Does inductive reasoning lead to knowledge?
in [Logic]
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From: Marshall on 9 Jan 2010 01:51 On Jan 8, 9:26 pm, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > dorayme wrote: > > In article <cWI1n.2906$%P5.1...(a)newsfe21.iad>, DanB wrote: > >> Marshall wrote: > > >>> if math is just a game, then > >>> what basis is there for claiming anything > >>> like "correctness" for any particular mathematical > >>> statement? > > >> Axioms that are 'accepted' as truth. > > > Why the qualifying quotes? > > > The point is that in a game, truth does not figure prominently. In > > maths and physics, truth is a bigish player. > > In math "truth" is whatever you develop logically from your axioms. Gödel's first incompleteness theorem proved that idea false. Marshall
From: Marshall on 9 Jan 2010 02:07 On Jan 8, 10:05 pm, DanB <a...(a)some.net> wrote: > Marshall wrote: > > > Show me how choosing some axioms that are > > 'accepted' as truth can make the right answer come > > out three. Ideally you will also show how accepting > > those axioms also makes case analysis come up with > > the answer three. > > Accepting an axiom determines results. I accepted no axioms, yet was able to determine the answer "four" to my question of how many unary functions are possible for a two-element algebra. This is a simple counterexample to you assertion. Also note that Gödel's first incompleteness theorem proved the existence of formulas that are true, yet do not follow from any axioms. > Are you getting this? I'm getting that you completely failed my simple challenge to show an arbitrary result following from some axioms, nor did you apparently even understand it. I'm getting that you have nothing to offer in the way of an argument other than "look it up." Marshall
From: Androcles on 9 Jan 2010 02:46 "Marshall" <marshall.spight(a)gmail.com> wrote in message news:43e98d31-7748-4755-b5dc-e2389bbc4c0b(a)m26g2000yqb.googlegroups.com... On Jan 8, 10:05 pm, DanB <a...(a)some.net> wrote: > Marshall wrote: > > > Show me how choosing some axioms that are > > 'accepted' as truth can make the right answer come > > out three. Ideally you will also show how accepting > > those axioms also makes case analysis come up with > > the answer three. > > Accepting an axiom determines results. I accepted no axioms, yet was able to determine the answer "four" to my question of how many unary functions are possible for a two-element algebra. This is a simple counterexample to you assertion. Also note that G�del's first incompleteness theorem proved the existence of formulas that are true, yet do not follow from any axioms. > Are you getting this? I'm getting that you completely failed my simple challenge to show an arbitrary result following from some axioms, nor did you apparently even understand it. I'm getting that you have nothing to offer in the way of an argument other than "look it up." Marshall ============================================ a = b (given) a^2 = ab (multiply both sides by a) a^2 - b^2 = ab-b^2 (subtract b^2 from both sides) (a+b)(a-b) = b(a-b) (factorize) a+b = b (divide both sides by a-b) b+b = b (substitute b for a) 2b = b (addition of b +b ) 2 = 1 (divide by b) Hence a = 2b since a = b. 2b+b = b (substitute 2b for a) 3 = 1 The axioms were followed, the result was arbitrary. An arbitrary result followed from some axiom. What we have is a well-known exception for which the axiom of division fails.
From: Michael Gordge on 9 Jan 2010 03:04 On Jan 8, 7:29 pm, chazwin <chazwy...(a)yahoo.com> wrote: > Free-will is an illusion. So you are saying there is no such thing as morality, because there is no choice, no such thing as right and wrong? So you're saying consciousness is only an illusion? So you believe that a supernatural power is totally responsible for your actions, a god, given that you have no choice because you have no free will to choose? MG
From: chazwin on 9 Jan 2010 06:31
On Jan 8, 10:29 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Jan 9, 12:33 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > > Find a PhD logician who thinks that's a good argument. > > > Marshall > > Speaking of a logical argument, you have never answered, how uncertain > are you that you can never be certain? > > Chazzzz says he can only ever be 99.999999% certain but Mortal says he > can only be 99.999% certain, so who is the smartest out of those two? > can you trump them? > > They both claim that they cant be certain of anything because of > something that doesn't exist by definition, the future, in other words > they are using something that does not exist, (the future) as a > requirement to be certain now. > > MG Your problem is that you think you are certain. Such is the root of all totalitarianism. |