Does inductive reasoning lead to knowledge?
in [Logic]
|
From: Zinnic on 18 Dec 2009 09:07 On Dec 17, 3:38 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Dec 18, 1:49 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. > > Have you added something important that I missed? Perhaps you are > quibbling about the different possible interpretations of "This is > probably such and such" and "This such and such is more likely than > not" > > > >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. > > First, it is simply not true. There is a little variation on a fallacy > called the Gambler's which goes: I won on the first pull of the pokie, > I won on the second... therefore... this *form* of induction does not > make things more likely in any sense at all.- Hide quoted text - > > - Show quoted text - It is common knowledge that the history of coin flips does not effect the outcome of a subsequent flip. But be honest. Would you not bet on the likelyhood of a continuation of the series if the previous 1,000 flips have had the same outcome? That is, would you not use induction to conclude that the coin is not fair?
From: Patricia Aldoraz on 18 Dec 2009 18:05 On Dec 18, 1:26 pm, M Purcell <sacsca...(a)aol.com> wrote: > 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. Here is an argument that could be described as a good probabilistic one: There are 100 balls in this bag There are 50 red ones _______________________________ The chance of any one being red is 50% But it is arguably one in which the conclusion cannot easily (from a conceptual point of view) be denied after accepting the premises. The premises seem to entail the conclusion. There is a relationship of necessity between the premises and the conclusion. But if you say This frog leaps. This other frog leaps. ..... __________________ Probably all frogs leap Then this is quite different, it does not follow, even by putting in the word probably. It is simply not any more probable than not, no matter how many frogs are examined. To suppose otherwise is to commit what dorayme calls a Reverse Gambler's Fallacy.
From: Patricia Aldoraz on 18 Dec 2009 18:12 On Dec 19, 12:49 am, Zinnic <zeenr...(a)gate.net> wrote: > 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. > If you had merely said that you would bet on the coin coming up tails again if it had always come up tails on countless occasions in the past, then no one would dispute your reasonableness. But you go on to say you use induction as if this is some sort of technique. And it is here where the real disagreements start. Induction is either not an argument form, or if it is, it is a manifestly inadequate one.
From: M Purcell on 18 Dec 2009 18:43 On Dec 18, 3:05 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Dec 18, 1:26 pm, M Purcell <sacsca...(a)aol.com> wrote: > > 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. > > Here is an argument that could be described as a good probabilistic > one: > There are 100 balls in this bag > There are 50 red ones > _______________________________ > The chance of any one being red is 50% > > But it is arguably one in which the conclusion cannot easily > (from a conceptual point of view) be denied after accepting > the premises. The premises seem to entail the conclusion. > There is a relationship of necessity between the premises > and the conclusion. That is mathematical induction. > But if you say > > This frog leaps. > This other frog leaps. > .... > __________________ > Probably all frogs leap > > Then this is quite different, it does not follow, even by putting in > the word probably. > It is simply not any more probable than not, no matter how many frogs > are examined. > To suppose otherwise is to commit what dorayme calls a Reverse > Gambler's Fallacy. Both the Gambler's Fallacy and it's reverse are post hoc fallacies. The validity of an inductive argument relies on the characteristic being generalized as well as the number of observations, a disproof of an inductive argument does not disprove all inductive arguments.
From: Rod Speed on 18 Dec 2009 19:33
Zinnic wrote: > On Dec 17, 3:38 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> > wrote: >> On Dec 18, 1:49 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. >> >> Have you added something important that I missed? Perhaps you are >> quibbling about the different possible interpretations of "This is >> probably such and such" and "This such and such is more likely than >> not" >> >>>> 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. >> >> First, it is simply not true. There is a little variation on a >> fallacy called the Gambler's which goes: I won on the first pull of >> the pokie, I won on the second... therefore... this *form* of >> induction does not make things more likely in any sense at all.- >> Hide quoted text - >> >> - Show quoted text - > > > It is common knowledge that the history of coin flips does not effect > the outcome of a subsequent flip. But be honest. Would you not bet on > the likelyhood of a continuation of the series if the previous 1,000 > flips have had the same outcome? That is, would you not use induction > to conclude that the coin is not fair? Nope, because I realise that the result of a particular coin toss is completely independant of what has happened before. |