The Definition of Points
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From: Lester Zick on 25 Apr 2007 13:31 On Wed, 25 Apr 2007 01:31:27 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Tue, 24 Apr 2007 19:08:46 -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: >>> >>>>> 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~~ >> >>If you already have truth values between 0 and 1, as in a probabilistic >>model, then not(x) is defined as 1-x, which is between 0 and 1 for x >>between 0 and 1. In that kind of system, not(x) is arithmetic. For >>uncorrelated x and y, and(x,y)=x*y, and or(x,y)=not(and(not(x),not(y))), >>or 1-(1-x)(1-y), or x+y-x*y. Where there is a correlation between x and >>y, it becomes hairier. I think that's what you're trying to address with >>your large and/or green apples? > >You're wasting your time. And you're wasting our time. So what? Hasn't stopped you so far. > Trust me. In God We Trust. All others pay cash. ~v~~
From: Lester Zick on 25 Apr 2007 14:03 On Tue, 24 Apr 2007 19:01:14 -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: >> >>>> We already know you think there are any number of points in the >>>> interval 0-1 so apriori declarations do not erase that inconsistency >>>> between different sets of assumptions. >>> I'm trying to keep it simple, and just discuss the mechanics of the most >>> basic kind of logic, where absolute "truth" exists. It doesn't, in real >>> science. >> >> I don't understand where you think absolute truth exists if not in >> real science. >> >> ~v~~ > >Absolute truth underlies the universe. Science only confirms a >theoretical truth to within some degree of accuracy, or disproves it. So this absolute truth thingie, Tony. Does it lie out there in space with the conjunctions you hypothecate and the dimensions Ben hypothecates? Can we conduct some experiments to demonstrate what you claim? Or are we forced to rely on your and Ben's philosophical tracts on these subjects instead? I'm inclined to the incontrovertible opinion personally there are three plus or minus 1/2pi dimensions, seven plus or minus 0.01 conjunctions, and two plus or minus e absolute truths but one can hardly ever tell for sure I suppose. Oh and don't forget the "is is" principle of Isis nee Parmenides. I'm sure we'll have to make room for it somewhere out there in space too. ~v~~
From: Lester Zick on 25 Apr 2007 14:27 On Tue, 24 Apr 2007 19:08:46 -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: >> >>>> 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~~ > >If you already have truth values between 0 and 1, as in a probabilistic >model, then not(x) is defined as 1-x, which is between 0 and 1 for x >between 0 and 1. In that kind of system, not(x) is arithmetic. For >uncorrelated x and y, and(x,y)=x*y, and or(x,y)=not(and(not(x),not(y))), >or 1-(1-x)(1-y), or x+y-x*y. Well, Tony, my problem comes with your apparent inference that 1=not 0 and 0=not 1. That can only be true in the context of TvN assumptions and mechanics where no intermediate values can exist and the physical constraints on bit representations in the system assure it. Otherwise you have no strict binary mechanics and representations both within and outside the limits 0-1 are possible. So either your mechanics is binary and non probabalistic or probabalistic and non binary. I don't see there is any other possibility. > Where there is a correlation between x and >y, it becomes hairier. I think that's what you're trying to address with >your large and/or green apples? Not really, Tony. I'm just trying to point out that the truth of combinatorial predicates is inherently problematic and not probablistic one way or the other. Let's suppose we ask whether the proposition "large green apples are large red apples" is true? The proposition itself is obviously false and on that basis should warrant a truth value of 0. But when we assign a truth value to a proposition the question is how do we do it? The fact is two of the predicates are true and one false. Does that mean t=0.000 or t=0.667? The same would apply to combinations of propositions. Are we supposed to be taking an arithmetic average or exercising some kind of intuitional insight? Not even to mention the weighting of predicates. I just can't imagine that all predicates have the same significance in terms of probablistic truth. Are we supposed to just adopt someones weighting opinions on the subject of truth? ~v~~
From: Lester Zick on 25 Apr 2007 14:45 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". 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. 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~~
From: Lester Zick on 25 Apr 2007 15:03
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. 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. 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~~ |