--- by J. L. Speranza
----- for the Grice Club
J was considering polyadicity and transitivity -- there is a lot of interesting thoughts by Grice on Russell's theory of relations as made popular by Davidson in his "Logical form of action sentences" -- and which allow Grice to play 'the linguistic botanist' -- Oxford variety. This is some vintage Grice --. The paper, "Actions and events" he did publish in his lifetime and it has not been overwhelmingly quoted but it should -- at least by those authors (not ovewhelming, I mean) who take the Griceian programme more or less seriously -- so that we just don't see them as only paying lip-service to Griceianism.
Grice writes of various problems with Davidson.
The very first is indeed, "the phenomenon of (so-called) "variable polyadicity"".
---- Grice notes -- qua Warden of the English language! --:
"There is considerable support in ordinary
language for the idea that verbs (and other
relational predicate expressions) carry
concealed within themslves ... a specification
of a given degree of polyadicity (or
"n-adicity")"
One wonders why he distinguishes between n-adicity (which I prefer) and polyadicity. I would think that if he wants to make a point he is going to make it about the number of arguments of a predicate be it 0 (as in propositional logic), 1, as in monadic predicates, 2, as in dyadic, and so on. Euclid, for example, would disregard 1 as a number -- 2 is a number -- but, given that we have the expression, 'twice' and 'thrice', would you say that '2' and '3' are MANY? (which is what 'poly-' means). Yes, via implicature. So one has to be careful. The term n-adicity seems to overcome this problem (but leaves untouched the issue of a proposition as a zero-adic predicate).
Grice continues:
Grice has two qualms here. The first (actually the second he lists) concerns the construction of a system, like System G:
"So far as the construction of logical systems is
concerned, it has been shown that restrictions of
n-adicity are not required for PREDICATE logic."
----
And what is the first qualm? Well, it's the one that interests him primarily and why he lists it first. Consider "meet"
---- Who did John meet in Vienna?
-- Answers:
----- 1. He met Bill
----- 2. He met Bill and Harry.
----- 3. He met Bill, Harry, and Bob.
-- This perplexes Grice -- and me. "If we ask whom John met in Vienna, we may get (answers 1-3)", "without any suggestion [or IMPLICATUM]," Grice adds, "that some RESTRICTIVE condition OR n-adicity is being violated."
---
This may be vis a vis: "Who did John MARRY in Vienna?" --. Or perhaps there is a better example where some condition IS being violated.
----
What IS variable polyadicity? "To exhibit variable polyadicity," Grice notes,
"an item would have to be (say) on occasion dyadid, on
occasion triadic, on occasion tetradic; and this boring
ascent could presumably be continued ad infinitum."
---
But what IS this item? It cannot be _just_ linguistic. Consider "meeting".
A meeting took place in Vienna. Those who met were John, Bill, Harry, and Bob.
----
"[A] meeting might be a single ITEM ...
which holds, variably, between two, three,
or more persons."
--- (But this nonlinguistic construal Grice finds anti-Davidsonian, and he is trying to be exegetical).
So, he turns to the linguistic side of variable polyadicity.
Grice notes:
"If we turn from the nonlinguistic to the linguistic world,
we find clearly single ITEMS, viz. predicates ... which exemplify
determinate forms of n-adicity."
----
An observation by Grice at this point is that:
"the embodiment of (say) dyadic AND triadicity are
distinct from one another."
I.e.
" --- met ---" (as in "John met Bill")
and
" --- met --- and ---" (as in "John met Bill and Harry")
"are structures which do NOT have common instances".
-- He may be having in mind that if it is a fact that John met Bill and Harry it would be odd (or underinformative, and thus against the pragmatic pressures imposed by the cooperative principle and such) to just leave Bill or Harry out of the picture.
The point boils down to the 'individuals or sets' involved. Instances "must contain JUST AS MANY ELEMENTS as the number n in the n-adicity of the predicate". Indeed, for otherwise, it's not even a well-formed formulae.
This in spite that the 'brick out of which the predicates are made' -- i.e. 'predicate LETTERS' "may or may NOT have assignable n-adicity".
----
The second part of "Actions and Events" is concerned with Grice's own proposal -- as an improvement over Davidson. If in his earlier part he referred to
'sink'
as originating the fallacious argument,
H. M. S. Pinafore sank the Bismark
---
Therefore, H. M. S. Pinafore sank
he now mentions,
'fall'
'fall in a --'
i. Mary fell in a ditch
----
Therefore: ib. Mary fell.
BUT:
"fall in trance"
ii. Mary fell in a trance
----
Therefore: Mary fell (ODD).
Grice: "My doubt may be illustrated by an example: the statement (i) from which it follows ib, but the statement ii, from which this conclusion does not follow."
---
Why?
Well, because "Mary fell into a ditch" "offers what I might call a 'specificatory modification'" -- from which the original utterance is entailed -- of "Mary fell".
"Mary fell in a ditch" "purports to tell us how, in what circumstances, in what context (or such-like) Mary fell, and in virtue of that fact it presupposes or involves a commitment to the truth of the statement that Mary fell."
----
But surely there are further problems!
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Much of this analysis seems to me clouded by the physical nature of human language. In Javascript, there are two distinct "equals" operators.
ReplyDeletea=7
means "Let the variable a have the value 7."
If a==7
means "If the variable a has the value 7."
We commonly read the a [operator] 7 part of the declaration as "a equals 7." But that's an English quirk, Logically, these are two different operators, two different "words" if you will.
It seems to me that the transitive and intransitive versions of verbs are two different "logical" words. What the Bismarck did to the Hood, and what the Hood did after being hit by the Bismarck are two different things. That they use the same word is not purely coincidental, but it is, I think, analytically irrelevant, i.e. it ought to be treated as if it were a coincidence.
Likewise, the literal and metaphoric uses of a word - "Mary fell", and "Mary fell into a trance" are different logical words. That's why "Mary fell into a trance" does not imply that Mary fell.
The question I have been trying to ask is why so much other stuff - i.e. more than that we are talking about the identical physical representation of two logically different words - needs to be said about a word that doesn't behave "logically," i.e., doesn't always mean the same exact thing the way logical operators must?
I know that I have raised the idea of usages being of one physical word being distinct logical words before, but I don't recall an explicit discussion of why that fact doesn't end the matter, and I'd be interested to see such.
while I find this somewhat interesting, at the same time I am reminded a bit of Russell's slightly disparaging remarks re ord.lang. --"who cares about the silly things silly people say"...actually Lord Russell sounded rather arrogant and british with that, but at times....the semantic discussion (including Grice, Davidson...even St Ludwig of the PI) tends to be "surface" oriented; ergo,...possibly trivial (tho "silly" a bit much)--it seems either one points out the problems of logic and semantics and relates the analysis to psychology (..or metaphysics, if one feels suitably grand) OR one just sticks to "normal science" for lack of a better term, clarifies the language, works towards better functionality or something .
ReplyDeleteIn his discussions of relations, Russell, however detestable, takes on Leibniz and Spinoza, and yet attempted to situate symbolic logic in regard to science (at least..pre-quantum). He's a bit of a functionalist, I guess, but touches on the metaphysical issues (relations as depending greatly on externalism, for one...which BR does affirm....as did Spinoza..perhaps one reason the postmods or Kantians of whatever sort still detest BR). Just in terms of functional propositions--or say programming-- Im not sure transitivity is that big of an issue, and then the translation issues also creep in (not to say english vs latin vs deutsch vs mandarin etc). J. the occasional-philistine.