Does inductive reasoning lead to knowledge?
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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.
From: chazwin on 9 Jan 2010 06:35 On Jan 9, 12:19 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jan 8, 8:19 am, DanB <a...(a)some.net> wrote: > > > Marshall wrote: > > > > Or again I ask: 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. > > That's supposed to be the basis? Just that noun > phrase by itself? > > And anyway, axioms themselves also come from > somewhere. They are not just arbitrary creations > of man. Er--- yes they are. They have to be. Who else thinks them, writes them and uses them? God? > > Suppose I want to investigate two-element algebras. > How many unary functions are possible? I claim that > there is only a single correct answer to that question: > four. This can be established by simple case analysis. > > If axioms are what it's all about, please demonstrate > so. 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. Axioms are statements that are accepted as truth, all conclusion formed from axioms are also accepted as true. none of this relies on sensory evidence and as such is not real. There are no integers, straight lines, or spheres in nature. These are all constructs of the human imagination. > > Marshall
From: chazwin on 9 Jan 2010 06:42 On Jan 9, 3:53 am, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Jan 8, 9:27 pm, chazwin <chazwy...(a)yahoo.com> wrote: > > > Hume pointed out this problem in the early 18th C, but despite these > > difficulties the last 200 years+ has used inductive methods to design > > all the wonders of technology and we have reached to moon. > > If "inductive methods" merely means "whatever scientists do when they > do the non-deductive bits of their work" naturally it is true. But > what use is this. That is not any answer to the problem of induction. > > > Whilst we > > have to always be aware that our inductive knowledge is a question of > > probabilistic truth. > > Nor is this. The problem of induction is not a search for 100% > probability. It is a search for anything over 50%. Until this is > understood, it is impossible to understand what so troubled Hume and > modern versions of the problem Hume's own answer to the problem of induction was mitigated skepticism. Which means that although law-like statements built from induction are not 100% certain, if they work they it is possible to have a pragmatic belief in them until they are replaced by something more accurate or probable. Thus Newtonian physics woks in most cases. But Hume would have approved of the change in science offered by Einstein.
From: chazwin on 9 Jan 2010 06:42 On Jan 9, 5:26 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > dorayme wrote: > > In article <cWI1n.2906$%P5.1...(a)newsfe21.iad>, DanB <a...(a)some.net> > > wrote: > > >> Marshall wrote: > > >>> if math is just a game, then > >>> what basis is there for claiming anything > >>> like "correctness" for any particular mathematical > >>> statement? > > >> Axioms that are 'accepted' as truth. > > > Why the qualifying quotes? > > > The point is that in a game, truth does not figure prominently. In > > maths and physics, truth is a bigish player. > > In math "truth" is whatever you develop logically from your axioms. Some > sets of axioms lead to interesting games, some don't. And some sets lead to > games that are actually useful. But none of it is real.
From: chazwin on 9 Jan 2010 06:46
On Jan 9, 6:51 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jan 8, 9:26 pm, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > > > > > > > dorayme wrote: > > > In article <cWI1n.2906$%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 No, you misunderstand. It is a complete affirmation of this position. The incompleteness is an expression of the unknown elements which lie outside the axioms and the determinate conclusions that are drawn from those axioms. |