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In a message dated 6/6/2002 1:43:17 PM Central Daylight Time, maikxlx@gmail.com writes:Well, there is surely no doubt as to this _expression_'s Totally bought some particular package, hey? If the trees are properly laid out, they retain linearity by projection. But OTOH such tree structures are often not best structures to begin with for the semantic part of an analysis, since they tend to break up what goes together and bring together unrelated chunks. Not all tree, of course, since just about any useful structural analysis can be made to look like a tree, but the usual ones. Similarly, there are any number (six or seven easily accessible) of notions of "logical form" which provide all manner of devices for scope or anaphora or... (look a Peirce's beta graphs for a topological rather than a linear one, for example). McCawley did not learn "All You Ever Wanted to Know About Logic" nor Linguistics neither. The examples you gave (later) are interesting precisely because they use, quite naturally, some alternate devises of the sort you mention. "If something.., then it" employs illegitmate ("Logically") anaphora (you should see a typical logician trying to deal with this the first time around). The second uses non-anaphoric "it" as an implicitly univerally quantifed variable -- not in the usual grammars. Both in standard logical form patterns. Complex expressions are usually complex regardless of how you do them; logic offers a variety of ways of doing them, each appropriate to different kinds of complexities and all conveniently interdefinable. And each also conveniently related to some sort of syntactic structure as well -- most language is logical as it stands. <The feeling I almost get is that we'd virtually have to pioneer our very own theoretical semantics to make it rigorous. > Probably not, given the variety that is available with a little digging. <These expressions were sloppy; the idea was to capture the real logical structure using naturalistic language. In the first sentence, the quantifier is implicit.> No, it is explicit and particular and scoped to the antecedent, though meant to stand for a universal with sentence scope. <One could also say "if anything at all is a man, it loves some woman or other."> Yes, "any" is context-leaper from a negative component to a sentence, a universal quantifier. <The second example also contains an implicit quantifier, as long as we agree that the first <it> is not an anaphor. The fact that these statements are sloppy rather illustrates the insight that concerns me: namely that logical expressions are at apparent odds with natural expressions to some extent.> It is possible to do all universals this way and thus do away with the notion of an explicit universal quantifier (which makes particulars a bitch and a half). <Well the idea of introducing the conditional construction was simply to express the implicational operation which appears in the logical _expression_. Besides clear quantifier scope, this is the other thing that arguably is not reflected in the simple predicate syntax.> Conditionality is not expressed in simple predicate syntax because it usually is not there semantically/ logically either. The "for all x, if...x... then ...x..." reading of universals came in in full flush with all the 1858 stuff, after more than 2000 years of doing right with "All S is/are P" (and, in fact, it is still in most logical systems, though hidden -- the S is suppressed and the universal is just "All is P", typically with a complex P). <At this point, please understand that I am only naming some issues here on my mind. I too do not know how And handles things in his conlang, though I vaguely gather it involves employing quantifiers at the higher tree level as would be demanded by straightforward logical representation. I would be satisfied with *any* syntax that veriably assigns every _expression_ in the language one, and exactly one, equivalent logical _expression_, and allows every possible logical _expression_ at least one linguistic _expression_. That seems to me the minimal requirement for any true loglang.> Much too easy and way too hard. Any logic is going to give an infinite number of equivalent forms for each _expression_ -- some trivial, some not at all. And any form can be taken as a Logical _expression_, an atom. You want, I suppose, a canonical form (defined some way other than "What my rules give" -- and lots of luck with that) and one that is derived in some explanatory way from the original _expression_ (ditto, for "explanatory"). I think it is enough if you get one that works every time you use the tools at hand -- and maybe never get one that is seriously wrong (unless the original is screwed us in unnoticed ways). <.) I suspect that overall, logicality is served well by them, which is not the same as saying they are verifiably rigorous.> I wonder what is going to count as "verifiably rigorous". Kamp goes on for nearly three hundred pages and at the end has to make intuitive punts (very well disguised, I think). I would as soon punt early on and get good results faster -- and tidier. |