Hardy's Paradox

Speranza

Or shall we say, Grice on Hardy's Paradox, or "Bertie and Harold," or "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!