Does inductive reasoning lead to knowledge?
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From: PD on 11 Jan 2010 18:05 On Jan 11, 8:53 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jan 11, 6:47 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Jan 8, 6:19 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > > > On Jan 8, 8:19 am, DanB <a...(a)some.net> wrote: > > > > > Marshall wrote: > > > > > > Or again I ask: if math is just a game, then > > > > > what basis is there for claiming anything > > > > > like "correctness" for any particular mathematical > > > > > statement? > > > > > Axioms that are 'accepted' as truth. > > > > That's supposed to be the basis? Just that noun > > > phrase by itself? > > > > And anyway, axioms themselves also come from > > > somewhere. They are not just arbitrary creations > > > of man. > > > Why yes, yes, they are. > > Your post almost demands the response "Oh no > they are not." But that wouldn't be much use, > would it? > > Do you feel the same way about the natural numbers? > Are they an arbitrary creation of man? > > Do you have any argument you'd care to supply to > justify your position? It's really a matter of definition more than anything, as far as I know. The natural numbers are a concept, but I don't think they are an axiom. On the other hand, there is a set of axioms (the Peano axioms) that are used to rigorously define them. Notice that one of the Peano axioms is precisely the one that ensures the *mathematical* sense of induction will work at all. 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. But if the latter, then there is a serious problem with Riemannian geometry, which disbands the validity of the fifth postulate. Since both of those systems seem to have equally good applications not only in the mind but to real life, it seems difficult to say that they are both objectively true. On the other hand, if they are arbitrary creations of man, then it makes sense how the geometries that stem from them both have value.
From: dorayme on 11 Jan 2010 18:16 In article <32273fb7-a5a3-4b24-b1f0-0f433d04aeba(a)e27g2000yqd.googlegroups.com>, PD <thedraperfamily(a)gmail.com> wrote: > > > I see. So when others do it, it is contemptible. When you do it, it is > > > justified. > > > > No, you don't see at all.. If you did, you would have detailed things a > > bit more and made at least some basic distinctions When most people I > > have come across on this usenet group do it, it is contemptible, yes. > > When I do it *back*, it is not praiseworthy and I am not proud of myself > > - but it is more justified. > > That's what I just said. No that is not at all what you just said. > Thanks for confirming it, you hypocritical > loon. Please call to have your medications adjusted. > Your puerile rote phrases and rude responses are noted. > > I expect high standards of decency when > > people talk to me, higher than you for example. And I am more violent > > than you towards them if they fail. That's me folks! If you don't accept > > this and do not want to be simply polite and stick to non personal > > topics, do not bother to talk to me. > > You reserve the right to abuse people even though you hate being > abused, and if people don't like it, they can just shut the hell up. > Again no, you just can't get it right can you? I reserve the right forcefully show contempt for your rudeness and ignorance. That is different to reserving a right to be rude when unprovoked. You are not very good at philosophy are you? You seem quite incapable of making basic distinctions and it is because of your blunt ignorance and low nature that you feel the need to burst out in foul accusations. You simply have no idea, confine yourself to talking with other foul mouthed mugs and nasties. You will find them at basketweavers over there ------> Now I am done with you, I pass you over to the good Patricia who can kick you in the balls when she has time to look at Google Groupers, you have forfeited the right to appear in my newsreader. Bye! -- dorayme
From: Marshall on 11 Jan 2010 21:45 On Jan 11, 3:05 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Jan 11, 8:53 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > On Jan 11, 6:47 am, PD <thedraperfam...(a)gmail.com> wrote: > > > On Jan 8, 6:19 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > > > > On Jan 8, 8:19 am, DanB <a...(a)some.net> wrote: > > > > > Marshall wrote: > > > > > > > Or again I ask: if math is just a game, then > > > > > > what basis is there for claiming anything > > > > > > like "correctness" for any particular mathematical > > > > > > statement? > > > > > > Axioms that are 'accepted' as truth. > > > > > That's supposed to be the basis? Just that noun > > > > phrase by itself? > > > > > And anyway, axioms themselves also come from > > > > somewhere. They are not just arbitrary creations > > > > of man. > > > > Why yes, yes, they are. > > > Your post almost demands the response "Oh no > > they are not." But that wouldn't be much use, > > would it? > > > Do you feel the same way about the natural numbers? > > Are they an arbitrary creation of man? > > > Do you have any argument you'd care to supply to > > justify your position? > > It's really a matter of definition more than anything, as far as I > know. I guess what you mean by that is, it depends on what the definition of "arbitrary creation of man" is? Please clarify. > The natural numbers are a concept, but I don't think they are an > axiom. On the other hand, there is a set of axioms (the Peano axioms) > that are used to rigorously define them. Notice that one of the Peano > axioms is precisely the one that ensures the *mathematical* sense of > induction will work at all. I wasn't suggesting that the natural numbers are an axiom; of course they are not. I was asking if you think the natural numbers are an arbitrary creation of man. It is harder to engage with your position when you don't clarify what it is. It has been proposed on this thread that math is just a game with no significance or utility, except by coincidence (this is bullshit.) It has been suggested that axioms are the source of truth in math, by fiat; Goedel's first incompleteness theorem proves this false. Here the question is whether axioms come from man or from nature. It seems to me that (relative to the axioms of the natural numbers at least) this question depends on whether the natural numbers themselves are man-made or not. If they are not, then the axioms that they obey are not, since the axioms derive from the numbers and the operations on them. > 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. I do not accept this dichotomy; it is much too impoverished to capture what is going on. > But if the latter, then there > is a serious problem with Riemannian geometry, which disbands the > validity of the fifth postulate. Since both of those systems seem to > have equally good applications not only in the mind but to real life, > it seems difficult to say that they are both objectively true. On the > other hand, if they are arbitrary creations of man, then it makes > sense how the geometries that stem from them both have value. Since I don't accept you dichotomy, I don't accept this argument; it depends on the earlier dichotomy. All that is to be gained from a discussion of Euclid's fifth is to observe that, if a consistent theory doesn't decide a formula one way or the other, then we may add that formula or its negation and get a new, consistent theory. This tells us nothing about where axioms come from. Marshall
From: Marshall on 11 Jan 2010 21:48 On Jan 11, 2:18 pm, John Stafford <n...(a)droffats.net> wrote: > In article <doraymeRidThis-F346EA.07284412012...(a)news.albasani.net>, > > dorayme <doraymeRidT...(a)optusnet.com.au> wrote: > > If you do not believe this, check the history of almost every thread I > > have been on. But, having experienced your weasel ways here, your > > unforthcomingness when the topic discussion gets pressing, you will not > > be able to see this even if you looked. You will skew all the stats and > > take unrepresentative cases for the main data, you will make very kind > > of simple scientific mistake. > > Likelihood of dorame == aldoraz is now 82%. What algorithms are you using? References, papers, etc? Marshall
From: Patricia Aldoraz on 11 Jan 2010 22:20
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. |