From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Sunday, March 02, 2014 12:13 AM
To: everything-list@googlegroups.com
Subject: Re: If it's all math, then where does math come from?
On 01 Mar 2014, at 11:53, Chris de Morsella wrote:
From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Saturday, March 01, 2014 12:23 AM
To: everything-list@googlegroups.com
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.
Finite sets are useful tools and help sequence ordering of operation as well
as ordering of inputs and outputs. Infinite sets make it more interesting
and useful. The set provides the means of attributing things and finding
things via attributes; i.e. a member of the class of things that has these
attributes. Relating things and remembering the relationships amidst dynamic
change is what sets provide. Naturally all manner of more specialized
containers can emerge.... Say ordered set for example.
By un-bounding collections it makes them useful universal entities.
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.
In some ways all other possible sets naturally emerge from the null set; in
a way as all numbers emerge from the bit.... The bit, if infinitely replicated
can express any number; if you can get this infinitely self-auto-replicating
bit off and running like inflation then the universe is in business.
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").
Yes, I agree, I can only imagine how Kurt Gödel's incompleteness theorem
must have hit Russell and Whitehead like a ton of bricks.
Chris
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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