The Definition of Points
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From: Lester Zick on 21 Mar 2007 19:29 On 21 Mar 2007 12:37:39 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >And yet you remain incapable of stating what these "limitations" are. >Why is that? Could it be because you can't actually think of any? More likely that you can't actually think. ~v~~
From: Lester Zick on 21 Mar 2007 19:31 On Wed, 21 Mar 2007 20:07:17 +0000 (UTC), stephen(a)nomail.com wrote: >But you cannot identify any actual limitation with either the analytical >(set base) approach, or the more traditional approach. Well to SOAP operettas straight lines might be one limitation. ~v~~
From: Bob Kolker on 21 Mar 2007 20:43 Hero wrote: > > And Lester Zick also gave an answer. > So, Bob, when Thales determined the height of the pyramids by > measuring the shadow, at that time, when his own shadow equalled his > own length -was he using a true theorem or did his theorem only became > true, after Euclid derived it from his axioms? He was using a correctly proved theorem (which was proved nowhere near a physical pyramid) and he was -interpreting- the mathematical objects in terms of actual physical measurements. This is the difference between pure math and applied math. One distinguishes purely abstract mathematical reasoning which has no counterpart in the physical world from applied mathematics in which there is a correspondence between the abstract objects and relation and physical objects and measurables. This view of mathematics as empirical content free is a relatively modern view. In the beginning, mathematics was thought to be talking about the world. But Euclidean geometry can't be -true- in the factual sense since there are non-Euclidean. Euclidean geometry is readily -applied- to flat spaces with a straightforward pythagorean metric. Bob Kolker
From: Tony Orlow on 21 Mar 2007 23:21 Lester Zick wrote: > On Wed, 21 Mar 2007 00:06:40 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Mon, 19 Mar 2007 18:04:27 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>> No one says a set of points IS in fact the constitution of physical >>>>> object. >>>>> Whether it is rightly the constitution of a mentally formed object >>>>> (such as a geometric object), that seems to be an issue of arbitration >>>>> and convention, not of truth. Is the concept of "blue" a correct one? >>>>> >>>>> PD >>>>> >>>> The truth of the "convention" of considering higher geometric objects to >>>> be "sets" of points is ascertained by the conclusions one can draw from >>>> that consideration, which are rather limited. >>>> >>>> "blue" is not a statement with a truth value of any sort, without a >>>> context or parameter. blue(sky) may or may not be true. >>> I disagree here, Tony. "Blue" is a predicate and like any other >>> predicate or predicate combination it is either true or not true. >> No, Lester. I hate to put it this way, but here, you're wrong. > > No need for any regret, Tony. I certainly don't mind being called on > errors or even called on non errors when there's something you think > is wrong. But we shall just have to see what we shall see here, Tony. > Very good. :) >> "Blue" is >> a descriptor for an object, a physical object as perceived by a human, >> if "blue" is taken to mean the color. It's an attribute that some >> humanly visible object may or may not have. The "truth" of "blue" >> depends entirely on what it is attributed to. Blue(moon) is rarely true. >> Blue(sky) is often true in Arizona, and not so often around here. > > So "blue" is not a predicate, Tony, as in "it is blue"? And this > predicate cannot be true or false? > Right. It(blue) and blue(it) have truth values between 0 and 1 inclusive, but "blue" has no more truth value than "it". Truth is a matter of how much one idea applies to another, or perhaps something less vague than that. >> One can assign an attribute to an object as a function, like I just did. >> One can also use a function to include an object in a set which is >> described by an attribute, like sky(blue) or moon(blue) - "this object >> is a member of that set". The object alone also doesn't constitute an >> entire statement. "Sky" and "moon" do not have truth values. Blue(sky) >> might be true less than 50% of the time, and blue(moon) less than 1%, >> but "blue" and "sky" and "moon" are never true or false, because that >> sentence no verb. There is no "is" there, eh, what? :) > > Tony, I think you're confusing the supposed truth or falsity of a > single predicate with the supposed truth or falsity of an abstract > proposition. For that matter we can always make a proposition > out of a single predicate by saying "it is blue (or whatever)". > Without defining "it", there is no measure of the truth value of the statement, "it is blue". Likewise, if I say, "the moon is thus", one cannot ascertain the truth value of that statement without knowing which "thus" the moon is asserted to satisfy. >>> However the difference is that a single predicate such as "blue" >>> cannot be abstractly analyzed for truth in the context of other >>> predicates. For example we could not analyze "illogical" abstractly in >>> the context of "sky" unless we had both predicates together as in >>> "illogical sky". But that doesn't mean single isolated predicates are >>> not either true or false. >> But, it does. In order for there to be a statement with a logical truth >> value, > > I'm not sure what the significance of "truth value" is, Tony. I deal > with truth and finite tautological regressions to self contradictory > alternatives as the basis for truth and not merely the assignment and > evaluation of truth values whatever that may mean. > Truth assumes values between 0, commonly known as "false", and 1, or "true". In Boolean logic there are only these two values, but statistics allows for the full spectrum. So, a statement has a truth value, which can perhaps be evaluated, and which will always fall within these bounds, quantitatively. >> there must be buried within it a logical implication, "this >> implies that". The only implication for "blue" alone is that such a >> thing as "blue" exists. Does "florange" exist, by virtue of the fact >> that I just used the word? >> >> If "blue" and "fast" are predicates, is "blue fast" a predicate? Does >> that sound wrong? How about "chicken porch"? Is that true or false? > > Well all predicates and predicate combinations are what they are, > Tony. They are expressions of logical implication. And they can range from true to false to self contradictory. Self-contradictory = automatically false. I > don't see the problem with that whether we're considering things > literally or even metaphorically for that matter. It's all one system > of predicates and predicate combinations which are either true or > false in combinations. Some predicate combinations appear silly > because we already understand the combinations are false and self > contradictory. But that isn't to say the predicates themselves cannot > be true or false alone or in other combinations in given instances. I think you need to distinguish between predicates and attributes and objects. Predicates are assignments of attributes to objects, and only predicates have truth values, true, fals, or somewhere in between. > >> The fast chicken on the blue porch, don't you agree? I see no >> contradiction in that.... > > Nor do I. Nor do I see any problem in evaluating the truth or falsity > of "it is blue". No special mystery there that I can see. > > ~v~~ Only, just, what is it? :) 01oo
From: Tony Orlow on 21 Mar 2007 23:24
Lester Zick wrote: > On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowhere(a)nowhere.com> > wrote: > >> Tony Orlow wrote: >>> There is no correlation between length and number of points, because >>> there is no workable infinite or infinitesimal units. Allow oo points >>> per unit length, oo^2 per square unit area, etc, in line with the >>> calculus. Nuthin' big. Jes' give points a size. :) >> Points (taken individually or in countable bunches) have measure zero. > > They probably also have zero measure in uncountable bunches, Bob. At > least I never heard that division by zero was defined mathematically > even in modern math per say. > > ~v~~ Purrrrr....say! Division by zero is not undefinable. One just has to define zero as a unit, eh? Uncountable bunches certainly can attain nonzero measure. :) |