Re: A profound lack of profundity

[Stathis Papaioannou]

On Tue, 22 Aug 2017 at 10:00 am, John Clark  wrote:

> On Mon, Aug 21, 2017  Stathis Papaioannou  wrote:
>
>> ​>​
>> Which one and only one outcome will I see when I toss the coin?
>>
>
> ​I can't tell you today, but tomorrow after the flip I
> 'll be able to say what the correct answer would have been. ​So it was a
> real question with a real answer, I just didn't know what it was yesterday.
>
>

But if the world split when you toss a coin, you would just give up on
English?

> --
Stathis Papaioannou

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Re: A profound lack of profundity

[John Clark]

On Mon, Aug 21, 2017  Stathis Papaioannou  wrote:

​>​
> Which one and only one outcome will I see when I toss the coin?
>

​I can't tell you today, but tomorrow after the flip I
'll be able to say what the correct answer would have been. ​So it was a
real question with a real answer, I just didn't know what it was yesterday.

​

John K Clark​

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Re: A profound lack of profundity

[John Clark]

On Mon, Aug 21, 2017 at 8:06 AM, Bruno Marchal  wrote:

​>> ​
>> now the experiment is over and with the benefit of all the new
>> ​ ​
>> found knowledge you've gained from it I just want to know your new
>> improved answer to the question  "What is the name of the one and only one
>> city I will end up seeing after I became two?".
>
>
> ​> ​
> Very easy. I open the door, notice the city of Moscow, and
> ​ [blah blah *BLAH*]
>

I don't what another paragraph of bafflegab! You claim  "What is the name
of the one and only one city I will end up seeing after I became two?" is a
real
​ and the answer is very easy to find, so let's hear it. Knowing what you
know today with the benefit of hindsight what one and only one city name
would you have ​answered the Helsinki man's
​
​question with?

We both know you've got no one word answer, and that means it wasn't a
question.​


> ​> ​
> write the result in my diary.
>

​Bruno, why do keep talking about that stupid diary? After the duplication
2 people will have identical copies of that diary in their hand, so how
does that help us determine which *ONE *of the *TWO* wrote it? ​


​> ​
> I bet "W v M", and it is the best prediction available.
>

​That was yesterday, I what to know what's the best you can do today and if
it's not better than the prediction made yesterday that proves it wasn't a
question.​

​>>​
>> I what to know what your new improved answer is.
>
>
> ​> ​
> In Helsinki, I knew (modulo comp) that I will find myself in W or M, but
> ​ [blah blah *BLAH*]​
>

​That's the same crap you said yesterday about what will happen today, the
fact that you can't do any better today about what already happened today
is yet more proof that it wasn't a question. ​

​

John K Clark​

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Re: A profound lack of profundity

[Stathis Papaioannou]

On Tue, 22 Aug 2017 at 8:39 am, John Clark  wrote:

> On Mon, Aug 21, 2017  Stathis Papaioannou  wrote:
>
> ​> ​
 While the outcome is certain for you, it is not certain for me.

>>>
>>> ​That's because the meaning of the personal pronoun "me" will always be
>>> uncertain in ​a world that contains "me" duplicating machines.
>>>
>>>
>>
>> And this uncertainty constitutes the irreducible indeterminacy.
>>
>
> ​It signifies nothing more profound than poor writing​ and silly pronoun
> usage.
>
> ​> ​
>> After the duplication there will be two copies, one with $2 and the other
>> with nothing. Neither of them has the same amount of money as before.
>>
>
> ​OK. So what?​
>
>
> ​>>​
>>> ​As so often happens in this ​thread nobody can say if the above is
>>> true or not because nobody knows who Mr. I is.
>>>
>>>
>>
>> ​> ​
>> Mr I is the person who remembers going into the duplicator,
>>
>
> ​Then Mr.I will see *2* cities. QED​
>
>
> ​>>​
>>  and there are two of them. Mr I has gone through this many times and
>> knows that half the time he ends up in Washington with $2 and half the time
>> in Moscow with no money, hence next time he enters the duplicator he
>> believes he has s 1/2 chance of doubling his money or losing it. You tell
>> him he is not even wrong,
>
>
> ​I would never tell him that after he went through the duplicator, but I
> would tell him that before.​
>
>
>> ​>> ​
>>> ​A game involves skill and gambling involves probability and this
>>> pointless procedure involves neither. ​
>>>
>>>
>>
>> ​> ​
>> Games can be games of chance rather than skill.
>>
>
> ​But chance is not involved, everything is 100% predicable and it's not
> even difficult.
>

It's 100% predictable for an external observer, but not for the person
going through duplication, who feels that he has survived as one or other
of the duplicated. You, John Clark, would say the same thing if you went
through duplication: "I thought before the duplication that I would turn
into a soup of gibberish and nonsense, but surprisingly, here I am in
Washington, and there is another copy of me in Moscow".

> --
Stathis Papaioannou

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Re: A profound lack of profundity

[John Clark]

On Mon, Aug 21, 2017  Stathis Papaioannou  wrote:

​> ​
>>> While the outcome is certain for you, it is not certain for me.
>>>
>>
>> ​That's because the meaning of the personal pronoun "me" will always be
>> uncertain in ​a world that contains "me" duplicating machines.
>>
>>
>
> And this uncertainty constitutes the irreducible indeterminacy.
>

​It signifies nothing more profound than poor writing​ and silly pronoun
usage.

​> ​
> After the duplication there will be two copies, one with $2 and the other
> with nothing. Neither of them has the same amount of money as before.
>

​OK. So what?​


​>>​
>> ​As so often happens in this ​thread nobody can say if the above is true
>> or not because nobody knows who Mr. I is.
>>
>>
>
> ​> ​
> Mr I is the person who remembers going into the duplicator,
>

​Then Mr.I will see *2* cities. QED​


​>>​
>  and there are two of them. Mr I has gone through this many times and
> knows that half the time he ends up in Washington with $2 and half the time
> in Moscow with no money, hence next time he enters the duplicator he
> believes he has s 1/2 chance of doubling his money or losing it. You tell
> him he is not even wrong,


​I would never tell him that after he went through the duplicator, but I
would tell him that before.​


> ​>> ​
>> ​A game involves skill and gambling involves probability and this
>> pointless procedure involves neither. ​
>>
>>
>
> ​> ​
> Games can be games of chance rather than skill.
>

​But chance is not involved, everything is 100% predicable and it's not
even difficult.

 John K Clark  ​

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Re: A profound lack of profundity

[Stathis Papaioannou]

On Tue, 22 Aug 2017 at 8:12 am, John Clark  wrote:

> On Mon, Aug 21, 2017 at , Stathis Papaioannou  wrote:
>
>
>> ​>
 ​>>​
 ​
  Why does this make the question not a question?
>>>
>>>
>>> ​>>​
>>> ​Because the string of words with a question mark at the end was "What
>>> is the name of the one and only one city I will see after I become two?". ​
>>>
>>
>> ​> ​
>> And the answer is, "Either Washington or Moscow, but not both".
>>
>
> ​I didn't know ​ "Either Washington or Moscow, but not both" was the name
> of a city, seems like quite a mouthful. Where is this one and only one
> oddly named city? Is "Either Washington or Moscow, but not both" in the
> USA or in Russia?
>

Which one and only one outcome will I see when I toss the coin?
Either heads or tails but not both.

> --
Stathis Papaioannou

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Re: A profound lack of profundity

[John Clark]

On Mon, Aug 21, 2017 at , Stathis Papaioannou  wrote:


> ​>
>>> ​>>​
>>> ​
>>>  Why does this make the question not a question?
>>
>>
>> ​>>​
>> ​Because the string of words with a question mark at the end was "What is
>> the name of the one and only one city I will see after I become two?". ​
>>
>
> ​> ​
> And the answer is, "Either Washington or Moscow, but not both".
>

​I didn't know ​ "Either Washington or Moscow, but not both" was the name
of a city, seems like quite a mouthful. Where is this one and only one
oddly named city? Is "Either Washington or Moscow, but not both" in the USA
or in Russia?

 John K Clark

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Re: Is math real?

[Brent Meeker]

On 8/21/2017 5:43 AM, Philip Benjamin wrote:


[*Philip Benjamin*]

There is a difference between mathematical proposition and 
mathematical operation. For example, quantum theory is a mathematical 
proposition




It includes more than mathematical propositions.  It includes 
interpretations of the mathematics that relates it to operations and 
observations in the physical world.


, but Quantum interpretation such as "Collapse", "Many Worlds" etc. is 
philosophy/religion deserving no mathematical operation.




What does it mean to "deserve a mathematical operation"?  Is it like 
having your matrix removed?


Brent

Genetics can be subjected to mathematical operation, but Common 
Descent is a philosophical speculation beyond mathematics. So is the 
/evidential Natural Selection. /It can be subjected to mathematical 
analysis, but the /un-evidential trans-speciation /is philosophy 
beyond mathematics.


*Philip Benjamin*




*From:* everything-list@googlegroups.com 
 on behalf of Bruno Marchal 


*Sent:* Sunday, August 20, 2017 4:50 PM
*To:* everything-list@googlegroups.com
*Subject:* Re: Is math real?

On 20 Aug 2017, at 17:31, Philip Benjamin wrote:


[*Philip Benjamin*]
This is the wrong question, "not even wrong"!! The right question is 
"are the THINGS/SUBJECTS which mathematics deal with real?



OK, we agree I think, but fundamentally, it is not even that, at least 
when we apply mathematics (in the natural science, or in metaphysics; 
theology, ...).


It is "do you agree with this or that mathematical proposition". 
(followed by "agreement" on definitions).


Now some mathematical proposition does not ask much, like most theorem 
in first order arithmetic (when the proof are not too long).


Some propositions ask us more, like when using set theory, or set 
theory + the choice axiom.


Some proposition asks for so much that we will never stop searching a 
proof, like Riemann hypothesis, which we know refutable in very 
elementary arithmetic in case it would be false.


But the question "is math real" is often answered in the negative by 
the conventionalist (like Goethe, Perhaps Bergson, and the early 
positivist in math).  In my opinion, this is not defensible, from a 
mathematical logical viewpoint, even before Gödel's theorem, and still 
much more non-defensible after.


See my other post to David for some precision. The mathematical real 
is very vast, and it is normal some part are more doubtful than other 
parts. Some part are real, but only phenomenologically so, like with 
physics when we assume computationalism, as I explained often here.



Bruno






Best regards
*Philip Benjamin*


*From:*everything-list@googlegroups.com 
> on behalf of David Nyman 
mailto:david.ny...@gmail.com>>

*Sent:*Sunday, August 20, 2017 3:24 PM
*To:*everything-list
*Subject:*Re: Is math real?


On 20 Aug 2017 2:46 p.m., "Bruno Marchal" > wrote:



On 19 Aug 2017, at 01:21, David Nyman wrote:


On 18 August 2017 at 18:13, Bruno Marchalmailto:marc...@ulb.ac.be>>wrote:


On 18 Aug 2017, at 15:39, David Nyman wrote:


He points at a mug and says that 'representations' (meaning
numbers) aren't to be confused with things themselves.



He confuses a number and a possible representation of a number.



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



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Re: Is math real?

[Brent Meeker]

On 8/21/2017 4:28 AM, Bruno Marchal wrote:


On 21 Aug 2017, at 01:21, Brent Meeker wrote:




On 8/20/2017 4:02 PM, David Nyman wrote:



On 20 Aug 2017 23:16, "Brent Meeker" > wrote:




On 8/20/2017 9:23 AM, Bruno Marchal wrote:


On 20 Aug 2017, at 17:24, David Nyman wrote:




On 20 Aug 2017 2:46 p.m., "Bruno Marchal" mailto:marc...@ulb.ac.be>> wrote:


On 19 Aug 2017, at 01:21, David Nyman wrote:


On 18 August 2017 at 18:13, Bruno Marchal
mailto:marc...@ulb.ac.be>> wrote:


On 18 Aug 2017, at 15:39, David Nyman wrote:


He points at a mug and says that 'representations'
(meaning numbers) aren't to be confused with things
themselves.



He confuses a number and a possible representation of
a number.

LIke many people confuse the (usual, standard)
arithmetical reality with a theory of the
arithmetical reality. Yet after Gödel we know that no
theories at all can represent or encompass the whole
of the arithmetical reality.

It is not much different that confusing a telescope
and a star, or a microscope and a bacteria, or a
finger and a moon, or a number and a numeral
("chiffre" in french).
But in math, it is quite frequent. In logic, such
distinction are very important. In Gödel's proof, we
need to distinguish a mathematical being, like the
number s(0), the representation of the number s(0),
which is the sequence of the symbol "s", "(", "0",
")" (and that is not a number, but a word), and the
representation of the representation of a number,
which, when we represent things in arithmetic will be
something like
2^3 * 3^4 * 5^5 *7^6, which will be some
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s( (0)...). (very long!).



But what is the 'thing itself' at which he points?


A mug. I guess.


​Just so.


The question will be "what is a mug in itself". A
materialist would say that it is a structured collection
of atoms, but a mechanist has to say something like "a
common pattern pointed at by some normal (in Gauss sense)
machine sharing some long (deep) histories. Something like
that.


Yeah, something like that. I enjoyed Frenkel's talk actually.
I like his enthusiasm for mathematics. It's funny though he
doesn't seem to appreciate his implicit assumptions, or indeed
that he is in fact expressing a particular metaphysical
position. Is math real? I mean, really real? Trouble is,
people assume that the answer is obvious, whether they think
it's yes or no.


We need only to agree on what we agree. The beauty of the
Church's thesis, is that it entails by "theoremata" the
existence of the emulation of all computations in elementary
arithmetic.

(Just that fact, and computationalism, should make us doubt
that we can take a primary physical reality for granted: it is
the dream argument with a vengeance).

The question is not "is math real", but do you believe that
2+0= 2, and a bit of logic.

I do not claim that the whole of philosophy or theology can
become science, but I do claim that if we assume mechanism,
then by Church's thesis, philosophy and theology becomes a
science, even in the usual empiricist sense.

There is something funny here. The theology of the machine is
ultra-non-empiricist, as the mystical machine claims that the
whole truth (including physics) is "in your head and nowhere
else". ("you" = any universal machine). But that is what makes
the machine theology testable, by comparing the physics in the
head of any (sound) universal machine with what we actually
observed.


Are you claiming that there is a one-to-one map between true
statements in mathematics and what I experience??


Well, only if you happen to be God, perhaps.

The problem with everythingism is that one doesn't experience
everything.


How would you know?


By direct inexperience...and I'm not God either.



How could we know by_inexperience_?


Do you know you are not experiencing being in Washington now?...that's how.

I think you can *only* believe in something by some experience (of 
inexperience) leading you to postulate something different from 
yourself, but that is not something you can experience. It can only be 
a belief.


That is why "primary matter" is an hypothesis in metaphysics, not in 
physics.


So is "primary arithmetic".

Brent

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Re: Is math real?

[Brent Meeker]

On 8/21/2017 4:19 AM, Bruno Marchal wrote:
Before Gödel, most mathematician, like Hilbert, were hoping that 
with the finite and the symbolic we could justify the consistency of 
the use of the infinities, but after Gödel we know that even with 
the infinities we cannot circumscribe and justify the consistency of 
the finite and the symbolic.


All the more reason to classify them as fiction - not part of the 
really real.


OK. But then Mechanism has to be assumed false, or you too would not 
exist (and I hope you believe that you exist, in a way or another).




Consistency is a attribute of propositions and logic.  Whether there are 
infinities that cannot be circumscribed has no relevance to my existence 
or whether consciousness can be realized by a computer.


Brent

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Re: Is math real?

[Brent Meeker]

On 8/21/2017 4:19 AM, Bruno Marchal wrote:

The problem with everythingism is that one doesn't experience everything.


Indeed. But that is a very general problem, and you could say "the 
problem with physicalism is that we don't experience primary matter, 
nor the whole physical reality.


But that's not a problem for physicalism.  It doesn't predict that we 
experience primary matter or the whole of physical reality.  It models 
us as localized and limited and reality as a process, not a totality.


Brent

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Re: A profound lack of profundity

[Bruno Marchal]

On 21 Aug 2017, at 18:59, Telmo Menezes wrote:


Bruno, sorry for the delay as usual -- I really appreciate your
replies but life gets in the way...


I understand. No problem.




On Sun, Aug 13, 2017 at 7:25 PM, Bruno Marchal   
wrote:


On 13 Aug 2017, at 01:46, Telmo Menezes wrote:


On Sat 12. Aug 2017 at 03:12, Bruce Kellett >

wrote:


On 12/08/2017 3:22 am, Bruno Marchal wrote:

On 11 Aug 2017, at 13:40, Bruce Kellett wrote:


Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you*  
expect when

pushing the button in Helsinki?


I expect to die, to be 'cut', according to the protocol. The  
guys in
W and M are two new persons, and neither was around in H to make  
any

prediction whatsoever.


Fair enough.

You think the digital mechanism thesis is wrong.


Correct.

There is a fundamental problem with your person-duplication thought
experiments. This is that the way in which you interpret the  
scenario

inherently involves an irreducible 1p-3p confusion. The first person
(1p) concerns only things that the person can experience directly  
for
himself. It cannot, therefore, involve things that he is told by  
other
people, because such things are necessarily third person (3p)  
knowledge



Things that are told by othet people reach us as 1p experiences. We  
accept
them (or not) based on our own internal models of reality. Some  
people trust
evangelical preachers, others trust what is published in Nature. It  
is only
by personal cognitive processes that we can make such choices.  
There is no

such thing as pure 3p knowledge, that is nonsensical.


There is no 3p knowledge as such. But there is still a 3p  
Theaetetical

possible knowledge, in a theoretical frame.

For example, just imagine that 2 + 2 = 4 is really really really  
really true

(imagine!), then I would say that if a machine is such that

(B_(that machine) "2 + 2 = 4") is true about that machine, then,  
assuming
Mechanism, (or not, I am not sure) we can say that the machine has  
a correct
3p knowledge, even 0p knowledge if the machine itself bet on  
Mechanism.


Isn't this the same as assuming an independent reality, that remains
consistent even when nobody is looking?


Yes. (But this can mean the same thing at different level). You need  
to believe in a minimal number of things and relation between things  
to have the notion of universal machine or number to make sense of the  
mechanist hypothesis.





I'm not disagreeing -- nor an I saying that such a reality does not
exist. Just that it's an untestable assumption (albeit a very common
and useful one).


Yes, and with mechanism we can limit the assumption to the sigma_1  
truth.


The universal machine(s) already say "tat tvam asi" to  the universal  
machine(s) :)


Note that the sigma_1 truth is NOT Löbian, but we can consider it as  
the "knower of the sigma_1 true proposition", or just let open if it  
is a thing (which it certainly is) or a person.




Assuming mechanism, ISTM that one would then assume that we are
"inside" the machine for which 2 + 2 = 4, which is what we do


The point is that 2 + 2 = 4 (and its friends) emulate all machines for  
which 2+2=4.






but then
Gödel has something to say.. Right?



Gödel missed Church's thesis, and was reluctant to both mechanism and  
materialism. But he is the first to realized that a very large class  
of computable functions, can be represented in arithmetic, and that  
through its arithmetization of meta-arithmetic he got an isomorphism  
between arithmetical relation and metamathematics.


Let me quote the footnote 9 of his 1931 paper:

"In other words, the above-described procedure provides an isomorphic  
image of the syestem PM in the domain of arithmetic, and all  
metamathematical arguments can equally be conducted in this isomorphic  
image".


But, he will miss explicitly the law of Post, alias Church's or  
Turing's thesis. I think that in his 1934 paper he explains that  
identifying computability with recursiveness, or formal system with RE  
set, would be premature and would need a more careful analysis. A bit  
like Post who see the thesis as a "natural law" of human psychology.  
After reading Turing's paper, Gödel is convinced by Church thesis, and  
consider rightly that the closure of the set of programmable functions  
for the diagonalization procedure is a kind of miracle. It is, indeed.


Only Post, who anticipated everything in the early 1920, including the  
Lucas-Penrose proof that we are not machine, and its correction, and  
even get a glimpse of immaterialism (but still added in a later  
footnote that this was a grave mistake, also changing his mind after  
reading Turing, and so missing that the immaterialism he saw was a  
consequence of mechanism).



Turing was a metaphysical naturalist. Gödel was skeptical on  
naturalism, materialism and mechanism.









So, we don't have third person (3p) knowledge, OK, it would be non  
sensical.

In fact knowledge is pure 1p.

But, in 

Re: A profound lack of profundity

[Telmo Menezes]

Bruno, sorry for the delay as usual -- I really appreciate your
replies but life gets in the way...

On Sun, Aug 13, 2017 at 7:25 PM, Bruno Marchal  wrote:
>
> On 13 Aug 2017, at 01:46, Telmo Menezes wrote:
>
>
> On Sat 12. Aug 2017 at 03:12, Bruce Kellett 
> wrote:
>>
>> On 12/08/2017 3:22 am, Bruno Marchal wrote:
>> > On 11 Aug 2017, at 13:40, Bruce Kellett wrote:
>> >>
>> >>> Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you* expect when
>> >>> pushing the button in Helsinki?
>> >>
>> >> I expect to die, to be 'cut', according to the protocol. The guys in
>> >> W and M are two new persons, and neither was around in H to make any
>> >> prediction whatsoever.
>> >
>> > Fair enough.
>> >
>> > You think the digital mechanism thesis is wrong.
>>
>> Correct.
>>
>> There is a fundamental problem with your person-duplication thought
>> experiments. This is that the way in which you interpret the scenario
>> inherently involves an irreducible 1p-3p confusion. The first person
>> (1p) concerns only things that the person can experience directly for
>> himself. It cannot, therefore, involve things that he is told by other
>> people, because such things are necessarily third person (3p) knowledge
>
>
> Things that are told by othet people reach us as 1p experiences. We accept
> them (or not) based on our own internal models of reality. Some people trust
> evangelical preachers, others trust what is published in Nature. It is only
> by personal cognitive processes that we can make such choices. There is no
> such thing as pure 3p knowledge, that is nonsensical.
>
>
> There is no 3p knowledge as such. But there is still a 3p Theaetetical
> possible knowledge, in a theoretical frame.
>
> For example, just imagine that 2 + 2 = 4 is really really really really true
> (imagine!), then I would say that if a machine is such that
>
> (B_(that machine) "2 + 2 = 4") is true about that machine, then, assuming
> Mechanism, (or not, I am not sure) we can say that the machine has a correct
> 3p knowledge, even 0p knowledge if the machine itself bet on Mechanism.

Isn't this the same as assuming an independent reality, that remains
consistent even when nobody is looking?
I'm not disagreeing -- nor an I saying that such a reality does not
exist. Just that it's an untestable assumption (albeit a very common
and useful one).

Assuming mechanism, ISTM that one would then assume that we are
"inside" the machine for which 2 + 2 = 4, which is what we do but then
Gödel has something to say.. Right?

> So, we don't have third person (3p) knowledge, OK, it would be non sensical.
> In fact knowledge is pure 1p.
>
> But, in the frame of some axiom in metaphysics, like Mechanism, I think that
> a part of mathematics becomes a 3p knowledge (arithmetic!). You can someone
> observe the arithmetical truth from outside, and "see" all the "diaries" of
> all machines, and their astonishment when "opening" the doors, or just
> through birth, when they find themselves in this or that galaxy or city ...

Assuming we're not crazy, ok.

> I think that for a believer in mechanism, who would based his belief from
> studying computer science (and not just obeying his doctor!), arithmetic and
> the core of computer science is 3p knowledge, and even 0p knowledge: Nagel's
> point of view of nowhere.

Ok, but I'm not sure what you mean by the distinction between 3p and
0p, or what you mean by 0p exactly. Is it something you can map to
"your" hypostases?

> That 3p knowledge, is of course still only an 1p belief, from the 1p view. I
> agree with you from the 1p view! I just make precise that in a theoretical
> frame, God can see that sometimes,  some-relative-states I should say, some
> of our belief are true. I do think that this is the case for 2 is a divisor
> of 24.

Ok, I think we agree. I have no qualm here.
My point remains: the argument that Bruce makes against your theory
can be made against any theory, or the scientific endeavor itself.

For me, John Clark is more mysterious. I don't bother with the
circular discussion anymore (we've been through the loop too many
times). I think he's just playing games with language, but I'm not
sure why. Maybe a protection mechanism. Some conclusions are indeed
scary,

All the best to you and everyone else here,
Telmo.

>
>
>>
>> -- knowledge which he does not have by direct personal experience. So
>> our subject does not know the protocol of the thought experiment from
>> direct experience (he has only been told about it, 3p). When he presses
>> the button in the machine, he can have no 1p expectations about what
>> will happen (because he has not yet experienced it). He presses the
>> button in the spirit of pure experimental enquiry -- "what will happen
>> if I do this?" His prior probability for any particular outcome is zero.
>> So when he presses the button in Helsinki, and opens the door to find
>> himself in Moscow, he will say, "WTF!". In particular, he will not have
>> gained any 1p knowledge of duplic

Re: Is math real?

[Bruno Marchal]

On 21 Aug 2017, at 14:43, Philip Benjamin wrote:


[Philip Benjamin]
There is a difference between mathematical proposition and  
mathematical operation.


OK. "2+2  =  2 * 2" is a mathematical proposition. "+" and "*" denotes  
operations.





For example, quantum theory is a mathematical proposition,


Hmm... OK. It is a theory. It is a list of assumptions, or their  
conjunction, about a reality, itself assumed (at the metalevel in  
physics, and at the base level in some physicalist metaphysics).






but Quantum interpretation such as "Collapse", "Many Worlds" etc.


The collapse is one more assumption.

 "many-worlds" is when we don't do that collapse assumption.

In fact "many-world", with the logician's weak sense of "world" is a  
mathematical consequence of QM without collapse, and assuming a  
collapse makes the SWE false, or not applicable to the observer in QM 
+collapse theory (a good reason to be suspicious about the collapse).







is philosophy/religion deserving no mathematical operation.


?  (this does not make sense to me).




Genetics can be subjected to mathematical operation,


?   (I guess we are not using "operation" in the same sense. What do  
you mean by "operation"? You mean perhaps "analysis". Then OK here,  
but I do not see why philosophy/religion would not be subjected to  
mathematical analysis. That is possible in some theory, but not in  
another theory---and indeed, I illustrate that once we assume the  
mechanist hypothesis in the cognitive sciences, then we do have the  
mean to use mathematics in metaphysics/religion.





but Common Descent is a philosophical speculation beyond mathematics.


I prefer to not separate philosophy from science. That separation is  
too much often used to allow absence of rigor in philosophy, and that  
is a very bad habit. Same for theology, metaphysics. I limit myself to  
hypothesis making a mathematical treatment operational, leading to  
testable conclusions.


I don't really believe in something called "science", but I do believe  
in scientific attitude, and this is independent of the domain of  
investigation.




So is the evidential Natural Selection. It can be subjected to  
mathematical analysis, but the un-evidential trans-speciation is  
philosophy beyond mathematics.


It will depend on your fundamental theory/assumption, I would say.

Bruno Marchal






Philip Benjamin


From: everything-list@googlegroups.com > on behalf of Bruno Marchal 

Sent: Sunday, August 20, 2017 4:50 PM
To: everything-list@googlegroups.com
Subject: Re: Is math real?


On 20 Aug 2017, at 17:31, Philip Benjamin wrote:


[Philip Benjamin]
This is the wrong question, "not even wrong"!! The right question  
is "are the THINGS/SUBJECTS which mathematics deal with real?



OK, we agree I think, but fundamentally, it is not even that, at  
least when we apply mathematics (in the natural science, or in  
metaphysics; theology, ...).


It is "do you agree with this or that mathematical proposition".  
(followed by "agreement" on definitions).


Now some mathematical proposition does not ask much, like most  
theorem in first order arithmetic (when the proof are not too long).


Some propositions ask us more, like when using set theory, or set  
theory + the choice axiom.


Some proposition asks for so much that we will never stop searching  
a proof, like Riemann hypothesis, which we know refutable in very  
elementary arithmetic in case it would be false.


But the question "is math real" is often answered in the negative by  
the conventionalist (like Goethe, Perhaps Bergson, and the early  
positivist in math).  In my opinion, this is not defensible, from a  
mathematical logical viewpoint, even before Gödel's theorem, and  
still much more non-defensible after.


See my other post to David for some precision. The mathematical real  
is very vast, and it is normal some part are more doubtful than  
other parts. Some part are real, but only phenomenologically so,  
like with physics when we assume computationalism, as I explained  
often here.



Bruno






Best regards
Philip Benjamin

From: everything-list@googlegroups.com > on behalf of David Nyman 

Sent: Sunday, August 20, 2017 3:24 PM
To: everything-list
Subject: Re: Is math real?



On 20 Aug 2017 2:46 p.m., "Bruno Marchal"  wrote:

On 19 Aug 2017, at 01:21, David Nyman wrote:


On 18 August 2017 at 18:13, Bruno Marchal  wrote:

On 18 Aug 2017, at 15:39, David Nyman wrote:

He points at a mug and says that 'representations' (meaning  
numbers) aren't to be confused with things themselves.



He confuses a number and a possible representation of a number.




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Re: Is math real?

[Philip Benjamin]

[Philip Benjamin]

There is a difference between mathematical proposition and mathematical 
operation. For example, quantum theory is a mathematical proposition, but 
Quantum interpretation such as "Collapse", "Many Worlds" etc. is 
philosophy/religion deserving no mathematical operation. Genetics can be 
subjected to mathematical operation, but Common Descent is a philosophical 
speculation beyond mathematics. So is the evidential Natural Selection. It can 
be subjected to mathematical analysis, but the un-evidential trans-speciation 
is philosophy beyond mathematics.

Philip Benjamin



From: everything-list@googlegroups.com  on 
behalf of Bruno Marchal 
Sent: Sunday, August 20, 2017 4:50 PM
To: everything-list@googlegroups.com
Subject: Re: Is math real?


On 20 Aug 2017, at 17:31, Philip Benjamin wrote:

[Philip Benjamin]
This is the wrong question, "not even wrong"!! The right question is "are the 
THINGS/SUBJECTS which mathematics deal with real?


OK, we agree I think, but fundamentally, it is not even that, at least when we 
apply mathematics (in the natural science, or in metaphysics; theology, ...).

It is "do you agree with this or that mathematical proposition". (followed by 
"agreement" on definitions).

Now some mathematical proposition does not ask much, like most theorem in first 
order arithmetic (when the proof are not too long).

Some propositions ask us more, like when using set theory, or set theory + the 
choice axiom.

Some proposition asks for so much that we will never stop searching a proof, 
like Riemann hypothesis, which we know refutable in very elementary arithmetic 
in case it would be false.

But the question "is math real" is often answered in the negative by the 
conventionalist (like Goethe, Perhaps Bergson, and the early positivist in 
math).  In my opinion, this is not defensible, from a mathematical logical 
viewpoint, even before Gödel's theorem, and still much more non-defensible 
after.

See my other post to David for some precision. The mathematical real is very 
vast, and it is normal some part are more doubtful than other parts. Some part 
are real, but only phenomenologically so, like with physics when we assume 
computationalism, as I explained often here.


Bruno





Best regards
Philip Benjamin


From: everything-list@googlegroups.com 
mailto:everything-list@googlegroups.com>> on 
behalf of David Nyman mailto:david.ny...@gmail.com>>
Sent: Sunday, August 20, 2017 3:24 PM
To: everything-list
Subject: Re: Is math real?



On 20 Aug 2017 2:46 p.m., "Bruno Marchal" 
mailto:marc...@ulb.ac.be>> wrote:

On 19 Aug 2017, at 01:21, David Nyman wrote:

On 18 August 2017 at 18:13, Bruno Marchal 
mailto:marc...@ulb.ac.be>> wrote:

On 18 Aug 2017, at 15:39, David Nyman wrote:

He points at a mug and says that 'representations' (meaning numbers) aren't to 
be confused with things themselves.


He confuses a number and a possible representation of a number.



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Re: A profound lack of profundity

[Bruno Marchal]

On 21 Aug 2017, at 01:49, John Clark wrote:

On Sun, Aug 20, 2017 at 10:02 AM, Bruno Marchal   
wrote:


​>> ​1-you​ = Homemade Baby Talk.​

​> ​1-you refer to your subjective, first person, experience.

​And ​your subjective first person, experience​ refers to  
the1-you.


Exact.





And round and round we go.​


Only if you put the personal diaries based definition of 1p in your  
subconscious.






​>> ​But I know you love homemade acronyms too so perhaps you  
prefer HBT.


​> ​Ad hominem.

​But it's true, it is a undeniable fact that you do love homemade  
acronyms and jargon. Sorry if you consider this predisposition of  
yours to be rather embarrassing


No. It is false. I use simple abbreviation in threads repeating long  
term. Anyway, this is ad hominem and distract from the issue.







​>​>>​ ​Washington or Moscow, each with a probability of 1/2.



​>> ​That's the same thing you said BEFORE the duplication,

​>​Indeed. I do the prediction lways before the experience. if  
not, it is not a prediction.


​After a coin flip I know a lot more and can say much more  
precisely ​about ​what the coin ended up doing than I could say  
before;


Like after pushing on the button, from all the 1p experiences  
accessible in our context.





​back​​ then all I could could say is it will land heads with  
50% probability, but now after the flip I can say the coin landed  
the way it landed with 100% certainty. That's a big improvement and  
I just want you to do the same thing.


You say before the experiment the best you ​could ​say is   
"Washington or Moscow, each with a probability of 1/2" but now the  
experiment is over and with the benefit of all the new​ ​found  
knowledge you've gained from it I just want to know your new  
improved answer to the question  "What is the name of the one and  
only one city I will end up seeing after I became two?".


Very easy. I open the door, notice the city of Moscow, and write the  
result in my diary. I know for sure I see that city, and only believe  
intellectually that I might have a doppelganger in Washington. Bth of  
us get the answer, and both of us could not predict it in Helsinki,  
for the obvious reason that a specific prediction is necessarily  
refuted by one copy. Morality, I bet "W v M", and it is the best  
prediction available.


You continue to abstract ourself from the question asked, which is  
about the 1p experience that anyone can live when duplicating oneself.





If your answer after the experiment isn't better than the one made  
before then it wasn't a question​ and it makes no sense to ​ 
even ​talk about probability​ AFTER the event.


​>> ​now that the duplication Is long over is that STILL the best  
you can say even now?


​> ​No, after the duplication, there is no more prediction. Only  
verification if my bet was correct or not. You can look at the  
detailed answer in previous post,


​I don't want a goddamn detailed answer,


Aaah! OK, but don't complain on the gibberish brought by you avoiding  
the "details".




the question "What is the name of the one and only one city I will  
end up seeing after I became two?" ​ ​requires only a one word  
answer!


Only if we were trying to prove that self-duplication leads to 3p- 
indeterminacy. But nobody has ever defended such a crap.






And if nobody can ever know what the one word answer is ever AFTER  
the experiment is over then it wasn't a question.


But somebody can. Indeed, two-body! Just listen to all copies, and of  
course, there are multiple, given the protocol. You are eliminating  
the opinion of all copies. You talk like if they have both become  
zombie. That means, you assume computationalism false, simply, but  
that end the reduction ad absurdum.




A string of words can be well formed and correctly follow all the  
rules of English grammar and yet have no meaning, and sticking a  
question mark on at the end doesn't help.  ​


​>> ​Regarding a coin, if the best we could say is "after the  
coin fell and everybody observed how it landed it turned ​out ​it  
fell heads or tails with a probability of 1/2"​ ​ then the very  
concept of probability would be utterly meaningless.


​> ​That is my point.

​If that was your point you made it well. You said that even AFTER  
the experiment is over and even with the benefit hindsight you say  
the best you could have told the Helsinki man ​about what he ended  
up seeing ​is  "Washington or Moscow, each with a probability of  
1/2"​, and that is utterly meaningless. ​


Then throwing a coin is deterministic too, as I would say the same, in  
that same retrospective way.





​>> ​But we can do better than that, much better, we can say "it  
turned out that after the coin was flipped in landed heads with 100%  
certainty" with no need to add and any ifs ands or buts​ ​ 
whatsoever. That's because "how will the coin land after it is  
flipped?" is a real question with a real answer, but "what one city  
and o

Re: Is math real?

[Bruno Marchal]

On 21 Aug 2017, at 01:21, Brent Meeker wrote:




On 8/20/2017 4:02 PM, David Nyman wrote:



On 20 Aug 2017 23:16, "Brent Meeker"  wrote:


On 8/20/2017 9:23 AM, Bruno Marchal wrote:


On 20 Aug 2017, at 17:24, David Nyman wrote:




On 20 Aug 2017 2:46 p.m., "Bruno Marchal"   
wrote:


On 19 Aug 2017, at 01:21, David Nyman wrote:

On 18 August 2017 at 18:13, Bruno Marchal   
wrote:


On 18 Aug 2017, at 15:39, David Nyman wrote:

He points at a mug and says that 'representations' (meaning  
numbers) aren't to be confused with things themselves.



He confuses a number and a possible representation of a number.

LIke many people confuse the (usual, standard) arithmetical  
reality with a theory of the arithmetical reality. Yet after  
Gödel we know that no theories at all can represent or encompass  
the whole of the arithmetical reality.


It is not much different that confusing a telescope and a star,  
or a microscope and a bacteria, or a finger and a moon, or a  
number and a numeral ("chiffre" in french).
But in math, it is quite frequent. In logic, such distinction  
are very important. In Gödel's proof, we need to distinguish a  
mathematical being, like the number s(0), the representation of  
the number s(0), which is the sequence of the symbol "s", "(",  
"0", ")" (and that is not a number, but a word), and the  
representation of the representation of a number, which, when we  
represent things in arithmetic will be something like
2^3 * 3^4 * 5^5 *7^6, which will be some  
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s( (0)...). (very long!).




But what is the 'thing itself' at which he points?


A mug. I guess.

​Just so.


The question will be "what is a mug in itself". A materialist  
would say that it is a structured collection of atoms, but a  
mechanist has to say something like "a common pattern pointed at  
by some normal (in Gauss sense) machine sharing some long (deep)  
histories. Something like that.


Yeah, something like that. I enjoyed Frenkel's talk actually. I  
like his enthusiasm for mathematics. It's funny though he doesn't  
seem to appreciate his implicit assumptions, or indeed that he is  
in fact expressing a particular metaphysical position. Is math  
real? I mean, really real? Trouble is, people assume that the  
answer is obvious, whether they think it's yes or no.


We need only to agree on what we agree. The beauty of the Church's  
thesis, is that it entails by "theoremata" the existence of the  
emulation of all computations in elementary arithmetic.


(Just that fact, and computationalism, should make us doubt that  
we can take a primary physical reality for granted: it is the  
dream argument with a vengeance).


The question is not "is math real", but do you believe that 2+0=  
2, and a bit of logic.


I do not claim that the whole of philosophy or theology can become  
science, but I do claim that if we assume mechanism, then by  
Church's thesis, philosophy and theology becomes a science, even  
in the usual empiricist sense.


There is something funny here. The theology of the machine is  
ultra-non-empiricist, as the mystical machine claims that the  
whole truth (including physics) is "in your head and nowhere  
else". ("you" = any universal machine). But that is what makes the  
machine theology testable, by comparing the physics in the head of  
any (sound) universal machine with what we actually observed.


Are you claiming that there is a one-to-one map between true  
statements in mathematics and what I experience??


Well, only if you happen to be God, perhaps.

The problem with everythingism is that one doesn't experience  
everything.


How would you know?


By direct inexperience...and I'm not God either.



How could we know by inexperience? I think you can *only* believe in  
something by some experience (of inexperience) leading you to  
postulate something different from yourself, but that is not something  
you can experience. It can only be a belief.


That is why "primary matter" is an hypothesis in metaphysics, not in  
physics.


Bruno





Brent

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Re: Is math real?

[Bruno Marchal]

On 21 Aug 2017, at 01:02, David Nyman wrote:




On 20 Aug 2017 23:16, "Brent Meeker"  wrote:


On 8/20/2017 9:23 AM, Bruno Marchal wrote:


On 20 Aug 2017, at 17:24, David Nyman wrote:




On 20 Aug 2017 2:46 p.m., "Bruno Marchal"  wrote:

On 19 Aug 2017, at 01:21, David Nyman wrote:

On 18 August 2017 at 18:13, Bruno Marchal   
wrote:


On 18 Aug 2017, at 15:39, David Nyman wrote:

He points at a mug and says that 'representations' (meaning  
numbers) aren't to be confused with things themselves.



He confuses a number and a possible representation of a number.

LIke many people confuse the (usual, standard) arithmetical  
reality with a theory of the arithmetical reality. Yet after  
Gödel we know that no theories at all can represent or encompass  
the whole of the arithmetical reality.


It is not much different that confusing a telescope and a star,  
or a microscope and a bacteria, or a finger and a moon, or a  
number and a numeral ("chiffre" in french).
But in math, it is quite frequent. In logic, such distinction are  
very important. In Gödel's proof, we need to distinguish a  
mathematical being, like the number s(0), the representation of  
the number s(0), which is the sequence of the symbol "s", "(",  
"0", ")" (and that is not a number, but a word), and the  
representation of the representation of a  
number,  which, when we  
represent things in arithmetic will be something like
2^3 * 3^4 * 5^5 *7^6, which will be some  
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s( (0)...). (very long!).




But what is the 'thing itself' at which he points?


A mug. I guess.

​Just so.


The question will be "what is a mug in itself". A materialist  
would say that it is a structured collection of atoms, but a  
mechanist has to say something like "a common pattern pointed at  
by some normal (in Gauss sense) machine sharing some long (deep)  
histories. Something like that.


Yeah, something like that. I enjoyed Frenkel's talk actually. I  
like his enthusiasm for mathematics. It's funny though he doesn't  
seem to appreciate his implicit assumptions, or indeed that he is  
in fact expressing a particular metaphysical position. Is math  
real? I mean, really real? Trouble is, people assume that the  
answer is obvious, whether they think it's yes or no.


We need only to agree on what we agree. The beauty of the Church's  
thesis, is that it entails by "theoremata" the existence of the  
emulation of all computations in elementary arithmetic.


(Just that fact, and computationalism, should make us doubt that we  
can take a primary physical reality for granted: it is the dream  
argument with a vengeance).


The question is not "is math real", but do you believe that 2+0= 2,  
and a bit of logic.


I do not claim that the whole of philosophy or theology can become  
science, but I do claim that if we assume mechanism, then by  
Church's thesis, philosophy and theology becomes a science, even in  
the usual empiricist sense.


There is something funny here. The theology of the machine is ultra- 
non-empiricist, as the mystical machine claims that the whole truth  
(including physics) is "in your head and nowhere else". ("you" =  
any universal machine). But that is what makes the machine theology  
testable, by comparing the  physics in the head of any  
(sound) universal machine with what we actually observed.


Are you claiming that there is a one-to-one map between true  
statements in mathematics and what I experience??


Well, only if you happen to be God, perhaps.


Exactly!





The problem with everythingism is that one doesn't experience  
everything.


How would you know?


Good question. Of course, with computationalism, we might not been  
able to experience everything here and now, but it is not obvious for  
the infinite term.


Bruno





David




Math is real? Which math? I doubt that sincere people doubt  
arithmetic, and I have never heard of parents who would have taken  
their kids out of a school for the reason that hey have been taught  
that 2+2=4; neither in the Western nor Eastern worlds.


I doubt the infinity of standard arithmetic.




Now, for limit and real numbers it is much less obvious. here  
intutionist and classical philosophy diverge. With Mechanism, it is  
better to considered analysis (and eventually physics) as universal  
machine mind tools. Gödel's incompleteness justifies partially why  
the machine needs to invent infinities to better figure out  
themselves. Before Gödel, most mathematician, like Hilbert, were  
hoping that with the finite and the symbolic we could justify the  
consistency of the use of the infinities, but after Gödel we know  
that even with the infinities we cannot circumscribe and justify  
the consistency of the finite and the symbolic.


All the more reason to classify them as fiction - not part of the  
really real.


Brent


The root of the undecidability is the Turing-universality. With the  

Re: Is math real?

[Bruno Marchal]

On 21 Aug 2017, at 00:16, Brent Meeker wrote:




On 8/20/2017 9:23 AM, Bruno Marchal wrote:


On 20 Aug 2017, at 17:24, David Nyman wrote:




On 20 Aug 2017 2:46 p.m., "Bruno Marchal"  wrote:

On 19 Aug 2017, at 01:21, David Nyman wrote:

On 18 August 2017 at 18:13, Bruno Marchal   
wrote:


On 18 Aug 2017, at 15:39, David Nyman wrote:

He points at a mug and says that 'representations' (meaning  
numbers) aren't to be confused with things themselves.



He confuses a number and a possible representation of a number.

LIke many people confuse the (usual, standard) arithmetical  
reality with a theory of the arithmetical reality. Yet after  
Gödel we know that no theories at all can represent or encompass  
the whole of the arithmetical reality.


It is not much different that confusing a telescope and a star,  
or a microscope and a bacteria, or a finger and a moon, or a  
number and a numeral ("chiffre" in french).
But in math, it is quite frequent. In logic, such distinction are  
very important. In Gödel's proof, we need to distinguish a  
mathematical being, like the number s(0), the representation of  
the number s(0), which is the sequence of the symbol "s", "(",  
"0", ")" (and that is not a number,  
but  a word), and the  
representation of the representation of a number, which, when we  
represent  things in  
arithmetic will be something like
2^3 * 3^4 * 5^5 *7^6, which will be some  
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s( (0)...). (very long!).




But what is the 'thing itself' at which he points?


A mug. I guess.

​Just so.


The question will be "what is a mug in itself". A materialist  
would say that it is a structured collection of atoms, but a  
mechanist has to say something like "a common pattern pointed at  
by some normal (in Gauss sense) machine sharing some long (deep)  
histories. Something like that.


Yeah, something like that. I enjoyed Frenkel's talk actually. I  
like his enthusiasm for mathematics. It's funny though he doesn't  
seem to appreciate his implicit assumptions, or indeed that he is  
in fact expressing a particular metaphysical position. Is math  
real? I mean, really real? Trouble is, people assume that the  
answer is obvious, whether they think it's yes or no.


We need only to agree on what we agree. The beauty of the Church's  
thesis, is that it entails by "theoremata" the existence of the  
emulation of all computations in elementary arithmetic.


(Just that fact, and computationalism, should make us doubt that we  
can take a primary physical reality for granted: it is the dream  
argument with a vengeance).


The question is not "is math real", but do you believe that 2+0= 2,  
and a bit of logic.


I do not claim that the whole of philosophy or theology can become  
science, but I do claim that if we assume mechanism, then by  
Church's thesis, philosophy and theology becomes a science, even in  
the usual empiricist sense.


There is something funny here. The theology of the machine is ultra- 
non-empiricist, as the mystical machine claims that the whole truth  
(including physics) is "in your head and nowhere else". ("you" =  
any universal machine). But that is what makes the machine theology  
testable, by comparing the physics in the head of any (sound)  
universal machine with what we actually observed.


Are you claiming that there is a one-to-one map between true  
statements in mathematics and what I experience??


Not at all. I am saying that the laws of physics can be found by  
introspection. Introspection lead to the opposite of what you say: we  
can only experience (1p) a tiny fraction of the physical reality and  
of the psychological reality and all what is "in the head" in the 1p  
view is far bigger than the head itself (in this metaphorical image).  
Only the "outer God" might see, or be defined, by the "whole  
(arithmetical) truth".





The problem with everythingism is that one doesn't experience  
everything.


Indeed. But that is a very general problem, and you could say "the  
problem with physicalism is that we don't experience primary matter,  
nor the whole physical reality. After Gödel, we know that even for the  
arithmetical reality, even an immortal being can only scratch it  
infinitesimally. Reality is big.







Math is real? Which math? I doubt that sincere people doubt  
arithmetic, and I have never heard of parents who would have taken  
their kids out of a school for the reason that hey have been taught  
that 2+2=4; neither in the Western nor Eastern worlds.


I doubt the infinity of standard arithmetic.


Good. That is why I do not assume it. Only 0, 1, 2, ... all the  
objects assumed to exist are finite. Mechanism is a Finitism. Like  
Plotinus' God, Infinity does not belongs to the beings. It is  
responsible (only) of the existence of the (finite) being. This does  
not prevent us to use infinity at the meta-level, like all sc

Re: A profound lack of profundity

[Stathis Papaioannou]

On 21 August 2017 at 11:16, John Clark  wrote:

> On Sun, Aug 20, 2017  Stathis Papaioannou  wrote:
>
> ​> ​
>> There are two people after the event,
>
>
> ​Yes.
> ​
>
>
>> ​> ​
>> and each has his own answer about which one and only one city he sees,
>
>
> ​Yes.​
>
>
>> ​>​
>>  Why does this make the question not a question?
>
>
> ​Because the string of words with a question mark at the end was "What is
> the name of the one and only one city I will see after I become two?". ​
>

And the answer is, "Either Washington or Moscow, but not both". Many people
have tried it and they all agree: "I ended up in Washington about half the
time and Moscow about half the time, but never both". Naturally, they will
expect next time they go through that they will end up in one or other city
with 1/2 probability. You will tell them that they are talking gibberish,
but they will ignore you.

>


-- 
Stathis Papaioannou
-- 
Stathis Papaioannou

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