Does inductive reasoning lead to knowledge?
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From: dorayme on 13 Jan 2010 21:33 In article <gIu3n.5701$ap2.3179(a)newsfe18.iad>, Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > Patricia Aldoraz wrote: > > On Jan 14, 1:15 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > >> dorayme wrote: > >>> In article <Vld3n.32973$Gf3.11...(a)newsfe22.iad>, > >>> Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >>>> dorayme wrote: > >>>>> In article <sCV2n.3785$ZB2.3...(a)newsfe13.iad>, > >>>>> Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >>>>>> dorayme wrote: > >>>>>>> Well, I don't know how you would work it so that one could see > >>>>>>> that there are no primes between 1 and 21 and such things without > >>>>>>> changing the *meanings* of the words used. > > ... > >>>> Let me repeat: Mathematics is a game of the mind. > >>> You can repeat it as much as you like. It does not make it true and it > >>> still needs an argument. > >> It's simply the way that it is. > > > > What is the way that there are no primes between 0 and 21? > > In the formal system T = {Ax(Sx=0) /\ Axy(x+y=S0) /\ Axy(x*y=S0)} > one would find there are no primes between 0 and 21. But that is not to understand how there are no primes between 1 and 21 without changing the meaning of the words. You might as well say that 'The world is round' is true in our normal English language but false in your idiolect or in some other community of speakers' language where the mark "round" means square. -- dorayme
From: J. Clarke on 13 Jan 2010 21:58 dorayme wrote: > In article <lzu3n.5697$ap2.105(a)newsfe18.iad>, > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > >> 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. >> > >> You either read it too quick or didn't know much about physics: I >> didn't say or imply the asteroid is flying; in a very low gravity >> the act of running would make you fly! >> > > You need more than physics on this stuff. You are still not > understanding it I am afraid. It is a common idiomatic expression and > it is not saying pigs could not fly in some contexts on other planets > or low gravity or in special apparatuses. It is not saying fly in the > sense that man will fly (leap) through the air on the moon in a lunar > hurdling race. Your physics seems to have made you unable to > understand the idea of pigs flying about the streets where you live > and perching on rooftops and very big strong branches. > > It is usually a sarcastic idiomatic expression to say that something > is highly unlikely. Of course pigs cannot fly because they have not > got the right anatomy to fly. You cannot make pigs fly because you > have whatever qualifications in physics and nor can you make it that > there are no primes between 1 and 21. > >>> >>>> 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 doesn't matter if you or I repeat anything: > > It *does* matter if you are needing to give an argument for something > and keep failing to do so. > >> we are debating about >> mathematics and what matters is the reasonings in the debate got to >> *be backed-up by _technical mathematical reasoning_*, not by >> blah-blah-blah! > > There is nothing technical about the claim that not all mathematics is > just a game. It is you that is doing the blahing (ie. misunderstanding > things and talking and saying irrelevant things). If you have > technical mathematical reasoning to show how there are no primes > between 1 and 21 without changing the meanings of the words, go > ahead, I would love to see it. I am not encouraged by the way you > have misunderstood the pigs idiomatic expression. In what set do you want this shown, and how is multiplication defined over that set? It's not a matter of "changing meanings". You're assuming that the integers constitute the only set of numbers and that multiplication is defined in a manner consistent with high school algebra.
From: J. Clarke on 13 Jan 2010 22:13 dorayme wrote: > In article <gIu3n.5701$ap2.3179(a)newsfe18.iad>, > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > >> Patricia Aldoraz wrote: >>> On Jan 14, 1:15 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: >>>> dorayme wrote: >>>>> In article <Vld3n.32973$Gf3.11...(a)newsfe22.iad>, >>>>> Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>>>> dorayme wrote: >>>>>>> In article <sCV2n.3785$ZB2.3...(a)newsfe13.iad>, >>>>>>> Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>>>>>> dorayme wrote: >>>>>>>>> Well, I don't know how you would work it so that one could see >>>>>>>>> that there are no primes between 1 and 21 and such things >>>>>>>>> without changing the *meanings* of the words used. >>> ... >>>>>> Let me repeat: Mathematics is a game of the mind. >>>>> You can repeat it as much as you like. It does not make it true >>>>> and it still needs an argument. >>>> It's simply the way that it is. >>> >>> What is the way that there are no primes between 0 and 21? >> >> In the formal system T = {Ax(Sx=0) /\ Axy(x+y=S0) /\ Axy(x*y=S0)} >> one would find there are no primes between 0 and 21. > > But that is not to understand how there are no primes between 1 and 21 > without changing the meaning of the words. You might as well say that > 'The world is round' is true in our normal English language but false > in your idiolect or in some other community of speakers' language > where the mark "round" means square. The definitions of the "words" are part of the game. You can define the "words" to mean anything you want to in mathematics as long as you state what definitions you are using.
From: Nam Nguyen on 13 Jan 2010 22:31 dorayme wrote: > In article <gIu3n.5701$ap2.3179(a)newsfe18.iad>, > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > >> Patricia Aldoraz wrote: >>> On Jan 14, 1:15 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: >>>> dorayme wrote: >>>>> In article <Vld3n.32973$Gf3.11...(a)newsfe22.iad>, >>>>> Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>>>> dorayme wrote: >>>>>>> In article <sCV2n.3785$ZB2.3...(a)newsfe13.iad>, >>>>>>> Nam Nguyen <namducngu...(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. >>> ... >>>>>> 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. >>>> It's simply the way that it is. >>> What is the way that there are no primes between 0 and 21? >> In the formal system T = {Ax(Sx=0) /\ Axy(x+y=S0) /\ Axy(x*y=S0)} >> one would find there are no primes between 0 and 21. > > But that is not to understand how there are no primes between 1 and 21 > without changing the meaning of the words. You might as well say that > 'The world is round' is true in our normal English language but false in > your idiolect or in some other community of speakers' language where the > mark "round" means square. > The "idiolect" language that the "sci.logic" [one forum the thread is in] and mathematics community are using is L = L(0, S, +, *). Why don't you you get _technical_ and translate "there are no primes between 1 and 21" into a _mathematical statement_ in that language. If you could translate then you'd understand why the statement "there are no primes between 0 and 21" is true in T. If you can't - and it seems you can't - you've just been babbling on the subject that you don't have a basic understanding. [That's is to say if you're not already a troll].
From: dorayme on 13 Jan 2010 23:51
In article <4ew3n.9166$V_3.8047(a)newsfe09.iad>, Nam Nguyen <namducnguyen(a)shaw.ca> wrote: As you are starting to insult me, it happens fairly regularly from people who make mistake after mistake in their arguments, (they get terribly frustrated you see), I will not be taking you seriously and being patient with you from now on. In the normal meaning of positive integers and prime numbers there are a number of primes between 1 and 21. You are trying to make out that mathematical statements do not have any intrinsic truth or falsity by simply denying that there are some established and widely known ways of interpreting the word and statements of *some* maths. The claim was made a while back that *all* maths was merely a game and I am denying this. If that makes me some sort of troll in your eyes when I respond to your rude personal remarks, then perhaps it is you being the real troll. One mark of a nutter and a troll is someone who flies off into personal abuse when he is not getting his way despite the number of times he repeats his sad barely articulate ideas. The maths that most normally educated people know applies to the world and is useful because there is more than syntactical gaming to it. You are merely pointing out, ad nauseam, without knowing how quite to do it well, that there is a lot of game to maths and especially sophisticated maths. I have never denied this. You are a one eyed and rather stupid man and you think that a few qualifications in maths or physics qualifies you to spout any kind of nonsense *about* maths. You are no more qualified to understand mathematical truth than a typist is to describe how the hell she types. Leave me alone and go to join Clarke in the basketweaving class. It is over there -----> -- dorayme |