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.
Bruno
David
Bruno
https://futurism.com/the-most-important-question-underlying-artificial-general-intelligence-research-is-math-real/
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