On 01 Mar 2014, at 11:53, Chris de Morsella wrote:
From: [email protected] [mailto:[email protected]
] On Behalf Of Bruno Marchal
Sent: Saturday, March 01, 2014 12:23 AM
To: [email protected]
Subject: Re: If it's all math, then where does math come from?
On 01 Mar 2014, at 06:16, Chris de Morsella wrote:
"If it's all math, then where does math come from?"
>>Strange to say, elementary maths just appears to be a fact. That
is, it is a fact that 1+1=2.
Somehow I do not find that satisfying; in what way and by what
evidence does this occur?
Especially - as I had posited if math is the fundamental thing -
even more fundamental than the emergent material universe. I could
see this logic in a pre-existing universe replete with 10 to a very
large number of atoms, but if math is to be the superstructure
underlying everything then I - speaking for myself - am not
satisfied by saying it just is a fact.
But do you agree with 1+1=2?
I agree that math is internally consistent
"1+1=2" is quasi-infinitely more simple than "math is internally
consistent".
I have few doubt that "1+1=2" makes sense, and is true, but a term
like "math" does not denote a theory for which "consistent" can make
sense.
and that within mathematical ontology it is self-consistent.
Furthermore it seems to crop up in reality again and again.
Patterns, equations, such as say the Fibonacci series manifesting in
so many unrelated places; the universe in its reduced symbol set of
"smeared" quarks and leptons; its constants and various cardinal
values and states such as spin, color, charge etc. - it does all
seem very binary and mathematical.
I however remain curious, where "1" came from, and even before 1,
Don't confuse the null set and the number 0.
I don't believe in set. Finite set theory is equivalent to Peano
Arithmetic (even more equivalent than "Turing equivalent"). But usual
set theory have much stronger axiom, like the axiom of infinity.
the null set... the set of nothing at all. The null set is a lot more
than nothing.
Yes, with the set theoretical principles of reflexion and
comprehension, you can get almost all sets from the null set.
It takes a great leap to get from nothing to the null set. At this
most reductionist of levels; is this where everyone gives up,
perhaps because it is unknowable.
I can see the logical progression from 1+1=2 to an ever inflating
infinite forest of numbers with infinite overlays of dynamism
operating over layer and layers of stochastic boundaries.
OK. But the point is that we can't prove the existence of null set, or
of the umber 0. We can't prove this from logic alone (= failure of
Russell and Whitehead "logicism").
Because the rest is sunday philosophy in my opinion.
Of course, in "my" theory 1+1=2 is just a theorem. The interesting
things is that "Chris believes (or not) in 1+1=2" is also a theorem.
Sure... an emergent phenomena; don't really have any existential
issues with my being, being emergent.... In fact I rather like the
idea of emerging into being. It fits with the brains massive
parallelism and lack of any central operating system (that we have
found). I emerge; therefore I am.
OK, I have no problem with this too.
Bruno
http://iridia.ulb.ac.be/~marchal/
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