Grice on 'an': from cardinal to indefinite -- and back

While Grice is considering the logical form of

(Vx)Fx

--i.e. some x is F.

he fails to recognise (in WoW:iii) the important distinction. He considers:

I met a woman this evening.

or

Jack is meeting a woman this evening.

"It would be otiose that if it's his significant other, Jill". "We mean, someone other than his wife, platonic friend, sister, daughter, etc." "We mean lover".

--

But cfr.

Jack is meeting ONE woman this evening.

Recall that 'a' is short for 'an', which is short for 'one'. This is of course different from the iota operator as cardinalised by Quine.

Recall that in Mathematical Logic, by Quine, which Grice read, the idea is

"The twelve Apostles were drunk"

gets the logical form

(i12x)Dx

i.e. there were twelve and twelve only things, called Apostles, which were drunk.

---

So "Jack meets one woman" becomes

(i1x)F(x, Jack)

----



The problem then has a long date. As Onions notes ("Etym. Dict. of the Engl. Lang. Oxford), the problem started with the Anglo-Saxons (or Old English as he prefers) who did not make a distinction between indefinite and cardinal "an".

So what we provide a philosophical rationale here for is:

"cardinal/ordinal" OE "an"

.
.
.

to 1. cardinal MnE "one"
2. indefinite MnE "an", "a".


The alleged distintion, functional, rather than in terms of 'physical devices' diachronically considered, "indefinite article" (an, a) and cardinal numeral
adjective ("one") seems slightly otiose.

Etc.

Levinson notes that the ORDINALS lack some of the implicatures that the cardinals have:

"Grice was the first to use 'implicature' in English"

makes sense because others did after him.

But

"Jesus was the first to resurrect" (as uttered by a faithful Christian) seems odd in that he was the only one.

Or

"My first wife is called Anne" -- when we know it's Sir Peter Strawson saying it.

Etc.

But 'first' is like a superlative, note the ending -st, as in 'best'. So the idea is that it's THE one (as in "Chorus Line", etc.)

Etc.