The Definition of Points
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From: Ben newsam on 26 Apr 2007 18:53 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. >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. >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? >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.
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 |