Does inductive reasoning lead to knowledge?
in [Physics]
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From: Patricia Aldoraz on 12 Jan 2010 19:18 On Jan 13, 8:48 am, PD <thedraperfam...(a)gmail.com> wrote: > On Jan 12, 3:19 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> > wrote: > > On Jan 13, 2:50 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > 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. > > > The other possibility that you missed, amazingly is that it is simply > > false. > > This seems to be a remarkable statement, since an axiom is by > definition assumed to be true. Thus it is difficult to imagine how one > would hold from the outset that the same statement is assumed to be > true and yet false. > No, you are confusing a number of things. An axiom that is deemed to be true is not by definition or otherwise *thereby* true. If someone comes along and proposes some few axioms and shows off how impressive that so few can generate so much, it is still an open question whether the axioms are true or false or perhaps something else.
From: Michael Gordge on 12 Jan 2010 21:22 On Jan 13, 9:36 am, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > Truth is something more powerful than mere > game playing or human belief or proposal. So what is it? MG
From: bigfletch8 on 12 Jan 2010 21:37 On Jan 13, 5:44 am, PD <thedraperfam...(a)gmail.com> wrote: > On Jan 12, 1:50 pm, dorayme <doraymeRidT...(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! > > > Ever seen a policeman fly in a Jumbo? BOfL
From: Nam Nguyen on 13 Jan 2010 01:02 dorayme wrote: > In article <sCV2n.3785$ZB2.3547(a)newsfe13.iad>, > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > >> dorayme wrote: > >>> Well, I don't know how you would work it so that one could see that >>> there are no primes between 1 and 21 and such things without changing >>> the *meanings* of the words used. >> Keep the "meanings"; just change the frameworks, axioms, models, or a >> combination of. >> > > You mean like "A pig can fly" can be changed into a truth by a Martian > with different "frameworks, axioms, models", but who means exactly what > we mean by "pig", and "fly" and "is". What an intriguing suggestion! Yes. Put a pig on a small enough asteroid that has low gravity and it could fly! (And you wouldn't need a Martian help for that). Trivial fact perhaps but nothing intriguing. Another example, keep the meaning of "It's raining" the same, but change the model at will to change the truth of it. It's all just a game of the mind. >> The point is mathematics is still just a game, even though it might be a >> useful one by no coincidence. > > The point is that it is not always just a game then. Let me repeat: Mathematics is a game of the mind.
From: dorayme on 13 Jan 2010 03:12
In article <Vld3n.32973$Gf3.11418(a)newsfe22.iad>, Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > dorayme wrote: > > 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 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! > > Yes. Put a pig on a small enough asteroid that has low gravity and it could > fly! (And you wouldn't need a Martian help for that). Trivial fact perhaps > but nothing intriguing. > I thought you might not be understanding: a pig on a flying object is not a pig flying in the normal meaning of the phrases. > Another example, keep the meaning of "It's raining" the same, but change the > model at will to change the truth of it. > > It's all just a game of the mind. > > >> 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. > > Let me repeat: Mathematics is a game of the mind. You can repeat it as much as you like. It does not make it true and it still needs an argument. Your above misunderstanding should surely make you pause before being quite so confident as to simply repeat it again without further supporting explanation and argument. -- dorayme |