On Monday, May 5, 2014 10:26:27 AM UTC-4, Bruno Marchal wrote: > > > On 05 May 2014, at 14:27, Craig Weinberg wrote: > > > > On Saturday, May 3, 2014 3:53:48 PM UTC-4, Bruno Marchal wrote: > > > On 02 May 2014, at 23:58, Craig Weinberg wrote: > > > > On Friday, May 2, 2014 11:15:40 AM UTC-4, Bruno Marchal wrote: > > > On 01 May 2014, at 20:42, Craig Weinberg wrote: > > > > On Friday, April 18, 2014 3:23:13 AM UTC-4, Bruno Marchal wrote: > > > On 16 Apr 2014, at 20:10, Craig Weinberg wrote: > > What generates Platonia? > > > > Nothing generates Platonia, although addition and multiplication can > generate the comp-relevant part of platonia, that is the UD or equivalent. > > Elementary arithmetic cannot be justified by anything less complex (in > Turing or logical sense). It is the minimum that we have to assume to start. > > > Saying that elementary arithmetic is the minimum that we have to start > doesn't make sense to me. Elementary arithmetic depends on many less > complex expectations of sequence, identity, position, motivation, etc. I > keep repeating this but I don't think that you are willing to consider it > scientifically. > > > To define, is a reasonable precise sense, "expectations", "sequence", > "identity", "position", or "motivation" (which I doubt is a simple notion) > you need arithmetic. > > > How can arithmetic exist without sequence and then define sequence? > > > If you agree on logic and > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > Then you can study how to define sequence in that theory. > > > Only because you have an a priori expectation of sequence which can be > inferred. Otherwise nothing is defined and you have only unrelated > statements. You need sense to draw them together and match your intuition. > > > No. Logic is the art of making derivation without sense. >
There is no art without sense. If logic could be accomplished without sense then it would be impossible to make an error in logic. There would be no need to formalize logic because it would be inescapable in every state of consciousness. That isn't what we see though. In fact, logic is very tenuous and requires a particularly sober intellect which is focused on modeling concepts in an impersonal sense. > That is even why so many people think that a machine which can reason is > just doing syntactical manipulation without understanding, and at the low > level, that's correct. > A derivation, in a formal theory, is valid or non valid, independently of > any of its possible interpretation (all those terms are well defined). > Syntactical manipulation is still sense, it just has relatively limited aesthetic qualities. > > > > > > Gödel is the fist who did that. He invented the "Gödel beta function", > based on a generalization of a famous chinese "lemma", about set of modular > equations in arithmetic. > > Eventually (not easy exercice) you can define from the axiom and the chine > lemma a representation of the exponential function, and with its you can > define a sequence in arithmetic by using the unique factorization of the > natural numbers. > > > But "eventually" means that you must follow a sequence of steps to do your > defining. You smuggle the expectation for sequence in from the start. > > > Hmm, ... I will not insist here, as this will be the object to the next > post in the math thread. > > > > > > > > It is not the existence of arithmetic, it is the existence of 0, s(0), > etc. + the basic relation that you can derive from the axioms. > > > "Derive" requires sequence and sense. > > > Not at all. > Does that mean that dead people would be good at deriving relations from axioms? > > > > > > > > > > > It is the same capacity to reason which tells me that 5-3=2 which tells me > that sequence can exist without arithmetic but arithmetic cannot exist > without sequence. > > > It is a bit imprecise. I can define sequence in *any* turing complete > language, and they are all equivalent for computationalism. > You can define a notion of sequence as primitive, instead of numbers, yes. > That is the case for LISP, somehow, which is close to combinators and > lambda calculus. > > Yo have never provide any theory, so I can't figure what you talk about. > > > The theory is that logic and arithmetic are particular continuations of > sense, not the other way around. > > > Sense is a vague term. Not two human being understand it in the same way. > It is a bit like God. Important notion, but hardly usable in theories. > If theories can't use sense, and sense is important, then surely it is the theories that should change. > > > > Before arithmetic can exist, there must exist a sense of expectation for > counting. Counting includes a sense of recursive steps as well as sequence, > comparison, memory, change, digits, etc. It cannot be primitive as it is a > manipulation of attention. > > > > Not at all. More in the math thread, but you might need to reread all > posts. > Sounds like a dodge. Craig -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
