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" <meeke...@verizon.net> 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" <marc...@ulb.ac.be>
wrote:
On 19 Aug 2017, at 01:21, David Nyman wrote:
On 18 August 2017 at 18:13, Bruno Marchal <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? 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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