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