Some Implicature

--- by JLS
------- for the GC


AS WE SEE, Grice gives TWO renderings for (Ex):

"some"

and

"at least one"

or rather:

"some"

'or' (Grice has it)

"at least one"

--- The 'or', rather than the 'and' is important because he is saying that either "some" OR "at least one" qualify the subject (In most romance languages, the 'or' is not necessary and 'and' will do).

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Now, to avoid the "That's SOME baby" implicature -- as uttered by pediatrician father-in-law of Kramer -- we would suggest to examine "all"

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Grice is using the quantifiers:

for ix, he has "the", which is just fine. And (ix) defines in terms of (x) and (Ex). Russellian definite descriptor: uniqueness and existence, entailed or implicated (in negative clauses).

So this leaves us with "all" and ""some" or "at least one"")

"One" usually gets corrupted to "a" -- and Grice analyses that, "I went to a house and saw a tortoise" -- odd if what we mean, is _my_ house (or my friend's house) and found MY tortoise-pet.

The problems with 'at least' are incredible, and we'll delay discussion of them.

The idea is that "at least 1" does NOT mean '1' (but I disagree). So that people like Boultinck are proposing that when we say,

"You have two lovely black eyes' --- after the boxing match

the Idea is that you have AT LEAST two and at MOST two lovely black eyes. I agree, but I do think that if one had "three" lovely black eyes, it is still true that one still has TWO lovely black eyes. So what Boultinck says it's part of the 'meaning' is just part of the implicature.

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So, this leaves us with "some" versus "all"

Grice uses

/\ to mean 'and'

and

\/ to mean 'or'


And in current logic -- not the one used by Grice -- who prefers the Russellian (x) and (Ex) -- that is the way you symoblise 'all' and 'some':

/\x.Fx

\/x.Fx

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Now, browsing the OED, I once found out that 'all' COULD take a singular number: "All man is mortal". This was odd for me to learn, but it's there. But in general, it's all MEN are mortal". In Roman, Boethius, etc., it's Omne homo est mortalis. So the distribution of the number is made easier in Latin than in English.

I would think Grice is thinking of "all" as followed by a PLURAL form. "All men are mortal". Since immediately after "all" he has "some", I assume he is also taking "some" to take the plural form, "SOME men are mortal". Recall this is logic, not literature.

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Warnock -- in "Metaphysics in Logic" -- and Strawson in "Introduction to Logical Theory" which credits Grice -- were well aware that there are unwanted 'implications' by the use of the plurarity: "Some of the authors who wrote Hamlet were born in Stafford-upon-Avon" is a true logical sentence. "Some (people) never learn" you can utter just on the basis of your _son_ never doing it, etc.

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The etymology of 'some' is VERY ENGLISH. I don't think we find a cognate of that in German, even. It is pretty obscure.

But in any case, it just means 'partiality' (versus 'totality'). The totality is carried by what philosophers (scholastic) called 'universalis' -- for the 'universe' of discourse as Venn would have it. The 'part-icularis' just participates on this and the only item it adds, unlike the 'universal' claim is not to much one about the particularity, but about the EXISTENCE.

"Barbara" requires no crosses in the Venn diagrams of interconnecting three sets.

But any syllogism involving "I" and "O" NECESSITATES the "crosses" that represent items or members of the set. It is THIS that marks what follows as per entailment from such utterances -- NEVER anything about plurality or 'partiality'. Odd, but --- logic.