On 18 August 2017 at 18:13, Bruno Marchal <[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. David > > Bruno > > > > > > > https://futurism.com/the-most-important-question-underlying- > artificial-general-intelligence-research-is-math-real/ > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
