The Definition of Points
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From: David R Tribble on 17 Apr 2007 18:42 Tony Orlow writes: >> ala L'Hospital's theft from the Bernoullis, and >> the division by 0 proscription. > Alan Smaill wrote: > and Zick was the one who claimed that he would use l'Hospital to work > out the right answer for 0/0. such a japester, eh? Geez. How many posts before someone points out that it's l'Hôpital's rule? L'Hospital is where you take someone after they get punched in the nose by a mathematician after saying "l'Hospital's rule". http://en.wikipedia.org/wiki/L%27Hopital%27s_Rule p.s. Those who disparage Wikipedia's accuracy always have the option of improving the articles themsleves.
From: Lester Zick on 17 Apr 2007 18:43 On Tue, 17 Apr 2007 13:39:45 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> I wasn't commenting on whether your assumptions are consistent with >> your axioms, Tony. I was asking whether your assumptions were true. >So, then. it's not true that every statement is either true or false. >What about the statement that every statement is true or false? That's >false? Perhaps it's not possible to determine the root of truth in any >deductive manner, but that determining truth of statements is an >infinite regress called "science". Have you considered that notion? Naturally. I don't know what you think you're talking about but the answer is still 46. ~v~~
From: Lester Zick on 17 Apr 2007 18:47 On Tue, 17 Apr 2007 13:39:45 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> Sure. Happens all the time. However if you're asking whether a >> statement must be one or the other the answer is no. There are >> problematic exceptions to the so called excluded middle. >Please eloborate. "Black is crows" is ambiguous in general terms and neither true nor false since "crows are black". Hence we find that "crows are black" is true but "black is not crows" is true too in general scientific terms. ~v~~
From: Lester Zick on 17 Apr 2007 18:48 On Tue, 17 Apr 2007 13:39:45 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> Well your phrase "exploring the meaning of truth" is ambiguous, Tony, >> because what you're really doing is exploring consequences of truth or >> falsity given assumptions of truth or falsity to begin with, which is >> an almost completely trivial exercise in comparison with the actual >> determination of truth in mechanically exhaustive terms initially. >> > >I am exploring the mechanics of truth, and its pursuit, which you are >not, really, as far as I can tell. You're exploring the mechanics of using truth once established but I see no indication you're exploring the mechanics of truth otherwise. ~v~~
From: Lester Zick on 17 Apr 2007 18:58
On Tue, 17 Apr 2007 13:39:45 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >>> The question about axioms is whether each one is justifiable and >>> sufficiently general enough to be accepted as "true" in some universal >>> sense. >> >> No the actual question is whether each and every axiom is actually >> true and demonstrably so in mechanically exhaustive terms. Otherwise >> there's not much point to the exhaustively rigorous demonstration of >> theorems in terms of axioms demanded of students if axioms themselves >> are only assumed true. >> >> ~v~~ > >I am saying that one can assume axioms for the sake of deduction, but >that the conclusions derived are only as reliable as the starting >axioms, and so there is an inductive process in deciding which axioms to >accept for the sake of one's "theory", expecially when looking for >universal truths that serve as axions in a TOE, depending on whether the >conclusions drawn fit the empirical evidence. Lots of axioms and conclusions fit the empirical evidence, Tony. That's the whole problem in determining which are actually true and why. Given various experimental circumstances the question is how to explain them all in terms of one another. Modern mathematikers just assume they can explain them one way to the exclusion of other ways and indulge in special pleading and excuses to justify their choices. It might help if we could just start from true assumptions to begin with for a change. You want to start by making certain assumptions for the sake of an argument and then argue the truth of the assumptions according to the apparent plausibility of the argument. Doesn't work that way. ~v~~ |