Or shall we say, "Hardy's Paradox, and how Popper deals with a phenomenon
identified by Grice."
The new film, "The man who knew infinity" has a lot of Griceian implicatures.
The first one is that the film is not set in Oxford. Grice went to Oxford. The
implicature is: "The other uni exists."
Once Gilbert Ryle was asked if he worked at Oxford University. "There's no such
thing -- that would be an anti-Ockham universal. There are colleges and there's
the sub-faculty of philosophy, etc. But there's no such thing as Oxford uni."
The second implicature is that part of the screenplay reads, "Principia
Mathematica." While the words are uttered, the ms of Newton's treatise is
shown, not Whitehead's and Russell's masterpiece that Grice revered. The
implicature: "The other Principia Mathematica exist" ("Principia" is neutral
plural, hence the 'exist').
The third implicature is Popperian, and reflected in the title of the film,
itself based on a bio.
i.The man who knew infinity.
Grice talked about infinity when he said that the implicature invited by (ii)
is "stever," a portmanteau word of 'stupid' + 'clever':
ii. I know that there are infinitely many stars.
I.e., as Grice notes, "to combine 'know' with 'infinite' is stever: one cannot
_know_ infinite". The title is possible sexist, too, in that "The person who
knew infnity" perhaps scans better. According to Popper, infinity belongs in
W3. His example of an interrelation between W3 and W2 relates precisely to
mathematics, where infinity figures. Popper's example is of a Griceian
mathematician, not a Cambridge mathematician, but let that go.
The fourth implicature is Griceian of the first rate. In his second John Locke
lecture on 'aspects of reason and reasoning,' Grice quotes Hardy directly --
not the Dorset pessimist novelist, but but the Cambridge mathematician, Harold
Hardy (played in the film by Jeremy Irons). Grice quotes Hardy as an example of
'reasoner'. And there is much about this in the film, with Hardy (convincingly
played by Irons) focusing on 'proofs' as in "Proofs" used by Lakatos in his
Popperian philosophy of mathematical revolutions. Hardy is into 'proofs' of
'theorems,' and rejects 'intuitionism'. I felt that Hardy's references to
intuitionism were 'avant-la-lettre', in that they were directed towards
Dummett! But Grice's point is that we have
A. Explicit reasoning
where we cannot skip ONE set from premise to conclusion. And then there's
B. INCOMPLETE reasoning.
Grice's point may be called "Hardy's Paradox": while Hardy praised for the need
of step-by-step proof, he would often skip one step or two in his pieces of
reasoning. The film does not show Hardy displaying much of mathematical proofs,
but one can get the idea.
The fifth implicature is about Grice's heterodoxy -- As an Oxonian he should
have had antipathetic feelings towards Russell (as J. L. Austin should have had
antipathetic feelings towards Moore -- but Austin said, "Some like Witters but
Moore's MY man"). Russell was GRICE's man, and he dedicates one of his
unpublications to him, "Definite descriptions in Russell and in the
vernacular."
The film shows Russell being dismissed from Cambridge:
HARDY: Where are you going now?
I was expecting Russell (played by Jeremy Northam -- you can call "The man who
knew infinity" "Jeremy and Jeremy") to say, "London." To surpise all he says,
"Oxford, until Cambridge BEGS me to come back." Grice was enamoured with
Russell's and Whitehead's (or Whitehead's and Russell's "Principia
Mathematica") since he thought that Strawson should not have gotten offended by
Russell ("Mr. Strawson on referring", Mind). You see, Russell thought ordinary
language of the type Grice and Strawson spoke involved 'a few silly things
silly people say', as when we say:
iii. He went to bed and took off his trousers.
Surely (iii) is equivalent to:
iv. He took off his trousers and went to bed.
since 'p. q' is equivalent to 'q. p'. If we _feel_ that (iii) reports an event,
where the implicature is 'p, and then q', that's because there is a pragmatic
desideratum to the effect that our conversational contributions should provide
"ORDERLY" reports. Russell knew this, Whitehead knew this, and Grice knew this.
Strawson didn't. As L. J. Cohen later, Strawson would argue that 'and' carries
a different SENSE from Russell's and Whitehead's ".". But he is wrong. "And"
has only SENSE and is commutative. The 'then' implicature is cancellable:
v. He took off his trousers and went to bed; but of course I don't want to
implicate the events happened in the order I describe them as happening.
Jeremy Northam plays 'Bertie' (as Hardold Hardy calls him) sympathetically,
much more than the one who plays him as a really hateful character in "Tom and
Viv" (on the life of T. S. Eliot). But them Northam has a lot of class, and it
shows!
Irons plays a wonderful Hardy. And the film will help to make his theories
better known in Oxford, even among non-mathematical philosophers!
Cheers,
Speranza
