What I think about the role of formal methods
I will end by considering four slogans, rejecting two and endorsing two.
I am a supporter of formal methods in philosophy. This is not to say that I believe that all philosophy must be made with their help. My friend and older colleague, the late Stig Kanger, who liked to provoke, used to say that philosophy that cannot be mathematized is not philosophy. And there is Quineís famous line: philosophy of science is philosophy enough. I donít subscribe to either slogan (and I donít know whether Kanger or Quine really did either). My own view is that formal methods are important for some parts of philosophy and indispensable for a few.
The value of formal methods lies in what they let you do but also to some extent in what they donít let you do. That they allow you to do things you cannot do without them is obvious. Rich Thomason once said something like this (in conversation about philosophers who spurn formal methods): Aristotle was very smart; todayís philosophers cannot realistically hope to improve on what he said without resorting to methods that were not available to him. This is a striking observation that would deserve to be hammered into a slogan, for example, Donít think you can outsmart Aristotle! or To go beyond a great philosopher, go beyond his methods!
But there are also things formal methods will not let you do. Formal methods impose discipline. It is of course possible for a formalist to devote himself to triviality. Even reputable technical journals occasionally contain nugatory papers that probably owe their existence to their authorsí need for tenure or promotion. But formal methods bring with them fairly definite standards of excellence, and so it is very difficult to get absolute rubbish published in a technical journal. For parts of the humanities, standards of excellence are, relatively speaking, less clear. For philosophy in particular, this lack is sometimes a problem. This is one reason why I deplore that the logic component in philosophy curricula in the countries with which I am familiar appears to be diminishing. It must be good, it seems to me, for all students of philosophy to be confronted with rigour at least once in their lifetime, a concept they are unlikely to meet outside mathematics or logic.
My exit line is due to Esaias Tegnťr, Swedish poet and bishop of Lund in the early nineteenth century. I donít know what he would have thought of having his words cited as a slogan in support of the use of formal methods in philosophy, but I like to think that he would have condoned it: