On 8/20/2017 4:02 PM, David Nyman wrote:
On 20 Aug 2017 23:16, "Brent Meeker" <meeke...@verizon.net <mailto: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 <mailto: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 <mailto: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. Brent -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
