Does inductive reasoning lead to knowledge?
in [Logic]
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From: M Purcell on 7 Jan 2010 11:24 On Jan 7, 7:45 am, jmfbahciv <jmfbahciv(a)aol> wrote: > M Purcell wrote: > > On Jan 6, 5:24 am, jmfbahciv <jmfbahciv(a)aol> wrote: > >> M Purcell wrote: > >>> On Jan 5, 5:54 am, jmfbahciv <jmfbahciv(a)aol> wrote: > >>>> M Purcell wrote: > >>>>> On Jan 4, 6:27 am, jmfbahciv <jmfbahciv(a)aol> wrote: > >>>>>> M Purcell wrote: > >>>>>>> On Jan 3, 6:48 am, jmfbahciv <jmfbahciv(a)aol> wrote: > >>>>>>>> John Stafford wrote: > >>>>>>>> <snip --piggy-backing another post> > >>>>>>>> I got to the library and looked up that induction-reasoning > >>>>>>>> web site. I had planned to watch myself think while doing > >>>>>>>> the test. Didn't happen. I popped out the answer to each > >>>>>>>> without thinking. > >>>>>>> You believe thinking is a physical activity unnecessary for answering > >>>>>>> questions? > >>>>>> Are you really trying to be ignorant? > >>>>> Are you really trying to watch yourself think without success? > >>>> I am successful. I was paid very well to do this kind of thing. > >>> Paid by whom to do what kind of thing? > >> the company who hired me and to be able to watch how people > >> do things which included how they did their thinking when > >> solving their problems. Often, we hadn't shipped yet, so > >> I used myself as the guinea pig in anticipation of how > >> our customers would act and think. > > > And you assumed everybody thinks like you do? > > Of course not. I simply am very good at being able > to figure out how other people think. > > > > > > > > >>>>>>>> If you call the process for finding those solutions > >>>>>>>> inductive reasoning, then I have to conclude that > >>>>>>>> inductive reasoning is in the hardware. I would > >>>>>>>> not use the word reasoning at all for that kind > >>>>>>>> of brain processing. > >>>>>>> The generalization of this test to all inductive reasoning is > >>>>>>> inductive reasoning. Apparently you are still not thinking. > >>>>>> There is a huge difference between conscious thinking and > >>>>>> automated thinking. One plans your survival the other > >>>>>> ensures you survive to carry those plans. > >>>>> A difference between survival and survival? > >>>> In business, it's called short-term and long-term. You > >>>> appear to be limited to short-term only. > >>> How did you arrive at this conclusion? > >> Your inability to think long term is clear from the nonsense > >> you type. > > > What is your reasoning to support this conclusion? > > The way you don't understand what is written in this thread. What is written in this thread that I don't understand? > You don't appear to have any critical analysis techniques. Do you judge by appearances or just judge? > Your habit of ignoring reality is part of it; it's called > cognitive dissonance. Gotta ignore something, how do you define reality? This happens when a person has an > inability to think in long-term scenarios. So my misunderstanding, appearance, and disinterest indicate immediate concerns?
From: M Purcell on 7 Jan 2010 11:30 On Jan 7, 8:11 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: > On Jan 7, 7:43 am, Errol <vs.er...(a)gmail.com> wrote: > > > On Jan 7, 12:23 pm, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > > > Seeing that axiomatic means "self evident', an axiomatic certainty is > > one that you do not have to check up because you already know what the > > answer will be. > > To my mind, that's a pretty childish notion of "axiomatic". It's the > one I was taught in grade school. It's the one I was forced to > unlearn in order to understand formal systems in mathematics. > > In the context of physics it's still a bit childish. You don't stop > checking an conjecture because you _know_ what the answer will be. > You stop checking when it's more work to check it again than the > resulting increase (or decrease!) in certainty is likely to be worth. > > Arguably, that works out to just about the same thing. At some point > your confidence in a conjecture is so high that you simplify things by > treating it as if it were absolute fact. But... Next thing you know, > your instruments get better, somebody checks again and darned if your > certainty wasn't misplaced. > > Can you give an example of something "self evident". > > Is the parallel postulate "self-evident". > Is the axiom of choice "self-evident". > Is the negation of the axiom of choice "self-evident". > > Are any of these three things "true"? > > > I can say "Any 5 digit positive integer starting with 9 will always be > > greater than any 5 digit positive integer starting with 7." > > > That is an axiomatic certainty, because I do have to play around with > > my calculator to check whether it is true or not. I know it is true. > > I would call it a deductive certainty. "Theorem" for short. It can > be deduced (aka proven) in a formal system within which certain > simpler and more general things are taken as axiomatic. > > In order to even make the statement in question you're pulling in a > signicant bit of well understood mathematics. The phrase "5 digit > positive integer starting with 9" pulls in the notion of "integer". > And the term "greater than" pulls in the notion of an order and of a > default ordering relation for the integers. You're also apparently > implying and pulling in the notion of simple decimal notation and a > big-endian digit ordering convention. Well over half the work in > proving this "axiomatic certainty" would likely be involved in filling > in defaults and specifying an environment within which you can > formally phrase it so that it is amenable to proof. > > The standard mathematical notion of integer is often formalized using > systems which are equiconsistent with other systems within which > various of the underlying axioms are negated. In particular, if the > axiom of infinity is negated it follows that there no such set as "the > positive integers" from which to select your "5 digit positive > integers starting with 9" and your supposed "axiomatic certainty" is > ill-formed on its face. > > [That's overstating things a bit. I do regard your statement as being > both meaningful and "true". It's provable in ZF. And with some > slight rephrasing, it's provable in ZF even with the axiom of infinity > negated. Just because the set of all positive integers does not exist > as a set would not mean that there isn't a set of just the "5 digit > integers". Indeed ZF-I+~I is able to prove the existence of such such > a set] > > If your notion of axiomatic certainty includes "follows from the > axioms" then we're good. The above claim is an axiomatic certainty. > Not because it's obvious. Not because you know it to be true without > looking. But because it follows from the axioms. I'll accept that definition.
From: PD on 7 Jan 2010 11:38 On Jan 7, 2:17 am, Michael Gordge <mikegor...(a)xtra.co.nz> wrote: > On Jan 7, 2:43 am, PD <thedraperfam...(a)gmail.com> wrote: > > > Ah, so I see the problem. You *assert* that anything that is certain > > must be derived from sensory evidence. > > Nope, you are a liar, I said, "certainty (as against an axiom) > required the non-contradictory identification and integration of > evidence, of sensory evidence" And the distinction in meaning from what I said is what? > > > And that therefore "axiomatic > > certainty" is, by virtue of your assertion, a contradiction in terms. > > Nope by YOUR definition of axiom being something accepted without any > evidence. That IS the definition of axiom. > > > OK, let's take an example. Let's use Euclid's Fifth Postulate. Is that > > certain or not? > > What is the sensory evidence? Shrug, if its not matter then it doesn't > matter. OK, so are you saying that Euclid's Fifth Postulate is not a postulate? If that is so, then why do you suppose it is called his fifth postulate? Is this a case of someone pointing to a zebra and calling it a zebra and you saying, "But by MY definition, that isn't a zebra, it's an anteater"? > > MG
From: J. Clarke on 7 Jan 2010 12:20 jmfbahciv wrote: > J. Clarke wrote: >> jmfbahciv wrote: > > <snip> >> >> FWIW, I think that everyone interested in this topic might want to >> read some Hume and some Popper--they both had goes at the question >> of the validity and utility of inductive reasoning, and Popper I >> understand discusses it specifically in the context of the scentific >> method. I don't know their work beyond that so can't suggest any >> readings--they're on my list but there's a lot in front of them. >> > > Popper is on my list. I'm not so sure about Hume since I've noticed > that it's the name used in their name-dropping to cause me to worship > the ground they trod on. I'm still trying to understand politics; > it doesn't help that I've been allergic to the subject all my life > :-). > > These people don't name-drop Popper as often. Do you have any > idea why this happens? Not really. Maybe it's that Hume is more famous.
From: dorayme on 7 Jan 2010 14:42
In article <hi4v5i92i43(a)news5.newsguy.com>, jmfbahciv <jmfbahciv(a)aol> wrote: > Patricia Aldoraz wrote: > > On Jan 6, 9:38 am, John Stafford <n...(a)droffats.net> wrote: > > > >> Methinks PD is a mathematician in which axiomatic certainty can occur. > > > > Axioms do not reside in mathematicians, they reside in systems. > > Oh, good grief. You don't even have high school math in your > background. > You are becoming quite a specialist at cowardly one line responses to posts by me and others, is this to hide the great analytical skills you boasted about recently? Do you ever have really good reasons for your views? -- dorayme |