by JLS
-- for the GC
-- So the point Warner is making is about implicit reasoning.
---- Warner writes:
"From "Everybody loves my baby, but
my baby don't love nobody but me" it
follows that I am my baby. However,
there is a clear sense [or way? JLS] in
which "Everybody loves my baby, but
my baby don't love nobody but me; therefore,
I am my baby" is not -- at least not for
most of us [emphasis mine. JLS] --
a COMPLETE piece of reasoning [emphasis mine. JLS].
Warner continues:
"A complete piece of reasoning,
would at least [emphasis mine. JLS]
point out that, assuming a universal
domain of quantification for 'everybody',
if everybody loves my baby, [...] since my
baby is included in 'everybody', my baby
loves my baby. But since my baby don't love
nobody but me, I must be my baby".
Q. E. D.
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in the usual proofs common to first-order logic texts it's shown that everyone includes baby, and thus "bLb", I believe. with the correct deduction that "everyone loves ...me" . But note that the language really says baby doesn't love anyone, except me (one person). Logic types translate that with like (x) (bLx -> x=a), do they not??
ReplyDeletehowever (if you'll allow some meta-izing) the translation itself into a universal seems dubious to me (if not the entire project of taking jazzy, colloquial speech and reducing to symbolic form). Baby doesn't love all. She doesn't love any, except for one (me). So it could probably be translated into uniqueness of a sort (I leave it as an exercise :) ).
But it's the typical sort of pedagogical hack anyway--they're setting up undecidability, Goedel, etc. with a near paradox (or at least...weirdness) Which is to say, allow self-referentiality, and the logic falls apart. Don't allow it, or allow type theory of some sort (or some set theory BS) and it's not that problematic.
I think you are right that we need to introduce the iota operator. To mark uniqueness, that is -- with the addition of the "=" identity symbol via some form of the Leibniz Law of the identity of indescirnibles. What I think the example may be used to show is, also that, people don't go with explicit ceteris paribus or exception clauses, but they should -- in terms of logical form. I would think the conclusion, "therefore, I am my baby" gets blocked if we understand "everybody" in "everybody loves my baby" to read, "everbody, EXCEPT my baby, loves my baby". In the case of the object of affection of baby, you are very right that baby's love is explicitly exclusive -- "she don't love nobody BUT me", with a unique _me_.
ReplyDeleteGrice found the topic of implicit reasoning fascinating -- (I wouldn't think all share his fascination). His example in the body of the book, Aspects of Reason, concerns an example well discussed by N. E. Allott, who contributes to this blog, in his PhD for UCL -- Allott thinks Grice means Hampshire -- but Grice calls him "Shropshire" ("I forget his name -- some shire of England", or words). In brief, or in the only way Grice heard of it, the argument run something like: The fact that a chicken continues running for 15 minutes after you behead it proves the immortality of the soul". Grice provides I believe something like 15 steps to prove that "explicitly".
Grice was ALSO fascinated by mathematicians like Hardy and would be amused that, of one mathematician, it was said that each proof that he ever presented on the board either lacked a step or contained an error!
---- So, the topic Warner is dealing with IS serious. I believe it gets solved by reliance on what Grice calls the Principle of Economy of Rational Effort. People don't SAY, "Everybody except my baby loves my baby". Since they don't, some of the things they say ARE loose, unGoedelian, etc. -- Some CAN expand the premisses explicitly, and Grice seems to think that the ability to be reasonable (if not rational) lies in this.
Kramer has expanded on these issues in the blog with references to the enthymeme which is exactly what Grice is having in mind. My PhD, whle focused on implicature, was really an essay on rationality, and so I should say I do share with Grice this idea about the importance of making explicit, by analysis, sometimes, what is at stake in things as basic as meaning and understanding -- before we proceed to meta-ethics, epistemology, and stuff.
I agree it's serious, in a sense--and interesting. Didn't mean to suggest otherwise--many of the issues you have raised remind me of Wittgenstein's comments on "the bewitchment of language"--whether conversation, ad slogans, pop songs, PunditSpeak etc-- it's like ...hypnosis, nearly.
ReplyDeleteMy beef is with the hack logic choppers (even high-powered sorts in ivy league or Steinford) who don't pay sufficient attention to the language and translation issues (or intention, really, however difficult it may be to flesh out). Enthymemes. Yes, but few take the time to point out the missing or incorrect premises
Kramer has expanded on these issues in the blog with references to the enthymeme which is exactly what Grice is having in mind.
ReplyDeleteWho, me? Cool.
Everybody loves my baby, too, but my baby only loves those who don't love her. This leaves her with plenty of time to gaze at her own lovely visage in the reflecting pool, but she can't figure out whether or not she loves herself...
Kramer is right. There are two tracks to take here. One is to proscribe self-love. After all, if we are defining, as J suggests, 'love' as a dyadic predicate, it is very logical that some dyadic predicates should NOT be reflexive. Why should love be?
ReplyDeleteIn this requirement, bLb, i.e. baby loves baby would be ill-formed. As when we say, I don't know, I'm shorter -- without specifying than who. Or, to use an example by Carnap, "Caesar but is is but".
The other track is indeed to proscribe the free-floating 'everybody' and add 'except my baby' -- rendering, 'everybody except my baby loves my baby'. This may be seen as a corollary of the impossibility of self-love as per the first track.
The moral of the song is obvious. She is well-loved. Note that if you replace, 'love' by 'make love', or even the F-word, the innuendo is lost: "everybody makes love to my baby, but my baby, etc.".
The moral is that the singer is some lucky fellow because everybody is in love with BABY to no avail, because THEIR love will never be requithed. But as Kramer notes, it is never stated that the singer LOVES Baby. You may say, 'it is implicated' by 'everybody' which SHOULD include 'the singer'.
But: if we have excepted Baby from everybody, why not except Singer as well?
Now, there's THIS other song, French I think, which brings some more free-floating quantifiers -- I like the augmented chords to it:
ReplyDelete"Everybody loves somebody sometimes"
Grice often played with titles of songs. I have identified a few:
ReplyDelete"Every nice girl loves a sailor" -- Grice's example of hyperbole. From music-hall song.
"Home Sweet Home" -- used as example of 'prolixity' in a music review -- "She sang 'Home Sweet Home' in ways that correponded closely with the score. (WoW:ii).
"Moon over Miami", "Tipperary" -- used in examples by Schiffer. WoW:5
"She was poor but she was honest" (Great War Song) -- used by Grice, 1961, Causal theory of perception -- for 'colouring' of "but"
"You're the cream in my coffee" -- late 1920s song used by Grice as example of metaphor. WoW:ii.
-- and there may be others. Personally he preferred opera! But as Richardson says in Grice's obituary, "he thought Wagner's Meistersinger was for children". He also liked Mahler, Song of the Earth.
American songs are my favourite --. Especially the Tin Palley variety happen to have an innuendo in every title. It was like illegal in the 1920s to the 1940s to write a SONG WITHOUT some innuendo or implicature in the title -- at least the novelty types. Or not.
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ReplyDeleteEdited--
ReplyDeleteThe Singer could be said to equivocate on "love" (as you suggest with make love, or the f-word)--in the first premise Singer means all desire, lusts for Baby, etc. But in the second premise (baby loves nobody but me) that seems to be....sexual, consumated actual, not potential. Not real profound, but seems pertinent to the relational problem (or "dyadic" preds. as you termed it).
So in that sense, the standard translation doesn't really work--. Love as in "Desire for" does not at all mean Love, or WUV, ie cohabitating, the ding-an sich as I am sure many a philosophastry student would attest to...
Very good. And thanks for clarifying the sense in which this IS a fallacy of equivocation -- with 'love' being used with different denotata, as it were, in premisse and conclusion. The issue is subtle, though. In that I would regard some of this 'ambiguity' or 'equivocation' as inherent to ALL terms (there's 'contextual ambiguity' as Grice best calls it, after Aristotle, in "Aristotle on the multiplicity of being", Pacific Philosophical Quarterly, 1988 (posthumous), and recall that one of the conversational maxims IS 'avoid ambiguity'. One wonders about the conclusion -- 'I am my baby' not only has to swallow that equivocation and come up with yet a third hybrid where 'love' means '... lusts for...' and '... consumates a sexual act with...'. This may show the point by Warner in making the reasoning explicit. That the Singer could NOT be meaning 'including Baby' but 'except Baby' in the first premisse -- and with some kind of 'theoretical construction' of '... loves ...' it may be said to carry sense:
ReplyDelete"Everybody, except Baby, has baby as object of desire. But my baby doesn't have, as object of dsire, nobody but me" -- Even THIS requires some implicature: that REQUITED love is better than unrequited love. In fact it is a big of a bragging. For why does singer care to TELL that 'Everybody loves Baby'. The point being that Baby is a DESIRABLE thing -- a universally desirably thing -- and that he is extra-confident that since Baby is committed, at time of Singing, to Baby, Singer can't care less.
Dyadic predicate allows for generalisations. I never understood tryadic predicates, for example. In "Actions and Events", Grice is precise about them -- in his attempt to enrich on Davidson. Grice notes the verb, 'sink'.
As monadic predicate, it is obvious:
"H. M. S. Pinafore sank" -- means, went down in the water.
"H. M. S. Pinafore sank the Bismarck" -- is a causative: MADE the Bismarck to go down in the water.
His point is that it's never good to disregard the polyadicity (as he calls it) of a predicate in an argument. For, he holds, only under very general circumstances could we say that the below is 'valid':
"H. M. S. Pinafore sank the Bismarck"
----
Therefore H. M. S. Pinafore sank.
---
Ditto with 'love'. "I love" seems ungrammatical. Dyadic is the norm with x =/= y, as it were (the good norm, even). Triadic? Well, Grice would have ANYTHING as triadic, e.g.: "... loves ... in the ...". (kitchen, etc.).
But I always found the way to determine the number of 'arguments' of a predicate pretty artificial and Grice seems to have agreed with me! (For Davidson, who is more of a logician than a philosopher, in some respects -- god bless his soul, I love him -- the point seems less crucial -- the whole point of Grice's essay is to project some problems for a PHILOSOPHICALLY motivated view of actions and events (NOT in that order -- Grice, like Davidson, holds events more basic, of course).
His point is that it's never good to disregard the polyadicity (as he calls it) of a predicate in an argument.
ReplyDeleteyes. Or Transitivity in the older jargon ( about which Russell, in "Principles of Mathematics" also had some interesting things to say--along with relations, quantification, paradox, and about all things logical and/or foundational, until Goedel arrives on the scene (or was it Alonzo Church...or Zermelo))
Good. I would think 'transitivity' may apply primarily to dyadic predicates, though?
ReplyDeleteI would think I can formalise 'transitivity' as:
(aRb & bRc) ) aRc
-- where ")" is the horseshoe. No?
I should get the quote where Grice introduces the polyadicity. He actually refers to it as "VARIABLE" polyacity, so I may paste some of his comments in a separate post.