To mock a mockingbird: Smullyaniana

Speranza

There was a recent post to the "Carnap Corner" on "Deep Learning Eternal Truth" by R. B. Jones (the founder of Carnap Corner, as it happens).

I thought I would drop a line (or two, as the implicature goes) about Smullyan.

That would be Raymond Merrill Smullyan, a very prolific philosopher whose interests seem to correspond, shall we say, with Carnap's and indeed, Jones's.

Jones makes in his post on "Deep Learning" a passing reference to the catastrophe (not a word Jones uses) brought by Goedel. And Smullyan then has a whole book on Goedelian paradoxes that should amuse Jones.

Smullyan's career is eclectic. He holds a MA, and a PhD from Princeton -- His dissertation being on "Theory of Formal Systems".

He is best known to Griceians for a passing reference in Grice's "Vacuous Names" and for Smullyan's "First Order Logic".

When Grice gave his second William James lecture on logic and conversation, he starts by referring to what he calls, yes, a 'commonplace' in philosophical logic. The commonplace that there is, or appears to be (Grice is so guarded it hurts), between:

not
and
or
if
all
some (if not all)
the

and their formal counterparts: ~, /\, \/, ), (Ax), (Ex), (ix).

And the commonplace is repeated by Smullyan.

Of course, Grice will go on to argue -- not so much in THAT lecture but the two following ones, especially Lecture V, concerning if/) -- that this commonplace RESTS ON A BIG MISTAKE!

The mistake is due to the inability -- by Smullyan and others, onto which we can add Carnap and Quine -- especially the Quine of "Methods of Logic", that P. F. Strawson refers to in his introduction to "Philosophical Logic" (Oxford readings in philosophy) -- to perceive an implicature.

It's not that 'and' and '/\' differ, but if we say:

i. Sally, in our alley, got pregnant and married.
ii. Sally, in our alley, married and got pregnant.

Logically, they are equivalent. If the 'implicatures' differ, that's because there are, to use Carnap's label, some 'pragmatic' or 'general features of discourse' (as Grice puts it in "Prolegomena", Lecture I), at play, so that if you are narrating events, you proceed orderly.

This was noted by Urmson before Grice, and indeed by the Greeks before the English! Urmson's example (in "Philosophical Analysis between the two war worlds") is amusing:

iii. Smith got into bed and took off his trousers.
iv. Smith took off his trousers and got into bed.

When Grice delievered his lecture on "Presupposition and Conversational Implicature" (in the original transcript) he used that example, but the segment was edited out when he included that lecture in his WoW (Way of Words).

There are other fascinating facets about Smullyan. He was, like Grice, fascinated with Dodgson, Goedel, Boole, Cantor, and all the interesting names that should fascinate a Carnapian.

Smullyan had a taste for paradoxes, but he never lost his faith that first-order logic was the solution to it all, almost!