Does inductive reasoning lead to knowledge?
in [Logic]
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From: J. Clarke on 7 Jan 2010 21:15 dorayme wrote: > In article <hi61qt019be(a)news1.newsguy.com>, > "J. Clarke" <jclarke.usenet(a)cox.net> wrote: > >> dorayme wrote: >>> In article <hi5uar0lbu(a)news4.newsguy.com>, >>> "J. Clarke" <jclarke.usenet(a)cox.net> wrote: >>> >>>>>> >>>>>> Would you be kind enough to define the words "axiom" and >>>>>> "axiomatic" as you are using them? >>>>> >>>>> Well, I have not been party to any deep discussion about this and >>>>> have not much used them here. But I am happy to speak to your >>>>> question anyway. An axiom is a proposition in a system of >>>>> propositions that is accepted as true without needing to be proved >>>>> from within the system. Usually the word is used where the >>>>> propositions are not merely conditionally held to be true but are >>>>> simply self evident (or at least more obviously true than any >>>>> other thing that we can think of that it could itself be derived >>>>> from). >>>> >>>> I see. When you say that something is "axiomatic" do you mean that >>>> you are stating an axiom or do you mean that you are deducing >>>> something from axioms? >>> >>> I don't go around ever saying this - but if I did I would probably >>> mean it was self-evident or something to be assumed for now, it >>> would depend on the context. Care to supply one? >> >> Just wanted to know how you defined the terms. Seems that you've >> got it mostly right, however you need to remember that axioms are >> _always_ made up rules, in both math and physics. > > I cannot *remember* what is not true! And it is not true that axioms > in maths or logic or physics are always *made up of rules*. I didn't say they were made up _of_ rules, I said that they were rules that someone made up. >> In math, which is really a logic game, the >> axioms don't necessarily have any basis in the physical universe, > > It is an open question whether it is not *just* a logic game. There > are semantics. And it is not clear what "having a basis in the > physical universe" really means. No, it is not an open question. Mathematics is a game, an intellectual exercise, any relation that it bears to practical reality is purely coincidental. A common toast among mathematicians is "here's to pure mathematics, may it never be of any use to anybody". >> while in >> physics they are established by long observation and are subject to >> change if a confirmed observation to the contrary is encountered. > > Now you contradict yourself, one hardly looks to observations to > verify the truth of something made up of rules. In physics the rules were selected because they bear some relation to observation. The observation does not verify the rules, the rules are the result of the observation.
From: Marshall on 7 Jan 2010 22:00 On Jan 7, 6:15 pm, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > > >> In math, which is really a logic game, the > >> axioms don't necessarily have any basis in the physical universe, > > > It is an open question whether it is not *just* a logic game. There > > are semantics. And it is not clear what "having a basis in the > > physical universe" really means. > > No, it is not an open question. Mathematics is a game, an intellectual > exercise, any relation that it bears to practical reality is purely > coincidental. That's bullshit. Marshall
From: dorayme on 7 Jan 2010 22:34 In article <hi65bt0115f(a)news5.newsguy.com>, "J. Clarke" <jclarke.usenet(a)cox.net> wrote: > >> Just wanted to know how you defined the terms. Seems that you've > >> got it mostly right, however you need to remember that axioms are > >> _always_ made up rules, in both math and physics. > > > > I cannot *remember* what is not true! And it is not true that axioms > > in maths or logic or physics are always *made up of rules*. > > I didn't say they were made up _of_ rules, I said that they were rules that > someone made up. > On my newsreader your previous words are *still* "axioms are _always_ made up rules, in both math and physics". It makes little difference because if someone makes a rule, there are rules he makes. And I am denying that all the axioms of physics or maths are rules. A rule is an instruction of some kind, many axioms if not all, do not even look anything of the kind. > >> In math, which is really a logic game, the > >> axioms don't necessarily have any basis in the physical universe, > > > > It is an open question whether it is not *just* a logic game. There > > are semantics. And it is not clear what "having a basis in the > > physical universe" really means. > > No, it is not an open question. Mathematics is a game, an intellectual > exercise, any relation that it bears to practical reality is purely > coincidental. Hardly! A coincidence is something particularly unlikely. Mathematics is a human activity and its outputs are not highly unlikely relationships with 'practical reality'. > A common toast among mathematicians is "here's to pure > mathematics, may it never be of any use to anybody". > It is a nice toast and it is true that some of the best maths may not turn out to be of any use to anyone. That does not make some of your previous remarks correct. We must not let it go to our heads that some bit of maths just happens to become useful a few hundred years later. It is not *a coincidence* that if I take out 4 apples from a barrel and then another 4, that I will have taken out 8 or that if there had been 200 to start with, there will now be 192. It is not a mere coincidental relationship between these practical goings on and that 4 + 4 = 8 or 200 - 8 = 192. > >> while in > >> physics they are established by long observation and are subject to > >> change if a confirmed observation to the contrary is encountered. > > > > Now you contradict yourself, one hardly looks to observations to > > verify the truth of something made up of rules. > > In physics the rules were selected because they bear some relation to > observation. The observation does not verify the rules, the rules are the > result of the observation. Not in any sense of "relationship" or "the result of" that anyone around these parts is explaining or understanding. It is a big and open question in the philosophy of science. I don't mind chatting further about it. -- dorayme
From: Androcles on 7 Jan 2010 22:49 "Marshall" <marshall.spight(a)gmail.com> wrote in message news:02992afd-889d-4a84-a905-27b4860735b7(a)21g2000yqj.googlegroups.com... On Jan 7, 6:15 pm, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > > >> In math, which is really a logic game, the > >> axioms don't necessarily have any basis in the physical universe, > > > It is an open question whether it is not *just* a logic game. There > > are semantics. And it is not clear what "having a basis in the > > physical universe" really means. > > No, it is not an open question. Mathematics is a game, an intellectual > exercise, any relation that it bears to practical reality is purely > coincidental. That's bullshit. Marshall =================================== Agreed. "Mathematics is a game, an intellectual exercise" = TRUE. "any relation that it bears to practical reality is purely coincidental" = bullshit. TRUE AND bullshit = bullshit.
From: J. Clarke on 7 Jan 2010 23:55
dorayme wrote: > In article <hi65bt0115f(a)news5.newsguy.com>, > "J. Clarke" <jclarke.usenet(a)cox.net> wrote: > >>>> Just wanted to know how you defined the terms. Seems that you've >>>> got it mostly right, however you need to remember that axioms are >>>> _always_ made up rules, in both math and physics. >>> >>> I cannot *remember* what is not true! And it is not true that axioms >>> in maths or logic or physics are always *made up of rules*. >> >> I didn't say they were made up _of_ rules, I said that they were >> rules that someone made up. >> > > On my newsreader your previous words are *still* "axioms are _always_ > made up rules, in both math and physics". It makes little difference > because if someone makes a rule, there are rules he makes. And I am > denying that all the axioms of physics or maths are rules. A rule is > an instruction of some kind, many axioms if not all, do not even look > anything of the kind. > >>>> In math, which is really a logic game, the >>>> axioms don't necessarily have any basis in the physical universe, >>> >>> It is an open question whether it is not *just* a logic game. There >>> are semantics. And it is not clear what "having a basis in the >>> physical universe" really means. >> >> No, it is not an open question. Mathematics is a game, an >> intellectual exercise, any relation that it bears to practical >> reality is purely coincidental. > > Hardly! A coincidence is something particularly unlikely. Mathematics > is a human activity and its outputs are not highly unlikely > relationships with 'practical reality'. > >> A common toast among mathematicians is "here's to pure >> mathematics, may it never be of any use to anybody". >> > > It is a nice toast and it is true that some of the best maths may not > turn out to be of any use to anyone. That does not make some of your > previous remarks correct. We must not let it go to our heads that some > bit of maths just happens to become useful a few hundred years later. > It is not *a coincidence* that if I take out 4 apples from a barrel > and then another 4, that I will have taken out 8 or that if there had > been 200 to start with, there will now be 192. It is not a mere > coincidental relationship between these practical goings on and that > 4 + 4 = 8 or 200 - 8 = 192. > >>>> while in >>>> physics they are established by long observation and are subject to >>>> change if a confirmed observation to the contrary is encountered. >>> >>> Now you contradict yourself, one hardly looks to observations to >>> verify the truth of something made up of rules. >> >> In physics the rules were selected because they bear some relation to >> observation. The observation does not verify the rules, the rules >> are the result of the observation. > > Not in any sense of "relationship" or "the result of" that anyone > around these parts is explaining or understanding. It is a big and > open question in the philosophy of science. I don't mind chatting > further about it. You do some grad work in mathematics and physics and get back to us. As things stand you need more background than can be provided via USENET to get to where you understand the issues under discussion. |