Professor of Philosophy
The subject of formal methods in philosophy is intriguing but also — for me at least — puzzling, in more than one way. One puzzle is not unlike the predicament of the character in Molière who is surprised to hear that he had been speaking French prose all his life long. What else could he have done? What other methods should — or could — I have possibly used in the philosophical work I have done? The first two major philosophers to influence me were Eino Kaila and G.H. von Wright. Neither spoke self-consciously of formal methods, but neither one hesitated to use in areas like epistemology and philosophy of science concepts and arguments using logic probability theory or other kinds of mathematics. I took such a methodology for granted.
The successes of such tactics encouraged and inspired me further. An early case in point in my education was the analysis of the phenomenon of bluffing in the game theory of von Neumann and Morgenstein. (I was introduced to this “formal method”, not by my philosophy teachers but by one of my mathematics professors, Gustaf Elfing who taught the first lecture course in Finland on this subject.) On the face of things, bluffing is a purely psychological ad hominem ploy calculated to mislead an opponent. Yet a formal game-theoretical analysis shows precisely what is involved. In the rational eyes of a game theorist, bluffing is nothing more and nothing less than the use of a mixed strategy.
I was fascinated by this “hidden hand” analysis, and I believe that there are many more opportunities for such analyses than philosophers have exploited. For instance, I suspect that there is a much more striking rationale of appeals to coherence in epistemology than has been generally recognized. Another important example is the presence of two different kinds of identification principles in the conceptual and linguistic practice of all of us which nevertheless remains largely unacknowledged even by philosophers who pretend that they are practicing explication of concepts in our everyday logically unexamined life. It takes a cognitively disturbed patient like Oliver Sacks’s “man who mistook his wife for a hat” to make us aware of the difference.
Although formal methods are thus for me the natural medium of philosophizing, my “philosophical mother tongue”, I have come to realize that the very idea of formal methods is full of ambiguities and problems. Formal methods are important only when they actually do some work instead of merely being another notation. Keynes emphasized the mathematical skills of his great predecessor Alfred Marshall at the same time as he noted that Marshall used advanced mathematics only sparingly. Marshall knew when mathematics really does some work. In the same spirit, Pat Suppes used to respond to the news that some scientist or philosopher had formalized and axiomatized some theory by asking: “But how many theorems has he proved?”
Now that job that formal methods are drafted to do is in the last analysis indistinguishable from the substantial task they are tools of dealing with. Whether or not Marshall McLuhan is right or not, in philosophical analysis method is part of the message. For instance, in adopting the usual epistemic logic one is in effect adopting one particular interpretation of the notion of knowledge. If you do not see this at once, you may consider the parallel case of the logic of visual cognition. If one analyzes visual cognition in terms of the possible situations one’s visual impressions rule out or admit, one is treating visual perception as pickup of information. In other words, one is in effect agreeing with a version of J.J. Gibson’s ecological theory of perception according to which “there can be sensationless perception, but never informationless perception.”