Does inductive reasoning lead to knowledge?
in [Logic]
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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$ZB2.3547(a)newsfe13.iad>, > > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > > > >> dorayme wrote: > > > >>> Well, I don't know how you would work it so that one could see that > >>> there are no primes between 1 and 21 and such things without changing > >>> the *meanings* of the words used. > > >> Keep the "meanings"; just change the frameworks, axioms, models, or a > >> combination of. > >> > > > > You mean like "A pig can fly" can be changed into a truth by a Martian > > with different "frameworks, axioms, models", but who means exactly what > > we mean by "pig", and "fly" and "is". What an intriguing suggestion! > > Yes. Put a pig on a small enough asteroid that has low gravity and it could > fly! (And you wouldn't need a Martian help for that). Trivial fact perhaps > but nothing intriguing. > I thought you might not be understanding: a pig on a flying object is not a pig flying in the normal meaning of the phrases. > Another example, keep the meaning of "It's raining" the same, but change the > model at will to change the truth of it. > > It's all just a game of the mind. > > >> The point is mathematics is still just a game, even though it might be a > >> useful one by no coincidence. > > > > The point is that it is not always just a game then. > > Let me repeat: Mathematics is a game of the mind. You can repeat it as much as you like. It does not make it true and it still needs an argument. Your above misunderstanding should surely make you pause before being quite so confident as to simply repeat it again without further supporting explanation and argument. -- dorayme
From: Errol on 13 Jan 2010 04:07 On Jan 13, 10:12 am, dorayme <doraymeRidT...(a)optusnet.com.au> wrote: > In article <Vld3n.32973$Gf3.11...(a)newsfe22.iad>, > Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > 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. > Maybe you could provide an example of how a pig might fly in the normal meaning of the phrases. Maybe the pig came to earth from planet zork in the 43rd dimension from our causal reference and has super powers on earth. Maybe an earth pig with swine flu was infected by a bird with bird flu while eating radioactive swill and grew wings. maybe a pig drank red bull Please enlighten me.
From: J. Clarke on 13 Jan 2010 09:15
dorayme wrote: > 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. It's simply the way that it is. Algebra over the real numbers is one of many different rings. Rings in general are only one subset of groups. There are axioms that define the properties of groups in general, then there are specific additional axioms that define particular kinds of groups, then there are additional axioms that define rings within groups. Then there are additional axioms that define particular kinds of rings. Then there are additional axioms which when applied to a specific kind of ring give us our everyday algebra. By applying different axioms you can define other algebras that work fine as mathematical systems but are not particularly useful for anything. |