Here’s my write-up of last night’s event — please add comments where I’ve missed things, got things wrong etc. In particular, this is my recollection of what Wilfrid said and isn’t based on his notes, so apologies if I’ve mangled anything.

The topic was introduced by Prof Wilfrid Hodges in what transpired to be his last engagement as a member of Queen Mary College staff. He opened with brief descriptions of Aristotle’s syllogistic logic, and the tradition that followed him. In particular he pointed out that this tradition often claimed that logic — broadly, the formal rules for making arguments or deductions — was at the very heart of all rationality.

Aristotle’s logical rules were good, but are they sufficient for rationality? It would seem that computer progammes, which are purely logical, would count as rational; the Curry-Howard Correspondence is a technical result in computer science that exhibits a clear relationship between programmes and arguments, or at least the special case of those mathematical arguments known as “proofs”. But is this satisfactory? Or is rationality something more?

The American philosopher C S Peirce put forward a “proof” that Aristotle’s rules for logic were sufficient for rationality. His argument proceeded by starting from an intuitive idea about how we reason and showing that this simply corresponds to a syllogism. But the act of reducing a real-world argument to a formal scheme is very messy and not at all straightforward. What’s more, real-life decisions are often not based on a specific set of well-defined hypotheses; we’d have to include a huge number of assumptions to write out the decision-making process in formal terms. That’s perhaps why it’s possible for two rational people who start with the same information and reach different conclusions; their previous experiences will come to bear in all kinds of complex ways.

What’s more, all this would take a huge amount of time, and in real life we don’t have that kind of time. There are also questions of epistemology — the status of our knowledge — and hence probability, too. We don’t need pure textbook logic to be rational but “bounded rationality“, which operates within human limits; perhaps this just *is* rationality.

In the ensuring discussion we touched on a wide range of topics. A few that I particularly remember were:

- The contention in some parts of Continental philosophy that “rationality” is culturally specific, and isn’t an absolute. I have some thoughts on this but as I didn’t get into them at the time I’ll hold my fire for another post.
- On a related note, there was some discussion of whether reason, however defined, was the only valid way of thinking. I was reminded of William S Burrough’s injunction to “abandon all rational thought” in the quest for creativity and new ideas. We didn’t explore that too much, or the relationship it has to the pragmatic process of forming our basic assumptions, which can’t be a purely rational process.
- The idea of “getting rid of your assumptions” or minimising them, and the impossibility of really doing so, which I think were recognised on all sides. This is one reason why rationality can’t be
*just*logic. In order to infer very much using your logical system you have to have some assumptions to get you started. - The existence of “deviant” logics different from Aristotle’s, including Buddhist logic. The Stanford Encyclopaedia gives a gloss on the Tetralemma which is probably the most relevant part. Wilfrid mentioned studies of the Buddhist tradition by Western logicians indicating that the actual “laws of thought” being formulated were not as radically different from Aristotle’s as first appeared; it was more of a superficial difference in presentation rather than a radical difference in rationality.
- On a similar tack I also mentioned Brouwer’s intuitionism, which is a logic that doesn’t assume the Law of the Excluded Middle. But as Wilfrid pointed out, this is a special logic designed to capture not “truth” but “provability”, and just because something is true doesn’t mean we can prove it (if it did, we’d be omniscient).
- The Wason Selection Test, and the fact that even trained logicians may find logical rules hard to apply in quite simple cases; but also the fact that the way we choose to reason is fitted to different situations (in this case, a psychology experiment), lending a sociological aspect to the problem.

Wilfrid summed up with the sentiment that, while people are not universally rational, and while we may not yet understand everything about rationality (or even everything about logic) we as a species can be optimistic about our chances of putting our relationships on ever more rational footings in the future, although that outcome was by no means certain.

It was a great discussion and I know I missed a lot out — as I said above, please feel free to add your own recollections, or follow up on things not said, below. In particular there were some interesting things said about Leibniz and Wittgenstein (not at the same time) that I don’t now recall well enough to try to write them down.

If you’d like to read something by Wilfrid and haven’t the necessary background for his mathematical work, this paper is relatively accessible and touches on many of the topics we talked about. If you enjoyed the Wason Selection Test but found it a bit easy then this is a real challenge.