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. > 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. > > 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. > > > > > > 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. 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. > > > > > >> It is, I think, your unwillingness to study a bit of math and logic which >> prevents you from seeing this. >> > > Just the opposite. It is your unwillingness to question the supremacy of > math and logic which prevents you from even seeing that there is something > to question. > > > On the contrary I did ask people to question anything I say, which is of > the type verifiable. That's how science work. > Then it is not a question of supremacy. Only a good lamp to search the key. > There are other lamps...other keys. Craig > > I stop when you attribute to me the contrary on point On which I insist a > lot. > > Bruno > > > > > >> You get a lot about the numbers with few axioms written in first order >> language. >> > > I don't see why any axioms would be possible. Where do they come from? Who > is writing them? > > >> I doubt you can define "expectation of sequence" in such a simple way. >> > > How can you doubt it? > > >> How will you define "sequence" without mentioning some function from N >> (the set of natural numbers) to some set? >> > > With rhythmic patterns and pointing - the way that everyone learns to > count. A horse can understand sequence without a formal definition derived > from set theory. What you are saying sounds to me like 'you cannot make an > apple unless you ask an apple pie how to do it'. > > >> >> Again, I remind you that "simple" means "simple in the 3p sharable >> sense", not "simple" in the 1p personal experiential sense. >> > > Why is that not an arbitrary bias? If I don't allow the possibility of 3p > without 1p, then simplicity can only be 1p. > > >> All scientists agree on the arithmetic axioms, >> > > If that's true, its an argument from authority, and it could be the reason > why all scientists fail to solve the hard problem. (which is exactly my > argument). > > >> and I have to almost lie to myself to fake me into doubting them. >> > > I can't remember what it was like before I learned arithmetic, but I can > still understand that we all live for years without those notions. There is > at least one culture today that has no arithmetic. > > >> Something like "expectation" might already have a different meaning for >> spiders, for different humans, etc. >> > > Either way, it is undeniably more primitive than arithmetic in my view. > > Craig > > >> Bruno >> >> >> 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 everything-li...@googlegroups.com <javascript:>. > To post to this group, send email to everyth...@googlegroups.com<javascript:> > . > Visit this group at http://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. 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