The Twelve Apostles: Algebra Meets Pragmatics

I have recently been having yet another round on whether Joan Rivers is lying when she says she is her thirties.

For Boolos, Joan Rivers is being 'trans-categorial'. Boolos, who knew Grice well, it's best to approach numericals via specific iota-operators. He relies on Quine.

Quine seemed to be thinking in the theory of types when he wrote ch. 44 on 'Numbers' for _Methods of Logic_. The definition of 'number', in
*non*-canonical positions, as I'd say -- as in, to use Quine's example,

"There are just as many Apostles as Muses."

(as opposed to "The Apostles are twelve") -- relies on that.

The logical form of: "The Apostles are 12" is


(EX)(x)(X(x) <-> apostle(x) & #X=12)

which reads:

"There exists a _relation_ X such that for all x, if x is an X, x is an apostle,
& the number of X's is 12."

Cfr.

http://web.mit.edu/philos/www/jjt-rlc-jc.html

J. J. Thompson et al writing for the online MIT memoir for Boolos:

"[Boolos's] key idea was to construe second-order variables as in effect _plural pronouns_, devices for referring in the plural to objects in the range of the first-order variables."

E.g. "years", as used by Joan Rivers.

"Donkey ears" -- as the Cockney says, come in twos.

I treasure my discussions with R. Helzerman on this.

Grice credits Boolos in "Vacuous Names". The blurb for Boolos's "Logic, logic, and logic" reads:

"George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gdel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has
provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume."



"[His] key idea was to construe second-order variables as in effect


_plural pronouns_,


devices for referring in the plural to objects in the range of the first-order variables."

But while written in Belgium (!), I mean, Vlaams, perhaps Boultinck remains my favourite numerical Gricean...

In terms of scalar implicature, we can, but then again we can not, postulate a scale

<9,8,7,6,5,4,3,2,1>

So that

1. Which month has 28 days?

yields

2. All months.

as _true_. Only a very antipathetic anti-Gricean will say that (2) is _false_. Yet, Joan Rivers says she is 37, and you think she is lying. Can an anti-Gricean at least have some _consistency_?

Etc.