The Virgin Birth of Points
in [Physics]
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From: Shrew_D on 6 Dec 2007 11:52 On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir <ElLoboViejo(a)RuddyMoss.com> wrote: >> 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. > >Since I cannot figure out what Lester means by "predicates" etc, I can >neither agree nor disagree. You can't agree that "shorthand" means "shorthand for something"?
From: Schlock on 6 Dec 2007 12:19 On Wed, 5 Dec 2007 21:26:44 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 6, 12:03 am, Schlock <schl...(a)truthless.net> wrote: >> On Wed, 5 Dec 2007 10:44:18 -0800 (PST), Randy Poe >> >> >> >> <poespam-t...(a)yahoo.com> wrote: >> >On Dec 5, 1:35 pm, Schlock <schl...(a)truthless.net> wrote: >> >> On Tue, 4 Dec 2007 16:47:35 -0800 (PST), Randy Poe >> >> >> <poespam-t...(a)yahoo.com> wrote: >> >> >> For if "square circles" is not a predicate combination then what is >> >> >> it? >> >> >> >A noun phrase. >> >> >> It's also thirteen letters of the alphabet. Hardly definitive for one >> >> so schooled in the black arts of dialectical evasion as yourself. >> >> >Perhaps you would have gotten more information >> >relevant to your query had you included the >> >rest of the paragraph, the part that said >> >"one third of a predicate". >> >> >And therefore not a predicate. >> >> I didn't realize predicates came in fractions. Is that anything like >> "a little bit pregnant"? > >No, it's like writing a fragment of Anything like "a definition is shorthand for"?
From: Wolf Kirchmeir on 6 Dec 2007 13:46 Shrew_D wrote: > On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir > <ElLoboViejo(a)RuddyMoss.com> wrote: > >>> 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. >> Since I cannot figure out what Lester means by "predicates" etc, I can >> neither agree nor disagree. > > You can't agree that "shorthand" means "shorthand for something"? Well, of course. The term defined is shorthand for the description. I thunk that was obvious. But that doesn't explain what Lester means by "predicates." For example, he seems to think "not" is a predicate, hence his famous "regression to self contradiction", which he then contradicts to create a tautology that he claims is "universally true." See? I thought not. ;-)
From: Shrew_D on 6 Dec 2007 13:52 On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir <ElLoboViejo(a)RuddyMoss.com> wrote: >Shrew_D wrote: >> 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: >[...] >>>> 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. > >Those pro forma conventions are the essence of the issue. Not if we're evaluating the significance of words used in definitions versus the words used in propositions. That's all I'm concerned with in the present context. >>>>>> 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. > >Sorry, you haven't understood my point. You seem to think I'm making >some sort of claim about unicorns and their features. I'm not. I'm just >equating a term with a string of other terms, is all. If I say that >'unicorn' is defined "a green wormlike critter...", then that's a >definition of the word 'unicorn', not a proposition about an animal, >real or imaginary. If I build a system using 'unicorn' and other terms, >by means of axioms and definitions, then I could _interpret_ the term >'unicorn' as referring to an animal. Or to a bus. Or the snowpile at the >end of my driveway. Or whatever. > >You see, a term is just that. If you like, replace 'unicorn' by T, and >the terms in its definition by X{g,w,h}. Then my definition becomes T = >X{g,w,h}. Which you may read as "T refers to a member of a class X >characterised by w, c and h". (And that reading assumes some conventions >about notation, BTW, which may or may not be th usual conventions.) Then I strenuously disagree. "Unicorns are wormlike creatures" is as much a proposition as any other combination of words or predicates and can be evaluated for truth just like any other proposition. >[...] >> I think there might be a definitive way to settle the issue. Consider >> the following: > >There is no issue, really. I've just told you what I mean by >'definition' and indirectly what I mean by 'proposition' and 'predicate' >You're looking for some real or correct meanings of these terms. There >aren't any. There are just meanings that we may or may not agree on, by >convention. There are certainly conventions and those conventions can flout truth as a concept. You just told me what you, and perhaps others, mean by "definition". But that doesn't mean your "definition of definition" is correct. People are free to use false definitions just as they are free to use false propositions. And apart from evaluating the words in each in relation to one another I can think of no way to determine the truth of either. >> 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. > >Let's assume you mean the usual grammatical sense for 'predicate'. Then >the answer is, no, the terms on _either_ side of a definition can be >used in propositions. So why is a definition important? Because it >enables us to distinguish between true and false propositions. I didn't say it couldn't, only that the truth of either could be evaluated in comparable terms because the words employed are the same whether you call them descriptors or predicates. >If a definition is true or false, in what sense is that so? In the sense as to whether the words in the combinations of words in the definition contradict one another. > For it to be >true/false, we must interpret a definition as a proposition. Or manifestations of a common form according to which the words in the combinations of words in either contradict one another. > There are >in my view two interpretations of a definition that will answer the case: > >a) the definition is shorthand for "When people use T, then (in some >context) they mean X{a,b,c...}." This is the form of a dictionary >definition, and it's easy to determine whether a definition is true in >this sense - which is why I deliberately made up an unconventional >definition of 'unicorn.' > >b) the definition asserts the existence of the referent of T. IOW, my >definition would not only define 'unicorn', it would also say something >about unicorns. That can only be so if the definition implicitly asserts >the existence of unicorns. But how can we decide of the definition is >true in this sense? > >Let's hunt for unicorns. You find something that you thinmk is one. You >yell, "Hey, Wolf, this 'ere thing 'ere wot I'm lookin' at has a horn at >its front end." I say, "Thass nice, is it green??" You say, "Yes >indeedy, and it's of a wormlike shape and configgerashun, too!" And I >say, "Is it really? Shrew, my friend, you've found a unicorn!" "Yass, >that I 'as", you say, and receive the congratulations of the assembled >multitudes. Does this event make the definition true? > >Before you answer with an eager Yes, consider this alternative case. >We've hunted high and low, and flushed every critter in our little >corner of the universe, and we have found not a single example of a >green, wormlike one a horn at front end. We've some with horns, and some >without. We've found critters of all colours imaginable, and some >colours we couldn't imagine. We've found critters of ever possible >shape. But not one combines the three features in my definition of >'unicorn.' So we may conclude that there are no unicorns in our corner >of the universe. Does that make the definition false? > >In short, the definition allows us to say something about the existence >of unicorns, but it does not itself assert the existence of unicorns. >Thus it is neither true nor false. I think you misunderstand your own argument here. Definitions don't say anything about the existence of anything defined. But they can say something about the non existence of anything defined if the words and combinations of words used in definitions are self contradictory. Certainly squircles cannot exist not because squares and circles are not true and don't exist but only because the combination of square circles is not true and cannot exist. And that combination represents the definition of squircles. You appear to consider that truth is somehow a positive conceptual product of propositions, that we can somehow define truth independent of falsehood and self contradiction. But the only conceptual product of propositions (as well as definitions) is the absence of self contradiction as the result of which we conclude truth. >> 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. > >Well, those pro forma conventions are crucial. They make the difference >between conversation and logical argument. Of course, usually we assume >the pro from conventions, and don't make them explicit. And that >implicitness may mislead us. Except it's not the pro forma conventions we're concerned with but combinations of words used to construct whatever the pro forma conventions describe. >> 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. > >Vocabulary is not sufficient to make a proposition true or false. But the combination of words in the vocabulary is. And that's exactly what both definitions and propositions do. > Hence >we may use the same vocabulary for definitions and propositions. Consider: > >1) "Socrates is a man, and he is mortal." >2) "Socrates is a man, or he is mortal." > >These propositions use the same vocabulary, but they have different >forms. Hence one can be true while the other is false. Write the truth >tables for them, and you'll see. (There are 3 such tables, since 'or' >has two distinct meanings.) > >Footnote: we create a definition when it gets tedious to use a long >string of terms that keeps turning up in our arguments. This is such a >handy trick, that mathematicians use it even prior to constructing >arguments with such a string of terms. That string of terms may of >course be a proposition, and usually is, but the definition isn't. But >the term used to replace the string of terms is then a proposition... Then I would only ask how one can combine any string of terms without making the combinations propositions whether definitions or not? The point I was getting at was that both definitions and propositions have the same form (once again apart from pro forma conventions) and both can be and have to be evaluatable according to a common standard for word combinations in general. >;-) Maybe that's what Lester had in mind - who knows? According to your own remarks above this seems plausible. But how you arrive at the exclusion for definitions above doesn't seem plausible. >> 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. > >Since I cannot figure out what Lester means by "predicates" etc, I can >neither agree nor disagree. > >HTH
From: Wolf Kirchmeir on 6 Dec 2007 14:29
Shrew_D wrote: > On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir > <ElLoboViejo(a)RuddyMoss.com> wrote: >[...] >> In short, the definition allows us to say something about the existence >> of unicorns, but it does not itself assert the existence of unicorns. >> Thus it is neither true nor false. > > I think you misunderstand your own argument here. Definitions don't > say anything about the existence of anything defined. But they can say > something about the non existence of anything defined if the words and > combinations of words used in definitions are self contradictory. Logically "X does not exist" is an existence proposition. Hence what you say following this claim is irrelevant to my point, which assumes that the definition of term T says nothing about the existence of the entity referred to by T. See, when you talk about term you are not talking about what they refer to. Eg, We had a cat named Alex. Now "Alex" is a Greek name. When I say that, I'm not talking about Alex-the-cat. We also had a friend named Alex, so we had to be sure we knew which Alex "Alex" referred. Context was usually enough for that. Terms are not the things refer to. Definitions restrict what terms refer to, but a definition says nothing about whether the referent actually exists. IOW, when I told you above you that "Alex" referred to my cat, you couldn't know whether I actually had a cat named Alex. Or whether I had a fiend named Alex. See? HTH |