On 07 Mar 2014, at 21:06, Gabriel Bodeen wrote:
On Friday, March 7, 2014 10:59:06 AM UTC-6, Bruno Marchal wrote:
On 07 Mar 2014, at 17:05, Gabriel Bodeen wrote:
An argument on its own merits is presumably either valid or
invalid, and either sound or unsound. Regarding UDA's soundness:
I have no problem saying Yes Doctor. Similarly I have no problem
with the Church thesis. But when it comes to Arithmetical Realism,
I don't know of any convincing reasons to believe it.
You don't believe in the prime numbers?
All theories presuppose arithmetical realism. Many notions, like the
notion of digital machine presupposes arithmetical realism. Comp or
just Church thesis don't make sense without AR.
AR is not an hypothesis in metaphysics, it is the name of the
beliefs in elementary arithmetic. It is a set of mathematical
hypothesis, together with its usual semantic the structure (N, +, *).
Heh, yes, I believe in prime numbers.
All right. That's arithmetical realism. Unless you believe that the
truth of "there are prime numbers" is a consequence of physics, or of
the existence of a primitive physical universe.
But in "The Origin of Physical Laws and Sensations" you wrote of AR
that it is "the assumption that arithmetical propositions ... are
true independently of me, you, humanity, the physical universe (if
that exists), etc."
Just to make it clear. Without this you cannot assess something like
"Church thesis", which identify all possible classes of computable
functions from N to N. Some could argue that this is even more
demanding than AR.
A couple other accounts of how things might be that I take seriously
are (1) physicalism in the sense that arithmetical propositions
might only be true when physically realized,
No problem, and indeed this would make comp false. of course, if you
really defend that thesis, you have to explain and prove the existence
of infinitely many prime numbers by using physics, and this without
presupposing addition and multiplication of integers. I am not even
sure how you will just defined what is prime number.
or even (2) relativism in the sense that arithmetical propositions
might only be true for humanlike brains,
OK, but same remark. Defined human-like brain, and give me a proof
that 1+1=2 from that definition.
with an alethiology of the sort preferred by the American pragmatist
school of philosophy.
keep in mind that you mention people who are Aristotelian, and the
point I do is only that IF comp is true, THEN such approach get
inconsistent or epistemologically non sensical.
And a third meta-account is that reality might be a way that doesn't
make sense to me.
Then indeed comp is false, but also physics, etc. No problem.
Four options plus an ignorance prior and little evidence gives me
about 25% confidence for each. :)
ONLY IF you develop your alternate assumptions. The idea that "1+1 is
prime" independently of human is far more simple (and used) than the
idea that "1+1 is prime" is relative to the human brain.
The axiomatic of natural numbers is far more simple than anything
else. You can always propose a much more complex theory to falsify a
simple set of axioms.
Then, with respect to the UDA, to make much more complex a theory just
to avoid a mathematical problem is not good science, imo.
I can present "my" theory(*). Can you present yours? I agree that comp
might be false, but today that is speculation, and it is useless to
speculate on the negation of a theory to avoid testing it.
Keep in mind that I do not defend comp, on the contrary I only show it
testable, and show that thanks to Gödel and QM, it works pretty well.
(*) Classical logic + (for all x and y):
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
or if you prefer
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
And this is not just the theory of numbers (on which most people
agree), it is proved to be, once comp is assumed at the meta-level,
the "theory of everything" including consciousness and physics.
(Something I try to explain to Liz and some others right now, and is
the result of my research.
Is that not simple and elegant :) Well, my point is only that this is
testable.
Bruno
-Gabe
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