On 8/21/2017 4:28 AM, Bruno Marchal wrote:
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" <[email protected]
<mailto:[email protected]>> 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" <[email protected]
<mailto:[email protected]>> wrote:
On 19 Aug 2017, at 01:21, David Nyman wrote:
On 18 August 2017 at 18:13, Bruno Marchal
<[email protected] <mailto:[email protected]>> 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_?
Do you know you are not experiencing being in Washington now?...that's how.
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.
So is "primary arithmetic".
Brent
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