New Anti-Cantor Attack
in [Logic]
|
Prev: Meami.org Publishes Polynomial Time Quicksort Algortihm:
Next: Methods of Proving all of Incompleteness in Logic in Trivially Short Proofs & a Challenge
From: |-|ercules on 3 Jun 2010 02:33 "Marshall" <marshall.spight(a)gmail.com> wrote .. > On Jun 2, 9:37 pm, Don Stockbauer <donstockba...(a)hotmail.com> wrote: >> On Jun 2, 9:54 pm, Marshall <marshall.spi...(a)gmail.com> wrote: >> > On Jun 2, 1:41 pm, Transfer Principle <lwal...(a)lausd.net> wrote: >> >> > > I indeed asserted that if two >> > > people posted identical arguments, one under the >> > > name of a well-known "crank" and one under that of >> > > a newbie, the "crank" would have a harder time >> > > getting people to agree with them. >> >> > This is exactly as it should be. >> >> Of course you'd believe in a fallacy, the "Argument Against the Man." > > Stupid people are less likely to produce useful > results than smart people, and therefor less worthy > of attention. This may appear to be a logical fallacy > to those who aren't looking carefully. > > > Marshall smart = normal = nothing new Herc
From: Aatu Koskensilta on 4 Jun 2010 10:47 Jim Burns <burns.87(a)osu.edu> writes: > Perhaps you can imagine my surprise that someone > as insightful as you would apparently miss my point. I didn't miss your point. I was hoping to prod you into presenting your thoughts on an issue I find interesting. As you note, when people say that probably P is not NP, probably the Riemann hypothesis is true, and so on, usually they're thinking of degrees of belief, or, at least, it is difficult to come up with any other coherent way of making sense of such assertions; that is, they mean just that most experts would be willing to bet a not insignificant sum that no refutation of these conjectures is forthcoming, and indeed we find people are happy to use algorithms, in the real world, in production systems, the correctness of which depend on the truth of such conjectures. This interpretation makes less sense in case of baffling claims such as "we have good evidence that PA is probably consistent" and so on sometimes put forth by logically innocent mathematicians. > Uhmm? Is there something about the philosophy of mathematics that > requires it to be applied only to mathematics? Is there something about the philosophy of horology that requires that it be applied only to horology? I'm unsure what sort of philosophy we're talking about here. I was baffled because there seemed to be nothing specifically about mathematics in the in-itself perfectly reasonable attitude or philosophy you described, and I didn't, and still don't, quite understand in what sense it is a philosophy of mathematics. Perhaps you meant it only in the sense people speak of their "philosophy of chess" or "philosophy of cooking", i.e. a general attitude or approach they apply when going about some activity or pastime? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 4 Jun 2010 11:54 David Bernier <david250(a)videotron.ca> writes: > Feferman also discusses ACA_0, a theory having to do with > arithmetic-sentence based analysis or something like that. ACA_0 is a conservative extension of PA in the language of second-order arithmetic -- that is, all of its theorems which can be expressed in the language of PA are provable in PA, and conversely. It has both number and set variables, and as axioms induction stated as a single sentence: For all sets X, if 0 is in X, and n+1 is in X whenever n is, then all numbers are in X. the usual axioms for successor, addition and multiplication, and a predicative comprehension schema: For any formula P containing no bound set variables, the universal closure of There exists a set X such that a number x is in X if and only if P(x). is an axiom. This theory is predicatively justified, in the sense that we can make predicativist sense of its axioms, and can provide arguments for them that are compelling on the predicativist conception of mathematics. (It is also finitely axiomatizable, unlike PA itself.) -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 4 Jun 2010 12:09 David Bernier <david250(a)videotron.ca> writes: > Poincare was an intuitionist Sure, but not in the sense the term is used today in foundations and mathematical logic. > Every natural number can be given a finite description, a numeral. > This is not so for a typical subset of N, P(N), P(P(N)), etc. Right, hence the qualms of various predicatively and vaguely constructively inclined mathematicians at the turn of the 20th century. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: MoeBlee on 4 Jun 2010 13:50
On Jun 2, 4:40 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > It amazes me how Clinton was ridiculed a decade ago for > asking for the definition of "is," He didn't ask for a definitionof 'is'. He correctly and legitimately pointed out that the answer to the question posed to him depends on which sense of the word 'is' was meant. MoeBlee |