Does inductive reasoning lead to knowledge?
in [Logic]
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From: Zinnic on 30 Dec 2009 17:36 On Dec 30, 1:36 pm, John Stafford <n...(a)droffats.net> wrote: > In article > <e6657e15-0ffc-4904-a0c8-6c95f8f8b...(a)j19g2000yqk.googlegroups.com>, > > Zinnic <zeenr...(a)gate.net> wrote: > > On Dec 29, 6:00 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> > > wrote: > > [...] > > You have agreed in earlier posts that the longer a sequence of > > identical outcomes, then the stronger becomes your suspicion that > > there is an underlying causative factor for the repetition ( I am > > aware that the repetition is not itself causative). > > That is, as the repetition continues it is "reasonable" (your word in > > the above quote) for a mere suspicion to become an assumption and, > > eventually, a confident 'assertion' that the repetition will continue > > (despite the fact that certainty is not attained.) > > In an inductive argument, the observation of a consistent behavior can > be a premise. The premise need only be strong enough that _if they are > true_, then the conclusion is _likely_ to be true. This is quite unlike > deductive reasoning where a _valid argument and sound conclusion_ are > guaranteed to be true. I agree! But I note that you use observed "consistent behaviour " as a premise in what you label an "inductive argument". > > Explain how the quote from your post above is not simply your 'dance > > on the head of a pin' in a convulated attempt to eliminate induction > > as a reasonable means of assuming/asserting premisses used in a > > subsequent deduction. > > Uh oh. Did PA actually write that induction was could not lead to > deduction? No PA did not write that! ! I believe dorapatsy is claiming that the inherent uncertainty of induction entails that it lacks a 'reasonable form' of argument. IMO, the inductive argument--that consistent repetition of an outcome is caused by an underlying, possibly unknown, factor-- is not unreasonable. It is the basis for much of life's rationale, including deductions from premises derived by 'reasonable' inductive processes. I stand to be corrected, but since dorapatsy has no interest in discussing anything with me I expect no clarification from him. Just cop-outs and more of the abuse that I now welcome as a badge of honor. ;-) Regards Zinnic
From: PD on 30 Dec 2009 18:22 On Dec 30, 3:03 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Dec 31, 3:57 am, PD <thedraperfam...(a)gmail.com> wrote: > > > On Dec 30, 1:20 am, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > > > > On Dec 30, 11:31 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > > > > In the above-quoted sentence, "axiomatic" functions as > > > > an adjective. It changes the meaning of the following > > > > noun via the rules of English syntax. > > > > Shrug, how does the adjective axiomatic change the meaning of > > > certainty. > > > > MG > > > Observational evidence is distinguished from axiomatic statements, > > though both are taken to have some level of certainty. > > What do you mean by certainty in the above statement and how does it > change in meaning when preceeded by the adjective axiomatic? > > MG The certainty of any assumption I make is certainly different than the certainty of something I see with my own eyes. Don't you agree?
From: PD on 30 Dec 2009 18:25 On Dec 30, 3:02 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Dec 31, 3:55 am, PD <thedraperfam...(a)gmail.com> wrote: > > > Well, for one thing, "axiom" means something very specific. > > The question is, how does certainty change in meaning by being > preceeded with the adjective axiomatic? > > MG Well, let's take an example: Euclid's Fifth Postulate, where "postulate" and "axiom" are taken to be synonymous. This postulate says that given a line and a point not on the line, there is one and only one line through the point that is parallel to the first line. This cannot be derived from the other four postulates (despite many attempts by mathematicians to do so), and so must be assumed as any other postulate. It also seems intuitively certain. However, in Riemannian geometry, it ain't true!
From: Michael Gordge on 30 Dec 2009 19:53 On Dec 31, 8:22 am, PD <thedraperfam...(a)gmail.com> wrote: > On Dec 30, 3:03 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > > > > > > > On Dec 31, 3:57 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Dec 30, 1:20 am, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > > > > > On Dec 30, 11:31 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > > > > > In the above-quoted sentence, "axiomatic" functions as > > > > > an adjective. It changes the meaning of the following > > > > > noun via the rules of English syntax. > > > > > Shrug, how does the adjective axiomatic change the meaning of > > > > certainty. > > > > > MG > > > > Observational evidence is distinguished from axiomatic statements, > > > though both are taken to have some level of certainty. > > > What do you mean by certainty in the above statement and how does it > > change in meaning when preceeded by the adjective axiomatic? > > > MG > > The certainty of any assumption I make is certainly different than the > certainty of something I see with my own eyes. Don't you agree? I have no idea what you mean by certainty, the question remains - What do you mean by certainty and what meaning does it have, how does the meaning of certainty change when preceeded by the adjective axiomatic? MG
From: Michael Gordge on 30 Dec 2009 19:56
On Dec 31, 8:25 am, PD <thedraperfam...(a)gmail.com> wrote: > Well, let's take an example: Euclid's Fifth Postulate, where > "postulate" and "axiom" are taken to be synonymous. The question remains unanswered - What meaning does certainty have and how does it change when preceeded by the adjective axiomatic. MG |