On 15/2/07 03:40, "Anthony Stadlen" <STADLEN@AOL.COM> wrote:
I hope our editors may allow me to discuss these "syllogisms", since they help in our discussion of what makes Shade's "syllogism" false. SKB's account seems unnecessarily complicated. Shade's "syllogism" is false simply because it has the form:
All x are M; A is not an x; therefore A is not M. (It does not matter that x is "other men" and A is "I" and M is "mortal".)
Anthony: I welcome your comments. The topic has its belly-laughs (SILLYGISMS) but is far from trivial, encapsulating the heart and soul of Western logic (judging from your impressive Blog, I know you’ll appreciate the predicate ‘Western.’). Syllogisms and their siblings play a significant role in ‘understanding’ Nabokov (well, for me, at least), more than, say, chess problems and butterflies! (Note VN’s comment that ‘butterflies have no connection with my literary work’ [paraphrase from Strong Opinions]).
I’m afraid that at the level of serious syllogistic scholarship, it iDOES matter that
1. “Other men die; but I am not another; therefore I’ll not die”
does NOT immediately match your suggested, clearly false template
2. “All x are M; A is not an x; therefore A is not M.”
My “unnescessary” complications are needed to disambiguate 1 in such a way that it leads to the ‘formal’ 2. My particular disambiguation does, in fact, agree with yours, so “all’s well that ends well!” [“we both end well” implies “we are both well” ? Or vice versa? ;=)) That does not rule out further analysis, proviided we maintain a Nabokovian mix of precision and fun!
As you point out later, in analysing “God is Love; Love is Blind; ergo God is Blind,” (Smullyan and others have written whole libraries of such ‘teasers’) one must watch for matching/linking tokens in the opening premises and decide whether they are, in some sense, cognate (semantically) rather than lexical ‘coincidences.’
Version 1. lacks an explicit quantifier e.g., ALL or SOME, which must be guessed from context (neither guess ‘fixes’ this particular invalid deduction, of course); next we have that strange BUT not found (or needed) in 2. The usual logical conjunction here is the simpler, implied AND! The BUT (the weirdness of which word has been noted by VN — refs to follow!) seems to be setting us up for some kind of surpriise, maybe a contradiction, as in (P BUT not-P) **; then we look for the link from “OTHER men” to “I am not ANOTHER” -- which is far from following the pattern “x [are M]” to “[A is] not an x.” We both seek the most NATURAL disambiguation for “I am not ANOTHER?” We ask “ANOTHER what [unstated]?” and kindly fill in for the lazy poser (poseur?) “ANOTHER MAN” or rather, to match the two x’s, “an OTHER MAN.”
BUT**, this is a poem and we are playing literary as well as logical games. IF one fills the incomplete “A is ANOTHER” with “A is ANOTHER MORTAL,” the conclusion (“A will not die”) IS tautoligical (yet still not a REAL syllogism.)
The wider implications of what may seem to be idle nit-picking to those bored by logic and its expression in natural language: VN’s so-called dichotomy ‘twixt the ‘particular’ and the ‘general.’ One can admire the particularity of say “ ... that delightful little car — a dark-blue two-seater, paid for on installments.” (Otchayanie). Yet — it rests on the magic & mystery of linguistic generalisation: the word ‘car’ itelf that somehow subsumes all past, present and future cars in all their diverse particulars. You might yearn for more details about Hermann’s vehicle — OK, it’s small, blue, 2-seater, hire-purchased? No model, engine-size, weight, tyre sizes, mpg? There are degrees of competing particularity — when is genug, genug?
Stan Kelly-Bootle
** See my Curmudgeon column “But, Having Said That ...” (ACM Queue, March 2006)
http://www.acmqueue.org/modules.php?name=Content&pa=showpage&pid=376