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Re: A syllogism and an epitaph
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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 you¹ll appreciate
the predicate Western.¹). Syllogisms and their siblings play a significant
role in understanding¹ Nabokov (well, for me, at least), more than, say,
chess problems and butterflies! (Note VN¹s comment that butterflies have no
connection with my literary work¹ [paraphrase from Strong Opinions]).
I¹m afraid that at the level of serious syllogistic scholarship, it iDOES
matter that
1. ³Other men die; but I am not another; therefore I¹ll not die²
does NOT immediately match your suggested, clearly false template
2. ³All x are M; A is not an x; therefore A is not M.²
My ³unnescessary² complications are needed to disambiguate 1 in such a way
that it leads to the formal¹ 2. My particular disambiguation does, in fact,
agree with yours, so ³all¹s well that ends well!² [³we both end well²
implies ³we are both well² ? 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 ³God is Love; Love is Blind; ergo God
is Blind,² (Smullyan and others have written whole libraries of such
teasers¹) 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.¹
Version 1. lacks an explicit quantifier e.g., ALL or SOME, which must be
guessed from context (neither guess fixes¹ 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 ³OTHER men² to ³I am
not ANOTHER² -- which is far from following the pattern ³x [are M]² to ³[A
is] not an x.² We both seek the most NATURAL disambiguation for ³I am not
ANOTHER?² We ask ³ANOTHER what [unstated]?² and kindly fill in for the lazy
poser (poseur?) ³ANOTHER MAN² or rather, to match the two x¹s, ³an OTHER
MAN.²
BUT**, this is a poem and we are playing literary as well as logical games.
IF one fills the incomplete ³A is ANOTHER² with ³A is ANOTHER MORTAL,² the
conclusion (³A will not die²) 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: VN¹s so-called
dichotomy twixt the particular¹ and the general.¹ One can admire the
particularity of say ³ ... that delightful little car a dark-blue
two-seater, paid for on installments.² (Otchayanie). Yet it rests on the
magic & mystery of linguistic generalisation: the word car¹ itelf that
somehow subsumes all past, present and future cars in all their diverse
particulars. You might yearn for more details about Hermann¹s vehicle OK,
it¹s 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 ³But, Having Said That ...² (ACM Queue, March
2006)
http://www.acmqueue.org/modules.php?name=Content&pa=showpage&pid=376
Search the archive: http://listserv.ucsb.edu/archives/nabokv-l.html
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> 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 you¹ll appreciate
the predicate Western.¹). Syllogisms and their siblings play a significant
role in understanding¹ Nabokov (well, for me, at least), more than, say,
chess problems and butterflies! (Note VN¹s comment that butterflies have no
connection with my literary work¹ [paraphrase from Strong Opinions]).
I¹m afraid that at the level of serious syllogistic scholarship, it iDOES
matter that
1. ³Other men die; but I am not another; therefore I¹ll not die²
does NOT immediately match your suggested, clearly false template
2. ³All x are M; A is not an x; therefore A is not M.²
My ³unnescessary² complications are needed to disambiguate 1 in such a way
that it leads to the formal¹ 2. My particular disambiguation does, in fact,
agree with yours, so ³all¹s well that ends well!² [³we both end well²
implies ³we are both well² ? 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 ³God is Love; Love is Blind; ergo God
is Blind,² (Smullyan and others have written whole libraries of such
teasers¹) 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.¹
Version 1. lacks an explicit quantifier e.g., ALL or SOME, which must be
guessed from context (neither guess fixes¹ 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 ³OTHER men² to ³I am
not ANOTHER² -- which is far from following the pattern ³x [are M]² to ³[A
is] not an x.² We both seek the most NATURAL disambiguation for ³I am not
ANOTHER?² We ask ³ANOTHER what [unstated]?² and kindly fill in for the lazy
poser (poseur?) ³ANOTHER MAN² or rather, to match the two x¹s, ³an OTHER
MAN.²
BUT**, this is a poem and we are playing literary as well as logical games.
IF one fills the incomplete ³A is ANOTHER² with ³A is ANOTHER MORTAL,² the
conclusion (³A will not die²) 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: VN¹s so-called
dichotomy twixt the particular¹ and the general.¹ One can admire the
particularity of say ³ ... that delightful little car a dark-blue
two-seater, paid for on installments.² (Otchayanie). Yet it rests on the
magic & mystery of linguistic generalisation: the word car¹ itelf that
somehow subsumes all past, present and future cars in all their diverse
particulars. You might yearn for more details about Hermann¹s vehicle OK,
it¹s 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 ³But, Having Said That ...² (ACM Queue, March
2006)
http://www.acmqueue.org/modules.php?name=Content&pa=showpage&pid=376
Search the archive: http://listserv.ucsb.edu/archives/nabokv-l.html
Search archive with Google:
http://www.google.com/advanced_search?q=site:listserv.ucsb.edu&HL=en
Contact the Editors: mailto:nabokv-l@utk.edu,nabokv-l@holycross.edu
Visit Zembla: http://www.libraries.psu.edu/nabokov/zembla.htm
View Nabokv-L policies: http://web.utk.edu/~sblackwe/EDNote.htm