The Definition of Points
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From: Lester Zick on 24 Apr 2007 18:04 On Tue, 24 Apr 2007 09:27:05 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> And I believe it obvious that the one "mechanism" has to be the >> process of "alternation" itself or there is no way to produce anything >> other than our initial assumption. A chain is no stronger than its >> weakest link and if you make dualistic apriori assumptions neither of >> which is demonstrably true of the other in mechanically exhaustive >> terms you already have the weakest link right there at the foundation. >> > >Again, please comment on my use of "not" to define the relationship >between true() and false(). Okay that's an improvement. But one of the things I don't see is how you produce and "truth values" between 0 and 1 using not. ~v~~
From: Lester Zick on 24 Apr 2007 18:06 On Tue, 24 Apr 2007 09:27:05 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> Well this comment is pure philosophy, Tony, because we only have your >> word for it. You can certainly demonstrate the "truth" of "truth" by >> regression to alternatives to "truth" by the mechanism of alternation >> itself and I have no difficulty demonstrating the "truth" of "truth" >> by regression to a self contradictory "alternatives to alternatives". >> Of course this is only an argument not a postulate or principle but >> then anytime you analyze "truth" you only have recourse to arguments. >> > >If you're discussing logic, you have the additional recourse to the >mechanics of logic itself, the basics of which are well understood, if >not widely. What kind of logic do you have in mind? Boolean conjunctive logic, truth value logic or what? I don't see these as mechanical. ~v~~
From: Lester Zick on 24 Apr 2007 18:07 On Tue, 24 Apr 2007 09:27:05 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >>> Truth tables and logical statements involving variables are >>> just that. If I say, 3x+3=15, is that true? No, we say that IF that's >>> true, THEN we can deduce that x=4. >> >> But here you're just appealing to syllogistic inference and truisms >> because your statement is incomplete. You can't say what the "truth" >> of the statements is or isn't until x is specified. So you abate the >> issue until x is specified and denote the statement as problematic. > >Right. The truth of the statement 3x+3=15 cannot be determined without >specifying x. That's my point. But my point is that even with x you still haven't established the truth of the axioms on which such statements are based. ~v~~
From: Lester Zick on 24 Apr 2007 18:08 On Tue, 24 Apr 2007 09:27:05 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> The difficulty with syllogistic inference and the truism is Aristotle >> never got beyond it by being able to demonstrate what if anything >> conceptual was actually true. The best he could do was regress >> demonstrations of truth to perceptual foundations which most people >> considered true, even if they aren't absolutely true. But even based >> on that problematic assumption he could still never demonstrate the >> conceptual truth of anything beyond the perceptual level. > >Now you're the one lapsing into philosophy, so I'll oblige. Where am I lapsing into philosophy? Just because I mention Aristotle? >The only thing we can ever really know is that we exist, ala Descartes. >Beyond that, there is always the chance that our perceptions are >entirely false. However, one has to ask oneself why that would be. Where >would these illusions come from? I don't see any explanation for why a >seemingly consistent universe should not be considered to be just what >it seems. So, we have to start with the assumption, and that's just what >it is, that this is not all an illusion, despite the fact that our >perceptions may be flawed or limited. Having accepted that, we apply >scientific method, either formally or intuitively, to detect "truths", >and the only measure of a truth is whether it consistently predicts >measurable facts from other measurable facts. Where we detect a formula >which "works", we have detected a "truth" of some sort or another. Of >course, we may never truly understand the most fundamental nature of >what we observe, but we can still "know" something about it, in that sense. ~v~~
From: Lester Zick on 24 Apr 2007 18:11
On Tue, 24 Apr 2007 09:27:05 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> And here the matter has rested for mathematics and science in general >> ever since. Empiricism benefitted from perceptual appearances of truth >> in their experimental results but the moment empirics went beyond them >> to explain results in terms of one another they were hoist with the >> Aristotelian petard of being unable to demonstrate what was actually >> true and what not. The most mathematicians and scientists were able to >> say at the post perceptual conceptual level was that "If A then B then >> C . . ." etc. or "If our axiomatic assumptions of truth actually prove >> to be true then our theorems, inferences, and so forth are true". But >> there could never be any guarantee that in itself was true. >Well, if the axiom systems we develop produce the results we expect >mathematically, then we can be satisfied with them as starting >assumptions upon which to build. My issue with transfinite set theory is >that it produces a notion of infinite "size" which I find >unsatisfactory. I accept that bijection alone can define equivalence >classes of sets, but I do not accept that this is anything like an >infinite "number". So, that's why I question the axioms of set theory. >Of course, one cannot do "experiments" on infinite set sizes. In math, >one can only judge the results based on intuition. I was discussing Aristotelian syllogistic inference and truisms here, Tony. So I don't know why you're talking transfinite sets and so on. ~v~~ |