Does inductive reasoning lead to knowledge?
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From: John Stafford on 31 Dec 2009 12:37 In article <hhian61d4f(a)news3.newsguy.com>, jmfbahciv <jmfbahciv(a)aol> wrote: > John Stafford wrote: > > Shouldn't we keep mathematic's proof by induction separate from > > inductive reasoning? > > It's the only thing I know which has been used to lead to knowledge. Knowledge of Natural Numbers, and what else? > >The subject is inductive reasoning which is not > > particularly rigorous except in special cases, IMHO. > > So you're saying that inductive reasoning is not the method > used in math. I don't see how the not-math type of thinking > could lead to any knowledge without some form of rigorous > method, especially in science. Inductive reasoning can occur in math, but in math the term 'inductive proof' is most common and entirely different that that used in philosophy which is 'inductive reason' (note - no claim of proof).
From: Marshall on 31 Dec 2009 12:42 On Dec 30, 10:07 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Dec 31, 10:53 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > On Dec 30, 1:02 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? > > > I gave you the specific relevant dictionary definition. > > How is it that you still don't know? > > Is your name PD? If so then explain what meaning does certainty have > prior to preceeding it with the adjective axiomatic and then explain > the meaning that certainty has by preceeding it with the adjective > axiomatic. You said the meaning of certainty changes, I am simply > asking from what to what. Yes you are, and the fact that you continue to do so despite your question having been answered repeatedly is remarkable. Normally when people have their questions answered, they don't keep asking them. My question is why you're not like that. I've asked it a few times, and you haven't answered. Putting these two facts together, I conclude that you are either perverse or remarkably stupid. Possibly both. Marshall
From: PD on 31 Dec 2009 13:50 On Dec 30, 6:53 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > 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? Certainty is a catch-all word that expresses both a continuous range and different flavors. I don't know of a definition of the word that would convey the meaning completely or distinctly, any more than one could do the same for "art" or "beauty".
From: M Purcell on 31 Dec 2009 15:55 On Dec 31, 12:04 pm, David Bernier <david...(a)videotron.ca> wrote: > jmfbahciv wrote: > > John Stafford wrote: > >> Shouldn't we keep mathematic's proof by induction separate from > >> inductive reasoning? > > > It's the only thing I know which has been used to lead to knowledge. > > >> The subject is inductive reasoning which is not particularly rigorous > >> except in special cases, IMHO. > > > So you're saying that inductive reasoning is not the method > > used in math. I don't see how the not-math type of thinking > > could lead to any knowledge without some form of rigorous > > method, especially in science. > > The statistician George Box is given as the originator of the saying: > All models are wrong, but some are useful. > > Perhaps model should be qualified by "statistical model". > > There is no Theory of Everything as of yet. So I'd suggest what > one arrives at in science is an approximation to perfect, certain > knowledge, but not the thing itself. Sometimes approximations are good enough and necessary to arrive at timely decisions. Even if our idealized mathematical models were accurate, the measurements used to verify them are imprecise. Science is practiced by imperfect human beings with limited prior knowledge and imagination. And the standard to which both are compared is a nature knowable by virtue of our limited senses, thus the Uncertainty Principle and an Universe expanding beyond our powers of observation. I believe our knowledge is based on comparisons with ourselves and fundamentally anthropomorphic.
From: dorayme on 31 Dec 2009 16:21
In article <hhian61d4f(a)news3.newsguy.com>, jmfbahciv <jmfbahciv(a)aol> wrote: > >The subject is inductive reasoning which is not > > particularly rigorous except in special cases, IMHO. > > So you're saying that inductive reasoning is not the method > used in math. He is not saying any such thing. If you had a single clue about philosophy, you would understand this. -- dorayme |