Does inductive reasoning lead to knowledge?
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From: chazwin on 9 Jan 2010 08:39 On Jan 9, 7:46 am, "Androcles" <Headmas...(a)Hogwarts.physics_r> wrote: > "Marshall" <marshall.spi...(a)gmail.com> wrote in message > > news:43e98d31-7748-4755-b5dc-e2389bbc4c0b(a)m26g2000yqb.googlegroups.com... > On Jan 8, 10:05 pm, DanB <a...(a)some.net> wrote: > > > Marshall wrote: > > > > Show me how choosing some axioms that are > > > 'accepted' as truth can make the right answer come > > > out three. Ideally you will also show how accepting > > > those axioms also makes case analysis come up with > > > the answer three. > > > Accepting an axiom determines results. > > I accepted no axioms, yet was able to determine the > answer "four" to my question of how many unary functions > are possible for a two-element algebra. This is > a simple counterexample to you assertion. > > Also note that G del's first incompleteness theorem proved > the existence of formulas that are true, yet do not > follow from any axioms. > > > Are you getting this? > > I'm getting that you completely failed my simple challenge > to show an arbitrary result following from some axioms, > nor did you apparently even understand it. I'm getting > that you have nothing to offer in the way of an argument > other than "look it up." > > Marshall > ============================================ > a = b (given) > a^2 = ab (multiply both sides by a) > a^2 - b^2 = ab-b^2 (subtract b^2 from both sides) > (a+b)(a-b) = b(a-b) (factorize) > a+b = b (divide both sides by a-b) > b+b = b (substitute b for a) > 2b = b (addition of b +b ) > 2 = 1 (divide by b) > Hence a = 2b since a = b. > 2b+b = b (substitute 2b for a) > 3 = 1 > > The axioms were followed, the result was arbitrary. > An arbitrary result followed from some axiom. > What we have is a well-known exception for which > the axiom of division fails. Interesting.
From: Androcles on 9 Jan 2010 09:35 "chazwin" <chazwyman(a)yahoo.com> wrote in message news:d5cb2f4d-c198-4316-92ba-ba4db19711dd(a)u7g2000yqm.googlegroups.com... On Jan 9, 3:53 am, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Jan 8, 9:27 pm, chazwin <chazwy...(a)yahoo.com> wrote: > > > Hume pointed out this problem in the early 18th C, but despite these > > difficulties the last 200 years+ has used inductive methods to design > > all the wonders of technology and we have reached to moon. > > If "inductive methods" merely means "whatever scientists do when they > do the non-deductive bits of their work" naturally it is true. But > what use is this. That is not any answer to the problem of induction. > > > Whilst we > > have to always be aware that our inductive knowledge is a question of > > probabilistic truth. > > Nor is this. The problem of induction is not a search for 100% > probability. It is a search for anything over 50%. Until this is > understood, it is impossible to understand what so troubled Hume and > modern versions of the problem Hume's own answer to the problem of induction was mitigated skepticism. Which means that although law-like statements built from induction are not 100% certain, if they work they it is possible to have a pragmatic belief in them until they are replaced by something more accurate or probable. Thus Newtonian physics woks in most cases. But Hume would have approved of the change in science offered by Einstein. ======================================= If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A. We don't need to assume Albert Einstein was a ranting lunatic, clearly his "definition" is absurd. http://www.androcles01.pwp.blueyonder.co.uk/Shapiro/Crapiro.htm Obviously it takes a different time for light to reach Mars from Earth than it does to return. If you are correct (which you are not) Hume would be an idiot.
From: Zinnic on 9 Jan 2010 09:47 On Jan 8, 9:53 pm, Patricia Aldoraz <patricia.aldo...(a)gmail.com> wrote: > On Jan 8, 9:27 pm, chazwin <chazwy...(a)yahoo.com> wrote: > > > Hume pointed out this problem in the early 18th C, but despite these > > difficulties the last 200 years+ has used inductive methods to design > > all the wonders of technology and we have reached to moon. > > If "inductive methods" merely means "whatever scientists do when they > do the non-deductive bits of their work" naturally it is true. But > what use is this. That is not any answer to the problem of induction. Wow! If B is merely not-A that is not any answer to the problem of B. See how the flounder flounders out of the water. (snicker). > > Whilst we > > have to always be aware that our inductive knowledge is a question of > > probabilistic truth. > > Nor is this. The problem of induction is not a search for 100% > probability. It is a search for anything over 50%. Until this is > understood, it is impossible to understand what so troubled Hume and > modern versions of the problem Anything over 50% except 100%? Perhaps 200%? Gee, if only more than 50% of your pronouncements were relevant they might give a clue as to what so troubles you and your mouthpiece!. You must swim deeper my little, flexuous, flopping, flat fish so that you can and lie on the bottom looking up adoringly from whatever side of your face focusses on your alter ego! . See what a sorry state you have brought us. Not a smidgen of insightful philosophy from the three of us (Dora-al-dora and me). Are we having fun yet? Zinnic p.s Justification for this post is to push the thread to the 1,000 mark. :-)
From: jmfbahciv on 9 Jan 2010 10:25 DanB wrote: > Marshall wrote: >> >> Or again I ask: if math is just a game, then >> what basis is there for claiming anything >> like "correctness" for any particular mathematical >> statement? > > Axioms that are 'accepted' as truth. No. Axioms lay a premise. then you can construct geometries and algebras based on that premise. You can do some amazing things just by tweaking one aspect of one premise in the math biz. When you see somebody talking about Lie algebras, you should immediately switch your viewpoint based on the axioms of that algebra. When somebody talks about a different algebra, your (if you knew any math) thinking would switch automatically to that algebra's premise. It's a shorthand form of communicating. /BAH
From: jmfbahciv on 9 Jan 2010 10:32
Michael Gordge wrote: > On Jan 9, 6:28 am, PD <thedraperfam...(a)gmail.com> wrote: >> And so is Euclid's Fifth Postulate a postulate or not? > > You have got my answer. > > MG Yup. We do know your answer--you don't know. /BAH |