Bellerophon didn't ride Pegasus

--- by JLS
-- for the GC

As J says, "Bellerophon [may ride] Pegasus".

Indeed, the issue is a tricky one.

This is predicate calculus -- not subject-and-predicate calculus. Yet Grice wants to say that

"Fa"

is

"a categorical subject-predicate sentence" (p. 123 of "Vacuous Names").

So far so good.

He goes on to discuss atomic formulae. "Socrates is wise" we understand. The other example of an atomic sentence he gives is:

"Bellerophon rode Pegasus".

The logical forms are different. For "Socrates is wise" it is indeed

Fa

---

For "Bellerophon rode Pegasus" it is, rather

Fab.

----

He does not give THAT logical form.

Yet he wants to say -- but does not say -- that, should we subscript "Fab" we would have

F3a1b2

---

For "Socrates is wise"

it has to be

F2a1

----

This is so obvious that it does not need a numerical device. It falls within the third feature regarding the scope-precedence of his natural deduction system --

to wit, that

"in an atomic formula the subscripts

of individual constants are always

higher than thta of the

predicate-constant."

This is, he says,

"in consonance with the fact that

[...] affirmative categorical subject-predicate

sentence"

among which he quotes,

"Bellerophon rode Pegasus"

'impl[ies]', or rather entails

'the non-vacuousness of the names which [it] contains.'

The topic had interested Strawson a few years earlier, in his "Identifying reference and truth-values" in Theoria, repr. in Logico-Linguistic Papers; and Strawson's observation was well received (for some reason) by the linguists of the day reading the philosophical literature:

Strawson's pair being:

"The king of France visited the Exhibition"

"The Exhibition was visited by the King of France".

---- It seems the presupposition, for Strawson, holds for 'topic' -- subject-position -- only, not for 'comment' position.

Mutatis mutandis, one may transfer the disanalogy or asymmetry to Grice's example:

"Bellerophon rode Pegasus"

----

Strictly,

S --> NP + VP

Subject: Bellerophon.
Predicate: rode Pegasus.

So,

"Bellerophon rode Pegasus"

implies, to use Grice's verb -- but 'entails' will do --

the non-vacuousness of "Bellerophon" -- never mind "Pegasus".