Does inductive reasoning lead to knowledge?
in [Logic]
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From: PD on 12 Jan 2010 10:50 On Jan 11, 9:20 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Jan 12, 10:05 am, PD <thedraperfam...(a)gmail.com> wrote: > > > The natural numbers are a concept, but I don't think they are an > > axiom. > > An axiom says something, the natural numbers simply exist. > > > I'll reiterate one of the examples I've cited in this thread: Euclid's > > fifth postulate. Now, either that is an arbitrary creation of man or > > it has some undeniable objective truth. > > These are not the only possibilities. Elaborate, please.
From: PD on 12 Jan 2010 10:51 On Jan 12, 12:58 am, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Jan 11, 11:45 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > I didn't see a yes or no anywhere in your answer, > > Thats encouraging, all you need do now is to expand non-contradictory > identification into your own ideas, e.g. lines that are parallel do > not converge, intersect and or diverge no matter how far their > journey. Still lacking a "yes" or "no" answer to a yes or no question. Is this a form of passive-aggressive behavior that is comfortable for you?
From: J. Clarke on 12 Jan 2010 10:30 jmfbahciv wrote: > Nam Nguyen wrote: >> Marshall wrote: >>> >>> It has been proposed on this thread that math is just a game >>> with no significance or utility, except by coincidence (this is >>> bullshit.) >> >> Mathematics is a game of the mind. > > Which can be written down on paper. > >> Whether or not that has any utility >> or significance, or that is by coincidence, or that is "bullshit" >> doesn't matter, to the fact that it's just a game. >> > Have you done any cost analysis lately? Or materials design? Or > built a bridge? Or figured out the load of the roof on your house? That sort of thing uses one branch of mathematics that coincidentally has real-world utility. This is a small subset of the totality of mathematics.
From: dorayme on 12 Jan 2010 14:50 In article <sCV2n.3785$ZB2.3547(a)newsfe13.iad>, Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > dorayme wrote: > > Well, I don't know how you would work it so that one could see that > > there are no primes between 1 and 21 and such things without changing > > the *meanings* of the words used. > > Keep the "meanings"; just change the frameworks, axioms, models, or a > combination of. > You mean like "A pig can fly" can be changed into a falsity by a Martian with different "frameworks, axioms, models", but who means exactly what we mean by "pig", and "fly" and "is". What an intriguing suggestion! > > > >>> That does not mean it is > >>> just a game nor that it is a coincidence that mathematics is useful to > >>> us. > >> It's a misconception that games in general have to be useless to human > >> beings. > > > > Who is falling for that misconception. Neither of us! But the question > > that is relevant is what sort of use. Mere use because it reduces stress > > levels is not much relevant! > > The point is mathematics is still just a game, even though it might be a > useful one by no coincidence. The point is that it is not always just a game then. -- dorayme
From: dorayme on 12 Jan 2010 15:27
In article <doraymeRidThis-BC9D1F.06504213012010(a)news.albasani.net>, dorayme <doraymeRidThis(a)optusnet.com.au> wrote: > You mean like "A pig can fly" can be changed into a falsity by a Martian > with different "frameworks, axioms, models", but who means exactly what > we mean by "pig", and "fly" and "is". What an intriguing suggestion! Oops (one ought to be especially careful to avoid typos when being mildly sarcastic <g>) read that as You mean like "A pig can fly" can be changed into a truth by a Martian with different "frameworks, axioms, models", but who means exactly what we mean by "pig", and "fly" and "is". What an intriguing suggestion! -- dorayme |