The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 4 Dec 2007 13:02 On Mon, 3 Dec 2007 09:11:41 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 2, 8:24 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Sun, 2 Dec 2007 16:16:36 -0800 (PST), Randy Poe >> >> <poespam-t...(a)yahoo.com> wrote: >> >> So if those people define a square to be a circle the definition is >> >> true? >> >> >If people define a "square" to be "a set of points in >> >a plane which is equidistant from a given point", >> >then for those people that is what will be meant by the >> >term "square". >> >> So if I define a circle to be "a set of points in a plane equidistant >> from any point" I haven't relied on geometric definitions for planes, >> lines, intersection and equidistance required to define points in the >> first place? > >Interesting strawman. I wonder why you substituted that >for what I wrote. Was it so you'd have something to >respond to? It would be so I'd have "someone" to respond to. You obviously have little respect for the words you use and less for the words I use so I have to put your words in context of what they actually imply so you'll at least have something intelligible to lip sync for a change. ~v~~
From: Lester Zick on 4 Dec 2007 18:18 On Tue, 4 Dec 2007 11:17:17 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 4, 12:55 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Mon, 3 Dec 2007 09:10:50 -0800 (PST), Randy Poe >> >> <poespam-t...(a)yahoo.com> wrote: >> >> >I'm not going to say something meaningless like "the definition >> >> >is true" since definitions are just shorthand, not things >> >> >which are true or false. >> >> >> So "squircles are square circles" is not a definition? >> >> >Why yes it is. You just told me that "squircles" is >> >a shorthand for "square circles". See how that works? >> >> Yes indeedy. "Squircles" is shorthand for the predicate combination >> "square circles". And you just admitted "squircles are square circles" >> is a definition. See how that works? > >Except for the assertion that "square circles" >is a predicate or a "predicate combination", sure. >See how that works? Except the assertion "square circles" is not a predicate combination. For if "square circles" is not a predicate combination then what is it? Obviously you don't see how that works. ~v~~
From: Wolf Kirchmeir on 5 Dec 2007 09:49 Shrew_D wrote: > On Tue, 04 Dec 2007 15:48:02 -0500, Wolf Kirchmeir > <ElLoboViejo(a)RuddyMoss.com> wrote: > >> Shrew_D wrote: >>> On Mon, 03 Dec 2007 20:33:19 -0500, Wolf Kirchmeir >>> <ElLoboViejo(a)RuddyMoss.com> wrote: [snip] >>>> Lester doesn't know what he means by "true", so it's not surprising he >>>> can't figure out what other people mean by it. Nor does he accept >>>> examples-of as ways of explaining what one means. Nevertheless, I will >>>> attempt such an explanation, for your edification, if not for his. >>>> >>>> Suppose I say, "A unicorn is a worm-like critter with a curly horn at >>>> the front end", he would ask whether that definition were true. As a >>>> definition, it's neither true nor false, actually. It's just a statement >>>> about what I mean by "unicorn." But if I were to construct propositions >>>> about unicorns, some of those might be true, and some might be false. It >>>> all depends on what axioms or assumptions about real critters are used >>>> to evaluate the truth/falsehood of such propositions. >>>> >>>> What Lester is incapable of grasping is that all mathematics is built on >>>> assumptions and definitions. In fact, mathematics could be characterised >>>> as the science of determining what assumptions and definitions make >>>> propositions true. There is more to it than that of course, but without >>>> assumptions and definitions, explicitly an unambiguously stated, it's >>>> impossible to determine whether a given mathematical statement is true. >>> Lester said "definitions are combinations of predicates". >> I no longer think that I can figure out what Lester means by this >> statement. His use of "predicate" is peculiar, to say the least. He >> seems to equate a grade-school grammatical notion of "predicate" with >> its logical meaning. > > I'm not sure I understand Lester's idea of predicate either. To my way > of thinking a predicate is just something predicated of something. On > the other hand I'm not sure I understand your own idea of a predicate > either. A predicate is part of a proposition. Back in the days when grammar and logic were considered the same subject of study, the term was invented to point to the part of the propositions that asserts something or other about the other part, which is called the subject. (Modern grammars use different terms, but "predicate" is still used in many primary /junior school grammars, and never in my experience properly explained.) However, fairly early on, a confusion arose, since the verb "be" is used to denote equivalence of terms. Consider A is B, or A = B. Grammatically, "is B" may be termed a predicate". Logically, it's not. See? (NB that most people with a grammar school education will argue that "is B" is a complement, and then they get into trouble when "is" is used as a synonym for "exists.") >>> Randy said >>> "definitions are just shorthand". Lester then asks if "definitions are >>> just shorthand, what are they shorthand for?". (Assuming I've got the >>> quotes right.) The obvious implication being the shorthand is short- >>> hand for "combinations of predicates". >> That would be Lester's assertion about definitions, but not necessarily >> Randy's. In my notional universe, a definition isn't shorthand, it's a >> class description 9see below.) A term is shorthand for a definition, though. > > But then what is a definition? A statement that a term stands for some description of a class/entity/etc. You've used them in math class: "Let a be...." >>> In fact this would seem to be born out by your own example of a >>> definition for unicorns with various predicates in combination. >> There are no predicates in my definition, merely descriptors. The "is" >> in my definition is an equivalence sign: it means you can replace >> "unicorn" with the definition wherever "unicorn" occurs. The descriptors >> can be used in predicates, such as "X has a horn at its front end." That >> may or may not be true about X - you'd have to take a look. > > But aren't horns predicated of unicorns in your definition? They seem > to be. No, the definition applies to the term "unicorn", _not_ to the entity /unicorn/. I didn't say "All unicorns are wormlike critters...", which would be a proposition. >>> I >>> agree shorthand can neither be true nor false because that's just a >>> matter of convention. But the predicates represented by the short- >>> hand might be when taken in combination. >>> >>> This in turn would lead to the proposition that if definitions are >>> combinations of predicates and propositions are combinations of >>> predicates and propositions can be evaluated for truth in terms of >>> those combinations of predicates, why couldn't definitions? >> Because a definition is not a proposition. It's just a expansion of a >> term. Definitions have the form "Let X stand for {a, b, c,...}", where X >> is the term, and {a,b,c,...} is the set of descriptors. Another way of >> putting is that a definition is a class description. But since a >> definition is not a proposition about the existence of the class, nor >> any of its members, it's neither true nor false. OTOH, if you assert "X >> exists", then within some system (or some model of some system) you will >> be able to prove that proposition to be true or false. > > But here there seems to be a subtle distinction between predicates and > "descriptors" which is somewhat elusive. Do you have an exact way to > decide which is which other than one occurs in definitions and the > other in propositions? I don't have trouble with the distinction. ;-) Look, any time you say "All X are....", or "Some X are...", you are stating a proposition, not a definition. Whenever you say "Let X be...", you are stating a definition, not a proposition. I said I was making a definition, so I didn't state it in explicit definition form, which would be: Let 'unicorn' stand for 'a green wormlike critter with a horn at its front end'. Does that make it clearer? If I had said "All unicorns are green wormlike critters a single horn at their fron ends", that would be a proposition. In a system which included my definition, that proposition would be true "by definition," as we say. In a system which did not include a definition of 'unicorn', it would be indeterminate. In a system which included a different definition of 'unicorn', it would be false. See? Keep in mind that a dictionary consists of definitions, not of existence propositions. That is, a dictionary merely tells you what people think they are talking about, not whether what they are talking about actually exists. Many people forget that, and insist that some word "really means" such and such. When they make that claim, they are confusing definitions with propositions. This is one of Lester's mistakes, actually - he thinks that what 'line' really means is whatever it was that he learned in grade school. >>> On the face of it I don't see anything wrong with this logic. I don't >>> know if it comprehends the entirety of mathematical and scientific >>> logic but it looks considerably more plausible than other approaches. >> IMO your error is assuming that Lester is using the same terminology as >> Randy. >> >> However, if a definition is a type of proposition, then your logic is >> valid. Since I deny that a definition is a proposition, I class your >> logic as valid but unsound. > > However I still don't understand the distinction you are drawing here. > Perhaps a definition is not a proposition. But what's the difference > between them? You suggest definitions entail descriptors rather than > predicates. But the words in one appear to be the same as the words in > the other. Or at least they can be. So I'm still at a loss as to how > you distinguish "descriptors" from "predicates". > >> Or so it seems to me. ;-) >> >> HTH Try this way of saying it: A predicate is a phrase in a proposition. It may or may not be identical with some phrase in a definition. It's a matter of syntax: the function of the phrase depends on the structure of the sentence. If the sentence states a proposition, then the phrase is a predicate. If it states a definition, then the phrase is a descriptor. The key is the verb: "be" in the sense of "=" indicates that you've got a definition. But having said all that, I know that others use the terms differently. It's unfortunate that there is no standard terminology for logic and grammar -- and the two subjects are closely intertwined. Logic may be understood as the study of which grammatical forms assert what kinds of propositions, and hence which grammatical forms can be used to construct logical arguments. I hope I've made my senses of these term clear enough. HTH
From: Shrew_D on 5 Dec 2007 13:20 On Wed, 05 Dec 2007 09:49:18 -0500, Wolf Kirchmeir <ElLoboViejo(a)RuddyMoss.com> wrote: >Shrew_D wrote: >> On Tue, 04 Dec 2007 15:48:02 -0500, Wolf Kirchmeir >> <ElLoboViejo(a)RuddyMoss.com> wrote: >> >>> Shrew_D wrote: >>>> On Mon, 03 Dec 2007 20:33:19 -0500, Wolf Kirchmeir >>>> <ElLoboViejo(a)RuddyMoss.com> wrote: [omitted] >>>> Randy said >>>> "definitions are just shorthand". Lester then asks if "definitions are >>>> just shorthand, what are they shorthand for?". (Assuming I've got the >>>> quotes right.) The obvious implication being the shorthand is short- >>>> hand for "combinations of predicates". >>> That would be Lester's assertion about definitions, but not necessarily >>> Randy's. In my notional universe, a definition isn't shorthand, it's a >>> class description 9see below.) A term is shorthand for a definition, though. >> >> But then what is a definition? > >A statement that a term stands for some description of a >class/entity/etc. You've used them in math class: "Let a be...." Except I meant in reference to propositions and how they differ other than pro forma conventions. >>>> In fact this would seem to be born out by your own example of a >>>> definition for unicorns with various predicates in combination. >>> There are no predicates in my definition, merely descriptors. The "is" >>> in my definition is an equivalence sign: it means you can replace >>> "unicorn" with the definition wherever "unicorn" occurs. The descriptors >>> can be used in predicates, such as "X has a horn at its front end." That >>> may or may not be true about X - you'd have to take a look. >> >> But aren't horns predicated of unicorns in your definition? They seem >> to be. > >No, the definition applies to the term "unicorn", _not_ to the entity >/unicorn/. I didn't say "All unicorns are wormlike critters...", which >would be a proposition. Are you saying "unicorns are wormlike critters" is not a proposition? If so I would strenuously disagree. >>>> I >>>> agree shorthand can neither be true nor false because that's just a >>>> matter of convention. But the predicates represented by the short- >>>> hand might be when taken in combination. >>>> >>>> This in turn would lead to the proposition that if definitions are >>>> combinations of predicates and propositions are combinations of >>>> predicates and propositions can be evaluated for truth in terms of >>>> those combinations of predicates, why couldn't definitions? >>> Because a definition is not a proposition. It's just a expansion of a >>> term. Definitions have the form "Let X stand for {a, b, c,...}", where X >>> is the term, and {a,b,c,...} is the set of descriptors. Another way of >>> putting is that a definition is a class description. But since a >>> definition is not a proposition about the existence of the class, nor >>> any of its members, it's neither true nor false. OTOH, if you assert "X >>> exists", then within some system (or some model of some system) you will >>> be able to prove that proposition to be true or false. >> >> But here there seems to be a subtle distinction between predicates and >> "descriptors" which is somewhat elusive. Do you have an exact way to >> decide which is which other than one occurs in definitions and the >> other in propositions? > >I don't have trouble with the distinction. ;-) Look, any time you say >"All X are....", or "Some X are...", you are stating a proposition, not >a definition. Whenever you say "Let X be...", you are stating a >definition, not a proposition. > >I said I was making a definition, so I didn't state it in explicit >definition form, which would be: Let 'unicorn' stand for 'a green >wormlike critter with a horn at its front end'. Does that make it clearer? > >If I had said "All unicorns are green wormlike critters a single horn at >their fron ends", that would be a proposition. In a system which >included my definition, that proposition would be true "by definition," >as we say. In a system which did not include a definition of 'unicorn', >it would be indeterminate. In a system which included a different >definition of 'unicorn', it would be false. See? > >Keep in mind that a dictionary consists of definitions, not of existence >propositions. That is, a dictionary merely tells you what people think >they are talking about, not whether what they are talking about actually >exists. Many people forget that, and insist that some word "really >means" such and such. When they make that claim, they are confusing >definitions with propositions. This is one of Lester's mistakes, >actually - he thinks that what 'line' really means is whatever it was >that he learned in grade school. I think there might be a definitive way to settle the issue. Consider the following: Are there any words or word combinations used as "descriptors" in definitions which cannot be used as predicates in propositions and conversely are there any words or word combinations which can be used as predicates in propositions which cannot be used as descriptors in definitions? If not then I see no viable distinction between the terms whether we call them descriptors or predicates and I see no reason both cannot be evaluated for truth, whatever that means. Frankly I can't think of any examples of words and word combinations which aren't applicable to both definitions and propositions (other than pro forma conventions). Nor does your definition for unicorns show evidence of any. So it looks to me like definitions are really mini propositions in the respect both definitions and propositions use the same vocabulary. And if there were categorical differences in vocabulary we'd have to have two different vocabularies with one vocabulary for definitions and one for propositions. However I think my original point regarding Randy's use of "short- hand" still stands because clearly the "shorthand" in a definition has to be "shorthand" for something and I think Lester is correct on this issue.
From: Lester Zick on 5 Dec 2007 13:30
On Tue, 4 Dec 2007 16:47:35 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >> >Except for the assertion that "square circles" >> >is a predicate or a "predicate combination", sure. >> >See how that works? >> >> Except the assertion "square circles" is not a predicate combination. > >Exactly. Exactly except you have no concept of irony whatsoever. ~v~~ |