### Re: What is more primary than numbers?

```

On 12/18/2018 6:20 AM, Bruno Marchal wrote:

By definition; soundness means that it reflect reality.

You're now messing with words.  What does "reflect reality" mean?  It
looks like an appeal to correspondence theory to truth.  But that
means to know a theory is sound you need to know what is true.

There are two definition of soundness.

Arithmetical soundness: it means that the theorem are true in (N, 0, +, *)

Exemple if the theory proves ExEyEx(x^3 + y^3 + z^3), if the theory is
sound, it means that there are (standard) natural numbers n, m, r such
that their sum of cube gives 33.

Soundness (in general): it means that what is proved in the theory is
true in all models/intepretations of the theory.

Completeness is the reverse of that one; a theory is complete if what
is true in all models is provable.

That's ambiguous.  Do you mean a theory is complete if whatever is true
in some model is provable, or do you mean that whatever is true in every
model is provable?   Since there are in general arbitrarily many models,
is completeness only knowable by a proof in a metatheory?

Not to confuse with Arithmetical Completeness: a theory is
arithmetically complete if it proves all truth in (N, +, *).

PA is a complete theory, like all first order theories (Gödel 1930)
PA is arithmetically  incomplete (Gödel 1931).

You can prove that PA is sound using a bit of set induction, like in
Analysis. Humans tend to trust Analysis, which assumes much more than
arithmetic.

Sound just means its theorems are tautologies, i.e. they are valid
inferences from the axioms.

You might makes number theorists a bit nervous if you say that Fermat
is a tautology. We use just “theorem”, and use only tautology for
classical propositional logic.

But they are conceptually the same.

Brent

Sound means true in all models (arithmetically sound means true in the
standard model (N, +, *).

Soundness implies consistency. But consistency does not imply
soundness. The robot describing the Venus of Milo in front of
another sculpture is consistent, but unsound.

All the machines I am talking about are supposed to be
arithmetically sound.

Meaning that what they "believe" are theorems.

No, meaning that the theorem/beliefs are true in the structure (N, +,
*). It means that if PA would prove ExEyEx(x^3 + y^3 + z^3), then
there are really numbers n, m, r, having their cube added to 33. With
PA + []f, you might be able to prove ExEyEx(x^3 + y^3 + z^3), but
still not know if such standard n, m, and r exist, because x, y and z
could be non standard natural numbers. PA + []f is typically unsound.
It asserts that there is proof of the false, but can prove that it not
0, nor 1, nor 2, nor 3, nor 4, etc. It is consistent, but not
omega-consistent.

Not that they "believe" everything that is true.  In fact you have
proven anything about what a person might or might not believe. Your
ideal machines do not include any concept of acting on "beliefs"
which is the real test of beliefs.

I have no clue why this could be true, except contingently, as I use
all this to derive physics from arithmetic, not for doing machine
acting in our local neighbourhood.

Bruno

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### Re: What is more primary than numbers?

```

On 12/18/2018 5:05 AM, Bruno Marchal wrote:

On 17 Dec 2018, at 21:43, Brent Meeker  wrote:

On 12/17/2018 2:55 AM, Bruno Marchal wrote:

Sure. Any argument showing that the primary universe exist would be a
refutation of Mechanism. That is why we do the test, but they confirm that the
primary universe do not exist, and actually, they refute already that a primary
universe can make sense. That is understood and normal for most physicists.
Only materialist philosophers (dogmatic believers) have a problem with this,
but they don’t argue. They insult, or talk with dismiss tones, etc.

You ask that a lot of work be done by the word "primary" when it's only meaning
seems to be "a place we start from”.

It means a place without which we cannot start at all.

To say that matter is primary means that we can’t explain matter without
assuming its existence, and so it means that matter appearance cannot be
entirely phenomenological.

Let me see if I can summarize your theory without all the arguments for it
which, I think, motivate extraneous objections.

Premises:
1. The reason a brain produces consciousness (and non-brains don't) is that a
brain instantiates a certain class of computations.
2. The class of conscious computations can be instantiated differently and
still produce the same conscious thoughts.

More or less OK.

3. Arithmetic exists.

That has no meaning. Ll what is asked here is just if you are OK with axioms
like

What does it mean to be "OK with axioms"??  I'm OK with any axiom anyone
wants to reason about.

1) If x = y and x = z, then y = z
2) If x = y then xz = yz
3) If x = y then zx = zy
4) Kxy = x
5) Sxyz = xz(yz)

Or like

Classical logic +
1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y))
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

Conclusions:
4. Arithmetic instantiates all possible computations and this includes the
class of conscious computations.

No, that is not a conclusion here. That is a theorem in arithmetic.

Theorems are conclusions of logical inferences.

Yes, for the second part, as all computation are emulated in any reality
satisfying the axiom above, then with mechanism, that includes all conscious
experiences.

5. All possible consciousness exists in arithmetic.
6. All physical reality exists as an inference from conscious thought and there
is no other evidence for it.

You forget that the physical reality is a FIRST PERSON inference and that it has to take into account all
computations (notably below its substitution level) making physics into a measure problem, and the measure
one has to obey to at least one of []p & p, or []p & <>t, or []p & <>t & p,
with p computable (sigma_1). All three give quantum logics, so there is still some room for different
“philosophies” according to which one is closer to nature.

I forget?? Have you proven those things from the above axioms.  I don't
think you've even shown there is  "FIRST PERSON" or a "physical reality".

Brent

I don't necessarily accept those, but I'm willing to consider them as a theory
of everything and see what they predict.  One thing you often repeat is that
you can derive QM from them.  So what is that derivation?

I reverse the representation by Goldblatt on the logic of those material
hypostases. That gives a quantum logic, and that is arithmetically complete,
and richer than the QL inferred on Nature, and if mechanism is correct, all
probabilities will be derived from a “Gleason theorem” in the semantic of some
of those material mode. It is technical, as we could expect, and it relies in
part to that important representation theorem of minimal quantum logic in the
modal logic B. We found such logic B-like for all three material
self-)referential modes.

Bruno

Brent

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### Re: What is more primary than numbers?

```

On 12/18/2018 4:48 AM, Bruno Marchal wrote:

It is disingenuous to imply that whomever believes "2+2=4" is thereby committed
to believing arithmetic is consistent or even that it is well defined.

What could mean “2+2=4” for someone not believing in the consistency of
elementary arithmetic?
One could easily believe 2+2=4 without believing there are infinitely
many numbers.

Brent

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### Re: What is more primary than numbers?

```

On 12/18/2018 4:29 AM, Bruno Marchal wrote:

But mathematical objects are completely defined by their axioms.

No, they are not. All theories containing a bit of arithmetic have an
infinity of  non isomorphic models/realities.

OK.  Then how do you judge the truth of unprovable propositions? You
can't rely on a model when there are an infinity of different ones.

Brent

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### Re: What is more primary than numbers?

```

On 12/17/2018 8:38 PM, Jason Resch wrote:

On Mon, Dec 17, 2018 at 12:26 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 10:46 PM, Jason Resch wrote:

On Mon, Dec 17, 2018 at 12:00 AM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 9:30 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 1:50 PM Jason Resch
mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

Are you claiming that there is an objective
arithmetical realm that is independent of any
set of axioms?

Yes. This is partly why Gödel's result was so
shocking, and so important.

And our axiomatisations are attempts to provide
a theory of this realm? In which case any
particular set of axioms might not be true of
"real" mathematics?

It will be either incomplete or inconsistent.

Sorry, but that is silly. The realm of integers
is completely defined by a set of simple axioms
-- there is no arithmetic "reality" beyond this.

The integers can be defined, but no axiomatic system
can prove everything that happens to be true about
them.  This fact is not commonly known and
appreciated outside of some esoteric branches of
mathematics, but it is the case.

All that this means is that theorems do not encapsulate
all "truth".

Where does truth come from, if not the formalism of the
axioms?  Do you agree that arithmetical truth has an
existence independent of the axiomatic system?

No.  You are assuming that arithmetic exists apart from
axioms that define it.

I am saying truth about the integers exists independently of any
system of axioms that are capable of defining the integers.

There are true things about arithmetic that are not provable
/within arithmetic/.

It's unclear what you mean by "within arithmetic".

But that is not the same as being independent of the axioms.
Some axioms are necessary to define what is meant by arithmetic.

You need to define what you're talking about before you can talk

But mathematical objects are completely defined by their axioms.

Are they?

Two is a mathematical object.
One of the properties of two is the number of primes it separates.
For example "3 and 5", "5 and 7", etc.

If mathematical objects are completely defined by their axioms, then
shouldn't this property be defined and known for two?  Yet we don't
even know the answer to this question, we don't know if it is infinite
or finite.  It might even be that no proof exists under the axioms we
currently use.

A fair point.  Although that means there may be no fact of the matter.

There is no possibility of ostensive or empirical definition.
That's the strength of mathematics; it's "truths" are independent
of reality, they are part of language.

But in any case, the axioms don't define arithmetical truth,
which is my only point.

No, but they define arithmetic, without which "arithmetical truth"
would be meaningless.

Was the physical universe meaningless before Newton?

The universe was defined as all that existed.   A question about the
physical universe was probably meaningless to Thag the caveman.

Brent

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### Re: What is more primary than numbers?

```

On 12/16/2018 12:58 PM, Jason Resch wrote:
It's not "my Platonic arithmetic theory" --- This is the a very
popular theory among mathematicians

and also the most commonly held ideas in philosophy of mathematics
among professional mathematicians.

Prominent mathematicians that were well known Platonists, include:

* Bertrand Russell
,^[12]

Russell wrote, "In mathematics we never know what we're talking about
nor whether what we say is true."  Russell was ready to accept anything
into mathematics, but I don't think that made him a Platonist.

* Alonzo Church ,^[12]

* Kurt Gödel ,^[12]

* W. V. O. Quine
,^[12]

Quine argued that what exists is whatever is posited by our accepted
theories of science.  He thought this meant that mathematics necessary
to science was "real", but I don't know what he thought of Harty Field.

Brent

* David Kaplan
,^[12]

* Saul Kripke ,^[12]

* Edward Zalta .^[13]

* John Conway
* Roger Penrose

https://plato.stanford.edu/entries/platonism/
https://en.wikipedia.org/wiki/Platonism#Modern_Platonism
https://www.quora.com/What-is-your-opinion-on-mathematical-Platonism

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### Re: What is more primary than numbers?

```

On 12/17/2018 11:12 AM, Bruno Marchal wrote:
We would discover that 2+2=3 below the Planck length.

The men's tennis doubles team had lunch with the mixed doubles
champions.  There were three at table, well above the Planck length.

Brent

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### Re: What is more primary than numbers?

```

On 12/17/2018 11:02 AM, Bruno Marchal wrote:

On 17 Dec 2018, at 07:10, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 9:42 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 10:27 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 4:43 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 2:04 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 8:56 AM Jason Resch
mailto:jasonre...@gmail.com>>
wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

But a system that is consistent can also prove
a statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical
theories?

Physical theories do not claim to prove theorems -
they are not systems of axioms and theorems. Attempts
to recast physics in this form have always failed.

Physical theories claim to describe models of reality.
You can have a fully consistent physical theory that
nevertheless fails to accurately describe the physical
world, or is an incomplete description of the physical
world.  Likewise, you can have an axiomatic system that is
consistent, but fails to accurately describe the integers,
or is less complete than we would like.

But it still has theorems.  And no matter what the theory
is, even if it describes the integers (another mathematical
abstraction), it will fail to describe other things.

ISTM that the usefulness of mathematics is that it's
identical with its theories...it's not intended to describe
something else.

A useful set of axioms (a mathematical theory, if you will)
will accurately describe arithmetical truth. E.g., it will
provide us the means to determine the behavior of a large
number of Turing machines, or whether or not a given equation
has a solution.  The world of mathematical truth is what we are
trying to describe.  We want to know whether there is a biggest
twin prime or not, for example.  There either is or isn't a
biggest twin prime.  Our theories will either succeed or fail
to include such truths as theorems.

This is begging the question. You taking one piece of
mathematics, arithmetic, and using it as a theory describing
another piece of mathematics, Turing machines.  And then you're
calling a successful description "true". But all you're showing
is that one contains the other.

I'm not following here.

Theorems are not "truths" except in the conditional sense that
it is true that they follow from the axioms and the rules of
inference.

I agree a theorem is not the same as a truth. Truth is independent
of some statement being provable in some system.

OK.

Truth is objective.  If a system of axioms is sound and consistent,
then a theorem in that system is a truth.

No, c.f. Donald Trump.

Assuming Donald Trump is sound.

We don’t know what truth is, but we can believe that some formula are
true about our domain investigation. When I assume x + 0 = x, I ask
people if they agree with this, about the natural numbers.

Then a theory is sound, if the rule of inference preserves truth.

If a theory appears to be unsound, we put it in the trash, simply.
That happens sometimes, usually when theories manage too much big objects.

But we can never be sure that system is sound and consistent (just
like we can never know if our physical theories reflect the physical
reality they attempt to capture).

But sometimes we can be sure that our theory does not reflect
reality, even if it is sound and consistent.

By definition; soundness means that it reflect reality.

You're now messing with words.  What does "reflect reality" mean? It
looks like an appeal to correspondence theory to truth.  But that means
to know a theory is sound you need to know what is true.

Sound just means its theorems are tautologies, i.e. they are valid
inferences from the axioms.

Soundness implies consistency. But consistency does not imply
soundness. The robot describing the Venus of Milo in front of another
sculpture is consistent, but unsound.

All the machines I am talking about are supposed to be arithmetically
sound.

Meaning that what they "believe" are theorems.  Not that they "believe"
everything that is true.  In fact you have proven anythi```

### Re: What is more primary than numbers?

```

On 12/17/2018 6:09 AM, Bruno Marchal wrote:
That is not "why" I hold the physical world to be real. I take the
physical world to be real because that is the definition of reality.

Given by Aristotle in his theology/metaphysics. But that was exactly
what Plato was skeptical about.
To identify real with physical requires a special act of faith, and
can be shown inconsistent with Mechanism. So this cannot be used to
study and test Mechanism. It assumes implicitly that Mechanism is false.

Sometimes you remember that your theory includes matter and only shows
that matter can be derivative. Other times to you seem to think it makes
matter unreal.

Brent

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### Re: What is more primary than numbers?

```

On 12/17/2018 5:36 AM, Bruno Marchal wrote:
Mathematics has deep relation with theology, no doubt, but is not a
religion by itself, unless you add some metaphysical hypothesis.

Like arithmetic exists.

Brent

With mechanism added, the arithmetical truth does get a religious
aspect, because we understand that we cannot define it without
assuming a bigger thing that we cannot define.

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### Re: What is more primary than numbers?

```

On 12/17/2018 2:55 AM, Bruno Marchal wrote:

Sure. Any argument showing that the primary universe exist would be a
refutation of Mechanism. That is why we do the test, but they confirm
that the primary universe do not exist, and actually, they refute
already that a primary universe can make sense. That is understood and
normal for most physicists. Only materialist philosophers (dogmatic
believers) have a problem with this, but they don’t argue. They
insult, or talk with dismiss tones, etc.

You ask that a lot of work be done by the word "primary" when it's only
meaning seems to be "a place we start from".

Let me see if I can summarize your theory without all the arguments for
it which, I think, motivate extraneous objections.

Premises:
1. The reason a brain produces consciousness (and non-brains don't) is
that a brain instantiates a certain class of computations.
2. The class of conscious computations can be instantiated differently
and still produce the same conscious thoughts.

3. Arithmetic exists.

Conclusions:
4. Arithmetic instantiates all possible computations and this includes
the class of conscious computations.

5. All possible consciousness exists in arithmetic.
6. All physical reality exists as an inference from conscious thought
and there is no other evidence for it.

I don't necessarily accept those, but I'm willing to consider them as a
theory of everything and see what they predict.  One thing you often
repeat is that you can derive QM from them.  So what is that derivation?

Brent

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### Re: What is more primary than numbers?

```

On 12/17/2018 2:16 AM, Bruno Marchal wrote:
Yes, you create a whole theology around not all truths are provable.
But you ignore that what is false is also provable.  Provable is only
relative to axioms.

I make my theory clear. (Kxy = x; Sxyz = xz(yz), elementary
arithmetic). False is not provable in that theory.

You mean a contradiction is not provable  within that theory.  As you
said above "false" is a relation to some separately known reality.

Of course, I can only hope that you believe that elementary arithmetic
is consistent, and true with respect to the standard model. But that
is always the case when we discuss with other people. We hope they
don’t believe in 2+2=5.

It is disingenuous to imply that whomever believes "2+2=4" is thereby
committed to believing arithmetic is consistent or even that it is well
defined.

Brent

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### Re: What is more primary than numbers?

```

On Monday, December 17, 2018 at 3:45:41 AM UTC-6, Bruno Marchal wrote:

On 15 Dec 2018, at 18:20, Philip Thrift > wrote:

On Saturday, December 15, 2018 at 10:44:41 AM UTC-6, Jason wrote:

Kids in school are taught the digits of Pi go on forever.

Also known as religious indoctrination.

What ?

Why the surprise, Bruno.  You're the one who says mathematical logic is
theology.

Brent

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### Re: What is more primary than numbers?

```

On 12/16/2018 11:02 PM, Jason Resch wrote:

On Mon, Dec 17, 2018 at 12:05 AM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 9:36 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 10:22 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 4:39 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 1:56 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 10:24 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only
need integers, addition, and
multiplication, and can define any
computable function. Therefore the
question of whether or not some
diophantine equation has a solution
can be made equivalent to the
question of whether some Turing
machine halts.  So you face this
problem of getting at all the truth
once you can define integers,

There's no surprise that you can't
get at all true statements about a
system  that is defined to be infinite.

But you can always prove more true
statements with a better system of
axioms.  So clearly the axioms are not
the driving force behind truth.

And you can prove more false statements
with a "better" system of axioms...which
was my original point.  So axioms are not
a "force behind truth"; they are a force
behind what is provable.

There are objectively better systems which
prove nothing false, but allow you to prove
more things than weaker systems of axioms.

By that criterion an inconsistent system is
the objectively best of all.

The problem with an inconsistent system is that it
does prove things that are false i.e. "not true".

However we can never prove that the system
doesn't prove anything false (within the
theory itself).

You're confusing mathematically consistency
with not proving something false.

They're related. A system that is inconsistent
can prove a statement as well as its converse.
Therefore it is proving things that are false.

But a system that is consistent can also prove a
statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

The difference is that mathematicians can't test their
theories.

Sure they can:  A set of axioms predicts a Diophantine
equation has no solutions.  We happen to find it does have a
solution.  We can reject that set of axioms.

Then the axioms must have also included enough to include
Diophantine equations (e.g. PA) so you have added axioms
making the system inconsistent and every proposition is a
theorem.  The only test of the theory was that it is
inconsistent.

There is also soundness
<https://en.wikipedia.org/wiki/Soundness> which I think more
accurately reflects my example above.

"...a system is sound when all of its theorems are tautologies."
Which is to say it is true that the theorem follows from the
axioms.  Not that it is true simpliciter.

Arithmetic soundness[edit

<https://en.wikipedia.org/w/index.php?title=Soundness=edit=5>]

If/T/is a theory whose objects of discourse can be interpreted
asnatural numbers <https://en.wikipedia.org/wiki/Natural_numbers>,
```

### Re: What is more primary than numbers?

```

On 12/16/2018 10:59 PM, Jason Resch wrote:

On Mon, Dec 17, 2018 at 12:03 AM Bruce Kellett > wrote:

On Mon, Dec 17, 2018 at 4:30 PM Jason Resch mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 1:50 PM Jason Resch
mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett
mailto:bhkellet...@gmail.com>>
wrote:

Are you claiming that there is an objective
arithmetical realm that is independent of any set
of axioms?

Yes. This is partly why Gödel's result was so
shocking, and so important.

And our axiomatisations are attempts to provide a
theory of this realm? In which case any particular
set of axioms might not be true of "real" mathematics?

It will be either incomplete or inconsistent.

Sorry, but that is silly. The realm of integers is
completely defined by a set of simple axioms --
there is no arithmetic "reality" beyond this.

The integers can be defined, but no axiomatic system
can prove everything that happens to be true about
them.  This fact is not commonly known and appreciated
outside of some esoteric branches of mathematics, but
it is the case.

All that this means is that theorems do not encapsulate
all "truth".

Where does truth come from, if not the formalism of the axioms?

You are equivocating on the notion of "truth". You seem to be
claiming that "truth" is encapsulated in the axioms, and yet the
axioms and the given rules of inference do not encapsulate all
"truth".

I think I worded that badly.  What I mean is given that truth does not
come from axioms (since they cannot encapsulate all of it), then where
does it come from?  Does it have an independent, uncaused,
transcendent existence?

Do you agree that arithmetical truth has an existence
independent of the axiomatic system?

I agree that there are true statements in arithmetic that are not
theorems in any particular axiomatic system. This does not mean
that arithmetic has an existence beyond its definition in terms of
some set of axioms. You cannot go from "true" to "exists", where
"exists" means something more than the existential quantifier over
some set. Confusing the existential quantifier with an ontology is
a common mistake among some classes of mathematicians.

I agree, let us ignore "exists" for now as I think it is distracting
from the current question of whether "true statements are true"
(independent of thinking about them, defining them, uttering them, etc.).

What I am curious to know is how how many of these statements you
agree with:

"2+2 = 4" was true:
1. Before I was born
2. Before humans formalized axioms and found a proof of it
3. Before there were humans
4. Before there was any conscious life in this universe
5. As soon as there were 4 physical things to count
6. Before the big bang / before there were 4 physical things

But "2+2=4" is easily seen as an empirical theory generalized from
experience.  How about "Every number has a successor."  Then the answers
aren't so easy.

Brent

There are syntactically correct statements in the system
that are not theorems, and neither are their negation
theorems.

Yes.

Godel's theorem merely shows that some of these statements
may be true in a more general system.

So isn't this like scientific theories attempting to better
describe the physical world, with ever more general and more
powerful theories?

Except that physics is not an axiomatic system, and does not
confuse theorems with truth. It is not useful to classify physical
theories as 'true' or 'false',

Isn't this what professors do with physics tests? Ask there students
to prove something or determine what some physical law says should
happen?  Then they grade an item as wrong if the answer given was
"false" under the working theory.

I've marked many a physics homework and test in my time and I've never
marked an answer "false".

Brent

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### Re: What is more primary than numbers?

```

On 12/16/2018 10:46 PM, Jason Resch wrote:

On Mon, Dec 17, 2018 at 12:00 AM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 9:30 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 1:50 PM Jason Resch
mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

Are you claiming that there is an objective
arithmetical realm that is independent of any set of
axioms?

Yes. This is partly why Gödel's result was so shocking,
and so important.

And our axiomatisations are attempts to provide a
theory of this realm? In which case any particular
set of axioms might not be true of "real" mathematics?

It will be either incomplete or inconsistent.

Sorry, but that is silly. The realm of integers is
completely defined by a set of simple axioms -- there
is no arithmetic "reality" beyond this.

The integers can be defined, but no axiomatic system can
prove everything that happens to be true about them.
This fact is not commonly known and appreciated outside
of some esoteric branches of mathematics, but it is the case.

All that this means is that theorems do not encapsulate all
"truth".

Where does truth come from, if not the formalism of the axioms?
Do you agree that arithmetical truth has an existence independent
of the axiomatic system?

No.  You are assuming that arithmetic exists apart from axioms
that define it.

I am saying truth about the integers exists independently of any
system of axioms that are capable of defining the integers.

There are true things about arithmetic that are not provable
/within arithmetic/.

It's unclear what you mean by "within arithmetic".

But that is not the same as being independent of the axioms.  Some
axioms are necessary to define what is meant by arithmetic.

You need to define what you're talking about before you can talk about
it.

But mathematical objects are completely defined by their axioms. There
is no possibility of ostensive or empirical definition. That's the
strength of mathematics; it's "truths" are independent of reality, they
are part of language.

But in any case, the axioms don't define arithmetical truth, which is
my only point.

No, but they define arithmetic, without which "arithmetical truth" would
be meaningless.

Brent

If they don't, then formalism, nominalism, fictionalism, etc. all
fall, and what is left is platonism.

Jason
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 9:42 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 10:27 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 4:43 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 2:04 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 8:56 AM Jason Resch
mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>>
wrote:

But a system that is consistent can also prove a
statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

Physical theories do not claim to prove theorems - they
are not systems of axioms and theorems. Attempts to
recast physics in this form have always failed.

Physical theories claim to describe models of reality.  You
can have a fully consistent physical theory that
nevertheless fails to accurately describe the physical
world, or is an incomplete description of the physical
world.  Likewise, you can have an axiomatic system that is
consistent, but fails to accurately describe the integers,
or is less complete than we would like.

But it still has theorems.  And no matter what the theory is,
even if it describes the integers (another mathematical
abstraction), it will fail to describe other things.

ISTM that the usefulness of mathematics is that it's
identical with its theories...it's not intended to describe
something else.

A useful set of axioms (a mathematical theory, if you will) will
accurately describe arithmetical truth.  E.g., it will provide us
the means to determine the behavior of a large number of Turing
machines, or whether or not a given equation has a solution.  The
world of mathematical truth is what we are trying to describe.
We want to know whether there is a biggest twin prime or not, for
example.  There either is or isn't a biggest twin prime.  Our
theories will either succeed or fail to include such truths as
theorems.

This is begging the question. You taking one piece of mathematics,
arithmetic, and using it as a theory describing another piece of
mathematics, Turing machines. And then you're calling a successful
description "true". But all you're showing is that one contains
the other.

I'm not following here.

Theorems are not "truths" except in the conditional sense that it
is true that they follow from the axioms and the rules of inference.

I agree a theorem is not the same as a truth. Truth is independent of
some statement being provable in some system.

OK.

Truth is objective.  If a system of axioms is sound and consistent,
then a theorem in that system is a truth.

No, c.f. Donald Trump.

But we can never be sure that system is sound and consistent (just
like we can never know if our physical theories reflect the physical
reality they attempt to capture).

But sometimes we can be sure that our theory does not reflect reality,
even if it is sound and consistent.

Brent

Jason
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 9:36 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 10:22 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 4:39 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 1:56 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 10:24 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need
integers, addition, and multiplication,
and can define any computable function.
Therefore the question of whether or not
some diophantine equation has a solution
can be made equivalent to the question
of whether some Turing machine halts.
So you face this problem of getting at
all the truth once you can define
integers, addition and multiplication.

There's no surprise that you can't get at
all true statements about a system  that
is defined to be infinite.

But you can always prove more true statements
with a better system of axioms.  So clearly
the axioms are not the driving force behind
truth.

And you can prove more false statements with a
"better" system of axioms...which was my
original point.  So axioms are not a "force
behind truth"; they are a force behind what is
provable.

There are objectively better systems which prove
nothing false, but allow you to prove more things
than weaker systems of axioms.

By that criterion an inconsistent system is the
objectively best of all.

The problem with an inconsistent system is that it does
prove things that are false i.e. "not true".

However we can never prove that the system doesn't
prove anything false (within the theory itself).

You're confusing mathematically consistency with
not proving something false.

They're related. A system that is inconsistent can
prove a statement as well as its converse. Therefore it
is proving things that are false.

But a system that is consistent can also prove a
statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

The difference is that mathematicians can't test their theories.

Sure they can:  A set of axioms predicts a Diophantine equation
has no solutions.  We happen to find it does have a solution.  We
can reject that set of axioms.

Then the axioms must have also included enough to include
Diophantine equations (e.g. PA) so you have added axioms making
the system inconsistent and every proposition is a theorem.  The
only test of the theory was that it is inconsistent.

There is also soundness
<https://en.wikipedia.org/wiki/Soundness> which I think more
accurately reflects my example above.

"...a system is sound when all of its theorems are tautologies." Which
is to say it is true that the theorem follows from the axioms.  Not that
it is true simpliciter.

Brent

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```

### Re: What is more primary than numbers?

```

On 12/16/2018 9:30 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett > wrote:

On Mon, Dec 17, 2018 at 1:50 PM Jason Resch mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

Are you claiming that there is an objective arithmetical
realm that is independent of any set of axioms?

Yes. This is partly why Gödel's result was so shocking, and so
important.

And our axiomatisations are attempts to provide a theory
of this realm? In which case any particular set of axioms
might not be true of "real" mathematics?

It will be either incomplete or inconsistent.

Sorry, but that is silly. The realm of integers is
completely defined by a set of simple axioms -- there is
no arithmetic "reality" beyond this.

The integers can be defined, but no axiomatic system can prove
everything that happens to be true about them.  This fact is
not commonly known and appreciated outside of some esoteric
branches of mathematics, but it is the case.

All that this means is that theorems do not encapsulate all "truth".

Where does truth come from, if not the formalism of the axioms?  Do
you agree that arithmetical truth has an existence independent of the
axiomatic system?

No.  You are assuming that arithmetic exists apart from axioms that
define it.  There are true things about arithmetic that are not provable
/within arithmetic/.  But that is not the same as being independent of
the axioms.  Some axioms are necessary to define what is meant by
arithmetic.

Brent

There are syntactically correct statements in the system that are
not theorems, and neither are their negation theorems.

Yes.

Godel's theorem merely shows that some of these statements may be
true in a more general system.

So isn't this like scientific theories attempting to better describe
the physical world, with ever more general and more powerful theories?

That does not mean that the integers are not completely defined by
some simple axioms. It means no more than that 'truth' and
'theorem' are not synonyms.

I agree with this.

Jason
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 4:43 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 2:04 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett
mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 8:56 AM Jason Resch
mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

But a system that is consistent can also prove a
statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

Physical theories do not claim to prove theorems - they are
not systems of axioms and theorems. Attempts to recast
physics in this form have always failed.

Physical theories claim to describe models of reality.  You can
have a fully consistent physical theory that nevertheless fails
to accurately describe the physical world, or is an incomplete
description of the physical world.  Likewise, you can have an
axiomatic system that is consistent, but fails to accurately
describe the integers, or is less complete than we would like.

But it still has theorems.  And no matter what the theory is, even
if it describes the integers (another mathematical abstraction),
it will fail to describe other things.

ISTM that the usefulness of mathematics is that it's identical
with its theories...it's not intended to describe something else.

A useful set of axioms (a mathematical theory, if you will) will
accurately describe arithmetical truth.  E.g., it will provide us the
means to determine the behavior of a large number of Turing machines,
or whether or not a given equation has a solution.  The world of
mathematical truth is what we are trying to describe.  We want to know
whether there is a biggest twin prime or not, for example.  There
either is or isn't a biggest twin prime.  Our theories will either
succeed or fail to include such truths as theorems.

This is begging the question. You taking one piece of mathematics,
arithmetic, and using it as a theory describing another piece of
mathematics, Turing machines.  And then you're calling a successful
description "true". But all you're showing is that one contains the
other.   Theorems are not "truths" except in the conditional sense that
it is true that they follow from the axioms and the rules of inference.

Brent

Jason
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 4:39 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/16/2018 1:56 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 10:24 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need
integers, addition, and multiplication, and
can define any computable function. Therefore
the question of whether or not some
diophantine equation has a solution can be
made equivalent to the question of whether
some Turing machine halts.  So you face this
problem of getting at all the truth once you
can define integers, addition and multiplication.

There's no surprise that you can't get at all
true statements about a system  that is
defined to be infinite.

But you can always prove more true statements with
a better system of axioms.  So clearly the axioms
are not the driving force behind truth.

And you can prove more false statements with a
"better" system of axioms...which was my original
point.  So axioms are not a "force behind truth";
they are a force behind what is provable.

There are objectively better systems which prove
nothing false, but allow you to prove more things than
weaker systems of axioms.

By that criterion an inconsistent system is the
objectively best of all.

The problem with an inconsistent system is that it does
prove things that are false i.e. "not true".

However we can never prove that the system doesn't
prove anything false (within the theory itself).

You're confusing mathematically consistency with not
proving something false.

They're related. A system that is inconsistent can prove a
statement as well as its converse. Therefore it is proving
things that are false.

But a system that is consistent can also prove a statement
that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

The difference is that mathematicians can't test their theories.

Sure they can:  A set of axioms predicts a Diophantine equation has no
solutions.  We happen to find it does have a solution.  We can reject
that set of axioms.

Then the axioms must have also included enough to include Diophantine
equations (e.g. PA) so you have added axioms making the system
inconsistent and every proposition is a theorem.  The only test of the
theory was that it is inconsistent.

Brent

--
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 2:04 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett <mailto:bhkellet...@gmail.com>> wrote:

On Mon, Dec 17, 2018 at 8:56 AM Jason Resch mailto:jasonre...@gmail.com>> wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

But a system that is consistent can also prove a statement
that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

Physical theories do not claim to prove theorems - they are not
systems of axioms and theorems. Attempts to recast physics in this
form have always failed.

Physical theories claim to describe models of reality. You can have a
fully consistent physical theory that nevertheless fails to accurately
describe the physical world, or is an incomplete description of the
physical world.  Likewise, you can have an axiomatic system that is
consistent, but fails to accurately describe the integers, or is less
complete than we would like.

But it still has theorems.  And no matter what the theory is, even if it
describes the integers (another mathematical abstraction), it will fail
to describe other things.

ISTM that the usefulness of mathematics is that it's identical with its
theories...it's not intended to describe something else.

Brentent

--
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```

### Re: What is more primary than numbers?

```

On 12/16/2018 1:56 PM, Jason Resch wrote:

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 10:24 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need integers,
addition, and multiplication, and can define any
computable function. Therefore the question of
whether or not some diophantine equation has a
solution can be made equivalent to the question of
whether some Turing machine halts.  So you face
this problem of getting at all the truth once you
can define integers, addition and multiplication.

There's no surprise that you can't get at all true
statements about a system  that is defined to be
infinite.

But you can always prove more true statements with a
better system of axioms.  So clearly the axioms are not
the driving force behind truth.

And you can prove more false statements with a "better"
system of axioms...which was my original point. So
axioms are not a "force behind truth"; they are a force
behind what is provable.

There are objectively better systems which prove nothing
false, but allow you to prove more things than weaker
systems of axioms.

By that criterion an inconsistent system is the objectively
best of all.

The problem with an inconsistent system is that it does prove
things that are false i.e. "not true".

However we can never prove that the system doesn't prove
anything false (within the theory itself).

You're confusing mathematically consistency with not proving
something false.

They're related. A system that is inconsistent can prove a
statement as well as its converse. Therefore it is proving things
that are false.

But a system that is consistent can also prove a statement that is
false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

So how is this different from flawed physical theories?

The difference is that mathematicians can't test their theories.

Brent

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### Re: What is more primary than numbers?

```Numbers are an abstraction and generalization from counting.   But
counting takes seeing some things a similar enough to be counted, yet
not identical.  I can count the dogs in my yard because what's a dog and
what's not seems clear. But it's hard to count trees in my yard:  Is
that a bush or a tree?  Is that sprout a tree, or does it have to grow
up first?

Brent

On 12/16/2018 1:29 AM, 'scerir' via Everything List wrote:

A /numerus/ (literally: "number"/i/) was the term used for a unit of
the Roman army .. In the
Imperial Roman army
(30 BC – 284 AD),
it referred to units of barbarian
allies who were not
integrated into the regular army structure of legions
and auxilia
.

I'm inclined to think that numbers - for there obiectivity - need a
good "counter" (somebody or somethink).

'I raised just this objection with the (extreme) ultrafinitist
Yessenin Volpin during a lecture of his. He asked me to be more
specific. I then proceeded to start with 2^1 and asked him whether
this is "real" or something to that effect. He virtually immediately
said yes. Then I asked about 2^2, and he again said yes, but with a
perceptible delay. Then 2^3, and yes, but with more delay. This
continued for a couple of more times, till it was obvious how he was
handling this objection. Sure, he was prepared to always answer yes,
but he was going to take 2^100 times as long to answer yes to 2^100
then he would to answering 2^1. There is no way that I could get very
far with this.' -Harvey M. Friedman

Dunno if in each every part of this universe there is a good
"counter". Maybe universe itself, as a whole, is a "counter"?.

'Paper in white the floor of the room, and rule it off in one-foot
squares. Down on one's hands and knees, write in the first square a
set of equations conceived as able to govern the physics of the
universe. Think more overnight. Next day put a better set of equations
into square two. Invite one's most respected colleagues to contribute
to other squares. At the end of these labors, one has worked oneself
out into the doorway. Stand up, look back on all those equations, some
perhaps more hopeful than others, raise one's finger commandingly, and
give the order "*Fly*!" Not one of those equations will put on wings,
take off, or fly. *Yet the universe "flies"*.(Wheeler on page 1208 of
_Gravitation_)

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### Re: What is more primary than numbers?

```

On 12/15/2018 10:24 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need integers,
addition, and multiplication, and can define any
computable function. Therefore the question of whether
or not some diophantine equation has a solution can be
made equivalent to the question of whether some Turing
machine halts. So you face this problem of getting at
all the truth once you can define integers, addition
and multiplication.

There's no surprise that you can't get at all true
statements about a system  that is defined to be infinite.

But you can always prove more true statements with a better
system of axioms. So clearly the axioms are not the driving
force behind truth.

And you can prove more false statements with a "better"
system of axioms...which was my original point.  So axioms
are not a "force behind truth"; they are a force behind what
is provable.

There are objectively better systems which prove nothing false,
but allow you to prove more things than weaker systems of axioms.

By that criterion an inconsistent system is the objectively best
of all.

The problem with an inconsistent system is that it does prove things
that are false i.e. "not true".

However we can never prove that the system doesn't prove anything
false (within the theory itself).

You're confusing mathematically consistency with not proving
something false.

They're related. A system that is inconsistent can prove a statement
as well as its converse. Therefore it is proving things that are false.

But a system that is consistent can also prove a statement that is false:

axiom 1: Trump is a genius.
axiom 2: Trump is stable.

theorem: Trump is a stable genius.

Brent

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### Re: What is more primary than numbers?

```

On 12/15/2018 6:07 PM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need integers, addition,
and multiplication, and can define any computable function.
Therefore the question of whether or not some diophantine
equation has a solution can be made equivalent to the
question of whether some Turing machine halts.  So you face
this problem of getting at all the truth once you can define
integers, addition and multiplication.

There's no surprise that you can't get at all true statements
about a system  that is defined to be infinite.

But you can always prove more true statements with a better
system of axioms.  So clearly the axioms are not the driving
force behind truth.

And you can prove more false statements with a "better" system of
axioms...which was my original point.  So axioms are not a "force
behind truth"; they are a force behind what is provable.

There are objectively better systems which prove nothing false, but
allow you to prove more things than weaker systems of axioms.

By that criterion an inconsistent system is the objectively best of all.

However we can never prove that the system doesn't prove anything
false (within the theory itself).

You're confusing mathematically consistency with not proving something
false.

Brent

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### Re: What is more primary than numbers?

```

On 12/15/2018 5:42 PM, Jason Resch wrote:

hh, but diophantine equations only need integers, addition, and
multiplication, and can define any computable function. Therefore
the question of whether or not some diophantine equation has a
solution can be made equivalent to the question of whether some
Turing machine halts.  So you face this problem of getting at all
the truth once you can define integers, addition and multiplication.

There's no surprise that you can't get at all true statements
about a system  that is defined to be infinite.

But you can always prove more true statements with a better system of
axioms.  So clearly the axioms are not the driving force behind truth.

And you can prove more false statements with a "better" system of
axioms...which was my original point.  So axioms are not a "force behind
truth"; they are a force behind what is provable.

Brent

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### Re: What is more primary than numbers?

```

On 12/15/2018 2:58 PM, Jason Resch wrote:

On Saturday, December 15, 2018, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/15/2018 7:43 AM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 1:09 AM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/14/2018 7:31 PM, Jason Resch wrote:

On Fri, Dec 14, 2018 at 8:43 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

Yes, you create a whole theology around not all truths
are provable.  But you ignore that what is false is also
provable.  Provable is only relative to axioms.

1. Do you agree a Turing machine will either halt or not?

2. Do you agree that no finite set of axioms has the power
to prove whether or not any given Turing machine will halt
or not?

3. What does this tell us about the relationship between
truth, proofs, and axioms?

What do you think it tells us.  Does it tell us that a false
axiom will not allow proof of a false proposition?

It tells us mathematical truth is objective and doesn't come from
axioms. Axioms are like physical theories, we can test them and
refute them if they lead to predictions that are demonstrably
false. E.g., if they predict a Turing machine will not halt, but
it does, then we can reject that axiom as an incorrect theory of
mathematical truth.  Similarly, we might find axioms that allow
us to prove more things than some weaker set of axioms, thereby
building a better theory, but we have no mechanical way of doing
this. In that way it is like doing science, and requires trial
and error, comparing our theories with our observations, etc.

Fine, except you've had to quailfy it as "mathematical truth",
meaning that it is relative to the axioms defining the Turning
machine.  Remember a Turing machine isn't a real device.

Brent

Ahh, but diophantine equations only need integers, addition, and
multiplication, and can define any computable function. Therefore the
question of whether or not some diophantine equation has a solution
can be made equivalent to the question of whether some Turing machine
halts.  So you face this problem of getting at all the truth once you
can define integers, addition and multiplication.

There's no surprise that you can't get at all true statements about a
system  that is defined to be infinite.

Brent

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### Re: What is more primary than numbers?

```

On 12/15/2018 7:43 AM, Jason Resch wrote:

On Sat, Dec 15, 2018 at 1:09 AM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/14/2018 7:31 PM, Jason Resch wrote:

On Fri, Dec 14, 2018 at 8:43 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

Yes, you create a whole theology around not all truths are
provable. But you ignore that what is false is also
provable.  Provable is only relative to axioms.

1. Do you agree a Turing machine will either halt or not?

2. Do you agree that no finite set of axioms has the power to
prove whether or not any given Turing machine will halt or not?

3. What does this tell us about the relationship between truth,
proofs, and axioms?

What do you think it tells us.  Does it tell us that a false axiom
will not allow proof of a false proposition?

It tells us mathematical truth is objective and doesn't come from
axioms. Axioms are like physical theories, we can test them and refute
them if they lead to predictions that are demonstrably false. E.g., if
they predict a Turing machine will not halt, but it does, then we can
reject that axiom as an incorrect theory of mathematical truth.
Similarly, we might find axioms that allow us to prove more things
than some weaker set of axioms, thereby building a better theory, but
we have no mechanical way of doing this. In that way it is like doing
science, and requires trial and error, comparing our theories with our
observations, etc.

Fine, except you've had to quailfy it as "mathematical truth", meaning
that it is relative to the axioms defining the Turning machine.
Remember a Turing machine isn't a real device.

Brent

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### Re: What is more primary than numbers?

```

On 12/14/2018 7:31 PM, Jason Resch wrote:
On Fri, Dec 14, 2018 at 8:43 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

Yes, you create a whole theology around not all truths are
provable.  But you ignore that what is false is also provable.
Provable is only relative to axioms.

1. Do you agree a Turing machine will either halt or not?

2. Do you agree that no finite set of axioms has the power to prove
whether or not any given Turing machine will halt or not?

3. What does this tell us about the relationship between truth,
proofs, and axioms?

What do you think it tells us.  Does it tell us that a false axiom will
not allow proof of a false proposition?

Brent

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### Re: What is more primary than numbers?

```

On 12/14/2018 11:32 AM, Jason Resch wrote:

On Fri, Dec 14, 2018 at 9:36 AM John Clark > wrote:

On Thu, Dec 13, 2018 at 8:21 PM Jason Resch mailto:jasonre...@gmail.com>> wrote:

>>The block universe changes along the time dimension and
special relativity deals with time, but the number 3 never
changes with time and has nothing to do with it.

/>Then you agree that there can be an objectively static object,/

Static with respect to what dimension? The block universe is a
mathematical 4D object  constructed in 1 dimension of time and 3
dimensions of space that follows Non-Euclidean geometry, and it
changes in time and it changes in space, if it didn't there would
be no details in the universe and everything would be a even
unchanging fog.

Special Relativity implies all points in time are equally real, and
moreover, cannot be sliced into any objective view of a "present",
each inertial reference frame can have its own view of what the
present is.

Which only shows that the idea of a reference frame defining a "present"
is inconsistent with relativity.  It is light cones that are
invariant...not specious "nows".

Brent

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### Re: What is more primary than numbers?

```

On 12/14/2018 10:41 AM, Philip Thrift wrote:
One type of objection might be that matter is a mystery, but math
isn't. But I think complexity theorists (like Chaitin) have shown that
math is a mystery too.

Actually the argument has been made the other way.  Math is not a
mystery, it is completely known as are fictional stories like "Moby
Dick". What is written down in all there is.  If you ask what was the
beam of the Pequod there is no corresponding fact.  But if you ask what
was the beam of the Pinta, there was such a value, even if you can't
find what it was.  So real things are more complex and are not
completely definable.

Brent

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### Re: What is more primary than numbers?

```

On 12/12/2018 3:19 AM, Bruno Marchal wrote:

On 10 Dec 2018, at 20:26, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/9/2018 11:38 PM, Philip Thrift wrote:

On Sunday, December 9, 2018 at 8:43:59 PM UTC-6, Jason wrote:

On Sun, Dec 9, 2018 at 2:02 PM Philip Thrift > wrote:

On Sunday, December 9, 2018 at 9:36:39 AM UTC-6, Jason wrote:

On Sun, Dec 9, 2018 at 2:53 AM Philip Thrift
wrote:

On Saturday, December 8, 2018 at 2:27:45 PM UTC-6,
Jason wrote:

I think truth is primitive.

Jason

As a matter of linguistics (and philosophy), *truth*
and *matter* are linked:

"As a matter of fact, ..."
"The truth of the matter is ..."
"It matters that ..."
...
[ https://www.etymonline.com/word/matter
<https://www.etymonline.com/word/matter> ]

I agree they are linked.  Though matter may be a few
steps removed from truth.  Perhaps one way to interpret
the link more directly is thusly:

There is an equation whose every solution (where the
equation happens to be */true/*, e.g. is satisfied when
it has certain values assigned to its variables) maps
its variables to states of the time evolution of the
wave function of our universe.  You might say that we
(literally not figuratively) live within such an
equation.  That its truth reifies what we call matter.

But I think truth plays an even more fundamental roll
than this.  e.g. because the following statement is
*/true/* "two has a successor" then there exists a
successor to 2 distinct from any previous number.
Similarly, the */truth/* of "9 is not prime" implies the
existence of a factor of 9 besides 1 and 9.

Jason

Schopenhauer 's view: "A judgment has /material
truth/ if its concepts are based on intuitive
perceptions that are generated from sensations. If a
judgment has its reason (ground) in another
judgment, its truth is called logical or formal. If
a judgment, of, for example, pure mathematics or
pure science, is based on the forms (space, time,
causality) of intuitive, empirical knowledge, then
the judgment has transcendental truth."
[ https://en.wikipedia.org/wiki/Truth
<https://en.wikipedia.org/wiki/Truth> ]

I guess I am referring to transcend truth here. Truth
concerning the integers is sufficient to yield the
universe, matter, and all that we see around us.

Jason

In my view there is basically just *material* (from matter)
truth and *linguistic* (from language) truth.

[
https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/
<https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/>
]

Relations and functions are linguistic: relational type
theory (RTT) , functional type theory (FTT) languages.

Numbers are also linguistic beings, the (fictional) semantic
objects of Peano arithmetic (PA).

Numbers can be "materialized" via /nominalization /(cf.
Hartry Field, refs. in [
https://en.wikipedia.org/wiki/Hartry_Field
<https://en.wikipedia.org/wiki/Hartry_Field> ]).

Assuming the primacy of matter assumes more and explains less,
than assuming the primacy of arithmetical truth.

Jason

In today's era of mathematics, Joel David Hamkins (@JDHamkins
<https://twitter.com/JDHamkins>) has shown there is a "multiverse"
of truths:

*The set-theoretic multiverse*
[ https://arxiv.org/abs/1108.4223 ]

/The multiverse view in set theory, introduced and argued for in
this article, is the view that there are many distinct concepts of
set, each instantiated in a corresponding set-theoretic universe.
The universe view, in contrast, asserts that there is an absolute
background set concept, with a corresponding absolute set-theoretic
universe in which every set-theoretic question has a definite
answer. The multiverse position, I argue, explains our experience
with the enormous diversity of set-theoretic possibilities, a
phenomenon that challenges the universe view. In particular, I argue
that the continuum hypothesis is settled on the multiverse view by
our extensive knowledge about how it behaves in the multiverse, and
as a result it can no longer be settled in the manner formerly hoped
for.

/
/
/
/
/
What this means```

### Re: What is more primary than numbers?

```

On 12/11/2018 10:34 AM, Philip Thrift wrote:

On Tuesday, December 11, 2018 at 12:13:14 PM UTC-6, Brent wrote:

On 12/9/2018 11:38 PM, Philip Thrift wrote:

On Sunday, December 9, 2018 at 8:43:59 PM UTC-6, Jason wrote:

On Sun, Dec 9, 2018 at 2:02 PM Philip Thrift
wrote:

On Sunday, December 9, 2018 at 9:36:39 AM UTC-6, Jason
wrote:

On Sun, Dec 9, 2018 at 2:53 AM Philip Thrift
wrote:

On Saturday, December 8, 2018 at 2:27:45 PM
UTC-6, Jason wrote:

I think truth is primitive.

Jason

As a matter of linguistics (and philosophy),
*truth* and *matter* are linked:

"As a matter of fact, ..."
"The truth of the matter is ..."
"It matters that ..."
...
[ https://www.etymonline.com/word/matter
]

I agree they are linked.  Though matter may be a few
steps removed from truth.  Perhaps one way to
interpret the link more directly is thusly:

There is an equation whose every solution (where the
equation happens to be */true/*, e.g. is satisfied
when it has certain values assigned to its variables)
maps its variables to states of the time evolution of
the wave function of our universe.  You might say
that we (literally not figuratively) live within such
an equation.  That its truth reifies what we call matter.

But I think truth plays an even more fundamental roll
than this.  e.g. because the following statement is
*/true/* "two has a successor" then there exists a
successor to 2 distinct from any previous number.
Similarly, the */truth/* of "9 is not prime" implies
the existence of a factor of 9 besides 1 and 9.

Jason

Schopenhauer 's view: "A judgment has /material
truth/ if its concepts are based on intuitive
perceptions that are generated from sensations.
If a judgment has its reason (ground) in another
judgment, its truth is called logical or formal.
If a judgment, of, for example, pure mathematics
or pure science, is based on the forms (space,
time, causality) of intuitive, empirical
knowledge, then the judgment has transcendental
truth."
[ https://en.wikipedia.org/wiki/Truth
]

I guess I am referring to transcend truth here. Truth
concerning the integers is sufficient to yield the
universe, matter, and all that we see around us.

Jason

In my view there is basically just *material* (from
matter) truth and *linguistic* (from language) truth.

[
https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/

]

Relations and functions are linguistic: relational type
theory (RTT) , functional type theory (FTT) languages.

Numbers are also linguistic beings, the (fictional)
semantic objects of Peano arithmetic (PA).

Numbers can be "materialized" via /nominalization /(cf.
Hartry Field, refs. in [
https://en.wikipedia.org/wiki/Hartry_Field
]).

Assuming the primacy of matter assumes more and explains
less, than assuming the primacy of arithmetical truth.

Jason

In today's era of mathematics, Joel David Hamkins (@JDHamkins
) has shown there is a
"multiverse" of truths:

*The set-theoretic multiverse*
[ https://arxiv.org/abs/1108.4223  ]

/The multiverse view in set theory, introduced and argued for in
this article, is the view that there are many distinct concepts
of set, each instantiated in a corresponding set-theoretic
universe. The universe view, in contrast, asserts that there is
an absolute background set concept, with a corresponding absolute
set-theoretic universe in which every set-theoretic question has
a definite answer. The multiverse position, I argue, explains our
experience with the enormous diversity of set-theoretic
possibilities, a phenomenon that challenges the universe view. In
```

### Re: Where Max Tegmark is really wrong

```

On 12/11/2018 12:04 PM, Philip Thrift wrote:

On Tuesday, December 11, 2018 at 1:53:50 PM UTC-6, agrays...@gmail.com
wrote:

On Tuesday, December 11, 2018 at 7:30:32 PM UTC, Philip Thrift wrote:

On Tuesday, December 11, 2018 at 1:02:52 PM UTC-6,
agrays...@gmail.com wrote:

On Tuesday, December 11, 2018 at 6:44:34 PM UTC, Philip
Thrift wrote:

On Tuesday, December 11, 2018 at 12:32:51 PM UTC-6,
agrays...@gmail.com wrote:

* As for physicists being materialists in the
sense of believing there is nothing underlying
matter as its cause, I have never heard that
position articulated by any physicist, in person
or on the Internet. AG *

Victor Stenger
*Materialism Deconstructed?*

https://www.huffingtonpost.com/victor-stenger/materialism-deconstructed_b_2228362.html

*I was once a member of Vic's discussion group. Vic
believed in the reality of matter, in the sense that if
you kick it, it kicks back. But he didn't deny the
possibility that there could be something more fundamental
underlying matter.  This denial is what Bruno claims is
the materialist position, but it surely wasn't Vic's
position. You know this, of course, being a member of that
group. Right? AG*

- pt

I hosted Vic in Dallas in 2014 for a talk. I got to know him
fairly personally .

Homages to philosophical materialism ("matter is the
fundamental substance in nature") is in his books. /Timeless
Reality/ in particular.

One can be open-minded, or /ironist /in Rorty's definition [
https://en.wikipedia.org/wiki/Ironism
], and he was that.

But despite all the "models" talk, I would confidently say he
was always a hardcore materialist.

- pt

Show me one instance, just one, where Vic denied something causal
and unknown underlying the existence of matter? This is Bruno's
model of materialism among physicists but it clearly doesn't apply
to Vic. AG

When Vic refutes that materialism ("all there is is matter") has been
refuted (as Vic did in his essay), he is asserting all there is is
matter. There is no matter + some ghosts behind matter. He wanted to
banish the ghosts (the immaterial).

Ghosts are agents.  The proposal that there is nothing more to matter
than mathematical relations, an idea advocated by Max Tegmark, Bruno
Marchal, Wheeler and others, is quite different from "ghosts".

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 12/14/2018 2:59 AM, Bruno Marchal wrote:

On 13 Dec 2018, at 21:24, Brent Meeker  wrote:

On 12/13/2018 3:25 AM, Bruno Marchal wrote:

But that is the same as saying proof=>truth.

I don’t think so. It says that []p -> p is not provable, unless p is proved.

So  []([]p -> p) -> p  or in other words Proof([]p -> p) => (p is true)  So in
this case proof entails truth??

But “[]([]p -> p) -> p” is not a theorem of G, meaning that "[]([]p -> p) -> p”
is not true in general for any arithmetic p, with [] = Gödel’s beweisbar.

The Löb’s formula is []([]p -> p) -> []p, not []([]p -> p) -> p.

For example []f -> f (consistency) is not provable. It will belong to G* \ G.

Another example is that []<>t -> <>t is false, despite <>t being true. In fact <>t ->
~[]<>t.
Or <>t -> <>[]f. Consistency implies the consistency of inconsistency.

I'm not sure how to interpret these formulae.  Are you asserting them for every
substitution of t by a true proposition (even though "true" is undefinable)?

No, only by either the constant propositional “true”, or any obvious truth you
want, like “1 = 1”.

Or are you asserting that there is at least one true proposition for which []<>t ->
<>t is false?

You can read it beweisbar (consistent(“1 = 1”)) -> (consistent (“1=1”), and
indeed that is true, but not provable by the machine too which this provability
and consistency referred to.

Nothing which is proven can be false,

Assuming consistency, which is not provable.

So consistency is hard to determine.  You just assume it for arithmetic.  But
finding that an axiom is false is common in argument.

Explain this to your tax inspector!

I have.  Just because I spent \$125,000 on my apartment building doesn't
mean it's appraised value must be \$125,000 greater.

If elementary arithmetic is inconsistent, all scientific theories are false.

Not inconsistent, derived from false or inapplicable premises.

Gödel’s theorem illustrate indirectly the consistency of arithmetic, as no one
has ever been able to prove arithmetic’s consistency in arithmetic, which
confirms its consistency, given that if arithmetic is consistent, it cannot
prove its consistency.

But it can be proven in bigger systems.

Gödel’s result does not throw any doubt about arithmetic’s consistency, quite
the contrary.

Of course, if arithmetic was inconsistent, it would be able to prove (easily)
its consistency.

Only if you first found the inconsistency, i.e. proved a contradiction.
And even then there might be a question of the rules of inference.

Brent

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### Re: What is more primary than numbers?

```

On 12/13/2018 4:15 AM, Bruno Marchal wrote:
See the bit about reversible computing:
https://en.wikipedia.org/wiki/Landauer%27s_principle (computations
that are reversible require no energy).

And they produce no results since they run both ways.  They are not
even computations in the CT sense.

They are computations in the CT sense.

CT computations halt.  A program that can just wander back an forth
at random doesn't halt.

?

There is no CT for the programs who always halt. Universal machine
would not exist. The price of being a universal machine is that not
only it does not always halt, but there is no mechanical procedure
deciding when it halts or not.

No, my point was that unless a program halts it has not computed
anything.  I objected to the above /"computations that are reversible
require no energy"/.   This is either a statement about the abstract
mathematical computation, in which case it is trivial, or it is a
statement about physically realized computations in which case it is
false because physically reversible computations have no direction.

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 12/13/2018 3:25 AM, Bruno Marchal wrote:

But that is the same as saying proof=>truth.

I don’t think so. It says that []p -> p is not provable, unless p is
proved.

So  []([]p -> p) -> p  or in other words Proof([]p -> p) => (p is true)
So in this case proof entails truth??

For example []f -> f (consistency) is not provable. It will belong to
G* \ G.

Another example is that []<>t -> <>t is false, despite <>t being true.
In fact <>t -> ~[]<>t.

Or <>t -> <>[]f. Consistency implies the consistency of inconsistency.

I'm not sure how to interpret these formulae.  Are you asserting them
for every substitution of t by a true proposition (even though "true" is
undefinable)?  Or are you asserting that there is at least one true
proposition for which []<>t -> <>t is false?

Nothing which is proven can be false,

Assuming consistency, which is not provable.

So consistency is hard to determine.  You just assume it for
arithmetic.  But finding that an axiom is false is common in argument.

which in tern implies that no axiom can ever be false.

Which is of course easily refuted.

Which makes my point that the mathematical idea of "true" is very
different from the common one.

“BBB” is true just in case it is the case that BBB.

But you can't know whether it is the case that 10^1 + 1 is the
successor of 10^1000 independent of the axioms, i.e. you assume it.

Brent

I am not sure, but the point is that no machine can prove []p -> p in
general. And the machine can know that, making her “modest” (Löbian).

Bruno

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 12/13/2018 3:18 AM, Bruno Marchal wrote:
*Automating Gödel'’s Ontological Proof of God’s Existence ¨ with
Higher-order Automated Theorem Provers*

http://page.mi.fu-berlin.de/cbenzmueller/papers/C40.pdf

Gödel took the modal logic S5 for its proof, which is the only logic
NOT available for the machines.

What about S5 makes it not available for machines?

Brent

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### Re: What is more primary than numbers?

```

On 12/12/2018 11:36 PM, Jason Resch wrote:

On Wed, Dec 12, 2018 at 10:44 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/12/2018 5:21 PM, Jason Resch wrote:

On Wed, Dec 12, 2018 at 6:04 PM Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/12/2018 3:29 AM, Bruno Marchal wrote:

On 11 Dec 2018, at 20:20, Brent Meeker
mailto:meeke...@verizon.net>> wrote:

On 12/11/2018 11:06 AM, Jason Resch wrote:

On Tue, Dec 11, 2018 at 12:53 PM Philip Thrift
mailto:cloudver...@gmail.com>> wrote:

On Tuesday, December 11, 2018 at 12:45:13 PM UTC-6,
Jason wrote:

On Tue, Dec 11, 2018 at 11:29 AM Brent Meeker
wrote:

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM
UTC-6, Jason wrote:

No one is refuting the existence of
matter, only the idea that matter is
primary.  That is, that matter is not
derivative from something more fundamental.

Jason

I can understand an (immaterial)
computationalism (e.g. *The universal
numbers. From Biology to Physics.* Marchal B
[
https://www.ncbi.nlm.nih.gov/pubmed/26140993
]) as providing a purely informational basis
for (thinking of) matter and consciousness,
but then why would *actual matter* need to
come into existence at all? Actual matter
itself would seem to be superfluous.

If actual matter is not needed for
experientiality (consciousness), and actual
matter does no exist at all, then we live in
a type of simulation of pure numericality.
There would be no reason for actual matter to
come into existence.

If it feels like matter and it looks like
matter and obeys the equations of matter how
is it not "actual" matter?  Bruno's idea is
that consciousness of matter and it's effects
are all we can know about matter. So if the
"simulation" that is simulating us, also
simulates those conscious thoughts about
matter then that's a "actual" as anything
gets. Remember Bruno is a theologian so all
this "simulation" is in the mind of
God=arithmetic; and arithmetic/God is the
ur-stuff.

It's not just Bruno who reached this conclusion.
from Markus Muller's paper:

In particular, her observations do not
fundamentally supervene on this “physical
universe”; it is merely a useful tool to
predict her future observations. Nonetheless,
this universe will seem perfectly real to her,
since its state is strongly correlated with
her experiences. If the measure µ that is
computed within her computational universe
assigns probability close to one to the
experience of hitting her head against a
brick, then the corresponding experience of
pain will probably render all abstract
insights into the non-fundamental nature of
that brick irrelevant.

Jason

What is the computer that running "her computational
universe"?

The very same that powers the equations that bring life to
our universe as you see it evolve.

What is its power supply?

Power is only required to erase information, and that is
only a concept of the physical laws of this universe.
Even the laws of our universe permit the creation of
computers which require no power to run.

See the bit about reversible computing:
https://en.wikipedia.org/wiki/Landauer%27s_principle
(computations that are reversible require no energy).

And they produce no results since they run both ways.  They
are not even computations in the CT sense.

They are computations in the CT sense.

CT computations halt.  A program that can just wander back an
forth at random doesn't halt.

A reversible computation can still halt. It doesn't have to be a
never ending circle, it just has to be p```

### Re: What is more primary than numbers?

```

On 12/12/2018 5:21 PM, Jason Resch wrote:

On Wed, Dec 12, 2018 at 6:04 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/12/2018 3:29 AM, Bruno Marchal wrote:

On 11 Dec 2018, at 20:20, Brent Meeker mailto:meeke...@verizon.net>> wrote:

On 12/11/2018 11:06 AM, Jason Resch wrote:

On Tue, Dec 11, 2018 at 12:53 PM Philip Thrift
mailto:cloudver...@gmail.com>> wrote:

On Tuesday, December 11, 2018 at 12:45:13 PM UTC-6, Jason
wrote:

On Tue, Dec 11, 2018 at 11:29 AM Brent Meeker
wrote:

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM UTC-6,
Jason wrote:

No one is refuting the existence of matter,
only the idea that matter is primary.  That
is, that matter is not derivative from
something more fundamental.

Jason

I can understand an (immaterial) computationalism
(e.g. *The universal numbers. From Biology to
Physics.* Marchal B [
https://www.ncbi.nlm.nih.gov/pubmed/26140993 ]) as
providing a purely informational basis for
(thinking of) matter and consciousness, but then
why would *actual matter* need to come into
existence at all? Actual matter itself would seem
to be superfluous.

If actual matter is not needed for experientiality
(consciousness), and actual matter does no exist
at all, then we live in a type of simulation of
pure numericality. There would be no reason for
actual matter to come into existence.

If it feels like matter and it looks like matter
and obeys the equations of matter how is it not
"actual" matter?  Bruno's idea is that
consciousness of matter and it's effects are all we
can know about matter.  So if the "simulation" that
is simulating us, also simulates those conscious
thoughts about matter then that's a "actual" as
anything gets.  Remember Bruno is a theologian so
all this "simulation" is in the mind of
God=arithmetic; and arithmetic/God is the ur-stuff.

It's not just Bruno who reached this conclusion. from
Markus Muller's paper:

In particular, her observations do not
fundamentally supervene on this “physical
universe”; it is merely a useful tool to predict
her future observations. Nonetheless, this universe
will seem perfectly real to her, since its state is
strongly correlated with her experiences. If the
measure µ that is computed within her computational
universe assigns probability close to one to the
experience of hitting her head against a brick,
then the corresponding experience of pain will
probably render all abstract insights into the
non-fundamental nature of that brick irrelevant.

Jason

What is the computer that running "her computational universe"?

The very same that powers the equations that bring life to our
universe as you see it evolve.

What is its power supply?

Power is only required to erase information, and that is only a
concept of the physical laws of this universe.  Even the laws
of our universe permit the creation of computers which require
no power to run.

See the bit about reversible computing:
https://en.wikipedia.org/wiki/Landauer%27s_principle
(computations that are reversible require no energy).

And they produce no results since they run both ways.  They are
not even computations in the CT sense.

They are computations in the CT sense.

CT computations halt.  A program that can just wander back an
forth at random doesn't halt.

A reversible computation can still halt. It doesn't have to be a never
ending circle, it just has to be possible to re-wind back to the
original state, in theory (by not throwing away information).

But the point is that there must be an entropic gradient to define which
way the computation goes if every step is reversible. Otherwise it
doesn't "go" anywhere.

All computations can be done reversibly.

OK.  Here's my result,  1029394857.   What two numbers did I add
to compute it?

Here you collapsed two operands down to one (you destroyed
information).  Had you preserved either of the other operands as
outputs in the circuit, the question co```

### Re: What is more primary than numbers?

```

On 12/12/2018 1:10 PM, Jason Resch wrote:
Right, which is what Bruno's result, Markus Muller's paper shows is
the case with arithmetical truth in its relation to physical systems.
Assuming arithemtical truth, one can explain how to derive physics
from it.

No.  You can claim it's consistent with a little bit of physics. And you
can claim that you "must be able to derive physics".

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 12/12/2018 9:18 AM, Bruno Marchal wrote:

On 12 Dec 2018, at 12:54, Philip Thrift > wrote:

On Wednesday, December 12, 2018 at 5:09:00 AM UTC-6, Bruno Marchal
wrote:

On 11 Dec 2018, at 12:58, Philip Thrift > wrote:

On Tuesday, December 11, 2018 at 5:41:49 AM UTC-6, Bruno Marchal
wrote:

On 11 Dec 2018, at 12:11, Philip Thrift
wrote:

Nothing is "confirmed" and "made precise".

(Derrida, Rorty, …)

That would make Derrida and Rorty into obscurantism.
Confirmation does not make an idea true, but it is better
than nothing, once we postulate some reality.

Some “philosophies” prevents the scientific attitude, like
some “religions” do, although only when they are used for
that purpose.  Some philosophies vindicate  their lack of
rigour into a principle. That leads to relativisme, and
obscurantism. It looks nice as anyone can defend any idea,
but eventually it hurts in front of the truth.

Bruno

Have you read some of the Opinions* or watched some of the
(youtube) lectures of Rutgers math professor Doron Zeilberger?

I've been following him like forever.

* e.g.

* *Mathematics is /so/ useful because physical scientists and
engineers have the good sense to largely ignore the
"religious" fanaticism of professional mathematicians, and
their insistence on so-called rigor, that in many cases is
misplaced and hypocritical, since it is based on "axioms"
that are completely fictional, i.e. those that involve the
so-called infinity.*

Mechanism proves this. Arithmetic, without infinity axiom, even
without the induction axiom, is the “ontological things”.
Induction axioms, infinity, physics, humans, etc. belongs to the
phenomenology. The phenomenology is not less real, but its is not
primary, it is second order, and that fiction is needed to
survive, even if fictionally.

Bruno

To experiential realists, phenomenal consciousness is a real thing.

That is what the soul of the machine ([]p & p) says to itself (1p)
correctly. It is real indeed. But it is non definable, and non
provable. The machine’s soul knows that her soul is not a machine, nor
even anything describable in any 3p terms.

To real (experiential) materialists (panpsychism), consciousness is
intrinsic to matter (like electric charge, etc.). So that would make
consciousness primary.

Then you better need to say “no” to the doctor who propose you a
digital body.

But are you OK that your daughter marry a man who got one such digital
body in his childhood, to survive some disease?

You might say yes, and invoke the fact that he is material. The point
will be that if he survives through a *digital* substitution, it can
be shown that no universal machine at all is unable to distinguish,
without observable clue, a physical reality from any of infinitely
many emulation of approximations of that physical reality at some
level of substitution (fine grained, with 10^100 decimals correct, for
example). Then, infinitely many such approximation exists in
arithmetic, even in diophantine polynomial equation, and the
invariance of the first person for “delays of reconstitution”
(definable by the number of steps done by the universal dovetailer to
get the relevant states) entails that the 1p is confronted with a
continuum. The math shows that it has to be a special (models of []p &
p, and []p & <>t & p. [] is the arithmetical “beweisbar” predicate of
provability of Gödel 1931. It is my generic Gödel-Löbian machine,
shortly: Löbian. They obeys to the formula of modesty of Löb: []([]p
-> p) -> []p. It represents a scheme of theorems of PA saying that PA
is close for the Löb rule: if you convince PA that the provability of
the existence of Santa Klauss entails the existence of Santa Klauss,
then PA will soon or later prove the existence of Santa Klauss.

But that is the same as saying proof=>truth.  Nothing which is proven
can be false, which in tern implies that no axiom can ever be false.
Which makes my point that the mathematical idea of "true" is very
different from the common one.

Brent

Put in another way, unless PA proves something, she will never prove
that the provability of something entails that something. PA is
maximally modest on her own provability ability.

In particular, with f the constant proposition false, consistency, the
~[]f, equivalent with []f -> f, is not provable, so []p -> p is in
general not provable and is not a theorem of PA.

Incompleteness enforces the nuances between

Truthp
Provable[]p
Knowable[]p & p
Observable[]p & <>t.  (t = propositional constant true, <> = ~[]~ =
consistent)

Sensible[]p & <>t

And incompleteness also doubles, or split,  the provable, the
observable and the sensible along the provable/true parts, G ```

### Re: What is more primary than numbers?

```

On 12/12/2018 3:29 AM, Bruno Marchal wrote:

On 11 Dec 2018, at 20:20, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/11/2018 11:06 AM, Jason Resch wrote:

On Tue, Dec 11, 2018 at 12:53 PM Philip Thrift
mailto:cloudver...@gmail.com>> wrote:

On Tuesday, December 11, 2018 at 12:45:13 PM UTC-6, Jason wrote:

On Tue, Dec 11, 2018 at 11:29 AM Brent Meeker
wrote:

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM UTC-6, Jason
wrote:

No one is refuting the existence of matter, only
the idea that matter is primary. That is, that
matter is not derivative from something more
fundamental.

Jason

I can understand an (immaterial) computationalism (e.g.
*The universal numbers. From Biology to Physics.*
Marchal B [
https://www.ncbi.nlm.nih.gov/pubmed/26140993 ]) as
providing a purely informational basis for (thinking
of) matter and consciousness, but then why would
*actual matter* need to come into existence at all?
Actual matter itself would seem to be superfluous.

If actual matter is not needed for experientiality
(consciousness), and actual matter does no exist at
all, then we live in a type of simulation of pure
numericality. There would be no reason for actual
matter to come into existence.

If it feels like matter and it looks like matter and
obeys the equations of matter how is it not "actual"
matter?  Bruno's idea is that consciousness of matter
and it's effects are all we can know about matter.  So
if the "simulation" that is simulating us, also
simulates those conscious thoughts about matter then
that's a "actual" as anything gets.  Remember Bruno is a
theologian so all this "simulation" is in the mind of
God=arithmetic; and arithmetic/God is the ur-stuff.

It's not just Bruno who reached this conclusion. from Markus
Muller's paper:

In particular, her observations do not fundamentally
supervene on this “physical universe”; it is merely a
useful tool to predict her future observations.
Nonetheless, this universe will seem perfectly real to
her, since its state is strongly correlated with her
experiences. If the measure µ that is computed within
her computational universe assigns probability close to
one to the experience of hitting her head against a
brick, then the corresponding experience of pain will
probably render all abstract insights into the
non-fundamental nature of that brick irrelevant.

Jason

What is the computer that running "her computational universe"?

The very same that powers the equations that bring life to our
universe as you see it evolve.

What is its power supply?

Power is only required to erase information, and that is only a
concept of the physical laws of this universe.  Even the laws of our
universe permit the creation of computers which require no power to run.

See the bit about reversible computing:
https://en.wikipedia.org/wiki/Landauer%27s_principle (computations
that are reversible require no energy).

And they produce no results since they run both ways. They are not
even computations in the CT sense.

They are computations in the CT sense.

CT computations halt.  A program that can just wander back an forth at
random doesn't halt.

All computations can be done reversibly.

OK.  Here's my result,  1029394857.   What two numbers did I add to
compute it?

Read and write needs some energy, but is not part of the computation,

A quantum computation stops when you read its output.  A CT computation
must halt to provide and output...otherwise you can't recognize an
output (and there would be no Halting Problem).

Brent

unless you run the couple “you + the computation concerned”. If not QM
would not be Turing universal, which it is.

Bruno

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### Re: What is more primary than numbers?

```

On 12/11/2018 11:06 AM, Jason Resch wrote:

On Tue, Dec 11, 2018 at 12:53 PM Philip Thrift <mailto:cloudver...@gmail.com>> wrote:

On Tuesday, December 11, 2018 at 12:45:13 PM UTC-6, Jason wrote:

On Tue, Dec 11, 2018 at 11:29 AM Brent Meeker
wrote:

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM UTC-6, Jason
wrote:

No one is refuting the existence of matter, only the
idea that matter is primary.  That is, that matter is
not derivative from something more fundamental.

Jason

I can understand an (immaterial) computationalism (e.g.
*The universal numbers. From Biology to Physics.* Marchal
B [ https://www.ncbi.nlm.nih.gov/pubmed/26140993 ]) as
providing a purely informational basis for (thinking of)
matter and consciousness, but then why would *actual
matter* need to come into existence at all? Actual matter
itself would seem to be superfluous.

If actual matter is not needed for experientiality
(consciousness), and actual matter does no exist at all,
then we live in a type of simulation of pure
numericality. There would be no reason for actual matter
to come into existence.

If it feels like matter and it looks like matter and obeys
the equations of matter how is it not "actual" matter?
Bruno's idea is that consciousness of matter and it's
effects are all we can know about matter.  So if the
"simulation" that is simulating us, also simulates those
conscious thoughts about matter then that's a "actual" as
anything gets.  Remember Bruno is a theologian so all this
"simulation" is in the mind of God=arithmetic; and
arithmetic/God is the ur-stuff.

It's not just Bruno who reached this conclusion. from Markus
Muller's paper:

In particular, her observations do not fundamentally
supervene on this “physical universe”; it is merely a
useful tool to predict her future observations.
Nonetheless, this universe will seem perfectly real to
her, since its state is strongly correlated with her
experiences. If the measure µ that is computed within her
computational universe assigns probability close to one to
the experience of hitting her head against a brick, then
the corresponding experience of pain will probably render
all abstract insights into the non-fundamental nature of
that brick irrelevant.

Jason

What is the computer that running "her computational universe"?

The very same that powers the equations that bring life to our
universe as you see it evolve.

What is its power supply?

Power is only required to erase information, and that is only a
concept of the physical laws of this universe. Even the laws of our
universe permit the creation of computers which require no power to run.

See the bit about reversible computing:
https://en.wikipedia.org/wiki/Landauer%27s_principle (computations
that are reversible require no energy).

And they produce no results since they run both ways.  They are not even
computations in the CT sense.

Brent

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### Re: What is more primary than numbers?

```

On 12/11/2018 9:52 AM, Philip Thrift wrote:

On Tuesday, December 11, 2018 at 11:29:13 AM UTC-6, Brent wrote:

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM UTC-6, Jason wrote:

No one is refuting the existence of matter, only the idea
that matter is primary.  That is, that matter is not
derivative from something more fundamental.

Jason

I can understand an (immaterial) computationalism (e.g. *The
universal numbers. From Biology to Physics.* Marchal B [
https://www.ncbi.nlm.nih.gov/pubmed/26140993
]) as providing a
purely informational basis for (thinking of) matter and
consciousness, but then why would *actual matter* need to come
into existence at all? Actual matter itself would seem to be
superfluous.

If actual matter is not needed for experientiality
(consciousness), and actual matter does no exist at all, then we
live in a type of simulation of pure numericality. There would be
no reason for actual matter to come into existence.

If it feels like matter and it looks like matter and obeys the
equations of matter how is it not "actual" matter? Bruno's idea is
that consciousness of matter and it's effects are all we can know
about matter.  So if the "simulation" that is simulating us, also
simulates those conscious thoughts about matter then that's a
"actual" as anything gets.  Remember Bruno is a theologian so all
this "simulation" is in the mind of  God=arithmetic; and
arithmetic/God is the ur-stuff.

Brent

I suppose that one can argue that *simulata* can replace *materia*
until the cows come home
.

(Simulata people think they are materia. Materia people think they are
simulata. ...)

But pragmatically, I'm not sure where this leads. Engineers still
think they are pushing matter around to make things. Not simulations
of the things they think are material.

The point is that there is no difference.  There is no distinction
except in the metaphysics used to talk about it.   Engineers don't do
metaphysics.

Bret

(For Kant, it was *noumena*.)

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 12/11/2018 3:58 AM, Philip Thrift wrote:

On Tuesday, December 11, 2018 at 5:41:49 AM UTC-6, Bruno Marchal wrote:

On 11 Dec 2018, at 12:11, Philip Thrift > wrote:

Nothing is "confirmed" and "made precise".

(Derrida, Rorty, …)

That would make Derrida and Rorty into obscurantism. Confirmation
does not make an idea true, but it is better than nothing, once we
postulate some reality.

Some “philosophies” prevents the scientific attitude, like some
“religions” do, although only when they are used for that purpose.
Some philosophies vindicate  their lack of rigour into a
principle. That leads to relativisme, and obscurantism. It looks
nice as anyone can defend any idea, but eventually it hurts in
front of the truth.

Bruno

Have you read some of the Opinions* or watched some of the (youtube)
lectures of Rutgers math professor Doron Zeilberger?

I've been following him like forever.

* e.g.

* *Mathematics is /so/ useful because physical scientists and
engineers have the good sense to largely ignore the "religious"
fanaticism of professional mathematicians, and their insistence on
so-called rigor, that in many cases is misplaced and hypocritical,
since it is based on "axioms" that are completely fictional, i.e.
those that involve the so-called infinity.*

Physics is to mathematics as sex is to masturbation.
--- Richard Feynman

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### Re: What is more primary than numbers?

```

On 12/11/2018 3:20 AM, Bruno Marchal wrote:
But only by abstracting from and generalizing some rules based
counting and then postulating that they apply to arbitrarily large
numbers of things.  For example, arithmetic assumes that you can add
1 to 10^1000 and get a different number.  But that is purely an
assumption.

I prefer to say that it is a theorem, from the usual assumption like
Kxy = x, Sxyz = xz(yz) +some definitions, or from x+0 = x, etc.

Counting could never confirm it.

You are right, but a physical confirmation is not a proof, it is just
an absence of refutation, inviting us to keep the theory if it is
simple, by Occam.

Right. It is a convenience.  Which is not a good reason to take it as
reality.

Brent

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### Re: Where Max Tegmark is really wrong

```

On 12/11/2018 2:12 AM, Bruno Marchal wrote:
When we say that God cannot be omniscient (for pure logical reason),
the atheists replies by saying that we cannot change the definition.
They would have said that Earth does not exist when it was discovered
that it is round! Of course, in science we change the definition *all
the time*.

But the Earth is defined ostensively.  Nobody changed the definition.
The definition of God is never ostensive and so it is subject to wildly
varying changes to serve the needs and prejudices of whomever wants
divine support for their theories.

*but for you their beliefs are the same? How ridiculous this is! AG*

Same belief in Matter (which is the God incompatible with Mechanism).
Same belief that God = the Christian God only (total oversight of a
millenium of scientific theology!).

They don’t have the same belief in God, but they share the same
definition (curiously enough).

What is curious about that.  If you have a different belief in fascism
than Siegfried Verbeke don't you have to share the same definition of
fascism; otherwise you would be having a different belief about a
different thing and you could no more disagree with him than my
believing eggs are a good breakfast would be disagreeing with you that
coffee is good at breakfast.  You have to agree on what you are talking
about in order to disagree on what you believe about it.

Brent

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### Re: What is more primary than numbers?

```

On 12/9/2018 11:38 PM, Philip Thrift wrote:

On Sunday, December 9, 2018 at 8:43:59 PM UTC-6, Jason wrote:

On Sun, Dec 9, 2018 at 2:02 PM Philip Thrift > wrote:

On Sunday, December 9, 2018 at 9:36:39 AM UTC-6, Jason wrote:

On Sun, Dec 9, 2018 at 2:53 AM Philip Thrift
wrote:

On Saturday, December 8, 2018 at 2:27:45 PM UTC-6,
Jason wrote:

I think truth is primitive.

Jason

As a matter of linguistics (and philosophy), *truth*
and *matter* are linked:

"As a matter of fact, ..."
"The truth of the matter is ..."
"It matters that ..."
...
[ https://www.etymonline.com/word/matter
]

I agree they are linked.  Though matter may be a few steps
removed from truth.  Perhaps one way to interpret the link
more directly is thusly:

There is an equation whose every solution (where the
equation happens to be */true/*, e.g. is satisfied when it
has certain values assigned to its variables) maps its
variables to states of the time evolution of the wave
function of our universe.  You might say that we
(literally not figuratively) live within such an
equation.  That its truth reifies what we call matter.

But I think truth plays an even more fundamental roll than
this.  e.g. because the following statement is */true/*
"two has a successor" then there exists a successor to 2
distinct from any previous number.  Similarly, the
*/truth/* of "9 is not prime" implies the existence of a
factor of 9 besides 1 and 9.

Jason

Schopenhauer 's view: "A judgment has /material truth/
if its concepts are based on intuitive perceptions
that are generated from sensations. If a judgment has
its reason (ground) in another judgment, its truth is
called logical or formal. If a judgment, of, for
example, pure mathematics or pure science, is based on
the forms (space, time, causality) of intuitive,
empirical knowledge, then the judgment has
transcendental truth."
[ https://en.wikipedia.org/wiki/Truth
]

I guess I am referring to transcend truth here. Truth
concerning the integers is sufficient to yield the
universe, matter, and all that we see around us.

Jason

In my view there is basically just *material* (from matter)
truth and *linguistic* (from language) truth.

[
https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/

]

Relations and functions are linguistic: relational type theory
(RTT) , functional type theory (FTT) languages.

Numbers are also linguistic beings, the (fictional) semantic
objects of Peano arithmetic (PA).

Numbers can be "materialized" via /nominalization /(cf. Hartry
Field, refs. in [ https://en.wikipedia.org/wiki/Hartry_Field
]).

Assuming the primacy of matter assumes more and explains less,
than assuming the primacy of arithmetical truth.

Jason

In today's era of mathematics, Joel David Hamkins (@JDHamkins
) has shown there is a "multiverse" of
truths:

*The set-theoretic multiverse*
[ https://arxiv.org/abs/1108.4223 ]

/The multiverse view in set theory, introduced and argued for in this
article, is the view that there are many distinct concepts of set,
each instantiated in a corresponding set-theoretic universe. The
universe view, in contrast, asserts that there is an absolute
background set concept, with a corresponding absolute set-theoretic
universe in which every set-theoretic question has a definite answer.
The multiverse position, I argue, explains our experience with the
enormous diversity of set-theoretic possibilities, a phenomenon that
challenges the universe view. In particular, I argue that the
continuum hypothesis is settled on the multiverse view by our
extensive knowledge about how it behaves in the multiverse, and as a
result it can no longer be settled in the manner formerly hoped for.

/
/
/
/
/
What this means is that for mathematics (a language category), truth
depends on the language.

I think Hamkins could say the same thing in French.  His example of the
continuum hypothesis just says that by adding as axioms different
undecidable propositions we get ```

### Re: What is more primary than numbers?

```

On 12/11/2018 12:31 AM, Philip Thrift wrote:

On Monday, December 10, 2018 at 7:05:17 PM UTC-6, Jason wrote:

No one is refuting the existence of matter, only the idea that
matter is primary.  That is, that matter is not derivative from
something more fundamental.

Jason

I can understand an (immaterial) computationalism (e.g. *The universal
numbers. From Biology to Physics.* Marchal B
[ https://www.ncbi.nlm.nih.gov/pubmed/26140993 ]) as providing a
purely informational basis for (thinking of) matter and consciousness,
but then why would *actual matter* need to come into existence at all?
Actual matter itself would seem to be superfluous.

If actual matter is not needed for experientiality (consciousness),
and actual matter does no exist at all, then we live in a type of
simulation of pure numericality. There would be no reason for actual
matter to come into existence.

If it feels like matter and it looks like matter and obeys the equations
of matter how is it not "actual" matter?  Bruno's idea is that
consciousness of matter and it's effects are all we can know about
matter.  So if the "simulation" that is simulating us, also simulates
those conscious thoughts about matter then that's a "actual" as anything
gets.  Remember Bruno is a theologian so all this "simulation" is in the
mind of  God=arithmetic; and arithmetic/God is the ur-stuff.

Brent

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### Re: What is more primary than numbers?

```

On 12/10/2018 7:37 AM, Jason Resch wrote:

On Monday, December 10, 2018, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/9/2018 6:42 PM, Jason Resch wrote:

On Sun, Dec 9, 2018 at 2:53 PM Brent Meeker mailto:meeke...@verizon.net>> wrote:

They are fundamental only in the sense that one can use them
as axioms.  So their fundamentalism is circular.

Brent

On 12/9/2018 7:36 AM, Jason Resch wrote:

But I think truth plays an even more fundamental roll than
this.  e.g. because the following statement is */true/* "two
has a successor" then there exists a successor to 2 distinct
from any previous number. Similarly, the */truth/* of "9 is
not prime" implies the existence of a factor of 9 besides 1
and 9.

That position was defensible before Godel, but not after.  He
showed mathematical truth cannot be based on axioms.

But he didn't show it could be based on something else.

We're talking about primary substances/foundations of reality. Those
things, that by their definition of being primary objects, are not
based on anything else.

That neither he, nor anyone else showed mathematical truth is or can
be based on something else would be expected if it is a primary object.

That's like saying "Sherlock Holmes companion is named Watson." is a
primary truth because it isn't derived from something else.

Brent

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### Re: What is more primary than numbers?

```

On 12/9/2018 6:42 PM, Jason Resch wrote:

On Sun, Dec 9, 2018 at 2:53 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

They are fundamental only in the sense that one can use them as
axioms.  So their fundamentalism is circular.

Brent

On 12/9/2018 7:36 AM, Jason Resch wrote:

But I think truth plays an even more fundamental roll than this.
e.g. because the following statement is */true/* "two has a
successor" then there exists a successor to 2 distinct from any
previous number.  Similarly, the */truth/* of "9 is not prime"
implies the existence of a factor of 9 besides 1 and 9.

That position was defensible before Godel, but not after.  He showed
mathematical truth cannot be based on axioms.

But he didn't show it could be based on something else.

Brent

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### Re: What is more primary than numbers?

```They are fundamental only in the sense that one can use them as axioms.
So their fundamentalism is circular.

Brent

On 12/9/2018 7:36 AM, Jason Resch wrote:
But I think truth plays an even more fundamental roll than this.  e.g.
because the following statement is */true/* "two has a successor" then
there exists a successor to 2 distinct from any previous number.
Similarly, the */truth/* of "9 is not prime" implies the existence of
a factor of 9 besides 1 and 9.

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### Re: What is more primary than numbers?

```

On 12/8/2018 2:46 PM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:13 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 12/8/2018 11:02 AM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift
mailto:cloudver...@gmail.com>> wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective statements
can be made (with or without objects to count).
For example, I can make and prove a statement about a number with
a million digits.  Despite that there are not that many things
(in my vicinity) to count.

But only by abstracting from and generalizing some rules based
counting and then postulating that they apply to arbitrarily large
numbers of things.  For example, arithmetic assumes that you can
add 1 to 10^1000 and get a different number.  But that is purely
an assumption. Counting could never confirm it.

So then we agree that numbers don't inherit their existence or
properties from from counting.

No, I agree that numbers do get their properties from counting by
generalization, but not that they exist.

Brent

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### Re: What is more primary than numbers?

```

On 12/8/2018 12:27 PM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 2:06 PM Philip Thrift > wrote:

On Saturday, December 8, 2018 at 1:02:25 PM UTC-6, Jason wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift
wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective
statements can be made (with or without objects to count).
For example, I can make and prove a statement about a number
with a million digits.  Despite that there are not that many
things (in my vicinity) to count.

But one counts things (things that are not numbers
themselves, in the primitive case). So the things one
counts + the one that counts must be more primary than
numbers.

2. Numbers come from lambda calculus (LC). But LC - a
programming language - needs a machine LCM to interpret LC
programs. So LC + LCM is more primary than numbers.

You can build computers and programs out of equations
concerning the arithmetical relationships that exist between
numbers.  See my post "Do we live in a Diophantine equation":

Jason

But what are /relations/? Are /relations/, or /functions/, then
primitive?

I think truth is primitive.

"True" means quite different things in different contexts.

Brent

cf. *Relations Versus Functions at the Foundations of Logic:
Type-Theoretic Considerations*
https://mally.stanford.edu/Papers/rtt.pdf

What language are /equations/ written in?

Things only need to be written for purposes of communication. Writing
a description has no bearing on the ontological status of the thing
described.

Jason
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### Re: What is more primary than numbers?

```

On 12/8/2018 11:02 AM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift > wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective statements can be
made (with or without objects to count).
For example, I can make and prove a statement about a number with a
million digits.  Despite that there are not that many things (in my
vicinity) to count.

But only by abstracting from and generalizing some rules based counting
and then postulating that they apply to arbitrarily large numbers of
things.  For example, arithmetic assumes that you can add 1 to 10^1000
and get a different number.  But that is purely an assumption.  Counting
could never confirm it.

Brent

But one counts things (things that are not numbers themselves, in
the primitive case). So the things one counts + the one that
counts must be more primary than numbers.

2. Numbers come from lambda calculus (LC). But LC - a programming
language - needs a machine LCM to interpret LC programs. So LC +
LCM is more primary than numbers.

You can build computers and programs out of equations concerning the
arithmetical relationships that exist between numbers.  See my post
"Do we live in a Diophantine equation":

Jason

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### Re: Chaos makes axioms unnecessary

```

On 12/5/2018 11:00 AM, Philip Thrift wrote:

"How many axioms would be needed [to model nature]?...if we look at
the universe in totality and not bracket any subset of phenomena, t*he
mathematics we would need would have no axioms at all* It is only
the way we look at the universe that gives us the illusion of structure."

Chaos Makes the Multiverse Unnecessary
by Noson S. Yanofsky
November 29, 2018
[
http://nautil.us/issue/66/clockwork/chaos-makes-the-multiverse-unnecessary-rp
]
/Science predicts only the predictable, ignoring most of our chaotic
universe./

A point we discussed with Vic.  POVI doesn't apply to everything. Only
some things are POVI and those are the things science is interested in.

Brent

Noson S. Yanofsky is a professor of computer science at Brooklyn
College of The City University of New York.

[ http://www.sci.brooklyn.cuny.edu/~noson/ ]

- pt

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### Re: Where Max Tegmark is really wrong

```

On 12/4/2018 11:50 AM, Philip Thrift wrote:

On Tuesday, December 4, 2018 at 1:46:44 PM UTC-6, Brent wrote:

On 12/4/2018 12:06 AM, Philip Thrift wrote:

Can you give an example of "truth in the programming" and how
it differs from the mathematical idea of true and the
correspondence theory of truth?

Brent

Truth in programming follows the Brouwerian concept of truth:
[ https://plato.stanford.edu/entries/brouwer/
]

/There is no determinant of mathematical truth outside the
activity of thinking; a proposition only becomes true when the
subject has experienced its truth (by having carried out an
appropriate mental construction); similarly, a proposition only
becomes false when the subject has experienced its falsehood (by
realizing that an appropriate mental construction is not possible)./

*There is no determinant of mathematical truth outside the
activity of computing;* a proposition only becomes true when the
program has produced  its truth (by having carried out an
appropriate computational construction); similarly, a proposition
only becomes false when the program has produced its falsehood
(by computing that an appropriate computational construction is
not possible).

I didn't ask for examples of circular definitions.

Brent

In what sense is type theory circular logic?

First, I didn't ask for a logic, I asked for examples to the different
ideas of truth.  Instead you provided some assertions about "where truth
is determined" and about becoming true...which were circular.

"a proposition only becomes*/true/* when the subject has experienced its
*/truth/*"

" a proposition only becomes /*true*/ when the program has produced  its
*/truth/*"

Third, neither your post nor the article on Brouwer said anything about
type theory.

https://plato.stanford.edu/entries/type-theory-intuitionistic/

Brent

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### Re: The most accurate clock ever

```

On 12/4/2018 6:28 AM, John Clark wrote:

Brent Meekerwrote:

/> Neither does a cesium clock measure the change in strength of 2
large gravitational fields.  It measures the difference in
gravitational potential. /

Same thing, a gravitational field describes the gravitational
potential at every point.

/> //So I compared the change in gravitational potential when
moving the clock up 1cm to the change in potential when
Cavendish's torsion balance moved the sensing weights the smallest
change in distance he said he could measure 0.25mm with the
weights 9" (0.23m) from the cannon balls. The ratio of these two
potentials is the product of three terms: The ratio of masses
(1.37e25 lbm/348 lbm) The ratio distances squared
(0.23m/6.4e6m)^2. The ratio of smallest measurable changes
(0.01m/0.00025m).  Work it out yourself./

Brent, Cavendish's torsion balance was only sensitive enough to
measure the Gravitational constant to one part in 100, and even today
with the newest and best torsion balance money can buy you can only
get 11.6 parts per MILLION.

New Torsion Balance

To measure the difference in Earth's gravity at 2 points one
centimeter higher from the surface than the other you'd need to do
better than 3 parts per BILLION. This new clock can do that, 3,900
times better than the best modern torsion balance.

But that's because finding the value of G depends on scaling the result
by that ratio of masses (1.37e25 lbm/348 lbm).  The way you are looking
at consider how far you would have to move the cesium clock from the
surface of the 348lbm cannon ball in order to detect the change in
gravitational time dilation affecting the clock.  It's the number I
cited, far bigger than the 0.25mm Cavendish cited as the limit of his
measurement.

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 12/4/2018 3:05 AM, Bruno Marchal wrote:

… where Omnès added “time to be irrational” ...

1. Histories originate at an emitter e and end at screen locations s
on a screen S.
2. At each s there is a history bundle histories(s). A weight w(s) is
computed from the bundle by summing the unit complex numbers of the
histories and taking the modulus.
3. The weight w(s) is sent back in time over a single history h*(s)
selected at random (uniformly) from histories(s).
4. At e, the weights w(s) on backchannel of h*(s) are received (in
the "present" time)

5. A single history h*(s*) is then selected from the distribution in 4.

"5.”  follows from mechanism as a first person view. No need of Omnès
mysterious selection.

The first person view is a view of the result of the sum over the
bundle; not of a single history. How would one perceive a history?

Brent

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### Re: Extended Wigner’s Friend

```

On 12/4/2018 1:02 AM, Philip Thrift wrote:

Fay Dowker [ https://en.wikipedia.org/wiki/Fay_Dowker ] gives a short
summary of "sum over histories" here (and why she prefers it to other
interpretations).

She says she prefers it to Copenhagen because Copenhagen doesn't give an
picture of what happens between preparation and measurement. She says
she prefers it to Bohmian QM because it doesn't conflict with
relativity.  But she doesn't say anything about other interpretations
such as Everett's relative state interpretation.

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 12/4/2018 12:25 AM, Philip Thrift wrote:

On Monday, December 3, 2018 at 9:00:26 PM UTC-6, Brent wrote:

On 12/3/2018 8:50 AM, Bruno Marchal wrote:

On 3 Dec 2018, at 10:35, Philip Thrift > wrote:

On Sunday, December 2, 2018 at 8:17:54 PM UTC-6, Brent wrote:

On 12/2/2018 5:14 PM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 4:25:04 PM UTC-6, Brent wrote:

On 12/2/2018 11:42 AM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 8:13:48 AM UTC-6,
agrays...@gmail.com wrote:

*
*
*Obviously, from a one-world perspective, only one
history survives for a single trial. But to even
grossly approach anything describable as
"Darwinian", you have to identify characteristics
of histories which contribute positively or
negatively wrt surviving but I don't see an
inkling of that. IMO, Quantum Darwinism is at best
a vacuous restatement of the measurement problemt;
that we don't know why we get what we get. AG*

In the *sum over histories* interpretation - of the
double-slit experiment, for example - each history
carries a unit complex number - like a gene - and this
gene reenforces (positively) or interferes
(negatively) with other history's genes in the sum.

But I thought you said the ontology was that only one
history "popped out of the Lottery machine"?  Here you
seem to contemplate an ensemble of histories, all those
ending at the given spot, as being real.

Brent

All are real until all but one dies.
RIP: All those losing histories.

The trouble with that is the Born probability doesn't apply
to histories, it applies to results.  So your theory says
nothing about the probability of the fundamental ontologies.

Brent

The probability distribution on the space of histories is
provided by the path integral.

Except that isn't true. A probability (or probability density) is
provided for a bundle of histories joining two events.  It doesn't
not provide a probability of a single history.

Brent

That's why you add to that "pick any history at random from the bundle":

But the probability didn't apply to that history.  The Born rule gave
the probability of the bundle.  To it is false that, "The probability
distribution on the space of histories is provided by the path integral."

1. Histories originate at an emitter e and end at screen locations s
on a screen S.
2. At each s there is a history bundle histories(s). A weight w(s) is
computed from the bundle by summing the unit complex numbers of the
histories and taking the modulus.
3. The weight w(s) is sent back in time over a single history h*(s)
selected at random (uniformly) from histories(s).
4. At e, the weights w(s) on backchannel of h*(s) are received (in the
"present" time)

5. A single history h*(s*) is then selected from the distribution in 4.

How is it selected?  Above you said "at random".  But that implies there
is already a probability measure defined on the histories. How is this
probability measure determined?  Or put another way how do you determine
what histories to consider to form the bundles in step 2?

Brent

See the *Wheeler-Feynman computer*:
[ https://codicalist.wordpress.com/2018/09/25/retrosignaling-in-the-quantum-substrate/
]

- pt
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### Re: Where Max Tegmark is really wrong

```

On 12/4/2018 12:06 AM, Philip Thrift wrote:

Can you give an example of "truth in the programming" and how it
differs from the mathematical idea of true and the correspondence
theory of truth?

Brent

Truth in programming follows the Brouwerian concept of truth:
[ https://plato.stanford.edu/entries/brouwer/ ]

/There is no determinant of mathematical truth outside the activity of
thinking; a proposition only becomes true when the subject has
experienced its truth (by having carried out an appropriate mental
construction); similarly, a proposition only becomes false when the
subject has experienced its falsehood (by realizing that an
appropriate mental construction is not possible)./

*There is no determinant of mathematical truth outside the activity of
computing;* a proposition only becomes true when the program has
produced  its truth (by having carried out an appropriate
computational construction); similarly, a proposition only becomes
false when the program has produced its falsehood (by computing that
an appropriate computational construction is not possible).

I didn't ask for examples of circular definitions.

Brent

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### Fwd: tricolor consciousness compression

```

Forwarded Message

"That's teleportation for ya!"

http://smbc-comics.com/comic/teleporter

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### Re: Extended Wigner’s Friend

```

On 12/3/2018 5:47 PM, Mason Green wrote:

Here’s a recent editorial I found in the magazine arguing against Many-Worlds
on the grounds that it denies the reality of experience or the self.
(https://www.quantamagazine.org/why-the-many-worlds-interpretation-of-quantum-mechanics-has-many-problems-20181018/)

Well, if we don’t want many-worlds or subjectivism, than the only other option
looks like it’d be to modify QM itself. Some form of digital physics might
work, otherwise we could have objective collapse (either random, or else
there’s something/someone outside the universe choosing which path the universe
follows).

Remember, QM is not compatible with general relativity.  It is often
assumed that the problem is finding a quantum theory of spacetime. But
the long sought theory may also require some modification of QM or
otherwise throw light on the measurement problem.  For example,
Penrose's gravitationally induced collapse might work out.

Brent

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### Re: Extended Wigner’s Friend

```
You should read Scott Aaronson's take:

https://www.scottaaronson.com/blog/?p=3975

Brent

On 12/3/2018 5:15 PM, Mason Green wrote:

There’s a new article in Quanta Magazine
about a thought experiment that poses trouble for certain interpretations of
quantum mechanics.

Specifically it implies that either 1. there are many worlds, 2. quantum
mechanics will need to be modified (as in objective collapse theories), or 3.
reality is subjective (solipsism?). Exciting stuff!

-Mason

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 12/3/2018 8:50 AM, Bruno Marchal wrote:

On 3 Dec 2018, at 10:35, Philip Thrift > wrote:

On Sunday, December 2, 2018 at 8:17:54 PM UTC-6, Brent wrote:

On 12/2/2018 5:14 PM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 4:25:04 PM UTC-6, Brent wrote:

On 12/2/2018 11:42 AM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 8:13:48 AM UTC-6,
agrays...@gmail.com wrote:

*
*
*Obviously, from a one-world perspective, only one
history survives for a single trial. But to even
grossly approach anything describable as "Darwinian",
you have to identify characteristics of histories which
contribute positively or negatively wrt surviving but I
don't see an inkling of that. IMO, Quantum Darwinism is
at best a vacuous restatement of the measurement
problemt; that we don't know why we get what we get. AG*

In the *sum over histories* interpretation - of the
double-slit experiment, for example - each history carries
a unit complex number - like a gene - and this gene
reenforces (positively) or interferes (negatively) with
other history's genes in the sum.

But I thought you said the ontology was that only one
history "popped out of the Lottery machine"?  Here you seem
to contemplate an ensemble of histories, all those ending at
the given spot, as being real.

Brent

All are real until all but one dies.
RIP: All those losing histories.

The trouble with that is the Born probability doesn't apply to
histories, it applies to results.  So your theory says nothing
about the probability of the fundamental ontologies.

Brent

The probability distribution on the space of histories is provided by
the path integral.

Except that isn't true. A probability (or probability density) is
provided for a bundle of histories joining two events.  It doesn't not
provide a probability of a single history.

Brent

I agree, and this statement can be made rather rigorously in the
approach of Griffith and Omnes, except that Omnes eventually add an
axiom of irrationality to extract a unique physical reality from the
formalism. He said it, at least, explicitly: like saying “and now
there is a miracle”. He says that at this stage, we need
irrationalism. But that appears in the last ten sentences of a rather
quite rational book.
Well, the point is that we can generalise the Born rule for making
sense on some probabilities on "consistent histories”.
(But I am in trouble (now) on how to handle the GHZ state in term of
(Griffith and Omnes)-histories (3-particle-GHZ = 1/sqrt(2)(up up up +
down down down)).

*Backward causation, hidden variables and the meaning of completenes*s
[ https://www.ias.ac.in/article/fulltext/pram/056/02-03/0199-0209 ]

/Feynman’s path integral approach, calculation of the probability of
the outcome in question depends on an integration over the possible
individual paths between the given initial state and the given final
state, each weighted by a complex number. The fact that the weights
associated with individual paths are complex makes it impossible to
interpret them as real valued probabilities, associated with a
classical statistical distribution of possibilities./

/
/
/However, there is no such difficulty at the level of the entire
‘bundle’ of paths which comprise the path integral. If we think of
the hidden reality as the instantiation not of one path rather than
another but of one entire bundle rather than another, then the
quantum mechanical probabilities can be thought of as classical
probability distributions over such elements of reality. (For
example, suppose we specify the boundary conditions in terms of the
electron source, the fact that two slits are open, and the fact that
a detector screen is present at a certain distance on the opposite
side of the central screen. We then partition the detector screen, so
as to define possible outcomes for the experiment. For each element
O_i of this partition, there is a bundle B_i of Feynman paths,
constituting the path integral used in calculating the probability of
outcome O_i . We have a classical probability distribution/

/over the set of such B_i ./

One could stop at /history bundles/ as the sample space, or the
"hidden reality" could be that /one history/ is selected at random
from the history bundle. That could occur with t*ime symmetry*
(retrocausality): The one path is chosen at random from a history
bundle at the source in the present from the distribution determined
on the history bundles in the future.

With mechanism, the randomness and the unicity is a first person
(plural) experience only, and seems to me no more astonishing than in
the amoeba duplication, or than in the Helsinki—> ```

### Re: Where Max Tegmark is really wrong

```

On 12/3/2018 7:31 AM, Bruno Marchal wrote:

On 2 Dec 2018, at 21:06, Brent Meeker  wrote:

On 12/2/2018 4:52 AM, Bruno Marchal wrote:

Language have no relation with truth a priori. Theories might have. Semantics
are truth “by definition”, by relativising it to the notion of model/reality.

Then what is this "true" and "false" which you attribute to the propositions of
modal logic?

In  classical logic, truth is any object in a set of two objects, or it is the
supremum in a Boolean algebra. In propositional logic a “world” is defined by
any function from the set of atomic letters to {t, f}.

Right.  T and F are just formal markers in logic and the rules of
inference are supposed to preserve T.

Then if the theory is “rich enough”, truth can be meta-defined by “satisfied by
the structure (N, 0, s, +, *).
Of course, this presuppose the intuitive understanding of 2+2=4, etc.

In our case, as all modal formula are arithmetical formula, it is the usual
informal mathematical notion just above (arithmetical truth, satisfaction by
the usual standard model).

That's satisfaction relative to some particular axioms and rules of
inference.

That one can be define by V(‘p’) means the same as p. It is Tarski’s idea that ‘p’
is true when p, or when it is the case that p. Like wise, to say
Provable-and-true(p) we use []p & p.

That's the correspondence theory of truth, which is what ordinary
discourse and physics assume.  So there are at least three kinds of
"true". To which we might add the Trump theory of truth, "If it makes me
look good it's true."

I recommend the book by Torkel Franzen “Inexhaustibility” for a more detailed
explanation of the concept of truth.

I have the book but I haven't read it (so many books, so little time).

Brent

We can come back, but I suggest to come back on this only when we need it, as
this is an very rich and complex subject by itself.

Bruno

Brent

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### Re: The most accurate clock ever

```

On 12/3/2018 5:24 AM, John Clark wrote:
On Sun, Dec 2, 2018 at 11:54 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

>>If you are on the Earth's surface and you raise a clock by one
centimeter you've increased its distance from the earth's
center by one part in 637,000,000, it is now 1.16
times further away. The intensity of the gravitational field
is proportional to the square of the distance so gravity was
1.31 times stronger before you raised raised the
clock. Cavendish did not have a scale good enough to measure
that, even today the very best (and very expensive) lab weight
scale might be able to measure a change of 1.001 but the
clock can do several hundred times better.

> He was measuring the change in a much smaller gravitational field.

Cavendish was measuring the displacement of a torsion balance parallel
to the Earth's surface caused by a weak but constant gravitational
field, there was no change whatsoever in the gravitational field
parallel to the Earth's surface at any time during the exparament. If
he had 2 *PRECISELY* identical cannonballs on the ends of a rod,
placed a pivot point *PRECISELY*at the center and place one
cannonball one centimeter higher than the other he would have
transformed his torsion balance into a weight balance and
theoretically he could have observed that the balance moved and
measured the small difference in strength in the large field at 2
different places, but Cavendish couldn't come close to achieving the
sort of precision required to do that 220 years ago, we can't even do
that today.

/> He was measuring the difference between the force on the
torsion balance with the cannon balls present vs absent. /

Cavendishsetup the exparament but nothing moved because the torsion
balance was held in place by a thread, he then sealed the room and did
nothing for 2 days to let the air currents settle down. He then
carefully burned through the thread freeing the torsion balanceand
observed its movement from far away through a telescope so his own
movements wouldn't disturb anything. At no time did he measure the
very small change of strength of 2 very large gravitational fields
because a torsion balancecan't do that, you'd need either a super good
weight balance or a super good clock.

Neither does a cesium clock measure the change in strength of 2 large
gravitational fields.  It measures the difference in gravitational
potential.  So I compared the change in gravitational potential when
moving the clock up 1cm to the change in potential when Cavendish's
torsion balance moved the sensing weights the smallest change in
distance he said he could measure 0.25mm with the weights 9" (0.23m)
from the cannon balls. The ratio of these two potentials is the product
of three terms: The ratio of masses (1.37e25 lbm/348 lbm)  The ratio
distances squared (0.23m/6.4e6m)^2. The ratio of smallest measurable
changes (0.01m/0.00025m).  Work it out yourself.

Brent

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### Re: Where Max Tegmark is really wrong

```

On 12/3/2018 9:59 AM, Philip Thrift wrote:

But that is close to the solipsist move. The fact that we cannot
define truth does not entail that some notion of truth does not
make sense. In particular, Peano arithmetic can already define an
infinity of approximation of truth, namely sigma_i and pi_i truth
(the truth of the sentences will a finite and fixed number of
quantifier, as opposed to finite sentences with an arbitrary
finite number of quantifier).

We can invoke truth, but we can develop meta-discourse relating
truth to theories, like we cannot invoke our own consciousness
does not prevent us to try theories about it.
It is a bit like “I cannot study my own brain”, but I can still
infer some theories of my brain by looking at the brain of others
and then assuming that I am not different.

So are do these theories produce true or false propositions?

Bruno

A different perspective (!) of "truth" comes from - vs. PA (Peano
arithmetic) - *PLT* (programming language theory - the legacy to a
large extent of John C. Reynolds
[ https://en.wikipedia.org/wiki/John_C._Reynolds - who was originally
a theoretical physicist ], and sort of in parallel the whole
type-theory gang). Rather than an external "god-like" notion of truth,
truth is in the programming.

- pt

Can you give an example of "truth in the programming" and how it differs
from the mathematical idea of true and the correspondence theory of truth?

Brent

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### Re: The most accurate clock ever

```

On 12/2/2018 7:04 PM, John Clark wrote:
On Sun, Dec 2, 2018 at 4:29 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

/> The Earth is 3.9e22 times heavier than Cavendishes cannon ball. /

The mass of the earth is irrelevant because we're talking about
measuring the difference in the strength of gravity as distance
increases not its absolute value.

>> In 1798 technology was good enough for Cavendish to measure
the gravitational attraction between 2 cannonballs a few
inches apart (andby doing so determine the value of the
Gravitational Constant) but until a few months ago no
technology was good enough to measure the difference in
strength of a gravitational field that was 637,000,000
centimeters from the center of the Earth and one that was
637,000,001 centimeters from the center of the Earth. But the
technology is good enough now thanks to this new clock.

> /N//o.  The potential difference measured by the cesium clock when
raised 1cm relative to the Earth was 2.03e9 times bigger than the
smallest difference measured by Cavendish (assuming he could
measure 0.00025m deflection).  The Earth is 3.9e22 times heavier
than Cavendishes cannon ball.     So 300yrs ago Cavendishes
technology was good enough;/

If you are on the Earth's surface and you raise a clock by one
centimeter you've increased its distance from the earth's center by
one part in 637,000,000, it is now 1.16 times further away.
The intensity of the gravitational field is proportional to the square
of the distance so gravity was 1.31 times stronger before you
raised raised the clock. Cavendish did not have a scale good enough to
measure that, even today the very best (and very expensive) lab weight
scale might be able to measure a change of 1.001 but the clock can
do several hundred times better.

He was measuring the change in a much smaller gravitational field.

> (assuming he could measure 0.00025m deflection).

When Cavendish measured a deflection he was measuring the strength of
the attraction between 2 canon balls, he was not measuring the
difference in the gravitational field at 2 points. Cavendish used a
torsion balanceand its very good at measuring weak forces but it can't
measure the super small difference between 2 strong forces, to do that
he'd need a weight scale, or a super accurate clock.

He was measuring the difference between the force on the torsion balance
with the cannon balls present vs absent.

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 12/2/2018 5:14 PM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 4:25:04 PM UTC-6, Brent wrote:

On 12/2/2018 11:42 AM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 8:13:48 AM UTC-6,
agrays...@gmail.com wrote:

*
*
*Obviously, from a one-world perspective, only one history
survives for a single trial. But to even grossly approach
anything describable as "Darwinian", you have to identify
characteristics of histories which contribute positively or
negatively wrt surviving but I don't see an inkling of that.
IMO, Quantum Darwinism is at best a vacuous restatement of
the measurement problemt; that we don't know why we get what
we get. AG*

In the *sum over histories* interpretation - of the double-slit
experiment, for example - each history carries a unit complex
number - like a gene - and this gene reenforces (positively) or
interferes (negatively) with other history's genes in the sum.

But I thought you said the ontology was that only one history
"popped out of the Lottery machine"?  Here you seem to contemplate
an ensemble of histories, all those ending at the given spot, as
being real.

Brent

All are real until all but one dies.
RIP: All those losing histories.

The trouble with that is the Born probability doesn't apply to
histories, it applies to results.  So your theory says nothing about the
probability of the fundamental ontologies.

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 12/2/2018 11:42 AM, Philip Thrift wrote:

On Sunday, December 2, 2018 at 8:13:48 AM UTC-6, agrays...@gmail.com
wrote:

*
*
*Obviously, from a one-world perspective, only one history
survives for a single trial. But to even grossly approach anything
describable as "Darwinian", you have to identify characteristics
of histories which contribute positively or negatively wrt
surviving but I don't see an inkling of that. IMO, Quantum
Darwinism is at best a vacuous restatement of the measurement
problemt; that we don't know why we get what we get. AG*

In the *sum over histories* interpretation - of the double-slit
experiment, for example - each history carries a unit complex number -
like a gene - and this gene reenforces (positively) or interferes
(negatively) with other history's genes in the sum.

But I thought you said the ontology was that only one history "popped
out of the Lottery machine"?  Here you seem to contemplate an ensemble
of histories, all those ending at the given spot, as being real.

Brent

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### Re: The most accurate clock ever

```

On 12/2/2018 6:22 AM, John Clark wrote:
On Sat, Dec 1, 2018 at 6:59 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

> /But an ocean wave many feet high would change the gravitational
field less than would moving a centimeter relative to the Earth's
center of mass./

Not so. In 1798 technology was good enough for Cavendish to measure
the gravitational attraction between 2 cannonballs a few inches apart
(and by doing so determine the value of the Gravitational Constant)
but until a few months ago no technology was good enough to measure
the difference in strength of a gravitational field that was
637,000,000 centimeters from the center of the Earth and one that was
637,000,001 centimeters from the center of the Earth. But the
technology is good enough nowthanks to this new clock. And this isn't
the end of the line for clock technology, nobody has made one yet but
a Thorium Nuclear Clock would be even more accurate.

No.  The potential difference measured by the cesium clock when raised
1cm relative to the Earth was 2.03e9 times bigger than the smallest
difference measured by Cavendish (assuming he could measure 0.00025m
deflection).  The Earth is 3.9e22 times heavier than Cavendishes cannon
ball.     So 300yrs ago Cavendishes technology was good enough; it's
just hard to hang two Earth masses in a big box.

Brent

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### Re: Where Max Tegmark is really wrong

```

On 12/2/2018 4:52 AM, Bruno Marchal wrote:

Language have no relation with truth a priori. Theories might have.
Semantics are truth “by definition”, by relativising it to the notion
of model/reality.

Then what is this "true" and "false" which you attribute to the
propositions of modal logic?

Brent

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### Re: Where Max Tegmark is really wrong

```

On 12/2/2018 4:58 AM, Bruno Marchal wrote:

On 30 Nov 2018, at 19:22, Brent Meeker <mailto:meeke...@verizon.net>> wrote:

On 11/30/2018 1:15 AM, Bruno Marchal wrote:

Perspectivism is a form of modalism.

Nietzsche is vindicated.

Interesting. If you elaborate, you might change my mind on Nietzche,
perhaps!
All what I say is very close the Neoplatonism and Negative Theology
(capable only of saying what God is not).

Bruno

From https://plato.stanford.edu/entries/nietzsche/

6.2 Perspectivism

Much of Nietzsche’s reaction to the theoretical philosophy of his
predecessors is mediated through his interest in the notion of
perspective. He thought that past philosophers had largely ignored
the influence of their own perspectives on their work, and had
therefore failed to control those perspectival effects (/BGE/6;
see/BGE/I more generally). Commentators have been both fascinated and
perplexed by what has come to be called Nietzsche’s “perspectivism”,
and it has been a major concern in a number of large-scale Nietzsche
commentaries (see, e.g., Danto 1965; Kaulbach 1980, 1990; Schacht
1983; Abel 1984; Nehamas 1985; Clark 1990; Poellner 1995; Richardson
1996; Benne 2005). There has been as much contestation over exactly
what doctrine or group of commitments belong under that heading as
about their philosophical merits, but a few points are relatively
uncontroversial and can provide a useful way into this strand of
Nietzsche’s thinking.

Nietzsche’s appeals to the notion of perspective (or, equivalently in
his usage, to an “optics” of knowledge) have a positive, as well as a
critical side. Nietzsche frequently criticizes “dogmatic”
philosophers for ignoring the perspectival limitations on their
theorizing, but as we saw, he simultaneously holds that the operation
of perspective makes a positive contribution to our cognitive
endeavors: speaking of (what he takes to be) the perversely
counterintuitive doctrines of some past philosophers, he writes,

Particularly as knowers, let us not be ungrateful toward such
resolute reversals of the familiar perspectives and valuations
with which the spirit has raged against itself all too long… : to
see differently in this way for once,/to want/to see differently,
is no small discipline and preparation of the intellect for its
future “objectivity”—the latter understood not as “disinterested
contemplation” (which is a non-concept and absurdity), but rather
as the capacity to have one’s Pro and Contra/in one’s power/, and
to shift them in and out, so that one knows how to make precisely
the/difference/in perspectives and affective interpretations
useful for knowledge. (/GM/III, 12)

This famous passage bluntly rejects the idea, dominant in philosophy
at least since Plato, that knowledge essentially involves a form of
objectivity that penetrates behind all subjective appearances to
reveal the way things really are, independently of any point of view
whatsoever. Instead, the proposal is to approach “objectivity” (in a
revised conception) asymptotically, by exploiting the difference
between one perspective and another, using each to overcome the
limitations of others, without assuming that anything like a “view
from nowhere” is so much as possible. There is of course an implicit
criticism of the traditional picture of a-perspectival objectivity
here, but there is equally a positive set of recommendations about
how to pursue knowledge as a finite, limited cognitive agent.

Thanks. But I do not oppose perspectivism with Plato, and certainly
not with neoplatonism, which explains everything from the many
perspective of the One, or at least can be interpreted that way.

Pure perspectivism is an extreme position which leads to pure
relativism, which does not make sense, as we can only doubt starting
from indubitable things (cf Descartes). But Nietzsche might have been
OK, as the text above suggested a “revised conception” of objective.

With mechanism, you have an ablate truth (the sigma_1 arithmetical
truth), and the rest is explained by the perspective enforced by
incompleteness.

My reading of Nietzsche is he thought that there are many different
perspectives and one can only approach the truth by looking from
different perspectives but never taking one of them as definitive. This
goes along with his denial and rejection of being a system builder.  I
think he equated system builders with those who took their perspective
to be the only one.

Brent

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### Re: The most accurate clock ever

```

On 12/1/2018 7:06 AM, John Clark wrote:

On Thu, Nov 29, 2018 at 6:34 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

>> good enough for jet fighters to automatically land on
aircraft carriers without a pilot, even at night in a heavy
fog in a bad storm with the deck tossing up and down.

/> Unfortunately for that idea, the surface of the Earth, and
especially the ocean, varies by a lot more than a centimeter. /

If the ocean fluctuates up and down the intensity of the Earth's
gravitational field will fluctuate too and with exactly the same
rhythm, the change in gravity will be very very small but a clock this
good could detect it. In a practical system in wartime conditions the
error would probably be a few inches rather than a centimeter but that
would be good enough; even the best human fighter pilot only knows
where the deck of his aircraft carrier is within a foot or two when he
lands.

But an ocean wave many feet high would change the gravitational field
less than would moving a centimeter relative to the Earth's center of mass.

Brent

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### Re: Where Max Tegmark is really wrong

```

On 11/30/2018 1:15 AM, Bruno Marchal wrote:

Perspectivism is a form of modalism.

Nietzsche is vindicated.

Interesting. If you elaborate, you might change my mind on Nietzche,
perhaps!
All what I say is very close the Neoplatonism and Negative Theology
(capable only of saying what God is not).

Bruno

From  https://plato.stanford.edu/entries/nietzsche/

6.2 Perspectivism

Much of Nietzsche’s reaction to the theoretical philosophy of his
predecessors is mediated through his interest in the notion of
perspective. He thought that past philosophers had largely ignored the
influence of their own perspectives on their work, and had therefore
failed to control those perspectival effects (/BGE/6; see/BGE/I more
generally). Commentators have been both fascinated and perplexed by what
has come to be called Nietzsche’s “perspectivism”, and it has been a
major concern in a number of large-scale Nietzsche commentaries (see,
e.g., Danto 1965; Kaulbach 1980, 1990; Schacht 1983; Abel 1984; Nehamas
1985; Clark 1990; Poellner 1995; Richardson 1996; Benne 2005). There has
been as much contestation over exactly what doctrine or group of
commitments belong under that heading as about their philosophical
merits, but a few points are relatively uncontroversial and can provide
a useful way into this strand of Nietzsche’s thinking.

Nietzsche’s appeals to the notion of perspective (or, equivalently in
his usage, to an “optics” of knowledge) have a positive, as well as a
critical side. Nietzsche frequently criticizes “dogmatic” philosophers
for ignoring the perspectival limitations on their theorizing, but as we
saw, he simultaneously holds that the operation of perspective makes a
positive contribution to our cognitive endeavors: speaking of (what he
takes to be) the perversely counterintuitive doctrines of some past
philosophers, he writes,

Particularly as knowers, let us not be ungrateful toward such
resolute reversals of the familiar perspectives and valuations with
which the spirit has raged against itself all too long… : to see
differently in this way for once,/to want/to see differently, is no
small discipline and preparation of the intellect for its future
“objectivity”—the latter understood not as “disinterested
contemplation” (which is a non-concept and absurdity), but rather as
the capacity to have one’s Pro and Contra/in one’s power/, and to
shift them in and out, so that one knows how to make precisely
the/difference/in perspectives and affective interpretations useful
for knowledge. (/GM/III, 12)

This famous passage bluntly rejects the idea, dominant in philosophy at
least since Plato, that knowledge essentially involves a form of
objectivity that penetrates behind all subjective appearances to reveal
the way things really are, independently of any point of view
whatsoever. Instead, the proposal is to approach “objectivity” (in a
revised conception) asymptotically, by exploiting the difference between
one perspective and another, using each to overcome the limitations of
others, without assuming that anything like a “view from nowhere” is so
much as possible. There is of course an implicit criticism of the
traditional picture of a-perspectival objectivity here, but there is
equally a positive set of recommendations about how to pursue knowledge
as a finite, limited cognitive agent.

Brent

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### Re: Where Max Tegmark is really wrong

```

On 11/29/2018 11:08 PM, Bruno Marchal wrote:

On 28 Nov 2018, at 18:40, Philip Thrift <mailto:cloudver...@gmail.com>> wrote:

On Wednesday, November 28, 2018 at 9:03:42 AM UTC-6, Lawrence Crowell
wrote:

On Friday, November 9, 2018 at 6:51:06 PM UTC-6, Bruce wrote:

From: *Brent Meeker*

You're dodging my point.  The "issue" of how we have
subjective experience only seems to be an issue because in
comparison to the "objective" experience of matter where we
can trace long, mathematically define causal chains down
to...a Lagrangian and coupling constants or something
similar, which is long enough and esoteric enough that
almost everyone loses interest along the way.  But some
people (like Vic) are going to say, "But where does the
Langrangian and coupling constants come from?"  and "Why a
Lagrangian anyway?" My point is that when we can give a
similarly deep and detailed account of why you think of an
elephant when reading this, then nobody will worry about
"the hard problem of consciousness"; just like they don't
worry about "the hard problems of matter" like where that
Lagrangian comes from or why a complex Hilbert space.

Why can't I worry about those things? Where does the
Lagrangian come from? And why use a complex Hilbert space? I
don't think this is the underlying reason for saying that the
"hard problem" of consciousness dissolves on solving the
engineering problems. Solving the engineering problems will
enable us to produce a fully conscious AI -- but will we then
know how it works? We will certainly know where it came from.

Bruce

When it comes to science I have to back what Bruce says here. All
knowledge faces the limits of the Münchhausen trilemma, where we
have three possible types of arguments. The first is the basic
axiomatic approach, which generally is the cornerstone and
capstone of mathematics and science. The second is a "turtles all
the way down," where an argument is based on premises that have
deeper reasons, and this nests endlessly. Vic Stenger found this
to be of most interest with his "models all the way down." The
third is a circular argument which would mean all truth is just
tautology. The second and third turn out to have some relevancy,
where these are complement in Godel's theorem. While in general
we use the first in science and mathematics we generally can't
completely eliminate the other two. However, for most work we
have an FAPP limitation to how far we want to go. Because of that
if there is ultimately just a quantum vacuum, or some set of
vacua, that is eternal, we may then just rest our case there.

If one wants to do philosophy or theology that may be fine, but
one has to make sure not to confuse these as categories with the
category of science. Maybe as Dennett says, philosophy is what we
do when we do not understand how to ask the question right. In
that setting at best we can only do sort of "pre-science," but
not really science as such. Theology is an even looser area of
thought, and I generally see no connection with science at all.

LC

The "models almost all the way up ... and ... down" quote ("models"
replacing the original "turtles") came first from the philosopher of
science *Ronald Giere* [ https://en.wikipedia.org/wiki/Ronald_Giere ].

/In his book Scientific Perspectivism he develops a version of
perspectival realism in which he argues that scientific descriptions
are somewhat like colors, in that they capture only selected aspects
of reality, and those aspects are not bits of the world seen as they
are in themselves, but bits of the world seen from a distinctive
human perspective. /

You can compare this with the consequence of mechanism and
incompleteness, which enforces the 8 different self-referential
universal (Löbian) machine “perspective” on arithmetic when seen by
inside:

p (true)
Bp (provable).  (split in two)
Bp & p (knowable)
Bp & Dp (observable).  (split in two)
Bp & Dp & p (sensible).  (split in two)

It is a form of perspectivism, or modalism. The modal B and D (which
is the diamond -B-) obeys the same law for all correct Löbian machine
(universal machine aware of its universality), but can be very
different form one individual to another.

B is Gödel’s beweisbar, or some generalisation for arbitrary

/In addition to the color example, Giere articulates his
perspectivism by appeal to maps and to his own earlier and
influential work on scientific models. Maps represent the world, but
the representations they provide are conventional, affected by
interes```

### Re: If Quantum Mechanics can be derived using arithmetic only, how would that derivation begin?

```What can be inferred always depends on what you take as premises. If you
start from the Hilbert space formulation of QM or an equivalent
formulation/*and you premise that there is a probability interpretation
of  a state*/, then Gleason's theorem tells you that the Born rule
provides the unique probability values.

Brent

On 11/29/2018 10:23 AM, agrayson2...@gmail.com wrote:
*Regardless of rules of arithmetic and mathematical logic, I simply
don't believe that something like Born's Rule can be inferred without
actually observing a quantum interference pattern. AG*

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### Re: The most accurate clock ever

```

On 11/29/2018 6:28 AM, John Clark wrote:
In yesterday's issue of the journal Nature Scientists at the National
Institute of Standards and Technology (NIST) reported they have made a
new type of clock that is the most accurate ever, it's called a
Ytterbium Lattice Clock. It's about 100 times better than any previous
clock, if set at the time of the Big Bang 13.8 billion years ago today
it would be off by less than one second.

https://www.nature.com/articles/s41586-018-0738-2

It's so good the main source of error is due to General Relativity, if
you lift the clock up by just one centimeter the Earth's gravitational
field is slightly weaker and so the clock runs noticeably faster, that
may be why NIST is now working on a portable version of their
Ytterbium Lattice Clock. If GPS satellites had clocks this good they'd
know where they were relative to the Earth to within a centimeter and
so could tell users on the ground where they were within a centimeter;
and that would be more than good enough for jet fighters to
automatically land on aircraft carriers without a pilot, even at night
in a heavy fog in a bad storm with the deck tossing up and down.

Unfortunately for that idea, the surface of the Earth, and especially
the ocean, varies by a lot more than a centimeter.  Off the coast of CA
where the Pacific Missile range is, the "Earth's surface" as defined in
WGS84 is a few meters underwater.  That's why one must us local
corrections for GPS altitude.  But the local correction is still only an
average over tidal cycles, etc.

Brent

It would be by far the best instrument ever made to detect tiny
changes in the gravitational field, and that would make it much easier
to find things buried deep underground. The Earth just became more
transparent. It might even be used to detect Gravitational Waves and
Dark Matter.

John K Clark
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### Re: Where Max Tegmark is really wrong

```

On 11/28/2018 9:40 AM, Philip Thrift wrote:

On Wednesday, November 28, 2018 at 9:03:42 AM UTC-6, Lawrence Crowell
wrote:

On Friday, November 9, 2018 at 6:51:06 PM UTC-6, Bruce wrote:

From: *Brent Meeker*

You're dodging my point.  The "issue" of how we have
subjective experience only seems to be an issue because in
comparison to the "objective" experience of matter where we
can trace long, mathematically define causal chains down
to...a Lagrangian and coupling constants or something
similar, which is long enough and esoteric enough that almost
everyone loses interest along the way.  But some people (like
Vic) are going to say, "But where does the Langrangian and
coupling constants come from?"  and "Why a Lagrangian
anyway?" My point is that when we can give a similarly deep
and detailed account of why you think of an elephant when
reading this, then nobody will worry about "the hard problem
of consciousness"; just like they don't worry about "the hard
problems of matter" like where that Lagrangian comes from or
why a complex Hilbert space.

Why can't I worry about those things? Where does the
Lagrangian come from? And why use a complex Hilbert space? I
don't think this is the underlying reason for saying that the
"hard problem" of consciousness dissolves on solving the
engineering problems. Solving the engineering problems will
enable us to produce a fully conscious AI -- but will we then
know how it works? We will certainly know where it came from.

Bruce

When it comes to science I have to back what Bruce says here. All
knowledge faces the limits of the Münchhausen trilemma, where we
have three possible types of arguments. The first is the basic
axiomatic approach, which generally is the cornerstone and
capstone of mathematics and science. The second is a "turtles all
the way down," where an argument is based on premises that have
deeper reasons, and this nests endlessly. Vic Stenger found this
to be of most interest with his "models all the way down." The
third is a circular argument which would mean all truth is just
tautology. The second and third turn out to have some relevancy,
where these are complement in Godel's theorem. While in general we
use the first in science and mathematics we generally can't
completely eliminate the other two. However, for most work we have
an FAPP limitation to how far we want to go. Because of that if
there is ultimately just a quantum vacuum, or some set of vacua,
that is eternal, we may then just rest our case there.

If one wants to do philosophy or theology that may be fine, but
one has to make sure not to confuse these as categories with the
category of science. Maybe as Dennett says, philosophy is what we
do when we do not understand how to ask the question right. In
that setting at best we can only do sort of "pre-science," but not
really science as such. Theology is an even looser area of
thought, and I generally see no connection with science at all.

LC

The "models almost all the way up ... and ... down" quote ("models"
replacing the original "turtles") came first from the philosopher of
science *Ronald Giere* [ https://en.wikipedia.org/wiki/Ronald_Giere ].

/In his book Scientific Perspectivism he develops a version of
perspectival realism in which he argues that scientific descriptions
are somewhat like colors, in that they capture only selected aspects
of reality, and those aspects are not bits of the world seen as they
are in themselves, but bits of the world seen from a distinctive human
perspective. In addition to the color example, Giere articulates his
perspectivism by appeal to maps and to his own earlier and influential
work on scientific models. Maps represent the world, but the
representations they provide are conventional, affected by interest,
and never fully accurate or complete. Similarly, scientific models are
idealized structures that represent the world from particular and
limited points of view. According to Giere, what goes for colors,
maps, and models goes generally: science is perspectival through and
through./

And I would add that this is true of all thought, not just "scientific"
ideas.  We evolved to see the world in certain ways conducive to
survival and reproduction.  But as Vic used to say science works so it
has something to do with reality.

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 11/27/2018 12:43 PM, Philip Thrift wrote:

On Tuesday, November 27, 2018 at 2:05:04 PM UTC-6, agrays...@gmail.com
wrote:

On Tuesday, November 27, 2018 at 6:49:51 PM UTC, Philip Thrift wrote:

On Tuesday, November 27, 2018 at 12:17:08 PM UTC-6,
agrays...@gmail.com wrote:

On Tuesday, November 27, 2018 at 6:00:50 PM UTC, Philip
Thrift wrote:

On Tuesday, November 27, 2018 at 8:43:35 AM UTC-6,
agrays...@gmail.com wrote:

On Tuesday, November 27, 2018 at 9:27:46 AM UTC,
Philip Thrift wrote:

On Monday, November 26, 2018 at 3:43:14 PM
UTC-6, agrays...@gmail.com wrote:

*
*
*I checked the postulates in Feynman's
Sums Over Histories (in link provided by
Phil) and I see nothing related to waves,
as expected, and thus nothing about
collapse of anything. I would suppose the
same applies to Heisenberg's Matrix
Mechanics; no waves, no collapse. I
suppose you could say they just produce
correct probabilities, and imply nothing
about relative states other than their
probabilities (which wave mechanics does),
but certainly nothing about consciousness.
To summarize: you're right that they are
"no collapse" theories, but IMO they say
nothing about consciousness. AG*

In terms of the path-integral (PI)
interpretation [ interesting lecture:

https://www.perimeterinstitute.ca/videos/path-integral-interpretation-quantum-mechanics

], there is in effect no waves or wave
function, just paths, or histories, in the
sum-over-histories (SOH) terminology.

There is still "decoherence" in the SOH (a
single history is ultimately "realized"), but
it could be called "selection": a single
history is selected from the total ensemble of
multiple and interfering histories. E.g. a
single point on a screen is "hit" by a photon
in the double-slit experiment.

*Does "selection" add any insight to the
measurement problem; that is, why do we get what
we get? And if not, what is its value? TIA, AG *

If you look at it as a "selection of the fittest" (one
history surviving from an ensemble of histories), then
it's like a form of quantum Darwinism. The quantum
substrate is a cruel world where all histories (but
one) die.

That's not an explanation; rather, a vacuous statement of
the result. AG

But that is a criticism of Darwinism (*natural selection*) in
general.

*
*
*Ridiculous comparison IMO. Darwinism posits a changing
environment and competition among species for niches. Nothing
comparable in Quantum Darwinism other than all outcomes fail
except for one which succeeds in each single trial, which we knew
from the get-go. AG*

*Quantum Darwinism* is a theory claiming to explain the
emergence of the classical world
from the
quantum world
as due to *a
process of **Darwinian
natural
selection *;
where the many possible quantum states
are selected
against in favor of a stable pointer state
.
[ https://en.wikipedia.org/wiki/Quantum_Darwinism
]

- pt

As for "competition for niches", the histories are in a sense
competing. Perhaps there is some conservation principle at work, so
only one history can win.

I don't know. Physicists don't know. We're even. :)

In a delayed quantum erasure experiment I wonder if you would be
possible to make a weak measurement on the photon to be erased? Would
you get an ```

### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 11/27/2018 2:38 AM, Bruno Marchal wrote:

On 25 Nov 2018, at 15:41, John Clark > wrote:

On Sun, Nov 25, 2018 at 4:40 AM Philip Thrift > wrote:

Dennett's said:

“/The elusive subjective conscious experience—the redness of red, the
painfulness of pain—that philosophers call qualia? Sheer illusion/.”

The trouble with the above statement isn't so much that it's false,
the trouble is that it's silly. In the first place an illusion is a
misinterpretation of the senses, but pain is direct experience that
needs no interpretation. I would love to ask Mr. Dennett how things
would be different if pain was not an illusion, if he can't answer
that, and I don't think he could, then the statement "pain is a
illusion" contains no information.

And illusion itself is a conscious phenomena, so saying consciousness
is an illusion is just saying consciousness is consciousness which,
although true, is not very illuminating. When discussing any
philosophical issue the word "illusion" should be used very
cautiously. And if the topic involves consciousness or quala and
silliness is to be avoided the word "illusion" should never be used
at all because it explains nothing.

That us why we use synonymous like first person, phenomenological, etc.

For example, with mechanism, the matter that we see is not an
illusion, but the primary matter that we infer

What is this "primary matter" of which you speak?  molecules? atoms?
quarks? strings?   Who is it who every claims any one of these is
"primary"?  What theory depends on one of them being primary?  I think
you are beating a straw man to imply that others theories are wrong
therefore yours must be right.

Brent

from that seeing experience is an illusion, or a delusion. It is just
a wrong inference, as most illusion are.

Consciousness cannot be an illusion, indeed, but all content of
consciousness, minus being conscious, can be wrong.

Bruno

John K Clark

//

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 11/24/2018 5:39 AM, John Clark wrote:

On Fri, Nov 23, 2018 at 1:10 PM Philip Thrift > wrote:

/> Some in AI will say if something is just informationally
intelligent (or pseudo-intelligent) but not experientially
intelligent then it will not ever be remarkably creative - in
literature, music, painting, or even science./

Apparently being remarkably creative is not required to be supremely
good at Chess or GO or solving equations because pseudo-intelligence
will beat true-intelligence at those things every time. The goal posts
keep moving, true intelligence is whatever computers aren't good at. Yet.

> And it will not be conscious,

My problem is if the AI is smarter than me it will outsmart me, but if
the AI isn't conscious that's the computers problem not mine. And
besides, I'll never know if the AI is conscious or not just as I'll
never know if you are.

The question is whether the AI will ever infer it is not conscious. I
think Bruno correctly points out that this would be a contradiction. If
it can contemplate the question, it's conscious even though it can't
prove it.

Brent

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### Re: Adam and Eve’s Anthropic Superpowers

```

On 11/24/2018 1:53 AM, Philip Thrift wrote:

On Friday, November 23, 2018 at 4:11:26 PM UTC-6, Mason Green wrote:

Hi everyone,

I found an interesting blog post that attempts to refute the
Doomsday Argument. It suggests that different worlds ought to be
weighted by the number of people in them, so that you should be
more likely to find yourself in a world where there will be many
humans, as opposed to just a few. This would cancel out the
unlikeliness of finding yourself among the first humans in such a
world.

I’m curious as to what the contributors here think. (I’m new here,
I found out about this list through Russell’s Theory of Nothing
book).

-Mason

Without examining the theoretical details of this (or any)
probabilistic argument (including Bayesian ones), one general approach
is this: The theory may all be correct of course (given accepted
assumptions), but it's ultimately convincing when results are compared
to Monte Carlo computer experiments. (If you don't like don't "trust"
your software's random numbers, then you can get some from [
https://www.fourmilab.ch/hotbits/secure_generate.html ]).

Say in the case of "In front of you is a jar. This jar contains either
10 balls or 100 balls. The balls are numbered in order from 1 to
either 10 or 100." Then you you write a program that randomly creates
either a 10ball-jar with probability 0.50 (or any p) or a 100ball-jar
with probability 0.50 (or 1-p) and then pick a ball at random. You run
this 10,000 times (or whatever) and just get statistics.

You can do this for the Monte Hall problem - which has the irony that
Monte Carlo "solves" the Monte Hall problem!

The best intuition pump to solve the Monte Hall problem is to imagine
that there are 100 doors and Monte opens all the doors except the one
you chose and one otherdo you switch?

Brent

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### Re: Measuring a system in a superposition of states vs in a mixed state

```

On 11/14/2018 11:23 PM, Philip Thrift wrote:

On Wednesday, November 14, 2018 at 6:55:36 PM UTC-6,
agrays...@gmail.com wrote:

On Wednesday, November 14, 2018 at 10:20:09 PM UTC, Pierz wrote:

Obviously you can't measure the particle simultaneously in the
up and down state. Nobody believes that. Nobody is arguing it.

*Haven't you ever heard of physicists, some prominent who write
books about QM for the lay public, who assert that one of the
mysteries of QM is that a particle can be in two places at the
same time, or cats can be alive and dead simultaneously, or spin
can be Up and Dn simultaneously? If you haven't, you're not paying
attention. AG*

*
*
*"a particle can be in two places at the same time"*

A path-integral realist (one who is "starting from a framework in
which /histories/ are fundamental")* might formulate it this way:

"a particle can have multiple histories — only one of which survives
measurement"

Don't you need multiple histories to account for interference effects?

Brent

* *Hilbert Spaces from Path Integrals*
https://arxiv.org/abs/1002.0589

- pt
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### Re: Where Max Tegmark is really wrong

```

On 11/9/2018 4:51 PM, Bruce Kellett wrote:

From: *Brent Meeker* mailto:meeke...@verizon.net>>

You're dodging my point.  The "issue" of how we have subjective
experience only seems to be an issue because in comparison to the
"objective" experience of matter where we can trace long,
mathematically define causal chains down to...a Lagrangian and
coupling constants or something similar, which is long enough and
esoteric enough that almost everyone loses interest along the way.
But some people (like Vic) are going to say, "But where does the
Langrangian and coupling constants come from?"  and "Why a Lagrangian
anyway?" My point is that when we can give a similarly deep and
detailed account of why you think of an elephant when reading this,
then nobody will worry about "the hard problem of consciousness";
just like they don't worry about "the hard problems of matter" like
where that Lagrangian comes from or why a complex Hilbert space.

Why can't I worry about those things? Where does the Lagrangian come
from? And why use a complex Hilbert space? I don't think this is the
underlying reason for saying that the "hard problem" of consciousness
dissolves on solving the engineering problems. Solving the engineering
problems will enable us to produce a fully conscious AI -- but will we
then know how it works? We will certainly know where it came from.

I just meant those as current examples.  Suppose you find that
Lagrangians come from POVI, as Vic proposed.  Then one can ask, "Why
POVI?"  Vic implied it was a choice, but that didn't explain why is an
available choice.  So I think both the problem of consciousness and the
problem of matter are both "hard"; the problem of matter seems "easy"
because we've come a long way in 400yrs of solving the engineering
problems of matter.

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 11/5/2018 1:34 PM, Philip Thrift wrote:

On Monday, November 5, 2018 at 2:45:30 PM UTC-6, Brent wrote:

On 11/5/2018 8:54 AM, Philip Thrift wrote:

On Monday, November 5, 2018 at 6:56:42 AM UTC-6, John Clark wrote:

On Mon, Nov 5, 2018 at 3:40 AM Philip Thrift
wrote:

> I agree with those scientists who that say something
isn't truly intelligent unless it is also conscious.

Then you have no way of knowing if any of your fellow human
beings are "truly intelligent" because you have no way of
knowing if they are conscious or not. And if you were
outsmarted by something that was *NOT* "truly intelligent"
should you feel better or worse that if you were outsmarted
by something that was *WAS* "truly intelligent"?

/> For something to be fully conscious, or self aware, it
would want to "live". It would not want to be "shut
down".When Watson starts screaming, "Don't turn me off!",
then it might be conscious./

Unlike winning at Jeopardy that would be trivially easy to
program.

John K Clark

I think I would feel better being outsmarted by an unconscious
robot than a conscious robot.

Because you know the conscious robot would have an internal model
of the world in which it knew it had outsmarted you and from which
it would learn and plan future actions...like selling you a time
share.  Which I think gives some insight into what constitutes
consciousness and why it is inherent in high-level intelligence.

Brent

Actually I was thinking the conscious robot would /experience/ a
satisfaction that the sans-consciousness robot could not.

But is satisfaction so specific.  If it's just property of some
bio-matter, then you could simply append a bio-component to your
electronic computer to proved the experience.

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 11/5/2018 8:54 AM, Philip Thrift wrote:

On Monday, November 5, 2018 at 6:56:42 AM UTC-6, John Clark wrote:

On Mon, Nov 5, 2018 at 3:40 AM Philip Thrift > wrote:

> I agree with those scientists who that say something isn't
truly intelligent unless it is also conscious.

Then you have no way of knowing if any of your fellow human beings
are "truly intelligent" because you have no way of knowing if they
are conscious or not. And if you were outsmarted by something that
was *NOT* "truly intelligent" should you feel better or worse that
if you were outsmarted by something that was *WAS* "truly
intelligent"?

/> For something to be fully conscious, or self aware, it
would want to "live". It would not want to be "shut down".When
Watson starts screaming, "Don't turn me off!", then it might
be conscious./

Unlike winning at Jeopardy that would be trivially easy to program.

John K Clark

I think I would feel better being outsmarted by an unconscious robot
than a conscious robot.

Because you know the conscious robot would have an internal model of the
world in which it knew it had outsmarted you and from which it would
learn and plan future actions...like selling you a time share.  Which I
think gives some insight into what constitutes consciousness and why it
is inherent in high-level intelligence.

Brent

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### Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```

On 11/5/2018 12:40 AM, Philip Thrift wrote:

On Sunday, November 4, 2018 at 6:49:12 PM UTC-6, John Clark wrote:

On Sun, Nov 4, 2018 at 7:22 PM Philip Thrift > wrote:

/> By "experience", philosophers (like Galen Strawson, Philip
Goff) mean that which you have within yourself right now: the
awareness that/[...]

Awareness? But awareness is just another word for consciousness,
so when you say "/It's that experience (not just information) that
needs processing to produc/*/e consciousness/"*you're saying that
to produce consciousness you must process consciousness. I don't
find that very helpful.

> I assume I can be outsmarted by Watson on Jeopardy!

Then Watson't intelligence isn't very pseudo.

John K Clark

I agree with those scientists who that say something isn't truly
intelligent unless it is also conscious.

For something to be fully conscious, or self aware, it would want to
"live". It would not want to be "shut down". When Watson starts
screaming, "Don't turn me off!", then it might be conscious.

Why would being conscious entail not wanting to be turned off? Don't you
go to sleep at night?

Out fundamental drives have been shaped by evolution, not by
technology.  When Watson says, "I want a woman." that will be the time
to worry.

Brent

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### Re: Mathematical Universe Hypothesis

```

On 11/1/2018 4:02 PM, Philip Thrift wrote:

On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote:

On 11/1/2018 11:59 AM, Philip Thrift wrote:

On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:

On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift
wrote:

/> infinite time Turing machines are more powerful than
ordinary Turing machines/

That is true, it is also true that if dragons existed they
would be dangerous and if I had some cream I could have
strawberries and cream, if I had some strawberries.

/> How  "real" you think this is depends on whether you
are a *Platonist *or a*fictionalist*./

No, it depends on if you think logical contradictions can
exist, if they can then there is no point in reading any
mathematical proof and logic is no longer a useful tool for
anything.

John K Clark

Of course logics are fiction too. (They're just languages after all.)

OK.  Sentences written down are physical and not fictions. But can
"This page is blue." unless they have some meaning as
propositions.  But this must be a relation between a proposition
(an abstract thing) and a fact (the color of this page).

Brent

Sentences, like this one, are physical *only* in the sense that they
are (in this case) made up of electronic bits displayed on a screen
(as you are looking at right now, maybe on a laptop or smartphone) -
or they could be made up of ink strokes on paper, etc.

One can't read anything more into them physically that that. What one
reads out of them (a person looking at this sentence, or a computer
scanning one) is a difference matter.

There are no abstractions in an immaterial sense.

But there are abstractions in the sense that the same proposition is
instantiated in different substrates.   So the contradiction can be
between different instances, e.g. a spoken sentence can contradict a
written one.

Brent

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### Re: Mathematical Universe Hypothesis

```

On 11/1/2018 11:59 AM, Philip Thrift wrote:

On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:

On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > wrote:

/> infinite time Turing machines are more powerful than
ordinary Turing machines/

That is true, it is also true that if dragons existed they would
be dangerous and if I had some cream I could have strawberries and
cream, if I had some strawberries.

/> How  "real" you think this is depends on whether you are a
*Platonist *or a*fictionalist*./

No, it depends on if you think logical contradictions can exist,
if they can then there is no point in reading any mathematical
proof and logic is no longer a useful tool for anything.

John K Clark

Of course logics are fiction too. (They're just languages after all.)

OK.  Sentences written down are physical and not fictions.  But can they
blue." unless they have some meaning as propositions. But this must be a
relation between a proposition (an abstract thing) and a fact (the color

Brent

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### Re: Schrodinger bacteria

```

On 10/30/2018 3:39 PM, John Clark wrote:
On Tue, Oct 30, 2018 at 3:28 PM Brent Meeker <mailto:meeke...@verizon.net>> wrote:

> But they are really just showing that the bacterial antennae that
absorb photons are in a superposition of excited and not-excited.
The bacteria are not alive+dead.  They're only alive.

The same bacteria saw something and at the same time the bacteria
didn't see  something,

I think it takes a brain to "see something".  By you usage and electron
"sees something" when it jumps and energy level.

Brent

its analogous to you  seeing a dead cat and you not seeing a dead cat
at the same time.  The only difference is you're bigger.

John k Clark

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### Re: Mathematical Universe Hypothesis

```

On 10/30/2018 2:49 PM, Tomas Pales wrote:

On Tuesday, October 30, 2018 at 8:14:31 PM UTC+1, Brent wrote:

On 10/30/2018 4:01 AM, Tomas Pales wrote:

On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal
wrote:

Any object can be inconsistently defined. I can define the
moon by the set of squared circles.

The set of squared circles is the empty set. The moon is not an
empty set, it has a complex internal structure.

Anyway, the word "define" has two meanings which need to be
distinguished. "An object is /defined/" may mean:

1) "An object is /described/" (this usually means that there must
be someone who defines/describes the object)

2) "An object is /constituted/formed/" (this doesn't require
anyone to define the object, just as the fact that an object is
composed of parts doesn't require a composer)

Where did you come up with these?  To define an object means to
cite sufficient characteristics of the object so that it is
distinguished from all other objects.  It is described in the
sense of 1) supra, but the description need not be extensive;
simple ostensive definition by pointing suffices, which is
probably how you learned the definition of "Moon".

Your "definition" 2) makes no sense.  Listing all the constituents
of an object to what level?  atoms?  quantum fields?  And how does
that even suffice to distinguish an object from other objects with
the same constituents?  When you've tried to use your idea of
"consistently defined" you've resorted to including all relations
to other objects in the "consistent definition" which makes the
object distinct from other objects but which makes the definition
of an object unknowable.

In the first sense, an object is defined by someone. In the second
sense, an object is defined by its properties, parts and relations.

But those are to numerous and uncertain to ever be known.  And why would
you use the word "defined" instead of "constituted" when "defined"
clearly refers to making definite which can be done by much less than
listing all the constituents?

Brent

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### Re: Mathematical Universe Hypothesis

```The calculus problems that computers can solve exactly don't have
complex boundary conditions, including arbitrary dynamic terms, that are
only defined numerically.

Brent

On 10/30/2018 8:43 AM, John Clark wrote:

On Tue, Oct 30, 2018 at 2:22 AM Philip Thrift > wrote:

/> Engineers today are ultrafintiitists in practice: They design
airplanes and bridges with computer software that runs on
computers with a fixed, finite number of bits that are ever used. /

For over 40 years computers have been able to solve calculus problems
symbolically and get EXACT answers and do it better than any human
can, just look at  Mathematica. Sometimes engineers use numerical
approximations not because they think calculus is wrong, no engineer
is that dumb, but because sometimes the equations are so complex even
Mathematica can't find a solution and because an approximation is good
enough to make sure the bridge won't fall down

John K Clark

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### Re: Schrodinger bacteria

```But they are really just showing that the bacterial antennae that absorb
photons are in a superposition of excited and not-excited. The bacteria
are not alive+dead.  They're only alive.

Brent

On 10/30/2018 5:53 AM, John Clark wrote:
A group of scientists claim to have put 6 living green sulfur bacteria
into a Schrodinger Cat state, photons of light were hitting and not
hitting the bacteria at the same time. They want to see if they can do
the same thing to a Tardigrade which is much larger.

http://iopscience.iop.org/article/10.1088/2399-6528/aae224/meta

John K Clark
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### Re: Mathematical Universe Hypothesis

```

On 10/30/2018 4:01 AM, Tomas Pales wrote:

On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:

Any object can be inconsistently defined. I can define the moon by
the set of squared circles.

The set of squared circles is the empty set. The moon is not an empty
set, it has a complex internal structure.

Anyway, the word "define" has two meanings which need to be
distinguished. "An object is /defined/" may mean:

1) "An object is /described/" (this usually means that there must be
someone who defines/describes the object)

2) "An object is /constituted/formed/" (this doesn't require anyone to
define the object, just as the fact that an object is composed of
parts doesn't require a composer)

Where did you come up with these?  To define an object means to cite
sufficient characteristics of the object so that it is distinguished
from all other objects.  It is described in the sense of 1) supra, but
the description need not be extensive; simple ostensive definition by
pointing suffices, which is probably how you learned the definition of
"Moon".

Your "definition" 2) makes no sense.  Listing all the constituents of an
object to what level?  atoms?  quantum fields?  And how does that even
suffice to distinguish an object from other objects with the same
constituents?  When you've tried to use your idea of "consistently
defined" you've resorted to including all relations to other objects in
the "consistent definition" which makes the object distinct from other
objects but which makes the definition of an object unknowable.

Brent

When I say that an object is consistently or inconsistently defined, I
mean defined in the second sense. That's the existential/ontological
sense. An inconsistently defined object is not identical to itself, it
is not what it is, it does not have the properties it has. Such an
object is nonsense, it cannot exist, it is not really an object, it is
nothing. The definition of an object in the first sense is
true/accurate iff it corresponds to the definition of the object in
the second sense.

- and this I mean in the absolute sense, regardless of theory: an
object that is not identical to itself is inconsistent in any
theory. Such an object cannot exist. All other objects can exist
somewhere.

You are not using the (logical) terms in their standard meaning.
It is hard to follow. I don’t undersetand what you mean by object.

Sorry, by "object" I mean anything that exists. Not nothing.

With mechanism, the axiom of infinity leads to an inflation of
predictions, which is not what we are experiencing

That may mean that we live in a finite mathematical structure. Still,
that doesn't rule out the existence of infinite mathematical
structures. If they are consistent, why wouldn't they exist?

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### Re: Mathematical Universe Hypothesis

```

On 10/29/2018 3:38 AM, Tomas Pales wrote:
An object can be inconsistent in the sense that it can be
inconsistently defined - and this I mean in the absolute sense,
regardless of theory: an object that is not identical to itself is
inconsistent in any theory. Such an object cannot exist. All other
objects can exist somewhere.

You keep giving this convoluted formula or your theory in terms of
"consistently defined".   But you apparently want to include physical
laws in the measure of consistency AND the mere empirical fact (like the
elephant in my den) that violates no law of physics and certainly not
logic.  So your theory that every consistently defined object exists has
no standard except that the object either is observed to exist or can be
the subject of a sentence asserting its existence "in another
universe".  So baldly stated it is clear that it has no content whatsoever.

Brent

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