On 10 Mar 2014, at 16:16, Gabriel Bodeen wrote:

On Saturday, March 8, 2014 2:37:50 AM UTC-6, Bruno Marchal wrote:A couple other accounts of how things might be that I takeseriously are (1) physicalism in the sense that arithmeticalpropositions might only be true when physically realized,No problem, and indeed this would make comp false. of course, if youreally defend that thesis, you have to explain and prove theexistence of infinitely many prime numbers by using physics, andthis without presupposing addition and multiplication of integers. Iam not even sure how you will just defined what is prime number.Given a correspondence theory of truth and this kind of physicalism,mathematical theorems would be true if and only if there's acorresponding physical reality.

That is too much vague for me. I can interpret this in too much sense.

So, for example, if the universe is finite, then there wouldn't beinfinitely many prime numbers.

This is non sense. In my humble sincere feeling.

`Even if physicists get a knock down argument in favor of a finite`

`universe, that would not refute at all Euclid's theorem that there is`

`an infinity of prime.`

A prime number is just not a physical object.

Nor would there be infinitely many integers.

`That is ultrafinitism. That is why I make "arithmetical realism"`

`sometime explicit.`

In that case indeed we are out of the scope of my expertize.

`But if step 8 is correct, that moves will still prevent you to say`

`"yes" to the doctor, unless more and more ad ptolemaic redefinition of`

`"matter".`

But there would still be integers and primes.

`Thanks for reassuring me. I was about to close Platonia for`

`bankruptcy :)`

Numbers, addition, and multiplication would be patterns that ourbrains recognize in material things,

`With Church thesis, we have a notion of universal machine which`

`generalizes this, non trivially. Comp makes obvious the use of those`

`mathematical tools.`

at first due to experience counting objects, grouping them, andcounting groups. We abstract those patterns to symbolic form in ourheads or our writing for convenience, and we generalize the notationto cover a wide variety of patterns. But our process of abstractingand generalizing may omit important limitations (such as finitude)of the physical reality on which it was originally based.

`Assuming a physical reality at the start. For the mind body problem it`

`is better to be, at least methodologically agnostic, about that.`

`You describe well how humans got the numbers, but it is a projection`

`to believe that the notion of humans is more conceptually simple than`

`the notion of numbers.`

The question is only, do you agree on the axioms I gave.

`With comp, your "numbers are a human cultural construction" becomes`

`"numbers are universal machine cultural construction.`

or even (2) relativism in the sense that arithmetical propositionsmight only be true for humanlike brains,OK, but same remark. Defined human-like brain, and give me a proofthat 1+1=2 from that definition.Due to our shared evolutionary history, humans share nearly alltheir brain architecture in common. Due to our shared culturalhistory, many of the humans we regularly encounter share much oftheir set of background assumptions and beliefs in common. Itappears that there's no such thing as such a perfectly lucid anddetailed description or set of instructions that one person couldgive another that eliminates the need for the other person to grokthe meaning, i.e. to connect the ideas appropriately and fill in themissing information based on their own "wiring" and their ownexperience. (Take Edgar as an demonstration of this apparent fact. ;)

`That's why you publish, or put down thesis. You have to play the`

`academic game.`

`The academic is the worst of all systems, except for all the others`

`(to parody Churchill).`

Consequently, some suppose that communication with anextraterrestrial intelligence may fail due to there being an almosttotal mismatch in "wiring" and experience. (When language fails, wehumans resort to pointing at objects and pantomiming, but withoutshared sensory systems and emotional responses, even that may wellfail to be grokked by the alien.) It's also possible that thesymbolic structure of our mathematics is dependent on our "wiring"and experience; indeed there is some evidence that the way humansuse language is due to an evolutionarily recent genetic mutation.

That's a computationalist type of explanation, no problem.

For these two reasons, our mathematical definitions, theorems,proofs, etc may only be suitable for use by other humans, and so bya pragmaticist alethiology, only true for humans.

?

`If comp is true for human, that's what counts. It means that they can`

`survive through a relative universal numbers, but then, without adding`

`magic, what is true for all universal numbers is true for human true,`

`and universal numbers have an amazing theory of self-reference.`

The usual proofs then apply, because we're humans.

Cool.

with an alethiology of the sort preferred by the Americanpragmatist school of philosophy.keep in mind that you mention people who are Aristotelian, and thepoint I do is only that IF comp is true, THEN such approach getinconsistent or epistemologically non sensical.Hm. Can you elucidate what you mean by saying they areAristotelian? What is the key contrast?

The Aristotelian believes/assumes a primitive material universe.

`The Platonists believes/assume the idea that what we observe is the`

`shadow of something else.`

Four options plus an ignorance prior and little evidence gives meabout 25% confidence for each. :)ONLY IF you develop your alternate assumptions. The idea that "1+1is prime" independently of human is far more simple (and used) thanthe idea that "1+1 is prime" is relative to the human brain.The axiomatic of natural numbers is far more simple than anythingelse. You can always propose a much more complex theory to falsify asimple set of axioms.I don't know that the other cases I've mentioned are more complex.Physicalism just puts some mysterious "matter" first and makes mathderivative of it. That may be wrong, but it's hard to see why it'smore complex than comp's reversal of it.

`Comp assumes only the numbers, and the law of addition and`

`multiplication. Of the combinators with the laws of the application`

`and reduction.`

We search for an explanation for matter and consciousness.

The relativism described above isn't an additional supposition addedto math; it takes ideas from biology and linguistics to see whatconsequences there might be when they intersect with math.

`That relativism argues against comp, and even implicitly against`

`Church thesis. But my point is not that comp is true, just that with`

`comp, the theory QM + comp is redundant, and we have to justify QM (at`

`the least its logic) from self-reference. And up to now, it looks it`

`works.`

Bruno

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