On Wed, 26 Jul 2006 10:00:48 +0100, firstname.lastname@example.org wrote:
> > >Lester Zick wrote: >> >> email@example.com wrote: >> > >> >Lester Zick wrote: >> >> >> >>firstname.lastname@example.org wrote: >> >> > >> >> >Lester Zick wrote: >> >> >> > >[...] > >> >> >> >> In other words >> >> >> >> if Q is true (and it is) it isn't because it's a component of P. >> >> >> > >> >> >> > >> >> >> >You're right, even though Q is a component of P. >> >> >> >> >> >> Where do you see Q in P? >> >> > >> >> > >> >> >Don't you see it? Your previous sentence ("In other words if Q is >> >> >true..." etc.) is ambiguous in that regard. >> >> >> >> Well the fact is that I don't see it. I see how it might be inferred >> >> given collateral judgments. But I just don't see the actual Q you >> >> describe anywhere literally in P. That's been the focus of my problem >> >> with your contention all along. >> > >> > >> >Well, the terms "component" and "literally" are not rigorously defined, >> >AFAIK, so it's possible we don't disagree. >> > >> >Take the two sentences >> > >> >1) Jones smokes. >> >2) Jones smokes. >> > >> >Obviously, (1) and (2) are distinct occurrences of the same sentence. >> >Are they "literally" the same? It could be argued that they differ, >> >at least in their placement on the page (or screen), and so are not >> >literally the same. >> > >> >If we say that they _are_ literally the same, then in that sense Q >> >("Margaret Thatcher is a politician") does not literally occur >> >in P ("Margaret Thatcher is a man, and all men are politicians"), >> >nor does it occur in (if I may) P' = "Margaret Thatcher is a >> >male politician". If we take "is a component of" to mean >> >"occurs literally in" (in this sense) then Q is not a component >> >of P. >> > >> >If, on the other hand, we take "is a component of" in a somewhat >> >looser sense, such as "is (logically) equivalent to a part (or >> >subformula) of" then it can be shown that Q is a component of >> >P and of P'. >> > >> >E.g., "Margaret Thatcher is a male politician" is clearly >> >equivalent, logically, to "Margaret Thatcher is a man, and >> >Margaret Thatcher is a politician." In this formulation, Q >> >("Margaret Thatcher is a politician") is clearly a component, >> >in this last sense, to a part of a sentence that is logically >> >equivalent to P'. >> >> Okay I can see what you're getting at now. But my take on the problem >> would be that in your p "MT is a male politician" the predicate "male" >> designates a subset of the predicate "politician" and the predicate >> "MT" designates a subset of "male politician". > >I don't think so. The predicate "male politician" designates the >intersection of the predicates (when taken extensionally) "male" >and "politician" (and so is a subset of both).
Well I agree and disagree for the following reason, Herb. You use the noun form "politician" so I have to assume "male" is used as the adjective qualifying "politician". If you had used "political males" instead the reverse would be true. This is an ongoing difficulty in the evaluation of generic language. But you're correct that there is an intersection involved and that in mechanical terms they're really a subset of both.
> "Margaret Thatcher" >is not a predicate, it is the subject term of the sentence.
Actually names are predicates as well just not obviously so. They're what I call the lowest order predicate possible and the way I approach this problem overall is to use what I call a universal subject such as "it" to form predication like "it is MT a male politician" so we can see the overall order of predication in uniform terms consistent with other predications of other subjects.
> Also, >the reference of the term "Margaret Thatcher" is, presumably, not a set, >and hence, not a subset of anything. She is not an element of the set >of male politicians, which p' falsely and explicitly asserts, and >which p falsely and implicitly asserts.
Sure. That's why it's false. The real issue here is how this kind of false predication can arise at all in mechanical terms through the intersection of sets of predicates.
>> And I think the question >> to be answered is exactly how the compounding of predicates is done in >> real mechanical terms and not just in terms of logical equivalence. >> >> In other words the conjunction "and" does not just fall out of thin >> air. It designates separate disjoint operations which are compounded. > >Not following you at all, in either of these last two sentences.
Well let me suggest this. In conventional terms "A and not A" is considered to be self contradictory. At least this was Aristotle's opinion and remains the same in modern logic. However there is a mechanical difficulty with this interpretation. When we intersect and conjoin different predicates conjunctively we do so through different operations and at different times.So we can't really say "A and not A" are necessarily true together at one and the same time and if they're not necessarily true at one and the same time they aren't necessarily self contradictory since there is nothing to prevent "A" from changing into "not A".
On the other hand if I say "A not A" meaning "A is not A" I have one predication which denotes self contradiction necessarily through the use of one predicate "not" or "is not". In other words my point above was that logical reduction in conventional conjunctive terms does not necessarily denote mechanical reduction in tautological terms.
>> And I think the order of predication > >I don't think there is an order of predication, or if there is, >I don't think it matters in this context. In english it is more >natural to say "male politician" than "politician male": I don't >know why. But "MT is a politician, and MT is a man" is as >natural as "MT is a man, and MT is a politician" and is equivalent >in meaning.
I don't necessarily disagree however see above.
>> designates "male politician" >> first and "MT" as a subset of that subset second such that nowhere is >> there any objective indication of "MT is a politician". > >If all swans are birds, then if there is a black swan, there is >a black bird, no?
Yes this form of positive predication is legitimate. Where syllogistic inference gets into difficulties is with negative predications.
>> If you are to maintain otherwise I suspect we could find all sorts of >> potential logical equivalences which might be implied within any >> predication whether or not designated objectively. > >Again, not following you.
Well let's say in your example "MT is a male" and "MT is a politician" are both included of necessity in your predication. What about the conjunction "and"?Is it not a necessary part of your basic predication as well? In other words given "MT is a male politician" are we not looking at the mechanically conjoined predicates "male politician" of necessity and if so how can we disjoin them mechanically just because there can be other conceivable logical reductions of those predicates in other contexts? Once you've reduced the intersection of subsets to "MT is a male politician" you no longer have the sets themselves to work with so you can't really say you have any other constituent predicates to work with. In other words once you've predicated something the original sets themselves are gone and mechanically all we're left with is there intersection which is erroneous.
The fact that we can compensate for this difficulty after the fact by the use of conjunctive inferences doesn't alter the circumstance that all we have after a tautological regression and intersection of sets is the result and not the constituent sets to work with.