The Definition of Points
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From: Lester Zick on 29 Mar 2007 20:01 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >> "Been there and done what" exactly, Tony? "Exhaustive analysis for >> truth" is not at all the same as "exhaustive demonstrations of truth". >> All "exhaustive analysis for truth" means or can mean is that you've >> looked the problem over and can find nothing amiss. It just doesn't >> matter whether the "you" is just yourself or a godzillion others when >> you don't have any demonstrable basis for truth to begin with. "You" >> can't very well analyze anything for truth when you don't know exactly >> what's true or may be true. All you can really do is guess.And that's >> exactly what seers, mystics, and empirics do because that's all they >> can do. >It helps if you at least define your terms. Hey I can define my terms six ways to Sunday. It just doesn't matter when definition is the subject of definition. Then you're forced to go back to basic operations where definition itself is defined.Doesn't do much good to try to define universal definition in particular terms. And if you try nonetheless all you wind up with are parochial meanings anybody can deny just by saying they don't like or agree with your definitions. I'd really like to see someone define something without differences. ~v~~
From: Lester Zick on 29 Mar 2007 20:04 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> If you're interested in the breakdown of binary logical operators, lemme >>> know... >> >> I have no special interest in things studied in college, Tony. They're >> well known and well demonstrated in their own terms and just not a >> substitute for truth in exhaustive mechanical terms. >> > >They didn't teach me this analysis of the logical operators in college, >just the mechanics. This particular analysis is independent and fairly >recent. Not sure I understand what you mean by the "analysis" as opposed to the "mechanics" of logical operators, Tony. Either way they're binary as far as I know and not what we deal with in the real external world. ~v~~
From: Lester Zick on 29 Mar 2007 22:26 On Thu, 29 Mar 2007 16:56:18 -0600, "nonsense(a)unsettled.com" <nonsense(a)unsettled.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >> >>>>Finite addition never produces infinites in magnitude any more than >>>>bisection produces infinitesimals in magnitude. It's the process which >>>>is infinite or infinitesimal and not the magnitude of results. Results >>>>of infinite addition or infinite bisection are always finite. >>>> >>>> >>>>> Wrong. >>>> >>>>Sure I'm wrong, Tony. Because you say so? >>>> >>> >>>Because the results you toe up to only hold in the finite case. >> >> >> So what's the non finite case? And don't tell me that the non finite >> case is infinite because that's redundant and just tells us you claim >> there is a non finite case, Tony, and not what it is. >> >> >>> You can >>>start with 0, or anything in the "finite" arena, the countable >>>neighborhood around 0, and if you add some infinite value a finite >>>number of times, or a finite value some infinite number of times, you're >>>going to get an infinite product. If your set is one of cumulative sets >>>of increments, like the naturals, then any infinite set is going to >>>count its way up to infinite values. >> >> >> Sure. If you have infinites to begin with you'll have infinites to >> talk about without having to talk about how the infinites you >> have to talk about got to be that way in the first place. > > >Confused about absolute infinity? :-) Someone is. ~v~~
From: Lester Zick on 29 Mar 2007 22:52 On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Your "not a not b" has an assumed OR in it. Tony, let me ask you something: without an AND or any other conjunction how would you mechanize the OR conjunction you claim I assume? And if it's just there as a basic circumstance of nature how do you get from there to other conjunctions and logic especially when you consider there's no necessity for conjoined components to be present together at the same time? ~v~~
From: Tony Orlow on 30 Mar 2007 12:39
Lester Zick wrote: > On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Hi Lester - >> >> Glad you responded. I was afraid I put you off. This thread seems to >> have petered unlike previous ones I've participated in with you. I hope >> that's not entirely discouraging, as I think you have a "point" in >> saying points don't have meaning without lines, and that the subsequent >> definition of lines as such-and-such a set of points is somewhat >> circular. Personally, I think you need to come to grips with the >> universal circularity, including on the level of logic. Points and lines >> can be defined with respect to each other, and not be mutually >> contradictory. But, maybe I speak too soon, lemme see... > > Hey, Tony - > > Yeah I guess I'm a glutton for punishment with these turkeys. The > trick is to get finite regressions instead of circular definitions. We > just can't say something like lines are the set of all points on lines > because that's logically ambiguous and doesn't define anything. I > don't mind if we don't know exactly what points are in exhaustive > terms just that we can't use them to define what defines them in the > intersection of lines and in the first place. > > The problem isn't mathematical it's logical. In mathematics we try to > ascertain truth in exhaustively demonstrable terms. That's what > distinguishes mathematics from physics and mathematicians from > mathematikers and empirics. > > (By the way, Tony, I'm chopping up these replies for easier access and > better responsiveness.) > > ~v~~ Sounds like a good idea. I've certainly taken my licks around here too, but that's a big part of this process - debate. You win some and lose some. Or rather, some lose and some win, when it comes to ideas. And some just spar forever before they finally realize they're actually dancing together, like waves and particles, in a fluid universe. When you say it's not necessary to know exactly what points "are", that's somewhat true. We don't even know what mass "is", but as in science, we define objects by their properties and the predictions we can make. So, if we can characterize the relationship between points and lines, then we can define them relative to each other, which may be the best we can do. But, that is not what you desire. You want a "ground zero" starting point upon which all else is built. This is akin to set theorists' e operator: "is an element of". They start with that one operator, then supposedly measure is built upon that. Well, they do the same thing you are doing when you assume an implied OR in "not a not b", and then derive OR from AND, which you define as not(not a not b). They introduce the von Neumann ordinals defined solely by set inclusion, and yet, surreptitiously introduce the notion of order by means of this set. Order, '<', is another operator and should be recognized as such. One should allow that there are always two first elements or operators, whose interplay produces the whole we're considering. That's the Tao. It's not wrong. There is no single perspective, and there is no straight line. It's all circles. :) Tony 01oo |