Does inductive reasoning lead to knowledge?
in [Logic]
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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$V_3.8047(a)newsfe09.iad>, Nam Nguyen <namducnguyen(a)shaw.ca> wrote: As you are starting to insult me, it happens fairly regularly from people who make mistake after mistake in their arguments, (they get terribly frustrated you see), I will not be taking you seriously and being patient with you from now on. In the normal meaning of positive integers and prime numbers there are a number of primes between 1 and 21. You are trying to make out that mathematical statements do not have any intrinsic truth or falsity by simply denying that there are some established and widely known ways of interpreting the word and statements of *some* maths. The claim was made a while back that *all* maths was merely a game and I am denying this. If that makes me some sort of troll in your eyes when I respond to your rude personal remarks, then perhaps it is you being the real troll. One mark of a nutter and a troll is someone who flies off into personal abuse when he is not getting his way despite the number of times he repeats his sad barely articulate ideas. The maths that most normally educated people know applies to the world and is useful because there is more than syntactical gaming to it. You are merely pointing out, ad nauseam, without knowing how quite to do it well, that there is a lot of game to maths and especially sophisticated maths. I have never denied this. You are a one eyed and rather stupid man and you think that a few qualifications in maths or physics qualifies you to spout any kind of nonsense *about* maths. You are no more qualified to understand mathematical truth than a typist is to describe how the hell she types. Leave me alone and go to join Clarke in the basketweaving class. It is over there -----> -- dorayme
From: dorayme on 14 Jan 2010 00:10 In article <doraymeRidThis-171BFD.15513714012010(a)news.albasani.net>, dorayme <doraymeRidThis(a)optusnet.com.au> wrote: > In article <4ew3n.9166$V_3.8047(a)newsfe09.iad>, > Nam Nguyen <namducnguyen(a)shaw.ca> wrote: > > .... > Leave me alone and go to join Clarke in the basketweaving class. It is > over there -----> O... I forgot to give you a going-away present, to show I have no hard feelings towards you, The Desert Problem: <http://members.optushome.com.au/droovies/binHassad/desert.html> Should take you a couple of minutes with all your high and mighty maths. Took me a while to work it out but I did with simple logical reasoning and some elementary maths. Get that Clarke to help you, Stafford would not have a clue. Damn, I just remembered, you probably would not "get it" because it is not wrapped in scientistic exactness - remember your botching up of the idiomatic sarcasm about *meaning* and *pigs flying*? -- dorayme
From: J. Clarke on 14 Jan 2010 00:56
dorayme wrote: > 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. Yep, anybody who disagrees with you "insults you" and "makes mistake after mistake in their argumnents". > In the normal meaning of positive integers and prime numbers Now you are starting to state the rules of the game you want to play. But you don't seem to be aware that you are doing so. > there > are a number of primes between 1 and 21. Yes, over the integers using the normal definition of multiplication over the integers. But you had not specified that before. > 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. Yes, there are some conventions, however if you are writing a formal proof you do not simply assume those conventions. If you are proving something over the integers you state that that is what you are doing, for example. > The claim was made a while back that *all* maths was merely a game > and I am denying this. Deny it all you want to. That doesn't make it any less so. > 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. Pointing out that you do not know things that a first year grad student or keen senior in a math program knows is not making "rude personal remarks" nor is it "personal abuse". The fact that you take it as such reflects badly on you however. > The maths that most normally educated people know applies to the world > and is useful because there is more than syntactical gaming to it. But most "normally educated people" do not know much mathematics. They may think that they do but what they know is a particular, tiny, useful subset of a very large field. You are trying to characterize that field by assuming that that subset is the totality. > 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. But you have not shown any understanding of the place that that particular subset of mathematics has in the whole of mathematics. And you don't want to listen to anyone who tries to educate you, you just get mad at them and start going on about "basketweaving". That math that "normally educated people" know is something that one generates from a set of assumptions when one starts studying the nature of algebras. It is no more special than the system that Nam Nguyen presented except that by coincidence it happens to be useful for accounting and other purposes. > 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. Yeah, God forbid that anybody who actually knows something about a subject say anything about it. Leave that to the realm of the ignorant. > You are no more qualified to understand > mathematical truth than a typist is to describe how the hell she > types. Temper, temper. > Leave me alone and go to join Clarke in the basketweaving class. It is > over there -----> If you want to be left alone then maybe you should just stop responding to posts. |