The Definition of Points
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From: Lester Zick on 26 Apr 2007 19:12 On Thu, 26 Apr 2007 23:53:10 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Thu, 26 Apr 2007 12:39:35 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>On Thu, 26 Apr 2007 02:25:25 +0100, Ben newsam >><ben.newsam.remove.this(a)gmail.com> wrote: >>>What you fail to realise is that binary 1 and 0 are synonymous with >>>the terms "true" and "false". >> >>And what you fail to realize, Ben, is that you haven't proven this is >>true. It's merely an assumption on your part. If the terms "true" and >>"false" were truly synonymous with binary 1 and 0 in this sense why >>wouldn't the same apply to "figs" and "ideas" or any other pair of >>synonyms? > >If figs and ideas are mutually exlusive, and everything is either a >fig or an idea, then yes that would be fine. You think figs and ideas aren't mutually exclusive? I'd like to see one that is the other. >>There is no reason here to suggest any true synonomy between TvN >>binary 1 and 0 and "true" and "false" except a desire to systematize >>descriptions of "true" and "false" in binary mathematical terms but >>without extrapolating the truth of "true" and "false" in mechanically >>exhaustive terms to begin with. >> >>> Also synonymous would seem to be the >>>terms "mathematical" and your odd phrase "mechanically reduced >>>exhaustive universal". >> >>If we were merely assigning arbitrary aliases I would agree. The fact >>however is that what we're doing is trying to ascertain the truth of >>"true" and "false" in mechanical terms and not just assigning aliases. > >You are. I am not. To me, "1" and "0" are sufficient, and "true" and >"false" are adequate aliases for them. So apparently would be figs and ideas. >>Presuming we already understand TvN binary mathematical logic >>sufficiently, what's the purpose of assigning the aliases "true" and >>"false" to 1 and 0? Obviously it's to pretend real truth and falsehood >>share identical properties with mathematical binary 1 and 0 when in >>fact we know nothing of the kind until we can demonstrate they share >>identical properties. And the fact you call 1 and 0 by other names has >>no affect on the properties of 1 and 0 or on the properties associated >>with those other names. > >They are both mutually exclusive, and everything must be either one or >the other. If you think they are not synonymous, perhaps you could >point out how they are not? Or perhaps you could point out how they are synonymous? >>As for the phrase "mechanically reduced exhaustive universal terms" my >>purpose in using it was to illustrate my approach to the demonstration >>of the real or actual meanings of "true" and "false" whether or not we >>can draft any coincidence between those meanings and binary 1 and 0. What no response? Surely the mutually exclusive nature of 1 and 0 is no worse than the mutually exclusive nature of figs and ideas? Thus if we don't care a fig for your ideas your ideas are perforce false? ~v~~
From: Lester Zick on 26 Apr 2007 19:16 On Thu, 26 Apr 2007 16:14:35 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Tue, 24 Apr 2007 19:12:48 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> 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~~ >>> My empirical evidence gives me no reason to doubt that the system we're >>> referring to models all finite numbers quite well. I think the truth of >>> the axioms is measured by the truth of the facts it produces. You don't >>> really doubt that x must be 4, do you? >> >> What I doubt is that your "no reason to doubt" is not the same as the >> truth you claimed to have proven. I don't doubt that x can be 4 but I >> doubt that you've shown x is 4 or x must necessarily be 4 when all >> you've shown is that x can be 4 under certain assumptions of truth >> when you haven't demonstrated the truth of those assumptions of truth. > >x is a variable! It could be "banana", but that won't solve the >equation. Sheesh! Who cares whether it solves the equation if the equation does not determine the truth of x or 4? >> I wonder if you really understood what I was getting at with my essay >> on truisms and the nature of Aristotelian syllogistic inference? When >> we have problematic circumstances we can certainly say "If A then B". >> But that doesn't allow us to conclude "A" definitely is. And Aristotle >> had a great deal useful to say about the evaluation of truth given the >> facts of truth to begin with but he could never establish the fact of >> truth itself to begin with nor why and how facts of truth were true. > >You do that by testing the predictions of your deductions. If they don't >work, you got something wrong. And if they do work then you could still have something wrong. >> And when I say "truth" and "demonstrations of "truth" I'm talking >> about "truth" and not merely "truisms" such as "If A then B" whereas >> what you and the rest of mathematics insist on talking about are >> truisms such as "If axioms are true and our assumptions regarding >> logic are true then theorems are true" and "If boolean assumptions >> regarding truth and conjunctions and so forth are true then truth >> values etc. are true" and so on. >> >> ~v~~ > >And so on...... etcetera etcetera etcetera. ~v~~
From: Lester Zick on 26 Apr 2007 19:21 On Thu, 26 Apr 2007 16:12:00 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Tue, 24 Apr 2007 19:10:15 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> 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~~ >>> Well, machines can perform those operations just fine, so they seem >>> pretty mechanical to me. Are you trying to determine the mechanics of >>> induction rather than deduction? >> >> Except, Tony, your references to logic are all over the place. >> >> Where are these boolean conjunctions supposed to be? I've already >> shown there are no boolean conjunctions in strict mechanical terms and >> the only possible conjunction is "not" and compounding of "not". > >No, you didn't. Well that's good to know, Tony. My mistake. > You started with "not a not b", but interpreted as what >most people would call "not a or not b". Actually I started with "A B". > Then you compounded that with >not to get a and b. But, you started, really, with "or" implicit. Of course I did, Tony. Just as you started with true=1 and false=0. >You notice I like to write these operators as functions, and that's for >a reason. When you say "not(a) not(b)" those are two different truth >values WITHOUT a conjunction. A single truth value has one operator >outside parentheses. What you are actually talking about is >or(not(a),not(b)). And you're right, not(or(not(a),not(b))) is the same >as and(a,b). But it is not solely built upon not. not(x) can only take >one parameter, so you cannot form an expression of any more than one >parameter with not. You must have at least one of the non-trivial >two-place operators, most commonly or(x,y) or and(x,y) in discussion, >though NAND and NOR gates are used too. You started with an "or". > >If you disagree, then answer the question I asked forever ago about my >simple truth table. Just as you never answered the question I asked about my truth table. >> Then when you willy-nilly appeal to TvN binary logic you can't even >> show how you can accommodate both unambiguous truth values and >> probabalistic values in one scheme. > >Just did. Whatever you say is jake with me, Tony. >> I mean you can't have it both ways, Tony. Either your mechanics is TvN >> binary and non probablistic or probabalistic and non TvN binary. And >> just saying machines do it just fine doesn't mean you can have it both >> ways. >> >> ~v~~ > >One is a subset of the other. Duh. Just as you're a subset of both, Tony. ~v~~
From: Bob Kolker on 26 Apr 2007 21:13 Virgil wrote: > > How can we be sure that Zick isn't just an alter ego of Orlow? Have they ever been photographed or televised together? Bob Kolker
From: Ben newsam on 27 Apr 2007 04:11
On Thu, 26 Apr 2007 16:16:01 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: >Who cares whether it solves the equation if the equation does not >determine the truth of x or 4? It determines nothing, it *states* that two things are equal. In other words, it states that the two things being equal is "true". |