Does inductive reasoning lead to knowledge?
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From: M Purcell on 17 Dec 2009 21:26 On Dec 17, 3:53 pm, dorayme <doraymeRidT...(a)optusnet.com.au> wrote: > > The idea of a logic is that it involves some degree at least of > necessity, of force. Fuzzy logic or probability logic is not obviously > helpful to supply this logical force (though it may well be a productive > line of enquiry). Perhaps somewhat promising is some idea of multi > valued truth where nothing is necessarily true or false. This may start > to capture some sort of logic of what we consider our reasonable > practices. But I very much doub if out of all this will come out some > clear and useful idea of an inductive form of argument. The word seems > often to simply conjure up anything that is "not deductive but good" or > "the way science operates". Pretty vague stuff, I think you will agree! Inductive reasoning is probabilistic and pragmatic and I suspect it is instinctive as well. But it also seems useful in providing testable relationships the result of which may provide better deductive premises.
From: spudnik on 17 Dec 2009 21:33 as I understood it, fuzzy ogic is not a lot more than the application of probability to logic; when I stated that it "thus" could be used as a formalism for quantum mechanics, to a grad-student of Bart Kosko, the popularizer of FL, it seemed to be only a matter of a half of a year, before Kosko got a new book out to do that. (of course, Zadeh may have created FL, playing with Schroedinger's undead cat .-) as for inductive versus deductive reasoning, I only state, again & again, that *mathematically* they are "one-to-one" or isomorphic, as proven in a short, easy proof in *Mathematics Magazine*, many years ago. > Multi-valued truth is nonproductive in any particular case. thus: it'd be very difficult to prove that Universe is not infinite, because any telescope is limited in resolution etc.; likewise, much "missing matter" is a) the result of Einsteinmania (only using gravity), and b) not properly sensed (infrared sensing is required to reveal most optical data past "Z=1" -- which is, now, beginning to be done -- and so on). thus: dood, see my sig -- new translations into English of l'OEuvre. > Dude, ever hear of Fermat's principle? thus: why do "pass/nofail" philosophers of science bother with such a silly notion as Minkowski's phase-space of "time & space forevermore on an equal footing, sic/um, because you can draw a graph with time as one axis?" thus: what, standard construction?... if you do as with the trigon, cutting the edges parallel to the facets, you get tetrahedra & octahedra .... as is wellknown to every student of Bucky Fuller (which could just be me .-) >http://emis.impa.br/EMIS/journals/BAG/vol.41/no.2/b41h2her.pdf thus: was you champion of a name-dropping proof, or have you looked at his avowedly nonstandard approach? I can't even vouch for Smullyan's popular books, althoughI did develop an alternative to his method in the Sherlock Holmes one, re chess. --l'OEuvre! http://wlym.com http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon.pdf
From: Les Cargill on 18 Dec 2009 01:13 dorayme wrote: > In article <hgem2f$toi$1(a)news.eternal-september.org>, > Les Cargill <lcargill99(a)comcast.net> wrote: > >> dorayme wrote: >>> In article <daniel_t-EABA81.20233714122009(a)earthlink.us.supernews.com>, >> <snip> >>> But arguments in logic or mathematics do not seem to me to have >>> inductive elements. >> http://en.wikipedia.org/wiki/Mathematical_induction >> >> <snip> >> >> -- >> Les Cargill > > > Crucial from that URL is: > > "Mathematical induction should not be misconstrued as a form of > inductive reasoning, which is considered non-rigorous in mathematics > (see Problem of induction for more information). In fact, mathematical > induction is a form of deductive reasoning and can be quite rigorous." > The PMI works, and inductive logic doesn't*. So of course they are disparate. If you could, however map all swans to the natural numbers, and prove that swan(n).isWhite ==> swan(n+1).isWhite, then there ya go. *completely. <snip> -- Les Cargill
From: jmfbahciv on 18 Dec 2009 08:23 jbriggs444 wrote: <snip> Thread drift alert! > Don't get me wrong. You could be right. Finagle could be in charge I thought it was Murphy who was in charge. I never made anti-Finagle incantations. <snip> /BAH
From: Zinnic on 18 Dec 2009 08:49
On Dec 17, 11:12 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: > On Dec 17, 9:49 am, Zinnic <zeenr...(a)gate.net> wrote: > > > > > > > On Dec 17, 3:27 am, Patricia Aldoraz <patricia.aldo...(a)gmail.com> > > wrote: > > > > On Dec 17, 5:19 pm, Zinnic <zeenr...(a)gate.net> wrote: > > > > > On Dec 17, 12:12 am, dorayme <doraymeRidT...(a)optusnet.com.au> wrote:> In article <hgbr3n$vn...(a)news.eternal-september.org>, > > > > > . But as far as I can see there is no > > > > > > logical form of induction that makes any conclusion more likely than > > > > > not. > > > > > But as far as I can see there is no form of induction that is other > > > > than "more likely than not ". > > > > Please inform my naivette. > > > > Yes, sure, one can enumerate past instances of something and couch the > > > conclusion in cautious terms. This X was red, this Y was red..., > > > therefore This Z will probably be red. > > > That is an induction that Z is more likely than not to be red. > > > >But this would not change the problem of trying to justify that it is *logical* process. Anyone can > > > say the latter train of thoughts, the question is what makes it a > > > logical process rather than a description of how people behave. > > > To act on the above induction makes success more likely than not. > > That is pragmatic not logical. > > What makes you claim that "to act on the above induction makes success > more likely than not" if you also claim that there is no logical basis > for acting in such a manner. If a fair coin is flipped, logic cannot demonstrate that it will end up as tails even though if it has ended up as tails in the previous 200 flips. However, in this case I would bet on tails on the basis that the coin may not be fair. That is I would be use induction to make a pragmatic rather than a logical choice. > Don't get me wrong. You could be right. Finagle could be in charge > of everything and the minute you think you've figured out the rules, > he could decide to change them. Induction could turn out to be the > exact wrong thing to rely on. But what's your alternative? Reach > into the hot stove for the pot of gold that wasn't there last time > precisely because it wasn't there last time? That doesn't sound very > smart When one relies on induction, one is not betting against the odds :-) |