Does inductive reasoning lead to knowledge?
in [Logic]
|
From: Patricia Aldoraz on 10 Jan 2010 22:05 On Jan 9, 4:26 pm, "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. Why the quotes around "truth"? I use them because I am quoting a word. Why are you using them?
From: PD on 11 Jan 2010 09:44 On Jan 8, 3:38 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Jan 9, 6:26 am, PD <thedraperfam...(a)gmail.com> wrote: > > Desperate strawman garbage snipped, you haven't answered, .... [your question snipped]
From: PD on 11 Jan 2010 09:45 On Jan 8, 3:43 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Jan 9, 6:28 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > And so is Euclid's Fifth Postulate a postulate or not? > > You have got my answer. > > MG I didn't see a yes or no anywhere in your answer, and it was a yes or no question.
From: PD on 11 Jan 2010 09:47 On Jan 8, 6:19 pm, 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. Why yes, yes, they are. > > 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. > > Marshall
From: Marshall on 11 Jan 2010 09:53
On Jan 11, 6:47 am, PD <thedraperfam...(a)gmail.com> wrote: > On Jan 8, 6:19 pm, 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. > > Why yes, yes, they are. Your post almost demands the response "Oh no they are not." But that wouldn't be much use, would it? Do you feel the same way about the natural numbers? Are they an arbitrary creation of man? Do you have any argument you'd care to supply to justify your position? Marshall |