### Re: Numbers

```

On 03 May 2013, at 17:09, John Mikes wrote:

Never argue with a logician!
I try to insert some re-remarks into ''-induced lines below
John

On Fri, May 3, 2013 at 5:52 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 02 May 2013, at 18:03, John Mikes wrote:

Bruno asked: are you OK with this?  -  NO, I am not OK:

as I follow, 0 is NOT a number, it does not change a number.

0 * 1000 = 0.

read in English: 'zero times thousand is zero, - which is
-funny: it is not additional/subtractional only states that if I
take the '1000' NOT AT ALL I get nothing.  You are right: I have
no problem with 0.00089, 0s as position markers for the order of
magnitude of the 89. I have problems if (some of the) 0-s are NOT
zeros, like 0.20489: to use NUMBERS as position-markers (the dirty
trick of a decimal point -G)

Well, I have to say you are the first to refuse to 0 the number
status, with the notable exception of the greeks, but they did not
really discovered it.
I am sure you have no problem with expression like the
concentration of this product is 0.00089 cc. It uses the number 0,
which is very useful in the decimal or base notation of the natural
and real, and complex numbers.

But how do you   A D D  a number to another one if it is not
identified as a quantity?

quantity is already part of some interpretation, but you can use
it, it is very well.

so you do not IDENTIFY, you just INTERPRET? (and do so
'practically')

Yes, and if we are cautious enough, the reasoning and the conclusion
will not depend on the interpretation. It is not well known, but this
has made clear by Gödel, Henkin in the frame of the first order
predicate logic.

Can you add an electric train to the taste of a lolly-pop?

No, but those are not numbers.

How would you know, if you do not know what NUMBERS are? So far
(my) 'Ding an Sich' can be anything.

We might not know what numbers are, and be pretty sure what they are
not.

You speak about 'axioms' (- in my words they are inventions to
prove a theory's applicability.)

They are just hypotheses that we accept at the start for doing the
reasoning. Nobody ever says that an axiom is true, except in some
philosophical context.

does that mean  that 'an axiom is untrue'? if it is 'not true',
why should I accept the hypothesis based on it? Maria said I lack
a proposal substituting the accepted reasoning. Pardon me, I am not
smarter than those zillion wise men

who so far used 'numbers' - yet I have the right to question.

We don't know if the hypotheses are true. That does not entail that an
hypothesis is untrue. It means that we are agnostic. This should not
prevent us to reason as IF they are true, in case the theory
(hypotheses) shed light on some subject.

So no reversing please: proving the theory by axioms.

We never do that. We always prove FROM axioms, and we always know
that proving does not entail truth or knowledge. Only pseudo-
scientists believe that we can prove things about some reality.

I am not for 'proving', do not accept 'reality' and 'truth'. I am
just a simpleminded agnostic who asks questions.

And I am a simple minded agnostic who try to answer them. The point is
that proving does not mean at all making true. Proving just shows a
shatable path (for good willing people readu to do some work) between
hypothesis and consequences. It does not mean that the hypotheses, nor
the consequences, are true.

May I repeat the main question: is YOUR number a quantity?

Natural number have both. A quantity aspect, and an ordinality
aspects, like in the first, the second, the third, etc.

so you can add (two = II to three = III and get five = I) ??

That's correct.

Now I really do not get it. You marked the quantity-aspect by pegs
- au lieu de anything better.

? you did.

So WHAT is that
NUMBER TWO marked by 'II'? Do you COUNT them?
(what?)

In the theory I gave, two is the successor of one, and one is the
successor of zero, and zero is that unique number which is such that
when added to some number, it gives that number.

If THAT is your axiom then numbers are quantity specifiers.

You can see it that way, but we don't need to agree on this, as long
as you agree with the axioms given. Agreeing in science does not
mean that we believe those axioms to be true, but that we can
understand them and use it to develop some other theories.

Now 2+3 = 5 was not an axiom, but it can be derived from them easily.

As an agnostic I cannot agree in science or it's axiomatic bases
just to submerge into a conventional  belief system,
which includes the interlaced assumption-conclusion mass we call
'science'. Numbers, or not.

Science is agnostic. (well, before Nobel Prize and before pension, and
out of the coffee room, actually). When science is not agnostic it is
pseudo-religion or pseudo-science.

We may AGREE on that, but then ```

### Re: Numbers

```Bruno, I apologize for taking so much time from you to reply.
(to which mine is no knowledgeable match) rebuffs.

One question if you still can take one:

*JM: I would leave out mind, matter, consciousness*

*Br: Well, that is what I am working on. *

(Q: on 'leaving them out' or 'working on THEM'?)

And I offer my take developed over the past 2 decades of my agnostic
(religious non-faithful) belief system - not for an argument (I am not
ready for that) just as a MAYBE usable idea:
I INTERPRET (thanks for the word)
*
*
*mind* as the unknowable mentality we 'work with' - an agent we (you?) are
willing to assign to our (physiological/physical tool) brain as the tool,
though far from understanding it. Then again

*matter* as the interactive figment for our sensors (known and still
unknown ones) as effects of relations (some knowable) in that 'infinite
complexity' of which we have access only to a portion and which gave rise
to the greatest hypothesis of man: the FEELING and SCIENCE (physics) of
some 'material world'.
(I have no idea how other 'creatures' THINK about matter). And:

*consciousness *(not related to human terms) as the response to relations
in that 'infinite complexity'.

Thanks for providing the opportunity to think about these definitions. I
may improve on them and would be glad to do so.

John Mikes

On Sat, May 4, 2013 at 8:06 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 03 May 2013, at 17:09, John Mikes wrote:

Never argue with a logician!
I try to insert some re-remarks into ''-induced lines below
John

On Fri, May 3, 2013 at 5:52 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 02 May 2013, at 18:03, John Mikes wrote:

Bruno asked:* are you OK with this?*  -  NO, I am not OK:

as I follow, 0 is NOT a number, it does not change a number.

0 * 1000 = 0.

read in English: 'zero times thousand is zero, - which is
-funny: it is not additional/subtractional only states that if I take
the '1000' *NOT AT ALL* I get nothing.  You are right: I have no problem
with 0.000*89, 0*s as position markers for the order of magnitude of
the *89*. I have problems if (some of the) 0-s are NOT zeros, like 0.204*
89:* to use NUMBERS as position-markers (the dirty trick of a decimal
point -G)

Well, I have to say you are the first to refuse to 0 the number status,
with the notable exception of the greeks, but they did not really
discovered it.
I am sure you have no problem with expression like the concentration of
this product is 0.00089 cc. It uses the number 0, which is very useful in
the decimal or base notation of the natural and real, and complex numbers.

But how do you  * A D D * a number to another one if it is not
identified as a quantity?

quantity is already part of some interpretation, but you can use it, it
is very well.

so you do not IDENTIFY, you just INTERPRET? (and do so 'practically')

Yes, and if we are cautious enough, the reasoning and the conclusion will
not depend on the interpretation. It is not well known, but this has made
clear by Gödel, Henkin in the frame of the first order predicate logic.

Can you add an electric train to the taste of a lolly-pop?

No, but those are not numbers.

How would you know, if you do not know what NUMBERS are? So far (my)
'Ding an Sich' can be anything.

We might not know what numbers are, and be pretty sure what they are not.

You speak about 'axioms' (- in my words they are inventions to prove a
theory's applicability.)

They are just hypotheses that we accept at the start for doing the
reasoning. Nobody ever says that an axiom is true, except in some
philosophical context.

does that mean  that 'an axiom is untrue'? if it is 'not true', why
should I accept the hypothesis based on it? Maria said I lack a proposal
substituting the accepted reasoning. Pardon me, I am not smarter than
those zillion wise men
who so far used 'numbers' - yet I have the right to question.

We don't know if the hypotheses are true. That does not entail that an
hypothesis is untrue. It means that we are agnostic. This should not
prevent us to reason as IF they are true, in case the theory (hypotheses)
shed light on some subject.

So no *reversing* please: proving the theory by axioms.

We never do that. We always prove FROM axioms, and we always know that
proving does not entail truth or knowledge. Only pseudo-scientists
believe that we can prove things about some reality.

I am not for 'proving', do not accept 'reality' and 'truth'. I am just a

And I am a simple minded agnostic who try to answer them. The point is
that proving does not mean at all making true. Proving just shows a
shatable path (for good willing people readu to do some work) between
hypothesis and consequences. It does not mean that the hypotheses, nor the
consequences, are true.

May I repeat the main ```

### Re: Numbers

```

On 02 May 2013, at 18:03, John Mikes wrote:

Bruno asked: are you OK with this?  -  NO, I am not OK:

as I follow, 0 is NOT a number, it does not change a number.

0 * 1000 = 0.

Well, I have to say you are the first to refuse to 0 the number
status, with the notable exception of the greeks, but they did not
really discovered it.
I am sure you have no problem with expression like the concentration
of this product is 0.00089 cc. It uses the number 0, which is very
useful in the decimal or base notation of the natural and real, and
complex numbers.

But how do you   A D D  a number to another one if it is not
identified as a quantity?

quantity is already part of some interpretation, but you can use it,
it is very well.

Can you add an electric train to the taste of a lolly-pop?

No, but those are not numbers.

You speak about 'axioms' (- in my words they are inventions to prove
a theory's applicability.)

They are just hypotheses that we accept at the start for doing the
reasoning. Nobody ever says that an axiom is true, except in some
philosophical context.

So no reversing please: proving the theory by axioms.

We never do that. We always prove FROM axioms, and we always know that
proving does not entail truth or knowledge. Only pseudo-scientists
believe that we can prove things about some reality.

May I repeat the main question: is YOUR number a quantity?

Natural number have both. A quantity aspect, and an ordinality
aspects, like in the first, the second, the third, etc.

so you can add (two = II to three = III and get five = I) ??

That's correct.

If THAT is your axiom then numbers are quantity specifiers.

You can see it that way, but we don't need to agree on this, as long
as you agree with the axioms given. Agreeing in science does not mean
that we believe those axioms to be true, but that we can understand
them and use it to develop some other theories.

Now 2+3 = 5 was not an axiom, but it can be derived from them easily.

We may AGREE on that, but then numbers are indeed the products of
human thinking applied as humans think. Q E D

In which theory?

I do not assume the humans as primitive, I try to explain them in the
theory which assumes that human can be Turing emulated. The result is
that the physical laws evolve from the relation between numbers, and
this in a testable way. the advantage is that we get an explanation
(perhaps wrong, of course) of why we have consciousness and qualia.

Bruno: ...That's very good, but we can also develop general
statement. We would not have discover the universal number (the
computers) without agreeing on those principles.

That's a practicality and very fortunate.

It is also a conceptual very deep discovery. Before it, mathematicians
thought that no epistemiological concept (like computability) could
have a universal nature. They believe we could use Cantor's
diagonalization to refute all prtendion to universality in math, but
computability seems to be an exception (cf the Church Turing thesis).

Does not enlighten the problem of what 'numbers' may be, if not
quantifiers.

The problem is what mind and matter are. The numbers are tools that we
use, and we don't even try to explain them, if only because we can
already explain (in the comp theory) why it is impossible to
understand what they are from anything simpler than them.

BrunO  :)

JOhn

On Thu, May 2, 2013 at 4:54 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 01 May 2013, at 22:09, John Mikes wrote:

Bruno asked why I have problems how to figure out 'numbers'.

In his texts (as I remember and I have no quotes at hand) the
world can be construed from a large enough amount of numbers in
simple arithmetical ways (addition-subtraction). Also: numbers do
not mean quantities.
If his older post with pegs (II=two, =four etc.) is OK, the
'words' two and four DO mean quantities. If not, as 'numbers' they
are meaningless combinations of letters (sounds?) we could call the
series any way, as well as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other
language (eins,zwei,drei, - egy, kettő, három) as they developed
in diverse domains/lifestyles. The 'numbers' would be like Ding an
Sich (German) however used as qualifiers for quantities if so
applied (see Bruno's 'pegs' above).

The terms we are using are not important. All we need is some
agreement on some theory.
Most things we need for the natural numbers can be derived from the
following axioms (written in english):

any number added to zero gives the number we started with (= x + 0 =
x)

0 is not the successor of any natural number
if two numbers are different, then they have different successors
a number x added to a successor of a number y gives a successor of
the sum of x and y.

Are you OK with this?

In science we know that we cannot define what we are ```

### Re: Numbers

```Never argue with a logician!
I try to insert some re-remarks into ''-induced lines below
John

On Fri, May 3, 2013 at 5:52 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 02 May 2013, at 18:03, John Mikes wrote:

Bruno asked:* are you OK with this?*  -  NO, I am not OK:

as I follow, 0 is NOT a number, it does not change a number.

0 * 1000 = 0.

read in English: 'zero times thousand is zero, - which is
-funny: it is not additional/subtractional only states that if I take the
'1000' *NOT AT ALL* I get nothing.  You are right: I have no problem with
0.000*89, 0*s as position markers for the order of magnitude of the *89*.
I have problems if (some of the) 0-s are NOT zeros, like 0.204*89:* to use
NUMBERS as position-markers (the dirty trick of a decimal point -G)

Well, I have to say you are the first to refuse to 0 the number status,
with the notable exception of the greeks, but they did not really
discovered it.
I am sure you have no problem with expression like the concentration of
this product is 0.00089 cc. It uses the number 0, which is very useful in
the decimal or base notation of the natural and real, and complex numbers.

But how do you  * A D D * a number to another one if it is not
identified as a quantity?

quantity is already part of some interpretation, but you can use it, it
is very well.

so you do not IDENTIFY, you just INTERPRET? (and do so 'practically')

Can you add an electric train to the taste of a lolly-pop?

No, but those are not numbers.

How would you know, if you do not know what NUMBERS are? So far (my)
'Ding an Sich' can be anything.

You speak about 'axioms' (- in my words they are inventions to prove a
theory's applicability.)

They are just hypotheses that we accept at the start for doing the
reasoning. Nobody ever says that an axiom is true, except in some
philosophical context.

does that mean  that 'an axiom is untrue'? if it is 'not true', why
should I accept the hypothesis based on it? Maria said I lack a proposal
substituting the accepted reasoning. Pardon me, I am not smarter than
those zillion wise men
who so far used 'numbers' - yet I have the right to question.

So no *reversing* please: proving the theory by axioms.

We never do that. We always prove FROM axioms, and we always know that
proving does not entail truth or knowledge. Only pseudo-scientists
believe that we can prove things about some reality.

I am not for 'proving', do not accept 'reality' and 'truth'. I am just a

May I repeat the main question: is YOUR number a quantity?

Natural number have both. A quantity aspect, and an ordinality aspects,
like in the first, the second, the third, etc.

so you can add (two = *II *to three = *III* and get five = *I*) ??

That's correct.

Now I really do not get it. You marked the quantity-aspect by pegs - au
lieu de anything better. So WHAT is that
NUMBER TWO marked by 'II'? Do you COUNT them?
(what?)

If THAT is your axiom then numbers are quantity specifiers.

You can see it that way, but we don't need to agree on this, as long as
you agree with the axioms given. Agreeing in science does not mean that we
believe those axioms to be true, but that we can understand them and use it
to develop some other theories.

Now 2+3 = 5 was not an axiom, but it can be derived from them easily.

As an agnostic I cannot agree in science or it's axiomatic bases just
to submerge into a conventional  belief system,
which includes the interlaced assumption-conclusion mass we call
'science'. Numbers, or not.

We may AGREE on that, but then numbers are indeed the products of human
thinking applied as humans think. *Q E D *

In which theory?

Maybe in the overall 'belief' that we can understand the world.

I do not assume the humans as primitive, I try to explain them in the
theory which assumes that human can be Turing emulated. The result is that
the physical laws evolve from the relation between numbers, and this in a
testable way. the advantage is that we get an explanation (perhaps wrong,
of course) of why we have consciousness and qualia.

Please do not forget all those knowables we may acquire later on - they
may change the 'physical Law' of yesterday
even the Turing emulation of the 'HUMAN'. Which raises again the
question how reliable the numbers may be. (If we agree in their
identification).

*
*
*Bruno: ...**That's very good, but we can also develop general
statement. We would not have discover the universal number (the computers)
without agreeing on those principles.*
*
*
That's a practicality and very fortunate.

It is also a conceptual very deep discovery. Before it, mathematicians
thought that no epistemiological concept (like computability) could have a
universal nature. They believe we could use Cantor's diagonalization to
refute all prtendion to universality in math, but computability seems to be
an exception (cf the Church Turing ```

### Re: Numbers

```

On 01 May 2013, at 22:09, John Mikes wrote:

Bruno asked why I have problems how to figure out 'numbers'.

In his texts (as I remember and I have no quotes at hand) the
world can be construed from a large enough amount of numbers in
simple arithmetical ways (addition-subtraction). Also: numbers do
not mean quantities.
If his older post with pegs (II=two, =four etc.) is OK, the
'words' two and four DO mean quantities. If not, as 'numbers' they
are meaningless combinations of letters (sounds?) we could call the
series any way, as well as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other
language (eins,zwei,drei, - egy, kettő, három) as they developed in
diverse domains/lifestyles. The 'numbers' would be like Ding an
Sich (German) however used as qualifiers for quantities if so
applied (see Bruno's 'pegs' above).

The terms we are using are not important. All we need is some
agreement on some theory.
Most things we need for the natural numbers can be derived from the
following axioms (written in english):

any number added to zero gives the number we started with (= x + 0 = x)
0 is not the successor of any natural number
if two numbers are different, then they have different successors
a number x added to a successor of a number y gives a successor of the
sum of x and y.

Are you OK with this?

In science we know that we cannot define what we are talking about,
but we can agree on some principles about them.

More reasonably sounds the idea of my wife, Maria, who assigns the
primitive development of quantities originally to proportions:
larger (amount) - smaller (amount) evolving in some thousand
centuries into the process of 'counting' the included units.

That's very good, but we can also develop general statement. We would
not have discover the universal number (the computers) without
agreeing on those principles.

I published on this list my thought for developing the Roman
numbering signs. I started with 2 - a PAIR of hands etc. (not with
one, which means only the existence) and branching into 5 (as
fingers, as in pentaton music) already as 'many'.

OK.

I still have no idea what description could fit 'number' in Bruno's
usage (I did not study number -  theory - to keep my common sense
(agnostic?) thinking free).

See above.

Bruno

John Mikes

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### Re: Numbers

```Bruno asked:* are you OK with this?*  -  NO, I am not OK:

as I follow, 0 is NOT a number, it does not change a number.
But how do you  * A D D * a number to another one if it is not identified
as a quantity? Can you add an electric train to the taste of a lolly-pop?
You speak about 'axioms' (- in my words they are inventions to prove a
theory's applicability.) So no *reversing* please: proving the theory by
axioms.

May I repeat the main question: is YOUR number a quantity?
so you can add (two = *II *to three = *III* and get five = *I*) ??
If THAT is your axiom then numbers are quantity specifiers.
We may AGREE on that, but then numbers are indeed the products of human
thinking applied as humans think. *Q E D *
*
*
*Bruno: ...**That's very good, but we can also develop general statement.
We would not have discover the universal number (the computers) without
agreeing on those principles.*
*
*
That's a practicality and very fortunate. Does not enlighten the problem of
what 'numbers' may be, if not quantifiers.
JOhn

On Thu, May 2, 2013 at 4:54 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 01 May 2013, at 22:09, John Mikes wrote:

Bruno asked why I have problems how to figure out *'numbers'*. * *

In his texts (as I remember and I have no quotes at hand) the world can
be construed from a large enough amount of numbers in simple arithmetical
ways (addition-subtraction). Also: numbers do not mean quantities.
If his older post with pegs (II=two, =four etc.) is OK, the 'words'
two and four DO mean quantities. If not, as 'numbers' they are meaningless
combinations of letters (sounds?) we could call the series any way, as well
as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other
language (eins,zwei,drei, - egy, kettő, három) as they developed in diverse
domains/lifestyles. The 'numbers' would be like Ding an Sich (German)
however used as qualifiers for quantities if so applied (see Bruno's 'pegs'
above).

The terms we are using are not important. All we need is some agreement on
some theory.
Most things we need for the natural numbers can be derived from the
following axioms (written in english):

any number added to zero gives the number we started with (= x + 0 = x)
0 is not the successor of any natural number
if two numbers are different, then they have different successors
a number x added to a successor of a number y gives a successor of the sum
of x and y.

Are you OK with this?

In science we know that we cannot define what we are talking about, but we
can agree on some principles about them.

Bruno: *...We would not have discover(ed) the universal number (the
computers) without agreeing on those principles. *
*
*
To have discovered the 'universal number'(?) (i.e. computers)
is fine but that does not imply understanding on numbers:
like numbers are such as to be applicable for... etc.
My agnosticism needs more than that. Sorry.

More reasonably sounds the idea of my wife, Maria, who assigns the
primitive development of quantities originally to proportions: larger
(amount) - smaller (amount) evolving in some thousand centuries into the
process of 'counting' the included units.

That's very good, but we can also develop general statement. We would not
have discover the universal number (the computers) without agreeing on
those principles.

I published on this list my thought for developing the Roman numbering
signs. I started with 2 - a PAIR of hands etc. (not with one, which means
only the existence) and branching into 5 (as fingers, as in pentaton music)

OK.

I still have no idea what description could fit *'number'* in Bruno's
usage (I did not study number -  theory - to keep my common sense
(agnostic?) thinking free).

See above.

Bruno

John

John Mikes

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to ```

### Re: Numbers

```

On Wednesday, May 1, 2013 4:09:03 PM UTC-4, JohnM wrote:

Bruno asked why I have problems how to figure out *'numbers'*. * *

In his texts (as I remember and I have no quotes at hand) the world can
be construed from a large enough amount of numbers in simple arithmetical
ways (addition-subtraction). Also: numbers do not mean quantities.
If his older post with pegs (II=two, =four etc.) is OK, the 'words'
two and four DO mean quantities. If not, as 'numbers' they are meaningless
combinations of letters (sounds?) we could call the series any way, as well
as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other
language (eins,zwei,drei, - egy, kettő, három) as they developed in diverse
domains/lifestyles. The 'numbers' would be like Ding an Sich (German)
however used as qualifiers for quantities if so applied (see Bruno's 'pegs'
above).

More reasonably sounds the idea of my wife, Maria, who assigns the
primitive development of quantities originally to proportions: larger
(amount) - smaller (amount)

Yes, I think that is a good place to start. Larger and smaller are
aesthetic qualities - feelings which we use to discern objects from one
another and changes in objects (the pond is larger after it rains).

Craig

evolving in some thousand centuries into the process of 'counting' the
included units. I published on this list my thought for developing the
Roman numbering signs. I started with 2 - a PAIR of hands etc. (not with
one, which means only the existence) and branching into 5 (as fingers, as
in pentaton music) already as 'many'.

I still have no idea what description could fit *'number'* in Bruno's
usage (I did not study number -  theory - to keep my common sense
(agnostic?) thinking free).

John Mikes

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### Re: Numbers in the Platonic Realm

```

On 02 Dec 2012, at 19:33, meekerdb wrote:

On 12/2/2012 1:07 AM, Bruno Marchal wrote:

On 30 Nov 2012, at 21:28, meekerdb wrote:

On 11/30/2012 10:02 AM, Roger Clough wrote:

And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

True in logic and formal mathematics is just marker T that is
preserved by the rules of inference.

This makes no sense. You confuse the propositional constant T, with
the semantical notion of truth. The first is expressible/definable
formally (indeed by T, or by 0 = 0 in arithmetic), the second is
not (Tarski theorem).

On the contrary, I'm pointing out that they are NOT the same thing.

Apology, but it was not clear.

Bruno

Brent

When we say that truth is preserved by the rules of inference, we
are concerned with the second notion.

In applications it is interpreted as if it were the correspondence
meaning of 'true'.

Like in arithmetic. Truth of ExP(x) means that it exists a n such
that P(n), at the metalevel, which is the bare level in logic
(that explains many confusion).

But like all applications of mathematics, it may be only
approximate.

Yes, but for arithmetic it is pretty clear, as we share our
intuition on the so-called standard finite numbers.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 30 Nov 2012, at 21:28, meekerdb wrote:

On 11/30/2012 10:02 AM, Roger Clough wrote:

And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

True in logic and formal mathematics is just marker T that is
preserved by the rules of inference.

This makes no sense. You confuse the propositional constant T, with
the semantical notion of truth. The first is expressible/definable
formally (indeed by T, or by 0 = 0 in arithmetic), the second is not
(Tarski theorem). When we say that truth is preserved by the rules of
inference, we are concerned with the second notion.

In applications it is interpreted as if it were the correspondence
meaning of 'true'.

Like in arithmetic. Truth of ExP(x) means that it exists a n such
that P(n), at the metalevel, which is the bare level in logic (that
explains many confusion).

But like all applications of mathematics, it may be only
approximate.

Yes, but for arithmetic it is pretty clear, as we share our intuition
on the so-called standard finite numbers.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 12/2/2012 1:07 AM, Bruno Marchal wrote:

On 30 Nov 2012, at 21:28, meekerdb wrote:

On 11/30/2012 10:02 AM, Roger Clough wrote:

And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

True in logic and formal mathematics is just marker T that is preserved by the rules
of inference.

This makes no sense. You confuse the propositional constant T, with the semantical
notion of truth. The first is expressible/definable formally (indeed by T, or by 0 = 0
in arithmetic), the second is not (Tarski theorem).

On the contrary, I'm pointing out that they are NOT the same thing.

Brent

When we say that truth is preserved by the rules of inference, we are concerned with the
second notion.

In applications it is interpreted as if it were the correspondence meaning of
'true'.

Like in arithmetic. Truth of ExP(x) means that it exists a n such that P(n), at the
metalevel, which is the bare level in logic (that explains many confusion).

But like all applications of mathematics, it may be only approximate.

Yes, but for arithmetic it is pretty clear, as we share our intuition on the so-called
standard finite numbers.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

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### Re: Re: Numbers in the Platonic Realm

```Hi meekerdb

My reaction is that nothing is perfect in this world anyway.

[Roger Clough], [rclo...@verizon.net]
12/1/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: meekerdb
Time: 2012-11-30, 15:28:31
Subject: Re: Numbers in the Platonic Realm

On 11/30/2012 10:02 AM, Roger Clough wrote:
And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

True in logic and formal mathematics is just marker T that is preserved by
the rules of inference.  In applications it is interpreted as if it were the
correspondence meaning of 'true'.  But like all applications of mathematics, it
may be only approximate.

Brent

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

Hintakka's concept of truth is what is called pragmatic truth,
or scientific truth. It's the same as Peirce's-- namely, what
results when you carry out a particular protocol.

[Roger Clough], [rclo...@verizon.net]
11/30/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-02, 18:20:11
Subject: Re: Numbers in the Platonic Realm

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
Are you familiar with Jaakko Hintikka's ideas? I am using his concept
of game theoretic semantics to derive truth valuations.

I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.

Dear Bruno,

Hintikka's idea is to show how truth values can be coherently
considered to be the result of a process and not necessarily just some a
priori valuation. This makes Truth an emergent valuation, just as I
content all definite properties are emergent from mutual agreements
between entities. Properties, in the absence of the possibility of
measurement or apprehension of some type, do not exist; they are what
the 1p project onto existence. Nothing more.

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```
On 11/30/2012 9:10 AM, Roger Clough wrote:

Hi Stephen P. King
Hintakka's concept of truth is what is called pragmatic truth,
or scientific truth. It's the same as Peirce's-- namely, what
results when you carry out a particular protocol.

Dear Roger,

Sure, I agree. My point is that such is the only notion of truth
that is within our ability to grasp. We obtain the transcendent notions
of truth by abstraction in some infinite limit of the pragmatic truths.

[Roger Clough], [rclo...@verizon.net] mailto:rclo...@verizon.net]
11/30/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
*From:* Stephen P. King mailto:stephe...@charter.net
*Time:* 2012-11-02, 18:20:11
*Subject:* Re: Numbers in the Platonic Realm

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
Are you familiar with Jaakko Hintikka's ideas? I am using his
concept
of game theoretic semantics to derive truth valuations.

I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.

Dear Bruno,

Hintikka's idea is to show how truth values can be coherently
considered to be the result of a process and not necessarily just
some a
priori valuation. This makes Truth an emergent valuation, just as I
content all definite properties are emergent from mutual agreements
between entities. Properties, in the absence of the possibility of
measurement or apprehension of some type, do not exist; they are what
the 1p project onto existence. Nothing more.

--

--
Onward!

Stephen

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```

### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

No, we can grasp truth by correspondence.

And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

[Roger Clough], [rclo...@verizon.net]
11/30/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-30, 11:17:12
Subject: Re: Numbers in the Platonic Realm

On 11/30/2012 9:10 AM, Roger Clough wrote:

Hi Stephen P. King

Hintakka's concept of truth is what is called pragmatic truth,
or scientific truth. It's the same as Peirce's-- namely, what
results when you carry out a particular protocol.

Dear Roger,

Sure, I agree. My point is that such is the only notion of truth that is
within our ability to grasp. We obtain the transcendent notions of truth by
abstraction in some infinite limit of the pragmatic truths.

[Roger Clough], [rclo...@verizon.net]
11/30/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-02, 18:20:11
Subject: Re: Numbers in the Platonic Realm

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
Are you familiar with Jaakko Hintikka's ideas? I am using his concept
of game theoretic semantics to derive truth valuations.

I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.

Dear Bruno,

Hintikka's idea is to show how truth values can be coherently
considered to be the result of a process and not necessarily just some a
priori valuation. This makes Truth an emergent valuation, just as I
content all definite properties are emergent from mutual agreements
between entities. Properties, in the absence of the possibility of
measurement or apprehension of some type, do not exist; they are what
the 1p project onto existence. Nothing more.

--

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 11/30/2012 10:02 AM, Roger Clough wrote:

And a transcendent truth could be arithmetic truth or
the truth of necessary logic.

True in logic and formal mathematics is just marker T that is preserved by the rules of
inference.  In applications it is interpreted as if it were the correspondence meaning of
'true'.  But like all applications of mathematics, it may be only approximate.

Brent

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

Plato in the end confessed that the best he
could offer was a likely story. I see no reason
to doubt his authority. Nor of the Bible,
for that matter.

Roger Clough, rclo...@verizon.net
11/5/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-03, 10:18:16
Subject: Re: Numbers in the Platonic Realm

On 11/3/2012 8:03 AM, Bruno Marchal wrote:

On 03 Nov 2012, at 11:46, Stephen P. King wrote:

On 11/3/2012 5:18 AM, Bruno Marchal wrote:
How can anything emerge from something having non properties? Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

Why does it have to be a theory? The concept of the One is a
fragment of a theory...

You make the same coinfusion again and again. The One is not the same
as the concept of the One.

Does the One have a Concept of The One as its unique 1p?

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```
On 11/5/2012 1:14 PM, Roger Clough wrote:

Hi Stephen P. King

Plato in the end confessed that the best he
could offer was a likely story. I see no reason
to doubt his authority. Nor of the Bible,
for that matter.

Dear Roger,

This tells me that you are OK with arguments from authority. This

--
Onward!

Stephen

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

I don't think there's a better standard of truth.

Roger Clough, rclo...@verizon.net
11/5/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-05, 13:39:57
Subject: Re: Numbers in the Platonic Realm

On 11/5/2012 1:14 PM, Roger Clough wrote:
Hi Stephen P. King

Plato in the end confessed that the best he
could offer was a likely story. I see no reason
to doubt his authority. Nor of the Bible,
for that matter.
Dear Roger,

This tells me that you are OK with arguments from authority. This

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```

On 03 Nov 2012, at 16:18, Stephen P. King wrote:

On 11/3/2012 8:03 AM, Bruno Marchal wrote:

On 03 Nov 2012, at 11:46, Stephen P. King wrote:

On 11/3/2012 5:18 AM, Bruno Marchal wrote:
How can anything emerge from something having non properties?
Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

Why does it have to be a theory? The concept of the One is a
fragment of a theory...

You make the same coinfusion again and again. The One is not the
same as the concept of the One.

Does the One have a Concept of The One as its unique 1p?

I think the inner God, alias the arithmetical 1p (not arithmetical
in the logician sense, but still applying to the machine) , alias Bp
p (Theaetetus on Bp) can be said to be a unique abstract person.

But it is not the 1p of the one, it is the 1p of the Man.

Open problem for me if Arithmetical truth can be seen as a person or
not.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 11/4/2012 12:01 PM, Bruno Marchal wrote:

[SPK] Does the One have a Concept of The One as its unique 1p?

I think the inner God, alias the arithmetical 1p (not arithmetical
in the logician sense, but still applying to the machine) , alias Bp
p (Theaetetus on Bp) can be said to be a unique abstract person.

But it is not the 1p of the one, it is the 1p of the Man.

Open problem for me if Arithmetical truth can be seen as a person or not.

Dear Bruno,

I am making a conjecture that Arithmetical truth (AT) cannot be
seen as a singular person and pursuing the consequences of that
conjecture. I claim that, at best, AT is the mutual consistent set of
predicates (?) within the individual 1p of at least 3 entities. This
follows from my definitions of information and Reality.

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```

On 02 Nov 2012, at 19:35, Stephen P. King wrote:

On 11/2/2012 12:23 PM, Bruno Marchal wrote:

On 01 Nov 2012, at 21:21, Stephen P. King wrote:

On 11/1/2012 11:23 AM, Bruno Marchal wrote:
[SPK] Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe.

?

Reread step 8. Step 7 and step 8 are the only steps where I
explicitly do assume a primitive physicalreality.

In step 8, it is done for the reductio ad absurdum.

Dear Bruno,

I have cut and pasted your exact words from SANE04 and you
still didn't understand... From: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf

...what  if we  don’t  grant a concrete robust  physical
universe?

Actually the 8th present step will  explain
that such a move is nevertheless without purpose. This will make
the notion of concrete and
existing universe completely devoid of  any  explicative  power.
It  will  follow  that  a  much
weaker and usual form of Ockham’s razor can be used to conclude
that not only physics has
been  epistemologically reduced  to  machine  psychology, but
that  ‘‘matter’’ has  been
ontologically reduced to ‘‘mind’’ where mind is defined  as the
object study of fundamental

machine psychology.

My claim is that neither physical worlds nor numbers (or any
other object that must supervene on mind) can be ontologically
primitive. Both must emerge from a neutral ground that is neither
and has no particular properties.

How can anything emerge from something having non properties? Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

thus it must stratify itself into Many. Each of the Many is claimed
to have aspects that when recombined cancel to neutrality.

[SPK] He goes on to argue that Occam's razor would demand that
we reject the very idea of the existence of physical worlds

Only of primitive physical worlds. And you did agree with this. I
just prove this from comp. That's the originality. A bit of
metaphysics is made into a theorem in a theory (comp).

Can we agree that physical worlds emerge somehow from sharable
aspects of multiple sheaves of computations?

This is what I have shown to be a consequence of comp.

I agree.

[SPK]  given that he can 'show' how they can be reconstructed or
derived from irreducible - and thus ontologically primitive -
Arithmetic 'objects' {0, 1, +, *} that are operating somehow
in an atemporal way. We should be able to make the argument run
without ever appealing to a Platonic realm or any kind of
'realism'. In my thinking, if arithmetic is powerful enough to
be a TOE and run the TOE to generate our world, then that power
should be obvious. My problem is that it looks tooo much like
the 'explanation' of creation that we find in mythology, whether
it is the Ptah of ancient Egypt or  the egg of Pangu or whatever
other myth one might like. What makes an explanation framed in
the sophisticated and formal language of modal logic any
different?

I use the self-reference logic, for obvious reason. Again, this
entails the sue of some modal logics, due to a *theorem* by
Solovay. All correct machine whose beliefs extend RA obeys to G
and G*. There is no choice in the matter.

That is not changed or involved by my argument.

I am very suspicions of special explanations' or 'natural
conspiracies'.  (This comes from my upbringing as a Bible-
believing Fundamentalist and eventual rejection of that
literalist mental straight-jacket.) As I see things, any
condition or situation that can be used to 'explain' some other
conceptually difficult condition or situation should be either
universal in that they apply anywhere and anytime

But even in your theory anywhere and anytime must be defined by
something more primitive, given that you agree that physics
cannot be the fundamental theory, given that the physical reality
is not primitive.

The concepts of where and when (positions in a space-time)
would seem to be rendered meaningless if there is no space-time
(or observers/measurements to define it), no? OH, BTW, I don't
think that we disagree that physics cannot be the fundamental
theory. Physics requires measurements/observations to be
meaningful. Where I agree with you is in your considerations of 1p
and observer indeterminacy. Where you and I disagree is on the
question of resources. Resources are required for computations to
run so there has to be the availability of resources involved in
*any* consideration of computations. Ignoring these considerations
by only considering computations as Platonic objects is wrong, IMHO.
You seem to be OK with computations as purely timeless objects
(in Platonia) that are such that ```

### Re: Numbers in the Platonic Realm

```
On 11/3/2012 5:18 AM, Bruno Marchal wrote:

How can anything emerge from something having non properties? Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

Why does it have to be a theory? The concept of the One is a
fragment of a theory...

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```
On 11/3/2012 5:18 AM, Bruno Marchal wrote:

I read Russell. Never found something that non sensical. If the basic
object have no properties, I don't see how anything can emerge from
it. You have to explain your point, not to refer to the literature.

Dear Bruno,

Did you notice that I distinguish between having no properties
and having no particular properties? The former is undefinable, the
latter is equivalent to having all possible properties. The word
particular seems to cause confusion. It is used to bracket one against
many, like a figure and its ground. It implies a choice...

--
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Stephen

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### Re: Numbers in the Platonic Realm

```

On 02 Nov 2012, at 23:12, Stephen P. King wrote:

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
I can understand these symbols because there is at least a way
to physically implement them.

Those notion have nothing to do with physical implementation.

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical
events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.

Dear Bruno,

Where is the evidence of the existence of a Platonic realm?

It is part of the assumption. We postulate arithmetic. I try to avoid
the use of platonic there, as I used the term in Plato sense. In
that sense Platonia = the greek Noùs, and it is derived from
arithmetic and comp.

All you need is the belief that 43 is prime independently of 43 is
prime.

The mere self-consistency of an idea is proof of existence

Already in arithmetic we have the consistence of the existence of a
prrof of the false, this certainly does not mean that there exist a
proof of the false. So self-consistency is doubtfully identifiable
with truth, and still less with existence.

but the idea must be understood by a multiplicity of entities with
the capacity to distinguish truth from falsehood to have any
coherence as an idea!

Not at all. 43 is prime might be true, even in absence of universe and
observer.

We cannot just assume that the mere existence of some undefined acts
to determine the properties of the undefined. Truth and falsity are
possible properties, they are not ontological aspects of existence.

Truth is no more a property than existence. It makes no sense.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 02 Nov 2012, at 23:16, Stephen P. King wrote:

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
You are the one saying that truth is limited to the means of
knowing!!!

Yes and no, Truth is limited to the *possibility* of knowledge of
it. In the absence of the possibility of a statement being true (or
false), there is not such thing as true or false.

I use the standard notion, which are simpler than possibility and
knowledge. I use only things like ExP(x) is true if there is a n
such that P(n), etc. read a textbook in logic, as you introduce
metaphysical baggage where logician have been able to discard them.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 02 Nov 2012, at 23:20, Stephen P. King wrote:

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
Are you familiar with Jaakko Hintikka's ideas? I am using his
concept of game theoretic semantics to derive truth valuations.

I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.

Dear Bruno,

Hintikka's idea is to show how truth values can be coherently
considered to be the result of a process and not necessarily just
some a priori valuation. This makes Truth an emergent valuation,
just as I content all definite properties are emergent from mutual
agreements between entities.

But how will you define entities? Where and how will the truth of
truth is an emergent valuation emerge?

What you say does not make sense for me. But if someone else

Properties, in the absence of the possibility of measurement or
apprehension of some type, do not exist; they are what the 1p
project onto existence. Nothing more.

Existence of what, of who, where, how?

It is very bad philosophy to throw doubt on scientific results just by
using non standard unclear philosophical  definition in a context
where honest scientist have no problem at all, and use what everybody
understand to show that there is some problem indeed, and attempt to
make a formulation of such problems.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 03 Nov 2012, at 11:46, Stephen P. King wrote:

On 11/3/2012 5:18 AM, Bruno Marchal wrote:
How can anything emerge from something having non properties?
Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

Why does it have to be a theory? The concept of the One is a
fragment of a theory...

You make the same coinfusion again and again. The One is not the same
as the concept of the One.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Re: Numbers in the Platonic Realm

```Hi Quentin Anciaux

Any statement that cannot be contradicted is always true.
As such these truths are called a priori. They were
here before the world or you or me was created.
Prime numbers seem to be such.

A posteriori truths are truths of existence called facts.
They may be contradicted, may not be always true
or false. Today it is raining is such.

Roger Clough, rclo...@verizon.net
11/3/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Quentin Anciaux
Time: 2012-11-02, 20:25:00
Subject: Re: Numbers in the Platonic Realm

2012/11/2 Stephen P. King

On 11/2/2012 1:23 PM, Bruno Marchal wrote:

I can understand these symbols because there is at least a way to physically
implement them.

Those notion have nothing to do with physical implementation.

? ? So your thinking about them is not a physical act?

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by platonic
arithmetical truth.

Dear Bruno,

? ? Where is the evidence of the existence of a Platonic realm? The mere
self-consistency of an idea is proof of existence but the idea must be
understood by a multiplicity of entities with the capacity to distinguish truth
from falsehood to have any coherence as an idea! We cannot just assume that the
mere existence of some undefined acts to determine the properties of the
undefined. Truth and falsity are possible properties, they are not ontological
aspects of existence.

Either? you can have emerging properties of nothing or you can't. Either there
is infinite regress or not, whatever is true (and one or the other is), it's
not an obstacle.

Quentin

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All those moments will be lost in time, like tears in rain.

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

The Platonic Realm doesn't exactly exist, because
it is non-contradictory truth beyond spacetime.
It is the a priori, the One, from which all things
come. Sometimes I think of it as Cosmic Mind,
Universal Intelligence, which has the attributes of God.

Roger Clough, rclo...@verizon.net
11/3/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-02, 18:12:19
Subject: Re: Numbers in the Platonic Realm

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
I can understand these symbols because there is at least a way to
physically implement them.

Those notion have nothing to do with physical implementation.

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.
Dear Bruno,

Where is the evidence of the existence of a Platonic realm? The
mere self-consistency of an idea is proof of existence but the idea must
be understood by a multiplicity of entities with the capacity to
distinguish truth from falsehood to have any coherence as an idea! We
cannot just assume that the mere existence of some undefined acts to
determine the properties of the undefined. Truth and falsity are
possible properties, they are not ontological aspects of existence.

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Stephen

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

1 + 1 =2 is a necessary truth, not a fact. It is always true.
A priori. So there are necessary truths such as arithmetical truths
which were here before the contingent world of facts was created.
And will always be.

Roger Clough, rclo...@verizon.net
11/3/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-02, 18:16:09
Subject: Re: Numbers in the Platonic Realm

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
You are the one saying that truth is limited to the means of knowing!!!

Yes and no, Truth is limited to the *possibility* of knowledge of
it. In the absence of the possibility of a statement being true (or
false), there is not such thing as true or false.

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### Re: Re: Numbers in the Platonic Realm

```Hi Stephen P. King

The platonic realm is nothing.
Intelligence is nothing.
Life itself is nothing.

Roger Clough, rclo...@verizon.net
11/3/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-11-02, 23:17:40
Subject: Re: Numbers in the Platonic Realm

On 11/2/2012 8:25 PM, Quentin Anciaux wrote:
Either you can have emerging properties of nothing or you can't.
Either there is infinite regress or not, whatever is true (and one or
the other is), it's not an obstacle.
Hi Questin,

It depends on whether you think of Nothing as merely an absence of
properties or a complete lack of existence. I believe in the former
case. I don't have problems with infinite regress as I understand that
an actual regress requires infinite stuff to be real. Explanation that
push the problem behind a insurmountable curtain are not infinite
regressive, they are merely evasions of the problem. They are attempt to
get people to stop asking hard questions.
I will not ever stop asking questions as I am not afraid of being
wrong or foolish.

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### Re: Numbers in the Platonic Realm

```
On 11/3/2012 8:03 AM, Bruno Marchal wrote:

On 03 Nov 2012, at 11:46, Stephen P. King wrote:

On 11/3/2012 5:18 AM, Bruno Marchal wrote:

How can anything emerge from something having non properties? Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously,

Why not? The One is not a theory.

Why does it have to be a theory? The concept of the One is a
fragment of a theory...

You make the same coinfusion again and again. The One is not the same
as the concept of the One.

Does the One have a Concept of The One as its unique 1p?

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### Re: Numbers in the Platonic Realm

```
On 11/3/2012 8:48 AM, Roger Clough wrote:

Hi Stephen P. King

1 + 1 =2 is a necessary truth, not a fact. It is always true.
A priori. So there are necessary truths such as arithmetical truths
which were here before the contingent world of facts was created.
And will always be.

Hi Roger,

It seems to me that is there are necessary truths that have no
connection to facts in any way, then they are unknowable. I am just
reversing that thought to define the relations between a priori and a
posteriori truths.

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Stephen

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### Re: Numbers in the Platonic Realm

```
On 11/3/2012 8:51 AM, Roger Clough wrote:

The platonic realm is nothing.
Intelligence is nothing.
Life itself is nothing.

1-1 = 0
2-2 = 0
3-3 = 0
...

--
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Stephen

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### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 21:21, Stephen P. King wrote:

On 11/1/2012 11:23 AM, Bruno Marchal wrote:
[SPK] Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe.

?

Reread step 8. Step 7 and step 8 are the only steps where I
explicitly do assume a primitive physical reality.

In step 8, it is done for the reductio ad absurdum.

Dear Bruno,

I have cut and pasted your exact words from SANE04 and you
still didn't understand... From: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf

...what  if we  don’t  grant a concrete robust  physical  universe?
Actually the 8th present step will  explain
that such a move is nevertheless without purpose. This will make the
notion of concrete and
existing universe completely devoid of  any  explicative  power.
It  will  follow  that  a  much
weaker and usual form of Ockham’s razor can be used to conclude that
not only physics has
been  epistemologically reduced  to  machine  psychology, but that
‘‘matter’’ has  been
ontologically reduced to ‘‘mind’’ where mind is defined  as the
object study of fundamental

machine psychology.

My claim is that neither physical worlds nor numbers (or any
other object that must supervene on mind) can be ontologically
primitive. Both must emerge from a neutral ground that is neither
and has no particular properties.

How can anything emerge from something having non properties? Magic?

[SPK] He goes on to argue that Occam's razor would demand that we
reject the very idea of the existence of physical worlds

Only of primitive physical worlds. And you did agree with this. I
just prove this from comp. That's the originality. A bit of
metaphysics is made into a theorem in a theory (comp).

Can we agree that physical worlds emerge somehow from sharable
aspects of multiple sheaves of computations?

This is what I have shown to be a consequence of comp.

[SPK]  given that he can 'show' how they can be reconstructed or
derived from irreducible - and thus ontologically primitive -
Arithmetic 'objects' {0, 1, +, *} that are operating somehow in
an atemporal way. We should be able to make the argument run
without ever appealing to a Platonic realm or any kind of
'realism'. In my thinking, if arithmetic is powerful enough to be
a TOE and run the TOE to generate our world, then that power
should be obvious. My problem is that it looks tooo much like the
'explanation' of creation that we find in mythology, whether it is
the Ptah of ancient Egypt or  the egg of Pangu or whatever other
myth one might like. What makes an explanation framed in the
sophisticated and formal language of modal logic any different?

I use the self-reference logic, for obvious reason. Again, this
entails the sue of some modal logics, due to a *theorem* by
Solovay. All correct machine whose beliefs extend RA obeys to G and
G*. There is no choice in the matter.

That is not changed or involved by my argument.

am very suspicions of special explanations' or 'natural
conspiracies'.  (This comes from my upbringing as a Bible-
believing Fundamentalist and eventual rejection of that
literalist mental straight-jacket.) As I see things, any condition
or situation that can be used to 'explain' some other conceptually
difficult condition or situation should be either universal in
that they apply anywhere and anytime

But even in your theory anywhere and anytime must be defined by
something more primitive, given that you agree that physics cannot
be the fundamental theory, given that the physical reality is not
primitive.

The concepts of where and when (positions in a space-time)
would seem to be rendered meaningless if there is no space-time (or
observers/measurements to define it), no? OH, BTW, I don't think
that we disagree that physics cannot be the fundamental theory.
Physics requires measurements/observations to be meaningful. Where I
agree with you is in your considerations of 1p and observer
indeterminacy. Where you and I disagree is on the question of
resources. Resources are required for computations to run so there
has to be the availability of resources involved in *any*
consideration of computations. Ignoring these considerations by only
considering computations as Platonic objects is wrong, IMHO.
You seem to be OK with computations as purely timeless objects
(in Platonia) that are such that somehow we finite entities can
create physical objects that can implement (in their dynamical
functions) instances of such, while I claim that computations are
equivalence classes of functions that physical systems can implement
*and* abstract objects. I see these two views as two poles of a
spectrum. There is a lot more detail in my considerations that I do
not have time to go into at this time...

My ```

### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 22:50, Stephen P. King wrote:

On 11/1/2012 12:04 PM, Bruno Marchal wrote:

On 01 Nov 2012, at 01:18, Stephen P. King wrote:

On 10/31/2012 12:45 PM, Bruno Marchal wrote:
can stop reading as you need to assume the numbers (or anything
Turing equivalent) to get them.

Dear Bruno,

So it is OK to assume that which I seek to explain?

You can't explain the numbers without assuming the numbers. This
has been foreseen by Dedekind, and vert well justified by many
theorem in mathematical logic. Below the number, you are lead to
version of ultrafinitism, which is senseless in the comp theory.

Dear Bruno,

I disagree with ultrafinitists, they seem to be the mathematical
equivalent of flat-earthers'.

*and* having some particular set of values and meanings.

I just assume

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

And hope you understand.

I can understand these symbols because there is at least a way
to physically implement them.

Those notion have nothing to do with physical implementation.

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.

Implementation and physical will be explained from them. A natural
thing as they are much more complex than the laws above.

Numbers are meaningless in the absence of a means to define
them. Theories do not free-float.

Truth is free floating, and theories lived through truth, they are
truth floating, even when false.

In the absence of some common media, even if it is generated by
sheaves of computations, there simply is no way to understand
anything.

Why ?

Because there is not way to know of them otherwise.

Our knowing as nothing to do with truth. If an asteroid would have
destroy Earth before the Oresme bishop dicovered that the harmonic
series diverge, she would have still diverge, despite no humans would
know it.

Unless you can communicate with me, I have no way of knowing
implementation of a mathematical statement, there is no meaning to
claims to truth ofsuch statements.

To claim, no. To be true is independent of the claim of the apes.

You must accept non-well foundedness for your result to work, but
you seem fixated against that.

1004.

You are often escaping answers by inappropriate mathematical

A statement, such as 2 = 1+1 or two equals one plus one, are
said truthfully to have the same meaning because there are
multiple and separable entities that can have the agreement on
the truth value. In the absence of the ability to judge a
statement independently of any particular entity capable of
understanding the statement, there is no meaning to the
concept that the statement is true or false. To insist that a
statement has a meaning and is true (or false) in an ontological
condition where no entities capable of judging the meaning, begs
the question of meaningfulness!
You are taking for granted some things that your arguments
disallow.

Do you agree that during the five seconds just after the Big Bang
(assuming that theory) there might not have been any possible
observers. But then the Big Bang has no more sense.

No, I don't. Why? Because that concept of the five seconds
just after the Big Bang is an assumption of a special case or
pleading. I might as well postulate the existence of Raindow Dash
to act as the entity to whom the Truth of mathematical statements
have absolute meaning. To be frank, I thing that the Big Bang
theory, as usually explained is a steaming pile of rubbish, as it
asks us to believe that thetotality of all that exists
sprang into being from Nothing.

I actually agree, by accident, on this. But this is not relevant
for my point.

It is very relevant to mine.

Imagine that we can show that some solution to GR equantion have
universe so poor that life cannot exist in there, would you say
that such universe cannot exist?

If there does not exist a means to show the solution there is
no solution.

Mathematical solipsism.

I believe that the totality of what exists is eternal, having no
beginning and no end.

I am OK with that. It is close to Platonism. But with comp we can
restrict this to the arithmetical truth (a highly non computable
structure, but still conceivable by universal numbers, relatively).

Well, can we work with that agreement?

Come on, you say that you can escape the consequence of comp, you have
to find the flaw, or to be ```

### Re: Numbers in the Platonic Realm

```
On 11/2/2012 5:29 AM, Platonist Guitar Cowboy wrote:
On Thu, Nov 1, 2012 at 10:55 PM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:

On 11/1/2012 12:23 PM, Platonist Guitar Cowboy wrote:

Don't get me started on reductionism! I don't believe in it
as I don't believe in ontologically primitive objects that
have particular properties.

Then I don't see how you can make an ontological bet. You're at
the table, betting on 24 or whatever, but you won't place your chips.

Hi Cowboy,

Where is the Doctor's Office? I want to make an appointment!
Until its tech is proven, I am taking Dr. McCoy's stance:

Dear Stephen,

That's funny. I'll follow you. But I know that show and all its
question ;)

The thing about where is the Doctors office? is a guarded
agreement on my saying Yes to the Doctor. So, I do accept the betting.

This fictional universe, and the doctor, accept UDA step 8 eventually,
as I will demonstrate through examples:

1) The transporter did work in the end, so the original series does
assume comp in this sense.

2) Kirk is probably not aware of reconstitution delay, when he gets
back, and they've all learned to live with this weirdness.

3) McCoy, or the doctor, also uses the transporter throughout the
series. So if you took an appointment and told him that you don't want
to be transported and cited this video: Just get up on that platform
and do it. We all do and it works in this fictional universe. Or are
you out of your Vulcan mind?

4) McCoy is simultaneously occupied by his soul and Spock's soul in
search for Spock which slowly kills him + makes him act very
strangely until Spock's soul is given a new body in Vulcan.

= Dr. McCoy understands after this, that his materialist bias is
offset by Vulcan's spiritual practice, who are all logicians since
childhood, and that spirit is transferable and independent of
particular physical bodies.

5) With the Doctor in Voyager extension of the show (who is a pure
medical doctor hologram/program, but realizes his universality and
demands his freedom, which the crew eventually grant him) = program,
strings of code, becomes conscious.

6) And the total denial of physical resources, in line with UDA step
8, needed for consciousness is here:

The species Q in the next Generation version of the show,
completely eliminate the need for physical resources to maintain or
run them. This species is clearly not limited by physical resources,
space, or time restraints.

Thus, your portrayal of McCoy's stance is not faithful to the
fictional universe of that television series, which does support Step
8 on numerous occasions :)

I agree with a weak version Step 8, one that allows for the
appearance of a robust physical universe but in the way I explained in
my posts yesterday.

Spacecowboy

Buckaroo? Banzai!

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### Re: Numbers in the Platonic Realm

```
On 11/2/2012 12:23 PM, Bruno Marchal wrote:

On 01 Nov 2012, at 21:21, Stephen P. King wrote:

On 11/1/2012 11:23 AM, Bruno Marchal wrote:
[SPK] Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe.

?

Reread step 8. Step 7 and step 8 are the only steps where I
explicitly do assume a primitive physical reality.

In step 8, it is done for the reductio ad absurdum.

Dear Bruno,

I have cut and pasted your exact words from SANE04 and you
still didn't understand... From:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf
http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf

...what  if we  don’t  grant a concrete robust  physical universe?
Actually the 8th present step will  explain
that such a move is nevertheless without purpose. This will make the
notion of concrete and
existing universe completely devoid of  any  explicative power.  It
weaker and usual form of Ockham’s razor can be used to conclude that
not only physics has
been  epistemologically reduced  to  machine  psychology, but that
‘‘matter’’ has  been
ontologically reduced to ‘‘mind’’ where mind is defined  as the
object study of fundamental

machine psychology.

My claim is that _/*neither physical worlds nor numbers (or any
other object that must supervene on mind) can be ontologically
primitive*/_. Both must emerge from a neutral ground that is neither
and has no particular properties.

How can anything emerge from something having non properties? Magic?

Dear Bruno,

No, necessity. The totality of existence, the One, cannot be
complete and consistent simultaneously, thus it must stratify itself
into Many. Each of the Many is claimed to have aspects that when
recombined cancel to neutrality.

[SPK] He goes on to argue that Occam's razor would demand that we
reject the very idea of the existence of physical worlds

Only of primitive physical worlds. And you did agree with this. I
just prove this from comp. That's the originality. A bit of
metaphysics is made into a theorem in a theory (comp).

Can we agree that physical worlds emerge somehow from sharable
aspects of multiple sheaves of computations?

This is what I have shown to be a consequence of comp.

I agree.

[SPK]  given that he can 'show' how they can be reconstructed or
derived from irreducible - and thus ontologically primitive -
Arithmetic 'objects' {0, 1, +, *} that are operating somehow in
an atemporal way. We should be able to make the argument run
without ever appealing to a Platonic realm or any kind of
'realism'. In my thinking, if arithmetic is powerful enough to be a
TOE and run the TOE to generate our world, then that power should
be obvious. My problem is that it looks tooo much like the
'explanation' of creation that we find in mythology, whether it is
the Ptah http://ancientegyptonline.co.uk/ptah.html of ancient
Egypt or  the egg of Pangu http://www.livingmyths.com/Chinese.htm
or whatever other myth one might like. What makes an explanation
framed in the sophisticated and formal language of modal logic any
different?

I use the self-reference logic, for obvious reason. Again, this
entails the sue of some modal logics, due to a *theorem* by Solovay.
All correct machine whose beliefs extend RA obeys to G and G*. There
is no choice in the matter.

That is not changed or involved by my argument.

am very suspicions of special explanations' or 'natural
conspiracies'.  (This comes from my upbringing as a
Bible-believing Fundamentalist and eventual rejection of that
literalist mental straight-jacket.) As I see things, any condition
or situation that can be used to 'explain' some other conceptually
difficult condition or situation should be either universal in that
they apply anywhere and anytime

But even in your theory anywhere and anytime must be defined by
something more primitive, given that you agree that physics cannot
be the fundamental theory, given that the physical reality is not
primitive.

The concepts of where and when (positions in a space-time)
would seem to be rendered meaningless if there is no space-time (or
observers/measurements to define it), no? OH, BTW, I don't think that
we disagree that physics cannot be the fundamental theory. Physics
requires measurements/observations to be meaningful. Where I agree
with you is in your considerations of 1p and observer indeterminacy.
Where you and I disagree is on the question of resources. Resources
are required for computations to run so there has to be the
availability of resources involved in *any* consideration of
computations. Ignoring these considerations by only considering
computations as Platonic objects is wrong, IMHO.
You seem to be OK with computations as purely timeless objects
(in Platonia) that are such that ```

### Re: Numbers in the Platonic Realm

```
On 11/2/2012 1:23 PM, Bruno Marchal wrote:
I can understand these symbols because there is at least a way to
physically implement them.

Those notion have nothing to do with physical implementation.

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.

Dear Bruno,

Where is the evidence of the existence of a Platonic realm? The
mere self-consistency of an idea is proof of existence but the idea must
be understood by a multiplicity of entities with the capacity to
distinguish truth from falsehood to have any coherence as an idea! We
cannot just assume that the mere existence of some undefined acts to
determine the properties of the undefined. Truth and falsity are
possible properties, they are not ontological aspects of existence.

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### Re: Numbers in the Platonic Realm

```
On 11/2/2012 1:23 PM, Bruno Marchal wrote:
bundles of arithmetic statements generate many individual observers
that in turn interact (which I model via a combination of cyclic
gossiping on graphs and bisimulations) with each other to define a
common physical world which in turn acts to implement the
arithmetic. It is a loop, an eternal cyclical process that never
exactly repeats. It is in this infinite loop that I see your UD.

It is not a loop. It is more like a recurring abyss, like the
Mandelbrot set.

Sure! I like the idea of a recurrent abyss!

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### Re: Numbers in the Platonic Realm

```
On 11/2/2012 1:23 PM, Bruno Marchal wrote:

You are the one saying that truth is limited to the means of knowing!!!

Yes and no, Truth is limited to the *possibility* of knowledge of
it. In the absence of the possibility of a statement being true (or
false), there is not such thing as true or false.

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### Re: Numbers in the Platonic Realm

```
On 11/2/2012 1:23 PM, Bruno Marchal wrote:
Are you familiar with Jaakko Hintikka's ideas? I am using his concept
of game theoretic semantics to derive truth valuations.

I read this. yes. I don't see relevant at all.
I do appreciate his linking of intention and intension, but it is a
bit trivial in the comp theory.

Dear Bruno,

Hintikka's idea is to show how truth values can be coherently
considered to be the result of a process and not necessarily just some a
priori valuation. This makes Truth an emergent valuation, just as I
content all definite properties are emergent from mutual agreements
between entities. Properties, in the absence of the possibility of
measurement or apprehension of some type, do not exist; they are what
the 1p project onto existence. Nothing more.

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### Re: Numbers in the Platonic Realm

```2012/11/2 Stephen P. King stephe...@charter.net

On 11/2/2012 1:23 PM, Bruno Marchal wrote:

I can understand these symbols because there is at least a way to
physically implement them.

Those notion have nothing to do with physical implementation.

Too much ambiguous. Even staying in comp I can answer yes and no.
Yes, because my human thinking is locally supported by physical events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.

Dear Bruno,

Where is the evidence of the existence of a Platonic realm? The mere
self-consistency of an idea is proof of existence but the idea must be
understood by a multiplicity of entities with the capacity to distinguish
truth from falsehood to have any coherence as an idea! We cannot just
assume that the mere existence of some undefined acts to determine the
properties of the undefined. Truth and falsity are possible properties,
they are not ontological aspects of existence.

Either  you can have emerging properties of nothing or you can't. Either
there is infinite regress or not, whatever is true (and one or the other
is), it's not an obstacle.

Quentin

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### Re: Numbers in the Platonic Realm

```
On 11/2/2012 8:25 PM, Quentin Anciaux wrote:
Either  you can have emerging properties of nothing or you can't.
Either there is infinite regress or not, whatever is true (and one or
the other is), it's not an obstacle.

Hi Questin,

It depends on whether you think of Nothing as merely an absence of
properties or a complete lack of existence. I believe in the former
case. I don't have problems with infinite regress as I understand that
an actual regress requires infinite stuff to be real. Explanation that
push the problem behind a insurmountable curtain are not infinite
regressive, they are merely evasions of the problem. They are attempt to
get people to stop asking hard questions.
I will not ever stop asking questions as I am not afraid of being
wrong or foolish.

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### Re: Numbers in the Platonic Realm

```
On 11/1/2012 1:19 AM, meekerdb wrote:

On 10/31/2012 6:58 PM, Stephen P. King wrote:

Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call those
functions:  phi_0, phi_1, phi_2, ...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and phi_x(y) are
defined (number) and that they are equal, OR they are both undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data.
u is the computer. u i said to emulate the program (machine, ...) x
on the input y.

So u could be any number, depending on how you enumerated the
functions and what bijection is used?

Brent
--

Oh, BTW, Bruno wrote the above ... not me.

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### Re: Numbers in the Platonic Realm

```On Thu, Nov 1, 2012 at 1:42 AM, Stephen P. King stephe...@charter.netwrote:

On 10/31/2012 6:14 PM, Platonist Guitar Cowboy wrote:

On Wed, Oct 31, 2012 at 7:59 PM, Stephen P. King stephe...@charter.netwrote:

Dear Cowboy,

One question. Was the general outline that I was trying to explain
make any sense to you? Without being obvious about it, I am trying to
finely parse the difference between the logic of temporal systems and the
logic of atemporal systems - such as the Platonic Realm - such that I might
show that reasonings that are correct in one are not necessarily correct in
the other.

This was not obvious to me, and going over the posts, I see how you're
leaning that way... but why not just say that, then? Don't get me wrong, I
love Joycean labyrinths as much as the next guy, but if the topic is on
some level tending towards sincerity, then I don't see the benefit in not
being obvious. Then again, I'm a Captain Obvious type. Should get the
shirt.

Hi Cowboy,

I am dyslexic, this colors/flavors everything I write

One problem that I have discovered (I thank Brent for bringing this up!)
is that in our reasoning we set up constructions - such as the person on
the desert island - that blur the very distinction that I am trying to
frame. We should never assume temporal situations to argue for relations
that are atemporal unless we are prepared to show the morphisms between the
two situations.

Isn't this already physical framework when you seem to be arguing for time
as primitive (n incompatible with comp to begin with, after which you seek
to carve out a distinction, when you've already mixed at the base?

My argument is that it is impossible to 'derive Becoming from Being,
but we can derive Being from Becoming. So why not work with the latter
idea? I am trying to get Bruno to admit, among other things, that he has to
assume a non-well founded logic for his result to work.;-)

I see less and less how you'd be able to do that, as I said, by making
process/linear time primitive in comp, and by assuming physical universe
with so many statements. Quantum Logic is part of the picture (see SANE
2004).

Bruno would have us, in step 8 of UDA, to not assume a concrete
robust physical universe. He goes on to argue that Occam's razor would
demand that we reject the very idea of the existence of physical worlds
given that he can 'show' how they can be reconstructed or derived from
irreducible - and thus ontologically primitive - Arithmetic 'objects' {0,
1, +, *} that are operating somehow in an atemporal way.

UDA does not contradict itself here. Restraints on processing power, on
memory and print capacities, implying time as some illusion emanating from
eternal primitives, don't exist when framed non-constructively, more like
sets of assignments, rather than operations in your sense, by which you
seem to mean physically primitive operations on par with ontologically
primitive arrow of time. Isn't this like cracking open the axioms, and then
complaining that the building has cracks in it?

There are simply a pile of concepts that are just assumed without
explanation in any discussion of philosophy/logic/math. My point is that a
theory must be have the capacity of being communicable ab initio for it to
even be considered. When I am confronted with a theory or a result or an
argument that seems to disallow for communicability I am going to baulk at
it!

And the possibility that you are baulking at your preconceptions rather
than engaging the theory has never happened to you? Happens to me all the
time.

We should be able to make the argument run without ever appealing to a
Platonic realm or any kind of 'realism'.

It's hard for me to see bets being made without some cash/investment/gap
of faith on the table.

Sure.

Then it would be easy for you to directly address the question: why assume
non-comp and then complain about comp's implications of time and physics
arising from dream interaction of universal numbers, therefore being not
primary or existing primitively?

In my thinking, if arithmetic is powerful enough to be a TOE and run the
TOE to generate our world, then that power should be obvious. My problem is
that it looks tooo much like the 'explanation' of creation that we find in
mythology, whether it is the
Ptahhttp://ancientegyptonline.co.uk/ptah.htmlof ancient Egypt or  the egg
of Pangu http://www.livingmyths.com/Chinese.htm or whatever other myth
one might like. What makes an explanation framed in the sophisticated and
formal language of modal logic any different?

Nothing, at its base. Appearances and looks can deceive, as numbers can
too.

Would this not make that deception something in our understanding and
not the fault of numbers? After all, numbers are supposedly the least
ambiguous of entities!

On the surface, but not when you look under the hood. That's a ```

### Re: Numbers in the Platonic Realm

```
On 11/1/2012 6:54 AM, Platonist Guitar Cowboy wrote:

On Thu, Nov 1, 2012 at 1:42 AM, Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net wrote:

On 10/31/2012 6:14 PM, Platonist Guitar Cowboy wrote:

On Wed, Oct 31, 2012 at 7:59 PM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:

[SPK]

One problem that I have discovered (I thank Brent for
bringing this up!) is that in our reasoning we set up
constructions - such as the person on the desert island
- that blur the very distinction that I am trying to
frame. We should never assume temporal situations to
argue for relations that are atemporal unless we are
prepared to show the morphisms between the two situations.

Isn't this already physical framework when you seem to be
arguing for time as primitive (n incompatible with comp to
begin with, after which you seek to carve out a distinction,
when you've already mixed at the base?

My argument is that it is impossible to 'derive Becoming from
Being, but we can derive Being from Becoming. So why not work with
the latter idea? I am trying to get Bruno to admit, among other
things, that he has to assume a non-well founded logic for his
result to work.;-)

I see less and less how you'd be able to do that, as I said, by making
process/linear time primitive in comp, and by assuming physical
universe with so many statements. Quantum Logic is part of the picture
(see SANE 2004).

Hi Cowboy,

I think of it this way: Change is fundamental (ala Heraclitus
http://plato.stanford.edu/entries/heraclitus/#PhiPri and Bergson
http://plato.stanford.edu/entries/bergson/#5) and Being is its
automorphism http://en.wikipedia.org/wiki/Automorphism. Is that a bit
more clear? Linear time (why 'linear'? Is there such a thing as
non-linear time? Cyclic time is still linear, AFAIK...) is, IMHO, change
+ a measure. Without a measure of change, there is no time; there is
just change. If we take relativity seriously, we might even claim that
there is no difference between change minus measure and staticness... I
should mention that any change that has no measure associated with it is
zeroth order change.
Without the means to compare two different things to each other,
does it make any sense to be able to make coherent statements about some
change in one relative to the other. If there is just one thing, how do
we know anything about its possible change(s) unless we are looking at
it and gauging (measuring) its change against some thing else that has
some measure associated - but our observation of it violates the
stipulation of if there is just one thing.

The idea that somehow the observer is irrelevant in physics and
philosophy is, IMHO, one of the worse errors ever. Sure, we need to
minimize and even eliminate observer bias and preferred reference
framing, but eliminating the observer and replacing it with some
ambiguous 'view from nowhere' is undiluted hogwash. This is where
realist chafe me, they act as if the universe of objects is out there
and has definite properties in the complete absence of any clear
explanation for how those properties came to be defined in the first
place. OK, OK, I will stop ranting...

Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe. He goes on to argue that
Occam's razor would demand that we reject the very idea of
the existence of physical worlds given that he can 'show' how
they can be reconstructed or derived from irreducible - and
thus ontologically primitive - Arithmetic 'objects' {0, 1, +,
*} that are operating somehow in an atemporal way.

UDA does not contradict itself here. Restraints on processing
power, on memory and print capacities, implying time as some
illusion emanating from eternal primitives, don't exist when
framed non-constructively, more like sets of assignments, rather
than operations in your sense, by which you seem to mean
physically primitive operations on par with ontologically
primitive arrow of time. Isn't this like cracking open the
axioms, and then complaining that the building has cracks in it?

There are simply a pile of concepts that are just assumed
without explanation in any discussion of philosophy/logic/math. My
point is that a theory must be have the capacity of being
communicable ab initio for it to even be considered. When I am
confronted with a theory or a result or an argument that seems
to disallow for communicability I am going to baulk at it!

And the possibility that you are baulking at your preconceptions
rather than engaging the theory has never happened to you? Happens to
me all the time.

OK, got any ideas what these might be other ```

### Re: Numbers in the Platonic Realm

```

On 31 Oct 2012, at 19:59, Stephen P. King wrote:

On 10/30/2012 7:36 PM, Platonist Guitar Cowboy wrote:

On Tue, Oct 30, 2012 at 11:39 PM, Stephen P. King stephe...@charter.net
wrote:

On 10/30/2012 5:39 PM, meekerdb wrote:

On 10/30/2012 2:27 PM, Stephen P. King wrote:

On 10/30/2012 5:15 PM, meekerdb wrote:

On 10/30/2012 1:53 PM, Stephen P. King wrote:

Dear Brent,

What is it that distinguishes between tokens and
propositions?

Tokens are the physical elements (e.g. letters, words, sounds)
that are used to represent a proposition in a particular language.

What determines the map between the letters, words, sounds
and the content of propositions?

The proposition is the abstracted meaning which is independent
of particular language.

Does this independence do so far as to disallow for an
arbitrary physical entity to know of it? Independence of
abstractions from particular individuals is not independence from
all.

So Zwei est ein und ein. are tokens expressing the same
proposition as Two equals one plus one. which is that 2=1+1.

That

Which 'that' do you refer to, the tokens or the proposition.

is true only because multiple persons came to believe that it is
true

You previously agreed that one person alone could come to know
that 2=1+1 or 17 is prime and express it symbolically, i.e. in
tokens.  So multiple persons are only necessary in order for the
tokens to be used for communicating from one to another; which is
the case whether the thing communicated is true or false.

In 10/30/2012 5:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of
symbols 17 is prime is an indicator of some particular
mathematical object and one of its particular properties, then
how does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is
prime not the concept that 17 is prime.  Could not a person who
grew up alone on an island realize that 17 has no divisors, and
he could even invent a private language in which he could write
down Peano's axioms.

Why are you using such trivial and parochial framing for
abstract questions? Why the reference to single individuals? Did
you not understand that I am claiming that meaningfulness requires
at least the possibility of interaction between many entities such
that each can evaluate the truth value of a proposition and thus
can truthfully claim to have knowledge of true statements?
A person that grew and died on a desert island may have
discovered for itself that 17 objects cannot be divided into equal
subsets, but our statements about that are mere figemnts of our
imagination as we could know nothing objective and non-imaginative
at all about that person. We are imagining ourselves to have
powers that we simply do not have. We are not omniscient voyeurs
of Reality and there is not anything that is.

How is an imaginary entity come to aquire a real 1p or actual
real properties? It might if that imaginary entity is deemed to
have 1p content within some narrative. But outside of that
getting us nowhere.

Brent

and acted to cause it to be true. Remove one person from the
multiplicity and the meaning still is there. Remove all of them
and the meaning vanishes.

This needs a cowboy's few cents:

Every bet on ontological primitive is, despite the infinite models
and conjectures we can weave from them, just that: a bet.

If this is stated clearly and honestly then it's cool, no matter if
it turns out an error, as we've eliminated something at least.

But this is unfortunately rarer than to pound people with real,
reality, authentic vs imaginary, artificial in discourse where
axioms are not shared: if somebody can demarcate this boundary
clearly for all discourse, then I fail to see/understand how
anybody could do this outside of being high with a smile on their
face and comic implication. My intelligence is limited insofar as I
cannot understand, how this is not some form of needless force, in
face of our vast ignorance.

Meaning is not some magical quality bestowed upon the discoverer of
a set of relations. That's everybody's flavor of semantics working
there.

As for human; if this is close to philosophical humanism
semantically, then it's safe to say that, paired with standard
model of physics, it's nice epistemologies with a lot of bs for its
close association to ideological atheism; particularly the
assertion no supernatural miracle shit when asserting singularity
as big bang is just that: another miracle; when the rules of the
humanist bet said no miracles.

m

Dear Cowboy,

One question. Was the general outline that I was trying to
explain make any sense to you? Without being obvious about it, ```

### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 00:58, Stephen P. King wrote:

On 10/31/2012 12:22 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 18:29, Stephen P. King wrote:

On 10/30/2012 12:38 PM, Bruno Marchal wrote:
No? If they do not have something equivalent to concepts, how
can they dream?

Yes, the universal numbers can have concept.

Dear Bruno,

Let's start over. Please plain in detail what is a universal
number and how it (and not ordinary numbers) have concepts or 1p.

I will give more detail on FOAR, soon or later. But let me explains
quickly.

Fix your favorite Turing universal system. It can be a programming
language, a universal Turing machine, or a sigma_1 complete theory,
or even a computer.

Dear Bruno,

That 'fixing occurs at our level only. We are free (relatively)
to fix our axiomatic objects from the wide variety that have been
proven to exist within the Mathematical universe of concepts or, if
we are clever, we can invent new concepts and work with them; but we
cannot do things in our logic that are self-contradictory unless we
make sure that the contradictions are not allowed to be pathological.

OK. No problem.

Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call
those functions:  phi_0, phi_1, phi_2, ...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and  phi_x(y)
are defined (number) and that they are equal, OR they are both
undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the
data. u is the computer. u i said to emulate the program
(machine, ...) x on the input y.

OK, but this does not answer my question. What is the ontological
level mechanism that distinguishes the u and the x and the y from
each other?

The one you have chosen above. But let continue to use elementary
arithmetic, as everyone learn it in school. So the answer is:
elementary arithmetic.

What I am trying to explain to you that ontological level objects
cannot have any logical mechanism that requires temporarily unless
you are assuming some form of Becoming as an ontological primitive.
Platonism, as far as I know, disallows this.

Indeed. becoming, like the whole physicalness, emerges from inside. It
is 1p (plural).

Bruno

Comp is the thesis that I can survive with a physical digital
computer in place of the physical brain, as far as it emulates me
close enough.

Comp gives a special role to computer (physical incarnation of a
universal number). The comp idea is that computer can supports
thinking and consciousness, and makes them capable of manifestation
relatively to other universal structure (physical universes if that

The lobian machines are only universal numbers, having the
knowledge that they are universal.
I can prove to any patient human that he/she is Löbian (I cannot
prove that he/she is sound or correct, note).

The UDA results is that whatever you mean by physical for making
comp meaningful, that physicalness has to emerge entirely and only,
from a 'competition' between all universal numbers. There is no
need to go out of arithmetic, and worst, there is no possible use
of going out of arithmetic, once betting on comp.

By arithmetic I mean arithmetical truth, or the standard model of
arithmetic, I don't mean a theory. I mean the whole set of true
arithmetical propositions, or of their Gödel numbers.

Bruno

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Stephen

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### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 01:18, Stephen P. King wrote:

On 10/31/2012 12:45 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 18:39, Stephen P. King wrote:

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them
for some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals
one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to
assert that the truth of, say  Two equals one plus one. depend
on some numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive

Then I can stop reading as you need to assume the numbers (or
anything Turing equivalent) to get them.

Dear Bruno,

So it is OK to assume that which I seek to explain?

You can't explain the numbers without assuming the numbers. This has
been foreseen by Dedekind, and vert well justified by many theorem in
mathematical logic. Below the number, you are lead to version of
ultrafinitism, which is senseless in the comp theory.

*and* having some particular set of values and meanings.

I just assume

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

And hope you understand.

I can understand these symbols because there is at least a way
to physically implement them.

Those notion have nothing to do with physical implementation.
Implementation and physical will be explained from them. A natural
thing as they are much more complex than the laws above.

In the absence of some common media, even if it is generated by
sheaves of computations, there simply isno way to understand
anything.

Why ?

You must accept non-well foundedness for your result to work, but
you seem fixated against that.

1004.

A statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value.
In the absence of the ability to judge a statement independently
of any particular entity capable of understanding the statement,
there is no meaning to the concept that the statement is true or
false. To insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities capable of
judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments
disallow.

Do you agree that during the five seconds just after the Big Bang
(assuming that theory) there might not have been any possible
observers. But then the Big Bang has no more sense.

No, I don't. Why? Because that concept of the five seconds just
after the Big Bang is an assumption of a special case or pleading.
I might as well postulate the existence of Raindow Dash to act as
the entity to whom the Truth of mathematical statements have
absolute meaning. To be frank, I thing that the Big Bang theory, as
usually explained is a steaming pile of rubbish, as it asks us to
believe that the totality of all that exists sprang into being from
Nothing.

I actually agree, by accident, on this. But this is not relevant for
my point. Imagine that we can show that some solution to GR equantion
have universe so poor that life cannot exist in there, would you say
that such universe cannot exist?

I believe that the totality of what exists is eternal, having no
beginning and no end.

I am OK with that. It is close to Platonism. But with comp we can
restrict this to the arithmetical truth (a highly non computable
structure, but still conceivable by universal numbers, relatively).

What we infer from our observations of Hubble expansion is just an
effect that follows, ultimately, from our finiteness.

Including time and space. So we do agree again.

I think Brent is right, and Quentin. You confuse 1+1=2 with human
expression for pointing on that proposition. You obviously needs
human to understand those  1+1=2 , but the content of 1+1=2
has simply no relation at all with the human, or with a physical
universe.

No, none of you have yet to be able to understand my counter-
argument. It is not complicated. We cannot assume to have something
when the means for its existence is not allowed. My claim is that
meaningfulness supervenes on the possibility of interaction of
*many* entities and is independent of any *one* (or some lesser
finite subset) of that Many.

But arithmetical truth is full of entities, even ```

### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 05:27, meekerdb wrote:

On 10/31/2012 11:52 AM, Bruno Marchal wrote:

I don't see why denying mathematical realism would entail saying
no to the doctor.

It implies not saying yes qua computatio. It implies NOT
understanding what Church thesis is about, as to show it consistent
you need the diagonalization, which use the excluded middle
principle.

You can still say yes, but only by using some magic.

The doctor isn't proposing to replace part of you brain with a
piece of Platonia, he has a real physical device to implant.

This is not related. That will follow step 8.

Here, you have to be arithmetical realist to get an idea of what a
computer is, and how it functions, as the physical one will
approximate it, well enough, it is hoped.

Of course you can say yes to the doctor, just because you trust
him. But comp is not saying yes to the doctor. Comp is the
doctrine that saying yes will indeed work, once the artificial
brain is a *computer*. The definition of computer makes no sense
with arithmetical realism.

?? If I'm a materialist I could say yes because I think the
artificial brain produces the same input/output signals.

But you need to be arithmetical realist to define what you mean by
same input-output.
Arithmetical realism is not a big deal. It means that you believe that
2+2=5 OR 2+2≠5.

I don't see why I would have believe in Platonia.

Comp use only arithmetical platonia, and that is just a poetical
expression to say that you believe that 17 is prime independently of
the existence of the Higgs boson.

I may believe that only some computations are instantiated and there
are no infinities.

OK, but again, that is different. That's the move toward physical
ultrafinitism. You can keep comp, up to step seven, and we are back on
the fact that step 8 (the movie-graph argument) makes such move
senseless.

But note that to just define the term computation, you need to be
arithmetical realist. But if there were no step 8, indeed, you might
have succeed in saving a form of materialism.  I still miss what you
don't understand in the step 8. you did not comment my recent answer
on this.
Maybe you could try to elaborate on your intuition. Why and how does a
primitive matter change something in a computation or in the
consciousness associated to it, and this in a Turing emulable manner?

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 06:19, meekerdb wrote:

On 10/31/2012 6:58 PM, Stephen P. King wrote:  (actually it was Bruno)

Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call
those functions:  phi_0, phi_1, phi_2, ...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and  phi_x(y)
are defined (number) and that they are equal, OR they are both
undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the
data. u is the computer. u i said to emulate the program
(machine, ...) x on the input y.

So u could be any number, depending on how you enumerated the
functions and what bijection is used?

Any number. I am not sure, the enumeration has to be given by an
algorithm.

But yes, the notion of computation, universality, etc. are intensional
notion, and makes sense only relatively to the other number. That is
why a often add relative before number.

This should be obvious. The doctor who scan your brain will also have
some flexibility in the encoding of your current local and relative
state.

I doubt it can encode it with the number 4, though.
You might say, that 4 is for the fourth compact disk on the shell
doctor, but then 4 is no more an encoding, but only a pointer to an
encoding.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 01 Nov 2012, at 14:25, Stephen P. King wrote:

But I agree with comp up to the strong version of step 8!

But then you have to find the flaw in step 8. as step 8 is done in
comp, without adding any assumptions, of course.

I accept comp with a weak version of step 8 or, I think
equivalently, a weak version of computational universality: A
computation is universal if it is not dependent on any one
particular physical system.

This is called functional, not universal. It has nothing to do with
Turing universality.

This implies, to me, that there is at least one physical system that
such a universal computation can be said to actually run on!

I don't see this.

This goes against the Parmenidean/Platonistic idea of computation as
static objects in eternity that are completely independent of
physical stuff!

Sorry but, by definition, computations are static objects in
arithmetic (or in fortanic, Lispic, combinatoric, lambdaic, etc
There are a lot of equivalent ontological choices here.).

The physicist have not (yet) found a definition of computation which
does not use that mathematical definition. This exists, though, has
*many* physical systems are in principle Turing universal. But Turing
universal is a mathematical, even arithmetical, (even in the strong
logician sense).

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 11/1/2012 11:23 AM, Bruno Marchal wrote:
[SPK] Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe.

?

Reread step 8. Step 7 and step 8 are the only steps where I explicitly
do assume a primitive physical reality.

In step 8, it is done for the reductio ad absurdum.

Dear Bruno,

I have cut and pasted your exact words from SANE04 and you still
didn't understand... From:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf
http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf

...what  if we  don't  grant a concrete robust  physical universe?
Actually the 8th present step will  explain
that such a move is nevertheless without purpose. This will make the
notion of concrete and
existing universe completely devoid of  any  explicative  power. It
weaker and usual form of Ockham's razor can be used to conclude that not
only physics has
been  epistemologically reduced  to  machine  psychology, but that
''matter'' has  been
ontologically reduced to ''mind'' where mind is defined  as the object
study of fundamental

machine psychology.

My claim is that _/*neither physical worlds nor numbers (or any
other object that must supervene on mind) can be ontologically
primitive*/_. Both must emerge from a neutral ground that is neither and
has no particular properties.

[SPK] He goes on to argue that Occam's razor would demand that we
reject the very idea of the existence of physical worlds

Only of primitive physical worlds. And you did agree with this. I just
prove this from comp. That's the originality. A bit of metaphysics is
made into a theorem in a theory (comp).

Can we agree that physical worlds emerge somehow from sharable
aspects of multiple sheaves of computations?

[SPK]  given that he can 'show' how they can be reconstructed or
derived from irreducible - and thus ontologically primitive -
Arithmetic 'objects' {0, 1, +, *} that are operating somehow in an
atemporal way. We should be able to make the argument run without
ever appealing to a Platonic realm or any kind of 'realism'. In my
thinking, if arithmetic is powerful enough to be a TOE and run the
TOE to generate our world, then that power should be obvious. My
problem is that it looks tooo much like the 'explanation' of creation
that we find in mythology, whether it is the Ptah
http://ancientegyptonline.co.uk/ptah.html of ancient Egypt or  the
egg of Pangu http://www.livingmyths.com/Chinese.htm or whatever
other myth one might like. What makes an explanation framed in the
sophisticated and formal language of modal logic any different?

I use the self-reference logic, for obvious reason. Again, this
entails the sue of some modal logics, due to a *theorem* by Solovay.
All correct machine whose beliefs extend RA obeys to G and G*. There
is no choice in the matter.

That is not changed or involved by my argument.

very suspicions of special explanations' or 'natural conspiracies'.
(This comes from my upbringing as a Bible-believing Fundamentalist
and eventual rejection of that literalist mental straight-jacket.) As
I see things, any condition or situation that can be used to
'explain' some other conceptually difficult condition or situation
should be either universal in that they apply anywhere and anytime

But even in your theory anywhere and anytime must be defined by
something more primitive, given that you agree that physics cannot be
the fundamental theory, given that the physical reality is not primitive.

The concepts of where and when (positions in a space-time)
would seem to be rendered meaningless if there is no space-time (or
observers/measurements to define it), no? OH, BTW, I don't think that we
disagree that physics cannot be the fundamental theory. Physics
requires measurements/observations to be meaningful. Where I agree with
you is in your considerations of 1p and observer indeterminacy. Where
you and I disagree is on the question of resources. Resources are
required for computations to run so there has to be the availability
of resources involved in *any* consideration of computations. Ignoring
these considerations by only considering computations as Platonic
objects is wrong, IMHO.
You seem to be OK with computations as purely timeless objects (in
Platonia) that are such that somehow we finite entities can create
physical objects that can implement (in their dynamical functions)
instances of such, while I claim that computations are equivalence
classes of functions that physical systems can implement *and* abstract
objects. I see these two views as two poles of a spectrum. There is a
lot more detail in my considerations that I do not have time to go into
at this time...

My Theory of comp: Sheaves of Computations/arithmetic - define -
particular physical states ```

### Re: Numbers in the Platonic Realm

```
On 11/1/2012 12:23 PM, Platonist Guitar Cowboy wrote:

Don't get me started on reductionism! I don't believe in it as I
don't believe in ontologically primitive objects that have
particular properties.

Then I don't see how you can make an ontological bet. You're at the
table, betting on 24 or whatever, but you won't place your chips.

Hi Cowboy,

Where is the Doctor's Office? I want to make an appointment! Until
its tech is proven, I am taking Dr. McCoy's stance:

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### Re: Numbers in the Platonic Realm

```

On 30 Oct 2012, at 18:29, Stephen P. King wrote:

On 10/30/2012 12:38 PM, Bruno Marchal wrote:
No? If they do not have something equivalent to concepts, how can
they dream?

Yes, the universal numbers can have concept.

Dear Bruno,

Let's start over. Please plain in detail what is a universal
number and how it (and not ordinary numbers) have concepts or 1p.

I will give more detail on FOAR, soon or later. But let me explains
quickly.

Fix your favorite Turing universal system. It can be a programming
language, a universal Turing machine, or a sigma_1 complete theory, or
even a computer.

Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call those
functions:  phi_0, phi_1, phi_2, ...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and  phi_x(y) are
defined (number) and that they are equal, OR they are both undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data.
u is the computer. u i said to emulate the program (machine, ...) x on
the input y.

Comp is the thesis that I can survive with a physical digital computer
in place of the physical brain, as far as it emulates me close enough.

Comp gives a special role to computer (physical incarnation of a
universal number). The comp idea is that computer can supports
thinking and consciousness, and makes them capable of manifestation
relatively to other universal structure (physical universes if that

The lobian machines are only universal numbers, having the knowledge
that they are universal.
I can prove to any patient human that he/she is Löbian (I cannot prove
that he/she is sound or correct, note).

The UDA results is that whatever you mean by physical for making comp
meaningful, that physicalness has to emerge entirely and only, from a
'competition' between all universal numbers. There is no need to go
out of arithmetic, and worst, there is no possible use of going out
of arithmetic, once betting on comp.

By arithmetic I mean arithmetical truth, or the standard model of
arithmetic, I don't mean a theory. I mean the whole set of true
arithmetical propositions, or of their Gödel numbers.

Bruno

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Onward!

Stephen

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### Re: Re: Numbers in the Platonic Realm

```Hi meekerdb

I think the = sign allows a concept to be predicated, such
as  2 = 1+1 where 1+1 is the predicate. A concept
and a predicate form a proposition, and you need
a proposition to judge whether something is true or false.

Roger Clough, rclo...@verizon.net
10/31/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: meekerdb
Time: 2012-10-30, 14:50:24
Subject: Re: Numbers in the Platonic Realm

On 10/30/2012 10:39 AM, Stephen P. King wrote:
On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems apply only to
the concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus one.
does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that the
truth of, say  Two equals one plus one. depend on some numbers or subject
having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A statement,
such as 2 = 1+1 or two equals one plus one, are said truthfully to have the
same meaning because there are multiple and separable entities that can have
the agreement on the truth value. In the absence of the ability to judge a
statement independently of any particular entity capable of understanding the
statement,

I think you are confusing the tokens 2 = 1+1 with the proposition 2 = 1+1.
The former requires someone who understands the notation to interpret it, but
the latter is the interpretation, i.e. the concept.  A concept has meaning by
definition, otherwise we say we cannot conceptualize it, e.g. klognee flarbles
myrable, and so there is nothing to assign a truth value to.

there is no meaning to the concept that the statement is true or false. To
insist that a statement has a meaning and is true (or false) in an ontological
condition where no entities capable of judging the meaning, begs the question
of meaningfulness!

That sounds like idealism, but whatever it is sll theories that will explain
the world to us are going to have to apply to times and places where there are
no humans.  So I guess the question is whether 2=1+1 means to you what it means
to the rest of us.  If it does it can be part of our explanation.

Brent

You are taking for granted some things that your arguments disallow.

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### Re: Numbers in the Platonic Realm

```

On 30 Oct 2012, at 18:39, Stephen P. King wrote:

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals
one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the truth of, say  Two equals one plus one. depend on some
numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive

Then I can stop reading as you need to assume the numbers (or anything
Turing equivalent) to get them.

*and* having some particular set of values and meanings.

I just assume

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

And hope you understand.

A statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value.
In the absence of the ability to judge a statement independently of
any particular entity capable of understanding the statement,
there is no meaning to the concept that the statement is true or
false. To insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities capable of
judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments
disallow.

Do you agree that during the five seconds just after the Big Bang
(assuming that theory) there might not have been any possible
observers. But then the Big Bang has no more sense.

I think Brent is right, and Quentin. You confuse 1+1=2 with human
expression for pointing on that proposition. You obviously needs human
to understand those  1+1=2 , but the content of 1+1=2 has simply
no relation at all with the human, or with a physical universe.

I asked you some time ago if you agree with the use of the excluded
middle in arithmetic. It asserts that for any arithmetical proposition
P, even highly non computably verifiable, you can accept as new
arithmetical truth the proposition asserting that P v ~P. Which
intuitive meaning that the proposition is unambiguously either true,
or false, despite you have no idea if it is P or ~P which is the true
one. To accept this means that you accept that such truth are
independent of the means to prove or verify them.

Even intuitionist (who are sort of mathematical solipsist) accept, for
P arithmetical, the proposition
~ ~ (P v ~P), which makes them already realist in the sense used in
comp.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 30 Oct 2012, at 19:52, meekerdb wrote:

On 10/30/2012 10:43 AM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals
one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to
assert that the truth of, say  Two equals one plus one. depend
on some numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive *and* having some particular set of values
and meanings. A statement, such as 2 = 1+1 or two equals one plus
one, are said truthfully to have the same meaning because there are
multiple and separable entities that can have the agreement on the
truth value. In the absence of the ability to judge a statement
independently of any particular entity capable of understanding
the statement, there is no meaning to the concept that the
statement is true or false. To insist that a statement has a
meaning and is true (or false) in an ontological condition where no
entities capable of judging the meaning, begs the question of
meaningfulness!
You are taking for granted some things that your arguments
disallow.

Hmm... but that's what arithmetical realism is all about... If you
deny meaning to '17 is prime' absent an entity which gives to it
its meaning... then you're simply negating arithmetical realism and
with it computationalism (ie: consciousness is emulable qua
computatio).

I don't see why denying mathematical realism would entail saying no
to the doctor.

It implies not saying yes qua computatio. It implies NOT
understanding what Church thesis is about, as to show it consistent
you need the diagonalization, which use the excluded middle principle.

You can still say yes, but only by using some magic.

The doctor isn't proposing to replace part of you brain with a piece
of Platonia, he has a real physical device to implant.

This is not related. That will follow step 8.

Here, you have to be arithmetical realist to get an idea of what a
computer is, and how it functions, as the physical one will
approximate it, well enough, it is hoped.

Of course you can say yes to the doctor, just because you trust him.
But comp is not saying yes to the doctor. Comp is the doctrine that
saying yes will indeed work, once the artificial brain is a
*computer*. The definition of computer makes no sense with
arithmetical realism.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```

On 30 Oct 2012, at 19:58, meekerdb wrote:
If there were no humans, no human level consciousness, would it
still be true that Holmes assistant is Watson?

If there are no humans, Conan Doyle would not have created the Holmes
and Watson characters, to which the use of the names refer, and the
question would be meaningless.

But in our branch of reality, it is true that Holmes assistant is
Watson (and not Crick, for example).

I a quiz, you would lose the point if you answer Crick to the
question what's the name of Holmes assistant?.

Holmes and Watson are sufficiently famous that we get the point such
names denote characters of some of the novels written by Doyle.

Even if the earth is destroyed, and no humans survive, it will remain
true that Watson was the assistant of Holmes, (in Conan  Doyle's
fiction) even if nobody care. Some alien might rediscovered that fact
when studying the humanity debris with some efficient tools.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 10/30/2012 7:36 PM, Platonist Guitar Cowboy wrote:

On Tue, Oct 30, 2012 at 11:39 PM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:

On 10/30/2012 5:39 PM, meekerdb wrote:

On 10/30/2012 2:27 PM, Stephen P. King wrote:

On 10/30/2012 5:15 PM, meekerdb wrote:

On 10/30/2012 1:53 PM, Stephen P. King wrote:

Dear Brent,

What is it that distinguishes between tokens and
propositions?

Tokens are the physical elements (e.g. letters, words, sounds)
that are used to represent a proposition in a particular language.

What determines the map between the letters, words, sounds
and the content of propositions?

The proposition is the abstracted meaning which is independent
of particular language.

Does this independence do so far as to disallow for an
arbitrary physical entity to know of it? Independence of
abstractions from particular individuals is not independence
from all.

So Zwei est ein und ein. are tokens expressing the same
proposition as Two equals one plus one. which is that 2=1+1.

That

Which 'that' do you refer to, the tokens or the proposition.

is true only because multiple persons came to believe that it is
true

You previously agreed that one person alone could come to know
that 2=1+1 or 17 is prime and express it symbolically, i.e. in
tokens.  So multiple persons are only necessary in order for the
tokens to be used for communicating from one to another; which is
the case whether the thing communicated is true or false.

In 10/30/2012 5:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:

[SPK] Unless multiple entities can agree that the sequence of
symbols 17 is prime is an indicator of some particular
mathematical object and one of its particular properties, then
how does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is
prime not the concept that 17 is prime.  Could not a person who
grew up alone on an island realize that 17 has no divisors, and
he could even invent a private language in which he could write
down Peano's axioms.

/*   Why are you using such trivial and parochial framing for
abstract questions? Why the reference to single individuals? Did
you not understand that I am claiming that meaningfulness
requires at least the possibility of interaction between many
entities such that each can evaluate the truth value of a
proposition and thus can truthfully claim to have knowledge of
true statements? *//*
*/
/*A person that grew and died on a desert island may have
discovered for itself that 17 objects cannot be divided into
equal subsets, but our statements about that are mere figemnts of
our imagination as we could know nothing objective and
non-imaginative at all about that person. We are imagining
ourselves to have powers that we simply do not have. We are not
omniscient voyeurs of Reality and there is not anything that is. */

How is an imaginary entity come to aquire a real 1p or actual
real properties? It might if that imaginary entity is deemed to
have 1p content within some narrative. But outside of that
getting us nowhere.

Brent

and acted to cause it to be true. Remove one person from the
multiplicity and the meaning still is there. Remove all of them
and the meaning vanishes.

This needs a cowboy's few cents:

Every bet on ontological primitive is, despite the infinite models and
conjectures we can weave from them, just that: a bet.

If this is stated clearly and honestly then it's cool, no matter if it
turns out an error, as we've eliminated something at least.

But this is unfortunately rarer than to pound people with real,
reality, authentic vs imaginary, artificial in discourse where
axioms are not shared: if somebody can demarcate this boundary clearly
for all discourse, then I fail to see/understand how anybody could do
this outside of being high with a smile on their face and comic
implication. My intelligence is limited insofar as I cannot
understand, how this is not some form of needless force, in face of
our vast ignorance.

Meaning is not some magical quality bestowed upon the discoverer of a
set of relations. That's everybody's flavor of semantics working there.

As for human; if this is close to philosophical humanism
semantically, then it's safe to say that, paired with standard model
of physics, it's nice epistemologies with a lot of bs for its close
association to ideological atheism; particularly the assertion no
supernatural miracle shit when asserting singularity as big bang is
just that: another miracle; when the rules of the humanist bet said
no ```

### Re: Numbers in the Platonic Realm

```On Wed, Oct 31, 2012 at 7:59 PM, Stephen P. King stephe...@charter.netwrote:

Dear Cowboy,

One question. Was the general outline that I was trying to explain
make any sense to you? Without being obvious about it, I am trying to
finely parse the difference between the logic of temporal systems and the
logic of atemporal systems - such as the Platonic Realm - such that I might
show that reasonings that are correct in one are not necessarily correct in
the other.

This was not obvious to me, and going over the posts, I see how you're
leaning that way... but why not just say that, then? Don't get me wrong, I
love Joycean labyrinths as much as the next guy, but if the topic is on
some level tending towards sincerity, then I don't see the benefit in not
being obvious. Then again, I'm a Captain Obvious type. Should get the
shirt.

One problem that I have discovered (I thank Brent for bringing this up!)
is that in our reasoning we set up constructions - such as the person on
the desert island - that blur the very distinction that I am trying to
frame. We should never assume temporal situations to argue for relations
that are atemporal unless we are prepared to show the morphisms between the
two situations.

Isn't this already physical framework when you seem to be arguing for time
as primitive (n incompatible with comp to begin with, after which you seek
to carve out a distinction, when you've already mixed at the base?

Bruno would have us, in step 8 of UDA, to not assume a concrete
robust physical universe. He goes on to argue that Occam's razor would
demand that we reject the very idea of the existence of physical worlds
given that he can 'show' how they can be reconstructed or derived from
irreducible - and thus ontologically primitive - Arithmetic 'objects' {0,
1, +, *} that are operating somehow in an atemporal way.

UDA does not contradict itself here. Restraints on processing power, on
memory and print capacities, implying time as some illusion emanating from
eternal primitives, don't exist when framed non-constructively, more like
sets of assignments, rather than operations in your sense, by which you
seem to mean physically primitive operations on par with ontologically
primitive arrow of time. Isn't this like cracking open the axioms, and then
complaining that the building has cracks in it?

We should be able to make the argument run without ever appealing to a
Platonic realm or any kind of 'realism'.

It's hard for me to see bets being made without some cash/investment/gap of
faith on the table.

In my thinking, if arithmetic is powerful enough to be a TOE and run the
TOE to generate our world, then that power should be obvious. My problem is
that it looks tooo much like the 'explanation' of creation that we find in
mythology, whether it is the
Ptahhttp://ancientegyptonline.co.uk/ptah.htmlof ancient Egypt or  the egg
of Pangu http://www.livingmyths.com/Chinese.htm or whatever other myth
one might like. What makes an explanation framed in the sophisticated and
formal language of modal logic any different?

Nothing, at its base. Appearances and looks can deceive, as numbers can too.

suspicions of special explanations' or 'natural conspiracies'.

Same here. My point with humanism + natural sciences, including standard
model, is that you have to be straight about your wager: there's my magic
primitive right there, warts and all.

Its deceiving to, on the one hand assert no miracles whatsoever, and then
ask for it at the instant of Big Bang. Human in this sense is both
deceptive through error and useful for power.

(This comes from my upbringing as a Bible-believing Fundamentalist and
eventual rejection of that literalist mental straight-jacket.) As I see
things, any condition or situation that can be used to 'explain' some other
conceptually difficult condition or situation should be either universal in
that they apply anywhere and anytime or are such that there must be a
particular configuration of events for them to occur. This principle (?)
applies to everything, be it the Big Bang initial state/singularity or
consciousness.

One point about the Big Bang. It seems to me that if we are
considering conditions in our current physical universe that involve
sufficiently small scales and/or high enough energies that there should be
the equivalent to the Big Bang initial conditions, thus the Big Bang should
be considered as an ongoing process even now and not some epochally special
event.

You argue both comp (universal, anywhere, eternal) and physically
primitive universe (current physical universe, ongoing process etc).
That's why I ask above why you burn your money before you put it on the
(comp) table and claim the game is rigged? Just because eternal is
foundation, doesn't imply that process isn't possible on some higher
level. Your alluding to mysticism points ```

### Re: Numbers in the Platonic Realm

```
On 10/31/2012 12:22 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 18:29, Stephen P. King wrote:

On 10/30/2012 12:38 PM, Bruno Marchal wrote:
No? If they do not have something equivalent to concepts, how can
they dream?

Yes, the universal numbers can have concept.

Dear Bruno,

Let's start over. Please plain in detail what is a universal
number and how it (and not ordinary numbers) have concepts or 1p.

I will give more detail on FOAR, soon or later. But let me explains
quickly.

Fix your favorite Turing universal system. It can be a programming
language, a universal Turing machine, or a sigma_1 complete theory, or
even a computer.

Dear Bruno,

That 'fixing occurs at our level only. We are free (relatively) to
fix our axiomatic objects from the wide variety that have been proven to
exist within the Mathematical universe of concepts or, if we are clever,
we can invent new concepts and work with them; but we cannot do things
in our logic that are self-contradictory unless we make sure that the
contradictions are not allowed to be pathological.

Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call those
functions:  phi_0, phi_1, phi_2, ...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and  phi_x(y) are
defined (number) and that they are equal, OR they are both undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data.
u is the computer. u i said to emulate the program (machine, ...) x on
the input y.

OK, but this does not answer my question. What is the ontological
level mechanism that distinguishes the u and the x and the y from each
other? What I am trying to explain to you that ontological level objects
cannot have any logical mechanism that requires temporarily unless you
are assuming some form of Becoming as an ontological primitive.
Platonism, as far as I know, disallows this.

Comp is the thesis that I can survive with a physical digital computer
in place of the physical brain, as far as it emulates me close enough.

Comp gives a special role to computer (physical incarnation of a
universal number). The comp idea is that computer can supports
thinking and consciousness, and makes them capable of manifestation
relatively to other universal structure (physical universes if that

The lobian machines are only universal numbers, having the knowledge
that they are universal.
I can prove to any patient human that he/she is Löbian (I cannot prove
that he/she is sound or correct, note).

The UDA results is that whatever you mean by physical for making comp
meaningful, that physicalness has to emerge entirely and only, from a
'competition' between all universal numbers. There is no need to go
out of arithmetic, and worst, there is no possible use of going out
of arithmetic, once betting on comp.

By arithmetic I mean arithmetical truth, or the standard model of
arithmetic, I don't mean a theory. I mean the whole set of true
arithmetical propositions, or of their Gödel numbers.

Bruno

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```
On 10/31/2012 12:45 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 18:39, Stephen P. King wrote:

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions,
not to numbers themselves.

Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals
one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the truth of, say  Two equals one plus one. depend on some
numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive

Then I can stop reading as you need to assume the numbers (or anything
Turing equivalent) to get them.

Dear Bruno,

So it is OK to assume that which I seek to explain?

*and* having some particular set of values and meanings.

I just assume

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

And hope you understand.

I can understand these symbols because there is at least a way to
physically implement them. In the absence of some common media, even if
it is generated by sheaves of computations, there simply is no way to
understand anything. You must accept non-well foundedness for your
result to work, but you seem fixated against that.

A statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value. In
the absence of the ability to judge a statement independently of any
particular entity capable of understanding the statement, there is
no meaning to the concept that the statement is true or false. To
insist that a statement has a meaning and is true (or false) in an
ontological condition where no entities capable of judging the
meaning, begs the question of meaningfulness!

You are taking for granted some things that your arguments disallow.

Do you agree that during the five seconds just after the Big Bang
(assuming that theory) there might not have been any possible
observers. But then the Big Bang has no more sense.

No, I don't. Why? Because that concept of the five seconds just
after the Big Bang is an assumption of a special case or pleading. I
might as well postulate the existence of Raindow Dash
http://3.bp.blogspot.com/-g3rGLKs9-t0/Tb2OVrEtc2I/AGU/3N5mSCci-_8/s1600/9234%2B-%2Bartist-Stinkehund%2Bcloud%2Brainbow_dash.png
to act as the entity to whom the Truth of mathematical statements have
absolute meaning. To be frank, I thing that the Big Bang theory, as
usually explained is a steaming pile of rubbish, as it asks us to
believe that the totality of all that exists sprang into being from
Nothing. I believe that the totality of what exists is eternal, having
no beginning and no end. What we infer from our observations of Hubble
expansion is just an effect that follows, ultimately, from our finiteness.

I think Brent is right, and Quentin. You confuse 1+1=2 with human
expression for pointing on that proposition. You obviously needs human
to understand those  1+1=2 , but the content of 1+1=2 has simply
no relation at all with the human, or with a physical universe.

No, none of you have yet to be able to understand my
counter-argument. It is not complicated. We cannot assume to have
something when the means for its existence is not allowed. My claim is
that/*meaningfulness */supervenes on the possibility of interaction of
*many* entities and is independent of any *one* (or some lesser finite
subset) of that Many.

I asked you some time ago if you agree with the use of the excluded
middle in arithmetic. It asserts that for any arithmetical proposition
P, even highly non computably verifiable, you can accept as new
arithmetical truth the proposition asserting that P v ~P. Which
intuitive meaning that the proposition is unambiguously either true,
or false, despite you have no idea if it is P or ~P which is the true
one. To accept this means that you accept that such truth are
independent of the means to prove or verify them.

We must us the principle to excluded middle to reason, but this
does not make the principle something external and independent of us.
This is a red herring, Bruno. It is not addressing my claim at all. You
seem to be stuck on the idea that only one entity can have or not have
some property or power and cannot reason about the possibility that
*many* may be required to solve some problems. A plurality is not a
multiplicity...

Even ```

### Re: Numbers in the Platonic Realm

```
On 10/31/2012 6:14 PM, Platonist Guitar Cowboy wrote:

On Wed, Oct 31, 2012 at 7:59 PM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:

Dear Cowboy,

One question. Was the general outline that I was trying to
explain make any sense to you? Without being obvious about it, I
am trying to finely parse the difference between the logic of
temporal systems and the logic of atemporal systems - such as the
Platonic Realm - such that I might show that reasonings that are
correct in one are not necessarily correct in the other.

This was not obvious to me, and going over the posts, I see how you're
leaning that way... but why not just say that, then? Don't get me
wrong, I love Joycean labyrinths as much as the next guy, but if the
topic is on some level tending towards sincerity, then I don't see the
benefit in not being obvious. Then again, I'm a Captain Obvious
type. Should get the shirt.

Hi Cowboy,

I am dyslexic, this colors/flavors everything I write

One problem that I have discovered (I thank Brent for bringing
this up!) is that in our reasoning we set up constructions - such
as the person on the desert island - that blur the very
distinction that I am trying to frame. We should never assume
temporal situations to argue for relations that are atemporal
unless we are prepared to show the morphisms between the two
situations.

Isn't this already physical framework when you seem to be arguing for
time as primitive (n incompatible with comp to begin with, after
which you seek to carve out a distinction, when you've already mixed
at the base?

My argument is that it is impossible to 'derive Becoming from
Being, but we can derive Being from Becoming. So why not work with the
latter idea? I am trying to get Bruno to admit, among other things, that
he has to assume a non-well founded logic for his result to work.;-)

Bruno would have us, in step 8 of UDA, to not assume a
concrete robust physical universe. He goes on to argue that
Occam's razor would demand that we reject the very idea of the
existence of physical worlds given that he can 'show' how they can
be reconstructed or derived from irreducible - and thus
ontologically primitive - Arithmetic 'objects' {0, 1, +, *} that
are operating somehow in an atemporal way.

UDA does not contradict itself here. Restraints on processing power,
on memory and print capacities, implying time as some illusion
emanating from eternal primitives, don't exist when framed
non-constructively, more like sets of assignments, rather than
operations in your sense, by which you seem to mean physically
primitive operations on par with ontologically primitive arrow of
time. Isn't this like cracking open the axioms, and then complaining
that the building has cracks in it?

There are simply a pile of concepts that are just assumed without
explanation in any discussion of philosophy/logic/math. My point is that
a theory must be have the capacity of being communicable ab initio for
it to even be considered. When I am confronted with a theory or a
result or an argument that seems to disallow for communicability I am
going to baulk at it!

We should be able to make the argument run without ever appealing
to a Platonic realm or any kind of 'realism'.

It's hard for me to see bets being made without some
cash/investment/gap of faith on the table.

Sure.

In my thinking, if arithmetic is powerful enough to be a TOE and
run the TOE to generate our world, then that power should be
obvious. My problem is that it looks tooo much like the
'explanation' of creation that we find in mythology, whether it is
the Ptah http://ancientegyptonline.co.uk/ptah.html of ancient
Egypt or  the egg of Pangu
http://www.livingmyths.com/Chinese.htm or whatever other myth
one might like. What makes an explanation framed in the
sophisticated and formal language of modal logic any different?

Nothing, at its base. Appearances and looks can deceive, as numbers
can too.

Would this not make that deception something in our understanding
and not the fault of numbers? After all, numbers are supposedly the
least ambiguous of entities!

very suspicions of special explanations' or 'natural conspiracies'.

Same here. My point with humanism + natural sciences, including
standard model, is that you have to be straight about your wager:
there's my magic primitive right there, warts and all.

Its deceiving to, on the one hand assert no miracles whatsoever, and
then ask for it at the instant of Big Bang. Human in this sense is
both deceptive through error and useful for power.

I think that we are too eager for explanations and are willing to
play fast and lose with concepts so long as we can hand wave problems away.

```

### Re: Numbers in the Platonic Realm

```
On 10/31/2012 11:52 AM, Bruno Marchal wrote:

I don't see why denying mathematical realism would entail saying no to the
doctor.

It implies not saying yes qua computatio. It implies NOT understanding what Church
thesis is about, as to show it consistent you need the diagonalization, which use the
excluded middle principle.

You can still say yes, but only by using some magic.

The doctor isn't proposing to replace part of you brain with a piece of Platonia, he
has a real physical device to implant.

This is not related. That will follow step 8.

Here, you have to be arithmetical realist to get an idea of what a computer is, and how
it functions, as the physical one will approximate it, well enough, it is hoped.

Of course you can say yes to the doctor, just because you trust him. But comp is not
saying yes to the doctor. Comp is the doctrine that saying yes will indeed work, once
the artificial brain is a *computer*. The definition of computer makes no sense with
arithmetical realism.

?? If I'm a materialist I could say yes because I think the artificial brain produces the
same input/output signals.  I don't see why I would have believe in Platonia.  I may
believe that only some computations are instantiated and there are no infinities.

Brent

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### Re: Numbers in the Platonic Realm

```
On 10/31/2012 6:58 PM, Stephen P. King wrote:

Enumerate the programs computing functions fro N to N, (or the equivalent notion
according to your chosen system). let us call those functions:  phi_0, phi_1, phi_2,
...  (the phi_i)

Let B be a fixed bijection from N x N to N. So B(x,y) is a number.

The number u is universal if phi_u(B(x,y)) = phi_x(y). And the equality means really
that either both phi_u(B(x,y)) and  phi_x(y) are defined (number) and that they are
equal, OR they are both undefined.

In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data. u is the computer.
u i said to emulate the program (machine, ...) x on the input y.

So u could be any number, depending on how you enumerated the functions and what bijection
is used?

Brent

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### Re: Numbers in the Platonic Realm

```

On 29 Oct 2012, at 22:38, Stephen P. King wrote:

On 10/29/2012 1:08 PM, Bruno Marchal wrote:

On 29 Oct 2012, at 14:36, Stephen P. King wrote:
[Bruno Marchal wrote:] So numbers are universal and can be
treated mathematically as always.

I agree, but the concept of numbers has no meaning prior to
the existence of objects that can be counted. To think otherwise
is equivalent to claiming that unspecified statements are true or
false even in the absence of the possibility of discovering the
fact.

Dear Bruno

I think you confuse numbers, and the concept of numbers.

No, I do not. My claim is that Numbers are objects in the mind
of conscious beings.

immediately, as comp needs the understanding of what a computer can
do, even in absence of any conscious observer.

If there does not exist worlds where entities to whom numbers are
concepts then there is no such thing as a concept of numbers in such
worlds.

But with comp, a conscious observer is explained by number relations.
We explain the concept of numbers, and of human understanding of
numbers, by number relations (computations).

My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not
to numbers themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

And then your argument is not valid, as with numbers, the miracle
is that we can specify the concept of numbers, as this result in
defining some arithmetical sigma_1 complete theory in terms of 0,
s(0), ... and the laws of addition and multiplication, that
everybody understands (unless philosophers?).

I am a philosopher! My argument rests only on the fact that the
'miracle' is exactly as you state it here: we exist and have a
concept of numbers and can ascertain the truth of arithmetic
statements. My claim is that truth valuations supervene on the
ability of consciousness to form concepts of numbers.

That is idealism, if not solipsism. In comp plotinus term, you confuse
the outer God (the objective ultimate truth) and the inner God, or the
sould of the individual inquirer.

I question the entire idea of numbers existing as separate Platonic
entities. In the absence of consciousness, there is no such thing as
a concept!

Again, we need only the relation between the numbers, not the concept
of numbers, which with comp will be explained by computation occurring
in the brain of some machine/number.

PS BTW, from a computer scientist perspective, your use of NP never
succeed to make sense. I don't dare to ask you to elaborate, as I
am afraid you might aggravate your case. The NP question is
fundamental and has many interesting feature, but it concerns a
local tractability issue, and is a priori, unless justification,
not relevant for the arithmetical body issue, nor number's theology
(including physics) issue, etc.

It is the argument is sound and is the same kind of argument as
what Kripke used to discuss the idea of possible worlds. In http://en.wikipedia.org/wiki/Possible_world

There is a close relation between propositions and possible
worlds. We note that every proposition is either true or false at
any given possible world; then the modal status of a proposition is
understood in terms of the worlds in which it is true and worlds in
which it is false.

All this presuppose numbers at the outset. World in Kripke are only
elements of any set having a binary relation. You must study the math,
not use the naive interpretation based on the use of common terms.

Solutions to equations or computations are not available until
after they are actually solved.

That is constructive thinking, again incompatible with comp, although
retrieved and explain for the subject. This is akin to your solipsism
above.
Of course it is hard to guess what you think as long as you don't
propose a theory.

My solution to this is to not go so far as you do in Step 8.

You can't make the conclusion of a reasoning false by stopping the
reasoning. This will only make you ignorant of a conclusion.

Let me try to be more explicit:

:

Instead of linking [the pain I feel] at space-time (x,t) to [a
machine state] at space-time
(x,t), we are obliged  to associate  [the pain  I  feel at  space-
time  (x,t)]  to a  type or a  sheaf of
computations  (existing  forever  in  the arithmetical  Platonia
which  is  accepted  as  existing

independently of  our  selves  with  arithmetical  realism).

Yes. That is already true in a concrete robust physical universe
(robust = own a non stopping  UD).

I am pointing out that the idea of computations ```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems apply only to the
concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some machine/numbers.
If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus one.
does.

Brent

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### Re: Numbers in the Platonic Realm

```

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not
to numbers themselves.

Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one
plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the truth of, say  Two equals one plus one. depend on some
numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 10/30/2012 12:38 PM, Bruno Marchal wrote:
No? If they do not have something equivalent to concepts, how can
they dream?

Yes, the universal numbers can have concept.

Dear Bruno,

Let's start over. Please plain in detail what is a universal number
and how it (and not ordinary numbers) have concepts or 1p.

--
Onward!

Stephen

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### Re: Numbers in the Platonic Realm

```
On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not
to numbers themselves.

Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one
plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the truth of, say  Two equals one plus one. depend on some
numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value. In
the absence of the ability to judge a statement independently of any
particular entity capable of understanding the statement, there is no
meaning to the concept that the statement is true or false. To insist
that a statement has a meaning and is true (or false) in an ontological
condition where no entities capable of judging the meaning, begs the
question of meaningfulness!

You are taking for granted some things that your arguments disallow.

--
Onward!

Stephen

--
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```

### Re: Numbers in the Platonic Realm

```2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply
only to the concepts of numbers and their constructions, not to numbers
themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus
one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that
the truth of, say  Two equals one plus one. depend on some numbers or
subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said truthfully
to have the same meaning because there are multiple and separable entities
that can have the agreement on the truth value. In the absence of the
ability to judge a statement independently of any particular entity capable
of understanding the statement, there is no meaning to the concept that
the statement is true or false. To insist that a statement has a meaning
and is true (or false) in an ontological condition where no entities
capable of judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny
meaning to '17 is prime' absent an entity which gives to it its meaning...
then you're simply negating arithmetical realism and with it
computationalism (ie: consciousness is emulable qua computatio).

Quentin

--
Onward!

Stephen

--
You received this message because you are subscribed to the Google Groups
Everything List group.
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For more options, visit this group at

--
All those moments will be lost in time, like tears in rain.

--
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To unsubscribe from this group, send email to
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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them
for some machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals
one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to
assert that the truth of, say  Two equals one plus one. depend
on some numbers or subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/
http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive *and* having some particular set of values
and meanings. A statement, such as 2 = 1+1 or two equals one plus
one, are said truthfully to have the same meaning because there
are multiple and separable entities that can have the agreement on
the truth value. In the absence of the ability to judge a
statement independently of any particular entity capable of
understanding the statement, there is no meaning to the concept
that the statement is true or false. To insist that a statement
has a meaning and is true (or false) in an ontological condition
where no entities capable of judging the meaning, begs the
question of meaningfulness!
You are taking for granted some things that your arguments
disallow.

Hmm... but that's what arithmetical realism is all about... If you
deny meaning to '17 is prime' absent an entity which gives to it its
meaning... then you're simply negating arithmetical realism and with
it computationalism (ie: consciousness is emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal by
definition! Individual entities are incapable of giving meaning to
things, be they puppies or prime numbers. It requires an *agreement
between many entities* to have meaningfulness. I claim that it takes at
least three entities...

If objects that are proposed to be real are not observable by
anyone then they don't exist! Where am I going off the rails? I think
that the problem here is that the distinction between not observable by
any particular entity and not observable by any entity are being
confused. I am reminded of Einstein's silly quip about the Moon still
existing even if he was not looking at it. The poor old fellow neglected
to notice that he was not the only entity that was capable of being
affected by the presence or non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

--
Onward!

Stephen

--
You received this message because you are subscribed to the Google Groups
Everything List group.
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For more options, visit this group at

```

### Re: Numbers in the Platonic Realm

```2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply
only to the concepts of numbers and their constructions, not to numbers
themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus
one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that
the truth of, say  Two equals one plus one. depend on some numbers or
subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said truthfully
to have the same meaning because there are multiple and separable entities
that can have the agreement on the truth value. In the absence of the
ability to judge a statement independently of any particular entity capable
of understanding the statement, there is no meaning to the concept that
the statement is true or false. To insist that a statement has a meaning
and is true (or false) in an ontological condition where no entities
capable of judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny
meaning to '17 is prime' absent an entity which gives to it its meaning...
then you're simply negating arithmetical realism and with it
computationalism (ie: consciousness is emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal by
definition! Individual entities are incapable of giving meaning to
things, be they puppies or prime numbers. It requires an *agreement between
many entities* to have meaningfulness. I claim that it takes at least three
entities...

If objects that are proposed to be real are not observable by
anyone then they don't exist! Where am I going off the rails? I think that
the problem here is that the distinction between not observable by any
particular entity and not observable by any entity are being confused. I
am reminded of Einstein's silly quip about the Moon still existing even if
he was not looking at it. The poor old fellow neglected to notice that he
was not the only entity that was capable of being affected by the presence
or non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or not
is not meaningful ? Only consciousness gives meaning to thing... yet it
seems absurd that truth value would disappear without consciousness.

Quentin

--
Onward!

Stephen

--
You received this message because you are subscribed to the Google Groups
Everything List group.
To post to this group, send email to everything-list@googlegroups.com.
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For more options, visit this group at

--
All those moments will be lost in time, like tears in rain.

--
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To unsubscribe from this group, send email to
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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:00 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their
constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing
them for some machine/numbers. If not, comp does not even
makes sense.

So your are agreeing?  Two has no truth value, but Two
equals one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to
assert that the truth of, say  Two equals one plus one.
depend on some numbers or subject having to discover it, or
prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/
http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an
ontological primitive *and* having some particular set of
values and meanings. A statement, such as 2 = 1+1 or two
equals one plus one, are said truthfully to have the same
meaning because there are multiple and separable entities
that can have the agreement on the truth value. In the
absence of the ability to judge a statement independently of
any particular entity capable of understanding the
statement, there is no meaning to the concept that the
statement is true or false. To insist that a statement has a
meaning and is true (or false) in an ontological condition
where no entities capable of judging the meaning, begs the
question of meaningfulness!
You are taking for granted some things that your arguments
disallow.

Hmm... but that's what arithmetical realism is all about... If
you deny meaning to '17 is prime' absent an entity which gives to
it its meaning... then you're simply negating arithmetical
realism and with it computationalism (ie: consciousness is
emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal
by definition! Individual entities are incapable of giving
meaning to things, be they puppies or prime numbers. It requires
an *agreement between many entities* to have meaningfulness. I
claim that it takes at least three entities...

If objects that are proposed to be real are not observable
by anyone then they don't exist! Where am I going off the rails? I
think that the problem here is that the distinction between not
observable by any particular entity and not observable by any
entity are being confused. I am reminded of Einstein's silly quip
about the Moon still existing even if he was not looking at it.
The poor old fellow neglected to notice that he was not the only
entity that was capable of being affected by the presence or
non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or
not is not meaningful ? Only consciousness gives meaning to thing...
yet it seems absurd that truth value would disappear without
consciousness.

Quentin

Unless multiple entities can agree that the sequence of symbols 17
is prime is an indicator of some particular mathematical object and one
of its particular properties, then how does 17 is prime come to mean
anything at all? Can you stop subconsciously assuming an invisible
observer whose sole job is to observe everything from infinity? It seems
that you cannot if what I am writing is mysterious to you!
How is it not absurd that meaningfulness exists in the absence of
anyone that can apprehend it? Please note that I am not considering the
absence of any one entity; I am considering the absence of all possible
entities in the degenerativeness or vanishing of meaningfulness. I am
asking Why is it OK to think that meaningfulness exists in the absence
of any means to determine it?.

--
Onward!

Stephen

--
You received this message because you are subscribed to the Google Groups
Everything List group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
For more options, visit this group at

```

### Re: Numbers in the Platonic Realm

```2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 2:00 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not to
numbers themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one
plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that
the truth of, say  Two equals one plus one. depend on some numbers or
subject having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said truthfully
to have the same meaning because there are multiple and separable entities
that can have the agreement on the truth value. In the absence of the
ability to judge a statement independently of any particular entity capable
of understanding the statement, there is no meaning to the concept that
the statement is true or false. To insist that a statement has a meaning
and is true (or false) in an ontological condition where no entities
capable of judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny
meaning to '17 is prime' absent an entity which gives to it its meaning...
then you're simply negating arithmetical realism and with it
computationalism (ie: consciousness is emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal by
definition! Individual entities are incapable of giving meaning to
things, be they puppies or prime numbers. It requires an *agreement between
many entities* to have meaningfulness. I claim that it takes at least three
entities...

If objects that are proposed to be real are not observable by
anyone then they don't exist! Where am I going off the rails? I think that
the problem here is that the distinction between not observable by any
particular entity and not observable by any entity are being confused. I
am reminded of Einstein's silly quip about the Moon still existing even if
he was not looking at it. The poor old fellow neglected to notice that he
was not the only entity that was capable of being affected by the presence
or non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or not
is not meaningful ? Only consciousness gives meaning to thing... yet it
seems absurd that truth value would disappear without consciousness.

Quentin

Unless multiple entities can agree that the sequence of symbols 17 is
prime is an indicator of some particular mathematical object and one of
its particular properties, then how does 17 is prime come to mean
anything at all? Can you stop subconsciously assuming an invisible observer
whose sole job is to observe everything from infinity? It seems that you
cannot if what I am writing is mysterious to you!
How is it not absurd that meaningfulness exists in the absence of
anyone that can apprehend it? Please note that I am not considering the
absence of any one entity; I am considering the absence of all possible
entities in the degenerativeness or vanishing of meaningfulness. I am
asking Why is it OK to think that meaningfulness exists in the absence of
any means to determine it?.

Well what you're explaining just feels like the egg and the chicken...
meaning is an internal view, if computationalism is true, observer and
meaning arise through computation... computation would be ontologically
real and primitive.

Quentin

--
Onward!

Stephen

--
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--
All those moments will be lost in time, like tears in rain.

--
You received this message because you are subscribed to the Google Groups
Everything List group.
To post to this group, send email to ```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 10:39 AM, Stephen P. King wrote:

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems apply only to the
concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus one.
does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that the truth of,
say  Two equals one plus one. depend on some numbers or subject having to discover
it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological primitive *and*
having some particular set of values and meanings. A statement, such as 2 = 1+1 or two
equals one plus one, are said truthfully to have the same meaning because there are
multiple and separable entities that can have the agreement on the truth value. In the
absence of the ability to judge a statement independently of any particular entity
capable of understanding the statement,

I think you are confusing the tokens 2 = 1+1 with the proposition 2 = 1+1.  The former
requires someone who understands the notation to interpret it, but the latter is the
interpretation, i.e. the concept.  A concept has meaning by definition, otherwise we say
we cannot conceptualize it, e.g. klognee flarbles myrable, and so there is nothing to
assign a truth value to.

there is no meaning to the concept that the statement is true or false. To insist that a
statement has a meaning and is true (or false) in an ontological condition where no
entities capable of judging the meaning, begs the question of meaningfulness!

That sounds like idealism, but whatever it is sll theories that will explain the world to
us are going to have to apply to times and places where there are no humans.  So I guess
the question is whether 2=1+1 means to you what it means to the rest of us.  If it does it
can be part of our explanation.

Brent

You are taking for granted some things that your arguments disallow.
--
Onward!

Stephen
--
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List group.

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 10:43 AM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply
only to
the concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one plus
one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that
the truth
of, say  Two equals one plus one. depend on some numbers or subject
having to
discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive
*and* having some particular set of values and meanings. A statement, such
as 2 =
1+1 or two equals one plus one, are said truthfully to have the same
meaning because
there are multiple and separable entities that can have the agreement on
the truth
value. In the absence of the ability to judge a statement independently of
any
particular entity capable of understanding the statement, there is no
meaning to
the concept that the statement is true or false. To insist that a statement
has a
meaning and is true (or false) in an ontological condition where no
entities capable
of judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny meaning to '17
is prime' absent an entity which gives to it its meaning... then you're simply negating
arithmetical realism and with it computationalism (ie: consciousness is emulable qua
computatio).

I don't see why denying mathematical realism would entail saying no to the doctor.  The
doctor isn't proposing to replace part of you brain with a piece of Platonia, he has a
real physical device to implant.

Brent

--
You received this message because you are subscribed to the Google Groups
Everything List group.
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To unsubscribe from this group, send email to
For more options, visit this group at

```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 11:00 AM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply
only to the concepts of numbers and their constructions, not to numbers
themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one
plus
one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the
truth of, say  Two equals one plus one. depend on some numbers or
subject
having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement,
such as 2 = 1+1 or two equals one plus one, are said truthfully to have
the
same meaning because there are multiple and separable entities that can
have
the agreement on the truth value. In the absence of the ability to
judge a
statement independently of any particular entity capable of
understanding the
statement, there is no meaning to the concept that the statement is
true or
false. To insist that a statement has a meaning and is true (or false)
in an
ontological condition where no entities capable of judging the meaning,
begs
the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny
meaning to
'17 is prime' absent an entity which gives to it its meaning... then you're
simply
negating arithmetical realism and with it computationalism (ie:
consciousness is
emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal by
definition!
Individual entities are incapable of giving meaning to things, be they
puppies or
prime numbers. It requires an *agreement between many entities* to have
meaningfulness. I claim that it takes at least three entities...

If objects that are proposed to be real are not observable by anyone
then
they don't exist! Where am I going off the rails? I think that the problem
here is
that the distinction between not observable by any particular entity and
not
observable by any entity are being confused. I am reminded of Einstein's
silly quip
about the Moon still existing even if he was not looking at it. The poor
old fellow
neglected to notice that he was not the only entity that was capable of
being
affected by the presence or non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or not is not
meaningful ? Only consciousness gives meaning to thing... yet it seems absurd that truth
value would disappear without consciousness.

If there were no humans, no human level consciousness, would it still be true that Holmes
assistant is Watson?

Brent

--
You received this message because you are subscribed to the Google Groups
Everything List group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
For more options, visit this group at

```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 11:22 AM, Stephen P. King wrote:

On 10/30/2012 2:00 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply
only to the concepts of numbers and their constructions, not to numbers
themselves.

Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.

So your are agreeing?  Two has no truth value, but Two equals one
plus
one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the
truth of, say  Two equals one plus one. depend on some numbers or
subject
having to discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to
have the same meaning because there are multiple and separable entities
that
can have the agreement on the truth value. In the absence of the
ability to
judge a statement independently of any particular entity capable of
understanding the statement, there is no meaning to the concept that
the
statement is true or false. To insist that a statement has a meaning
and is
true (or false) in an ontological condition where no entities capable of
judging the meaning, begs the question of meaningfulness!
You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny
meaning to
'17 is prime' absent an entity which gives to it its meaning... then you're
simply
negating arithmetical realism and with it computationalism (ie:
consciousness is
emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as unreal by
definition!
Individual entities are incapable of giving meaning to things, be they
puppies or
prime numbers. It requires an *agreement between many entities* to have
meaningfulness. I claim that it takes at least three entities...

If objects that are proposed to be real are not observable by anyone
then
they don't exist! Where am I going off the rails? I think that the problem
here is
that the distinction between not observable by any particular entity and
not
observable by any entity are being confused. I am reminded of Einstein's
silly
quip about the Moon still existing even if he was not looking at it. The
poor old
fellow neglected to notice that he was not the only entity that was capable
of
being affected by the presence or non-presence of the Moon!

You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or not is not
meaningful ? Only consciousness gives meaning to thing... yet it seems absurd that
truth value would disappear without consciousness.

Quentin

Unless multiple entities can agree that the sequence of symbols 17 is prime is an
indicator of some particular mathematical object and one of its particular properties,
then how does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is prime not the concept that
17 is prime.  Could not a person who grew up alone on an island realize that 17 has no
divisors, and he could even invent a private language in which he could write down Peano's
axioms.

Brent

Can you stop subconsciously assuming an invisible observer whose sole job is to observe
everything from infinity? It seems that you cannot if what I am writing is mysterious to
you!
How is it not absurd that meaningfulness exists in the absence of anyone that can
apprehend it? Please note that I am not considering the absence of any one entity; I am
considering the absence of all possible entities in the degenerativeness or vanishing of
meaningfulness. I am asking Why is it OK to think that meaningfulness exists in the
absence of any means to determine it?.

--
Onward!

Stephen
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To ```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:27 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 2:00 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King stephe...@charter.net
mailto:stephe...@charter.net

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and
provability of theorems apply only to the concepts
of numbers and their constructions, not to numbers
themselves.

Truth applies to proposition, or sentences
representing them for some machine/numbers. If not,
comp does not even makes sense.

So your are agreeing? Two has no truth value, but
Two equals one plus one. does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using
this to assert that the truth of, say  Two equals one
plus one. depend on some numbers or subject having to
discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/
http://iridia.ulb.ac.be/%7Emarchal/

Dear Bruno,

My point is that a number is not a capable of being
an ontological primitive *and* having some particular
set of values and meanings. A statement, such as 2 = 1+1
or two equals one plus one, are said truthfully to have
the same meaning because there are multiple and
separable entities that can have the agreement on the
truth value. In the absence of the ability to judge a
statement independently of any particular entity capable
of understanding the statement, there is no meaning to
the concept that the statement is true or false. To
insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities
capable of judging the meaning, begs the question of
meaningfulness!
You are taking for granted some things that your
arguments disallow.

Hmm... but that's what arithmetical realism is all about...
If you deny meaning to '17 is prime' absent an entity which
gives to it its meaning... then you're simply negating
arithmetical realism and with it computationalism (ie:
consciousness is emulable qua computatio).

Quentin

Hi Quentin,

Well, therefore I must reject arithmetical realism as
unreal by definition! Individual entities are incapable of
giving meaning to things, be they puppies or prime numbers.
It requires an *agreement between many entities* to have
meaningfulness. I claim that it takes at least three entities...

If objects that are proposed to be real are not
observable by anyone then they don't exist! Where am I going
off the rails? I think that the problem here is that the
distinction between not observable by any particular entity
and not observable by any entity are being confused. I am
reminded of Einstein's silly quip about the Moon still
existing even if he was not looking at it. The poor old
fellow neglected to notice that he was not the only entity
that was capable of being affected by the presence or
non-presence of the Moon!

You might have seen my definition of Reality. Do you
recall it?

So in your view, no humans (no consciouness) implies... 17 is
prime or not is not meaningful ? Only consciousness gives meaning
to thing... yet it seems absurd that truth value would disappear
without consciousness.

Quentin

Unless multiple entities can agree that the sequence of
symbols 17 is prime is an indicator of some particular
mathematical object and one of its particular properties, then how
does 17 is prime come to mean anything at all? Can you stop
subconsciously assuming an invisible observer whose sole job is to
observe everything from infinity? It seems that you cannot if what
I am writing is mysterious to you!
How is it not absurd that meaningfulness exists in the absence
of anyone that can apprehend it? Please note that I am not
considering the absence of any one entity; I am considering the
absence of all possible entities in the degenerativeness or
vanishing of meaningfulness. I am asking Why is it OK to think
that meaningfulness exists in the absence of any means to
determine it?.

```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:50 PM, meekerdb wrote:
I think you are confusing the tokens 2 = 1+1 with the proposition 2
= 1+1.  The former requires someone who understands the notation to
interpret it, but the latter is the interpretation, i.e. the concept.
A concept has meaning by definition, otherwise we say we cannot
conceptualize it, e.g. klognee flarbles myrable, and so there is
nothing to assign a truth value to.

Dear Brent,

What is it that distinguishes between tokens and propositions?

there is no meaning to the concept that the statement is true or
false. To insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities capable of
judging the meaning, begs the question of meaningfulness!

That sounds like idealism, but whatever it is sll theories that will
explain the world to us are going to have to apply to times and places
where there are no humans.  So I guess the question is whether 2=1+1
means to you what it means to the rest of us.  If it does it can be
part of our explanation.

http://en.wikipedia.org/wiki/Idealism
In philosophy, idealism is the group of philosophies which assert that
reality, or reality as we can know it, is fundamentally mental, mentally
constructed, or otherwise immaterial. Epistemologically, idealism
manifests as a skepticism about the possibility of knowing any
mind-independent thing. ... As an ontological doctrine, idealism goes
further, asserting that all entities are composed of mind or spirit.[2]
Idealism thus rejects physicalist and dualist theories that fail to
ascribe priority to the mind. An extreme version of this idealism can
exist in the philosophical notion of solipsism.

Does that seem like what I am claiming? NO! That is the wiki
definition of Idealism, and I agree with that definition and its
implications and I reject idealism.

Brent

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:58 PM, meekerdb wrote:
If there were no humans, no human level consciousness, would it still
be true that Holmes assistant is Watson?

Brent

If there there where no humans and no human level consciousness,
what meaning would the sentence It is true that Holmes assistant is
Watson have? It would be an empty syllogism at best for some non-human
with non-human consciousness to evaluate.

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of symbols
17 is prime is an indicator of some particular mathematical object
and one of its particular properties, then how does 17 is prime
come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is prime
not the concept that 17 is prime.  Could not a person who grew up
alone on an island realize that 17 has no divisors, and he could even
invent a private language in which he could write down Peano's axioms.

Why are you using such trivial and parochial framing for abstract
questions? Why the reference to single individuals? Did you not
understand that I am claiming that meaningfulness requires at least the
possibility of interaction between many entities such that each can
evaluate the truth value of a proposition and thus can truthfully claim
to have knowledge of true statements?
A person that grew and died on a desert island may have discovered
for itself that 17 objects cannot be divided into equal subsets, but our
statements about that are mere figemnts of our imagination as we could
know nothing objective and non-imaginative at all about that person. We
are imagining ourselves to have powers that we simply do not have. We
are not omniscient voyeurs of Reality and there is not anything that is.

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 1:53 PM, Stephen P. King wrote:

On 10/30/2012 2:50 PM, meekerdb wrote:
I think you are confusing the tokens 2 = 1+1 with the proposition 2 = 1+1.  The
former requires someone who understands the notation to interpret it, but the latter is
the interpretation, i.e. the concept.  A concept has meaning by definition, otherwise
we say we cannot conceptualize it, e.g. klognee flarbles myrable, and so there is
nothing to assign a truth value to.

Dear Brent,

What is it that distinguishes between tokens and propositions?

Tokens are the physical elements (e.g. letters, words, sounds) that are used to represent
a proposition in a particular language.  The proposition is the abstracted meaning which
is independent of particular language.  So Zwei est ein und ein. are tokens expressing
the same proposition as Two equals one plus one. which is that 2=1+1.

Brent

there is no meaning to the concept that the statement is true or false. To insist that
a statement has a meaning and is true (or false) in an ontological condition where no
entities capable of judging the meaning, begs the question of meaningfulness!

That sounds like idealism, but whatever it is sll theories that will explain the world
to us are going to have to apply to times and places where there are no humans.  So I
guess the question is whether 2=1+1 means to you what it means to the rest of us.  If
it does it can be part of our explanation.

http://en.wikipedia.org/wiki/Idealism
In philosophy, idealism is the group of philosophies which assert that reality, or
reality as we can know it, is fundamentally mental, mentally constructed, or otherwise
immaterial. Epistemologically, idealism manifests as a skepticism about the possibility
of knowing any mind-independent thing. ... As an ontological doctrine, idealism goes
further, asserting that all entities are composed of mind or spirit.[2] Idealism thus
rejects physicalist and dualist theories that fail to ascribe priority to the mind. An
extreme version of this idealism can exist in the philosophical notion of solipsism.

Does that seem like what I am claiming? NO! That is the wiki definition of Idealism,
and I agree with that definition and its implications and I reject idealism.

Brent

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of symbols 17 is prime is
an indicator of some particular mathematical object and one of its particular
properties, then how does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is prime not the concept
that 17 is prime.  Could not a person who grew up alone on an island realize that 17
has no divisors, and he could even invent a private language in which he could write
down Peano's axioms.

Why are you using such trivial and parochial framing for abstract questions? Why the
reference to single individuals? Did you not understand that I am claiming that
meaningfulness requires at least the possibility of interaction between many entities
such that each can evaluate the truth value of a proposition and thus can truthfully
claim to have knowledge of true statements?
A person that grew and died on a desert island may have discovered for itself that
17 objects cannot be divided into equal subsets,

So no additional entities are needed for a person know that 17 is prime and to express it
symbollically.  You seem to contradict what you just wrote in the prior paragraph.

Brent

but our statements about that are mere figemnts of our imagination as we could know
nothing objective and non-imaginative at all about that person. We are imagining
ourselves to have powers that we simply do not have. We are not omniscient voyeurs of
Reality and there is not anything that is.

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 5:15 PM, meekerdb wrote:

On 10/30/2012 1:53 PM, Stephen P. King wrote:

Dear Brent,

What is it that distinguishes between tokens and propositions?

Tokens are the physical elements (e.g. letters, words, sounds) that
are used to represent a proposition in a particular language.

What determines the map between the letters, words, sounds and the
content of propositions?

The proposition is the abstracted meaning which is independent of
particular language.

Does this independence do so far as to disallow for an arbitrary
physical entity to know of it? Independence of abstractions from
particular individuals is not independence from all.

So Zwei est ein und ein. are tokens expressing the same
proposition as Two equals one plus one. which is that 2=1+1.

That is true only because multiple persons came to believe that it
is true and acted to cause it to be true. Remove one person from the
multiplicity and the meaning still is there. Remove all of them and the
meaning vanishes.

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 5:21 PM, meekerdb wrote:

On 10/30/2012 2:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of
symbols 17 is prime is an indicator of some particular
mathematical object and one of its particular properties, then how
does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is
prime not the concept that 17 is prime.  Could not a person who
grew up alone on an island realize that 17 has no divisors, and he
could even invent a private language in which he could write down
Peano's axioms.

Why are you using such trivial and parochial framing for abstract
questions? Why the reference to single individuals? Did you not
understand that I am claiming that meaningfulness requires at least
the possibility of interaction between many entities such that each
can evaluate the truth value of a proposition and thus can truthfully
claim to have knowledge of true statements?
A person that grew and died on a desert island may have
discovered for itself that 17 objects cannot be divided into equal
subsets,

So no additional entities are needed for a person know that 17 is
prime and to express it symbollically.  You seem to contradict what
you just wrote in the prior paragraph.

Rubbish. You are projecting your concept of 17 is prime onto an
imaginary entity and discussing the idea of that entity with me, that
makes 3 people - not one; even if one - the person on the island - of
them is just in your and my mind.

Brent

but our statements about that are mere figemnts of our imagination as
we could know nothing objective and non-imaginative at all about that
person. We are imagining ourselves to have powers that we simply do
not have. We are not omniscient voyeurs of Reality and there is not
anything that is.

--
Onward!

Stephen

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:27 PM, Stephen P. King wrote:

On 10/30/2012 5:15 PM, meekerdb wrote:

On 10/30/2012 1:53 PM, Stephen P. King wrote:

Dear Brent,

What is it that distinguishes between tokens and propositions?

Tokens are the physical elements (e.g. letters, words, sounds) that are used to
represent a proposition in a particular language.

What determines the map between the letters, words, sounds and the content of
propositions?

The proposition is the abstracted meaning which is independent of particular
language.

Does this independence do so far as to disallow for an arbitrary physical entity to
know of it? Independence of abstractions from particular individuals is not independence
from all.

So Zwei est ein und ein. are tokens expressing the same proposition as Two equals
one plus one. which is that 2=1+1.

That

Which 'that' do you refer to, the tokens or the proposition.

is true only because multiple persons came to believe that it is true

You previously agreed that one person alone could come to know that 2=1+1 or 17 is prime
and express it symbolically, i.e. in tokens.  So multiple persons are only necessary in
order for the tokens to be used for communicating from one to another; which is the case
whether the thing communicated is true or false.

Brent

and acted to cause it to be true. Remove one person from the multiplicity and the
meaning still is there. Remove all of them and the meaning vanishes.

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```

### Re: Numbers in the Platonic Realm

```
On 10/30/2012 2:31 PM, Stephen P. King wrote:

On 10/30/2012 5:21 PM, meekerdb wrote:

On 10/30/2012 2:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of symbols 17 is prime
is an indicator of some particular mathematical object and one of its particular
properties, then how does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is prime not the concept
that 17 is prime.  Could not a person who grew up alone on an island realize that 17
has no divisors, and he could even invent a private language in which he could write
down Peano's axioms.

Why are you using such trivial and parochial framing for abstract questions? Why
the reference to single individuals? Did you not understand that I am claiming that
meaningfulness requires at least the possibility of interaction between many entities
such that each can evaluate the truth value of a proposition and thus can truthfully
claim to have knowledge of true statements?
A person that grew and died on a desert island may have discovered for itself that
17 objects cannot be divided into equal subsets,

So no additional entities are needed for a person know that 17 is prime and to express
it symbollically.  You seem to contradict what you just wrote in the prior paragraph.

Rubbish. You are projecting your concept of 17 is prime onto an imaginary entity
and discussing the idea of that entity with me, that makes 3 people - not one; even if
one - the person on the island - of them is just in your and my mind.

And another dozen people may be reading this.  What different does that make to the
question of whether one person alone can know a mathematical truth?  You seem to agree
that he can and yet deny it is meaningful at the same time.

Brent

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### Re: Numbers in the Platonic Realm

```
On 10/30/2012 5:39 PM, meekerdb wrote:

On 10/30/2012 2:27 PM, Stephen P. King wrote:

On 10/30/2012 5:15 PM, meekerdb wrote:

On 10/30/2012 1:53 PM, Stephen P. King wrote:

Dear Brent,

What is it that distinguishes between tokens and propositions?

Tokens are the physical elements (e.g. letters, words, sounds) that
are used to represent a proposition in a particular language.

What determines the map between the letters, words, sounds and
the content of propositions?

The proposition is the abstracted meaning which is independent of
particular language.

Does this independence do so far as to disallow for an arbitrary
physical entity to know of it? Independence of abstractions from
particular individuals is not independence from all.

So Zwei est ein und ein. are tokens expressing the same
proposition as Two equals one plus one. which is that 2=1+1.

That

Which 'that' do you refer to, the tokens or the proposition.

is true only because multiple persons came to believe that it is true

You previously agreed that one person alone could come to know that
2=1+1 or 17 is prime and express it symbolically, i.e. in tokens.  So
multiple persons are only necessary in order for the tokens to be used
for communicating from one to another; which is the case whether the
thing communicated is true or false.

In 10/30/2012 5:03 PM, Stephen P. King wrote:

On 10/30/2012 3:05 PM, meekerdb wrote:
[SPK] Unless multiple entities can agree that the sequence of
symbols 17 is prime is an indicator of some particular
mathematical object and one of its particular properties, then how
does 17 is prime come to mean anything at all?

I agree with that.  But you're talking about the tokens 17 is prime
not the concept that 17 is prime.  Could not a person who grew up
alone on an island realize that 17 has no divisors, and he could even
invent a private language in which he could write down Peano's axioms.

/*   Why are you using such trivial and parochial framing for abstract
questions? Why the reference to single individuals? Did you not
understand that I am claiming that meaningfulness requires at least
the possibility of interaction between many entities such that each
can evaluate the truth value of a proposition and thus can truthfully
claim to have knowledge of true statements? *//*
*//*A person that grew and died on a desert island may have
discovered for itself that 17 objects cannot be divided into equal
subsets, but our statements about that are mere figemnts of our
imagination as we could know nothing objective and non-imaginative at
all about that person. We are imagining ourselves to have powers that
we simply do not have. We are not omniscient voyeurs of Reality and
there is not anything that is. */

How is an imaginary entity come to aquire a real 1p or actual real
properties? It might if that imaginary entity is deemed to have 1p
content within some narrative. But outside of that narrative, it does

Brent

and acted to cause it to be true. Remove one person from the
multiplicity and the meaning still is there. Remove all of them and
the meaning vanishes.

--
Onward!

Stephen

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```

### Re: Numbers in Leibniz

```
On 10/29/2012 1:15 AM, Roger Clough wrote:

Hi Bruno

Still waiting for the storm to shut things down.

Numbers are not discussed specifically as far as I can find yet,
in my books on Leibniz. Which probably means that
they are simply numbers, with no ontological status.
Sort of like space or time. Inextended and everywhere.

Numbers are definitely not monads, because no
corporeal  body is attached.  Although they can
whenever thought of appear in the minds of
particular men in the intellects of their monads.

Hi Roger,

Physical bodies and, by extension, physical worlds follow from
mutually consistent aspects of the individual 1p of monads; they are not
attached. Leibniz, IMHO, bungled this badly in his discussions of the
that /they do not have any external aspect/. Monads do not see the
outsides of each other in any direct way. All that monads have as
percepts of that which is other than themselves are those aspects of
their own 1p that cannot be reconsidered as belonging to their identity
in the moment of the observation/appearance.

Leibniz does refer to a proposed universal
language, which is simply everywhere
as well as possibly in each head.  Numbers would
no doubt be the same, both everywhere and
in individual minds at times.

Yes, this is the Pre-Established Harmony, but as I have argued
before this concept is deeply flawed because it tries to claim that the
solution to NP-Hard problem (of choosing the best possible world) is
somehow accessible (for the creation of the monads by God) prior to the
availability of resources with which to actually perform the computation
of the solution. One cannot know the content of a solution before one
computes it, even if one is omniscient!

So numbers are universal and can be treated
mathematically as always.

I agree, but the concept of numbers has no meaning prior to the
existence of objects that can be counted. To think otherwise is
equivalent to claiming that unspecified statements are true or false
even in the absence of the possibility of discovering the fact.

--
Onward!

Stephen

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### Re: Numbers in Leibniz

```

On 29 Oct 2012, at 06:15, Roger Clough wrote:

Hi Bruno

Still waiting for the storm to shut things down.

Take care.

Numbers are not discussed specifically as far as I can find yet,
in my books on Leibniz. Which probably means that
they are simply numbers, with no ontological status.
Sort of like space or time. Inextended and everywhere.

I can be OK. I think that numbers are not even 'inextended' as
extension does not apply to them. Then, of course variant of
extension, like length in base 10, or number of Kb, can of course be
defined.

Numbers are definitely not monads, because no
corporeal  body is attached.

For me, numbers, body, language, machine, etc. are basically
synonymous. There are nuances, be they are not useful before they play
a (usually relative) rôle.

Although they can
whenever thought of appear in the minds of
particular men in the intellects of their monads.

Leibniz does refer to a proposed universal
language, which is simply everywhere
as well as possibly in each head.

I think Leibniz got the intuition of universal number (machine,
language, program, etc.).

Numbers would
no doubt be the same, both everywhere and
in individual minds at times.

OK.

So numbers are universal and can be treated
mathematically as always.

They are universal in that sense. But some numbers are universal in
the Turing sense, and, as language, might be closer to Leibniz
intuition. Such universal numbers can emulate the behavior of all
other number. typical incarnation: the brain, the computer, the three
bodies problem, the quantum zero body problem, game of life, fortran,
lisp, algol, c++, combinators, arithmetic, etc. They all faithfully
mirrors each other.

They are like the golem. You can instruct them by using words, or
numbers, so that they become slave, like your PC or MAC. Like the
golem, the math explain it is risky and that you can loose control.
With comp, you can make them becoming yourself, and an infinitely of

Bruno

Roger Clough, rclo...@verizon.net
10/29/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Roger Clough
Time: 2012-10-28, 18:31:25
Subject: Re: Re: A mirror of the universe.

Hi Bruno Marchal

I still haven't sorted the issue of numbers out.
I suppose I ought to do some research in my Leibniz books.

Aside from that, monads have to be attached to corporeal bodies,
and numbers aren't like that. I find the following unsatisfactory,
but since numbers are like ideas, they can be
in the minds of individual homunculi in individual monads,
but that doesn't sound satisfactoriy to me.
Not universakl enough.

My best guess for now is that the supreme monad (the One) undoubtedly
somehow possesses the numbers.

Hurricane coming.

Roger Clough, rclo...@verizon.net
10/28/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Time: 2012-10-27, 09:31:59
Subject: Re: A mirror of the universe.

On 26 Oct 2012, at 14:44, Roger Clough wrote:

Dear Bruno and Alberto,

I agree some what with both of you. As to the idea of a genetic
algorithm can isolate anticipative programs, I think that
anticipation
is the analogue of inertia for computations, as Mach saw inertia. It
is
a relation between any one and the class of computations that it
belongs
to such that any incomplete string has a completion in the
collections

of others like it. This is like an error correction or compression
mechanism.

--
Onward!

Stephen

ROGER: For what it's worth--- like Mach's inertia, each monad
mirrors the rest of the universe.

In arithmetic, each universal numbers mirrors all other universal
numbers. The tiny Turing universal part of arithmetical truth is

Bruno

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### Re: Numbers in Leibniz

```

On 29 Oct 2012, at 14:36, Stephen P. King wrote:

So numbers are universal and can be treated
mathematically as always.

I agree, but the concept of numbers has no meaning prior to the
existence of objects that can be counted. To think otherwise is
equivalent to claiming that unspecified statements are true or false
even in the absence of the possibility of discovering the fact.

I think you confuse numbers, and the concept of numbers.

And then your argument is not valid, as with numbers, the miracle is
that we can specify the concept of numbers, as this result in defining
some arithmetical sigma_1 complete theory in terms of 0, s(0), ... and
the laws of addition and multiplication, that everybody understands
(unless philosophers?).

Bruno

PS BTW, from a computer scientist perspective, your use of NP never
succeed to make sense. I don't dare to ask you to elaborate, as I am
afraid you might aggravate your case. The NP question is fundamental
and has many interesting feature, but it concerns a local tractability
issue, and is a priori, unless justification, not relevant for the
arithmetical body issue, nor number's theology (including physics)
issue, etc.

When you say:

Yes, this is the Pre-Established Harmony, but as I have argued
before this concept is deeply flawed because it tries to claim that
the solution to NP-Hard problem (of choosing the best possible
world) is somehow accessible (for the creation of the monads by God)
prior to the availability of resources with which to actually
perform the computation of the solution. One cannot know the content
of a solution before one computes it, even if one is omniscient!

I don't find any sense. I hope you don't mind my frankness. I wouldn't
say this if I did not respect some intuition of yours. But math and
formalism can't be a pretext for not doing the elementary reasoning in
the philosophy of mind. If you use math, you have to be clearer on the
link with philosophy or theology. To be understandable by others.

http://iridia.ulb.ac.be/~marchal/

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### Re: Numbers in the Platonic Realm

```
On 10/29/2012 1:08 PM, Bruno Marchal wrote:

On 29 Oct 2012, at 14:36, Stephen P. King wrote:
[Bruno Marchal wrote:] So numbers are universal and can be treated
mathematically as always.

I agree, but the concept of numbers has no meaning prior to the
existence of objects that can be counted. To think otherwise is
equivalent to claiming that unspecified statements are true or false
even in the absence of the possibility of discovering the fact.

Dear Bruno

I think you confuse numbers, and the concept of numbers.

No, I do not. My claim is that Numbers are objects in the mind of
conscious beings. If there does not exist worlds where entities to whom
numbers are concepts then there is no such thing as a concept of numbers
in such worlds. My argument is that concepts of truth and provability of
theorems apply only to the concepts of numbers and their constructions,
not to numbers themselves.

And then your argument is not valid, as with numbers, the miracle is
that we can specify the concept of numbers, as this result in defining
some arithmetical sigma_1 complete theory in terms of 0, s(0), ... and
the laws of addition and multiplication, that everybody understands
(unless philosophers?).

I am a philosopher! My argument rests only on the fact that the
'miracle' is exactly as you state it here: we exist and have a concept
of numbers and can ascertain the truth of arithmetic statements. My
claim is that truth valuations supervene on the ability of consciousness
to form concepts of numbers. I question the entire idea of numbers
existing as separate Platonic entities. In the absence of consciousness,
there is no such thing as a concept!

Bruno

PS BTW, from a computer scientist perspective, your use of NP never
succeed to make sense. I don't dare to ask you to elaborate, as I am
afraid you might aggravate your case. The NP question is fundamental
and has many interesting feature, but it concerns a local tractability
issue, and is a priori, unless justification, not relevant for the
arithmetical body issue, nor number's theology (including physics)
issue, etc.

It is the argument is sound and is the same kind of argument as
what Kripke used to discuss the idea of possible worlds.
http://www.philosophy-index.com/kripke/ In

There is a close relation between propositions and possible
worlds. We note that every proposition is either true or false at any
given possible world; then the modal status of a proposition is
understood in terms of the worlds in which it is true and worlds in
which it is false.

Solutions to equations or computations are not available until
after they are actually solved. My solution to this is to not go so far
as you do in Step 8. Let me try to be more explicit:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf :

Instead of linking [the pain I feel] at space-time (x,t) to [a machine
state] at space-time
(x,t), we are obliged  to associate  [the pain  I  feel at space-time
(x,t)]  to a  type or a  sheaf of
computations  (existing  forever  in  the arithmetical  Platonia which
is  accepted  as  existing

independently of  our  selves  with  arithmetical  realism).

I am pointing out that the idea of computations existing
independently of our selves is wrong in that it conflates *the meaning
and truth valuation of numbers* with *t**he existence of numbers as
Platonic objects*. It is absurd to refer to the claim that the truth of
17  is prime depends on any one person or entity, but the claim that
the truth of 17 is prime is knowable by any person is not absurd. If
we stipulate that the content of knowledge exists somehow prior to that
which knowledge supervenes upon, we are being absurd. The content of
knowledge and the ability of knowledge occur simultaneously or not at all.
Absent the concept of numbers there is no such thing as
valuations of numbers because the notion of Platonic objects considers
objects as existing independently as some singular perfect version
that is then plurally projected somehow into the physical realm, as we
see in the Allegory of the Cave. This is a one-to-many mapping, not a
one-to-one mapping.
How exactly is a type or sheaf a singular and perfect version
of each and every computation and yet be something that has individuated
valuations? Individual valuations of computations are only those that
occur as physical instantiations of computations and thus they do not
exist in Platonia. The Many exist in the physical worlds, no?
I propose a rephrasing of your statement above: We identify the 1p
qualia to a sheaf of computations (as bisimilar Boolean Algebras) that
is dual to physical machine states at diffeomorphically equivalent
space-time coordinates (x, y, z, t). This is a restatement of the Stone
duality into COMP-like terms. ;-) (The idea of ```

### Re: Re: Numbers and other inhabitants of Platonia are also inhabitantsofmonads

```Hi Richard Ruquist

Absolutely.

Roger Clough, rclo...@verizon.net
10/2/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Richard Ruquist
Time: 2012-10-01, 16:51:44
Subject: Re: Numbers and other inhabitants of Platonia are also

String theory and variable fine-structure measurements across the
universe suggest that the discrete and distinct monads are
ennumerable.

On Mon, Oct 1, 2012 at 4:32 PM, Stephen P. King  wrote:
On 10/1/2012 10:17 AM, Roger Clough wrote:

Hi Stephen P. King

Good idea, but unfortunately monads are not numbers,
numbers will now guide them or replace them.
Monads have to be associated with corporeal bodies down here in
contingia, where crap happens.

Hi Roger,

Roger Clough,rclo...@verizon.net 10/1/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-09-30, 14:22:03
Subject: Re: Numbers and other inhabitants of Platonia are also

On 9/30/2012 8:34 AM, Roger Clough wrote:

Hi Bruno Marchal

I'm still trying to figure out how numbers and ideas fit
so I have to rely on what Leibniz says otherwise about monads.

Previously I noted that numbers could not be monads because
monads constantly change. Another argument against numbers
whose identities persist, while ideas and numbers are not
created objects.

While numbers and ideas cannot be monads, they have to
be are entities in the mind, feelings, and bodily aspects
of monads. For Leibniz refers to the intellect of human
monads. And similarly, numbers and ideas must be used
in the fictional construction of matter-- in the bodily
aspect of material monads, as well as the construction
of our bodies and brains.

Dear Roger,

Bruno's idea is a form of Pre-Established Hamony, in that the
truth of the numbers is a pre-established ontological primitive.

--
Onward!

--
Onward!

Stephen

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### Re: Re: Numbers and other inhabitants of Platonia are also inhabitants ofmonads

```Hi Stephen P. King

Good idea, but unfortunately monads are not numbers,
numbers will now guide them or replace them.
Monads have to be associated with corporeal bodies down here in
contingia, where crap happens.

Roger Clough, rclo...@verizon.net
10/1/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-09-30, 14:22:03
Subject: Re: Numbers and other inhabitants of Platonia are also inhabitants

On 9/30/2012 8:34 AM, Roger Clough wrote:
Hi Bruno Marchal

I'm still trying to figure out how numbers and ideas fit
so I have to rely on what Leibniz says otherwise about monads.

Previously I noted that numbers could not be monads because
monads constantly change. Another argument against numbers
whose identities persist, while ideas and numbers are not
created objects.

While numbers and ideas cannot be monads, they have to
be are entities in the mind, feelings, and bodily aspects
of monads. For Leibniz refers to the intellect of human
monads. And similarly, numbers and ideas must be used
in the fictional construction of matter-- in the bodily
aspect of material monads, as well as the construction
of our bodies and brains.
Dear Roger,

Bruno's idea is a form of Pre-Established Hamony, in that the
truth of the numbers is a pre-established ontological primitive.

--
Onward!

Stephen

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```

```
Hi Roger Clough,

### ROGER:  Quanta are different from particles. They don't move
from A to B along particular paths through space (or even through
space), they move
through all possible mathematical paths - which is to say that they
are everywhere at once-
until one particular path is selected by a measurement (or selected
by passing through slits).

Do you agree with Everett that all path exists, and that the selection
might equivalent with a first person indeterminacy?

...
Note that intelligence requires the ability to select.

OK. But the ability to selct does not require intelligence, just
interaction and some memory.

Selection of a quantum path
(collapse or reduction of the jungle of  brain wave paths) produces
consciousness, according to Penrose et al. They call it orchestrated
reduction. .

Penrose is hardly convincing on this. Its basic argument based on
Gödel is invalid, and its theory is quite speculative, like the wave
collapse, which has never make any sense to me.

Why would the physical not be infinitely divisible and extensible,
especially if not real?

ROGER:  Objects  can be physical and also infinitely divisible,
but L considered this infinite divisibility to disqualify  an object
to be real because

there's no end to the process, one wouldn't end up with something
to refer  to.

In comp we end up with what is similar above the substitution level.
What we call macro, but which is really only what we can isolate.

The picture is of course quite counter-intuitive.

Personally. I substitute Heisenberg's uncertainty principle
as the basis for this view because the fundamental particles
are supposedly divisible.

By definition an atom is not divisible, and the atoms today are the
elementary particles. Not sure you can divide an electron or a Higgs
boson.
With comp particles might get the sme explanation as the physicist, as
fixed points for some transformation in a universal group or universal
symmetrical system.
The simple groups, the exceptional groups, the Monster group can play
some role there (I speculate).
ROGER: You can split an atom because it has parts, reactors do
that all of the time.
of this particular point, Electrons and other fundamental particles
do not have parts.

You lost me with the rest of this comment, but that's OK.

Yes. Atoms are no atoms (in greek άτομο means not divisible).
But if string theory is correct even electron are still divisible
(conceptually).

I still don't know with comp. Normally some observable have a real
continuum spectrum. Physical reality cannot be entirely discrete.

I'm still trying to figure out how numbers and ideas fit
so I have to rely on what Leibniz says otherwise about monads.

let me be explicit on this. I fixe once and for all a universal
system: I chose the programming language LISP. Actually, a subset of
it: the programs LISP computing only (partial) functions from N to N,
with some list representation of the numbers like (0), (S 0), (S S
0), ...

I enumerate in lexicographic way all the programs LISP. P_1, P_2,
P_3, ...

The ith partial computable functions phi_i is the one computed by P_i.

I can place on N a new operation, written #, with a # b = phi_a(b),
that is the result of the application of the ath program LISP, P_a, in
the enumeration of all the program LISP above, on b.

Then I define a number as being intensional when it occurs at the left
of an expression like a # b.

The choice of a universal system transforms each number into a
(partial) function from N to N.

A number u is universal if phi_u(a, b) = phi_a(b). u interprets or
understands the program a and apply it to on b to give the result
phi_a(b). a is the program, b is the data, and u is the computer. (a,
b) here abbreviates some number coding the couple (a, b), to stay
withe function having one argument (so u is a P_i, there is a
universal program P_u).

Universal is an intensional notion, it concerns the number playing the
role of a name for the function. The left number in the (partial)
operation #.

ROGER:  Despisers of religion would do well to understand
this point,  as follows:

Numbers, like all beings in Platonia  are intensional and necessary,
so are not contingent, as monads are. Thus, arithmetical theorems
and proofs
do not change with time, are always true or always false. Perfect,
heavenly,

eternal truths, as they say. Angelic. Life itself.  Free spirits.
..
Monads are intensional but are contingent, so they change (very
rapidly) with time (like other
inhabitants of Contingia). Monads are a bit corrupt like the rest of
us.
Although not perfect,  they tend to strive to be so, at least those
motivated  by
intellect (the principles of Platonia, so not entropic. Otherwise,
those dominated by the
lesser quality, passion, ```

### Re: Numbers and other inhabitants of Platonia are also inhabitants ofmonads

```
On 10/1/2012 10:17 AM, Roger Clough wrote:

Hi Stephen P. King

Good idea, but unfortunately monads are not numbers,
numbers will now guide them or replace them.
Monads have to be associated with corporeal bodies down here in
contingia, where crap happens.

Hi Roger,

Roger Clough,rclo...@verizon.net
10/1/2012

Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-09-30, 14:22:03
Subject: Re: Numbers and other inhabitants of Platonia are also inhabitants

On 9/30/2012 8:34 AM, Roger Clough wrote:

Hi Bruno Marchal

I'm still trying to figure out how numbers and ideas fit
so I have to rely on what Leibniz says otherwise about monads.

Previously I noted that numbers could not be monads because
monads constantly change. Another argument against numbers
whose identities persist, while ideas and numbers are not
created objects.

While numbers and ideas cannot be monads, they have to
be are entities in the mind, feelings, and bodily aspects
of monads. For Leibniz refers to the intellect of human
monads. And similarly, numbers and ideas must be used
in the fictional construction of matter-- in the bodily
aspect of material monads, as well as the construction
of our bodies and brains.

Dear Roger,

Bruno's idea is a form of Pre-Established Hamony, in that the
truth of the numbers is a pre-established ontological primitive.

--
Onward!

--
Onward!

Stephen

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