Vincent F. Hendricks and John Symons, eds.: Formal Philosophy.
Automatic Press 2005.
US$40.00 (cloth ISBN-13: 978-87-991013-1-3); US$26.00 (paper: ISBN-13: 978-87-991013-0-6).
Recently analytic philosophers have rediscovered the power and beauty of formal philosophy. Although this trend that can hardly be called new--think of philosophical giants such as Frege, the members of the Vienna Circle or the Polish school--events like the annual Formal Epistemology Workshops in the US, the 2006 Studia Logica conference titled Towards Mathematical Philosophy in Poland, the recent Mathematical Methods in Philosophy conference in Canada, and the upcoming first annual Synthese conference on David Lewis and the Future of Formal Methods in Philosophy certainly constitute a renewal of interest.
Formal Philosophy, edited by two eminent 'current generation' formal philosophers, offers a public forum to the who-is-who of formal philosophers of the 'last generation,' i.e. the very generation that cherished the applicability of mathematics in philosophy while facing the challenges of a hostile anti-formalist environment. Each contributor was asked to answer five relatively broad questions. This format triggered not just a sequence of insightful and entertaining reminiscences, it also allowed the editors to do something almost unheard of: to take an eclectic snapshot of modern analytic philosophy as a whole.
Where the Logical Empiricists used formal methods to clarify the philosophical presuppositions of scientific theories, modern formal philosophy seems driven by the mathematical structure of the philosophical mundane or, as van Benthem puts it, by the 'formal patterns in ordinary activities' (1). For example, modal logic and its analysis of idioms of natural language replaced first-order logic and set theory as the paradigms of logical endeavor, and accordingly not less than eleven contributors deal with modal logic. (There are exceptions: Fagot-Largeault says about Suppes' remark 'Don't waste your time with modal logic ... go to probability theory' , that it was the best advice she ever received.)
On the other hand, the interviewees' to-do list for young formal philosophers is heterogeneous and unclear. For instance, where Paris (151) calls upon the next generation to overcome the dark age in which inductive logic went out of fashion and to bridge the gaps between Carnap's and Kemeny's work and the new results in AI and Cognitive Science, Haack suggests more or less the opposite, guided by the thought that 'supportiveness of evidence does not depend on [logical] form alone' (89). Furthermore, though there are some typical answers to questions about the most important open philosophical problems--the mind-body problem and the understanding of mathematical intuition are mentioned--very few suggestions are given on how to tackle them or what formal philosophy's role might be.
Still, some of the interviews in Formal Philosophy also show remarkable coincidences. For example, I leave it for the reader to decide which of the following two quotations is van Benthem's and which is Fagot-Largeault's: 'collective rational agents are interactive .... The formal methodology available for the analysis of collective rationality may be found in the theory of games;' 'the dynamic stance making action and interactive processes a core topic ... has an interesting synchronicity in philosophy, logic, artificial intelligence, and computer science ... games seem the interactive model par excellence.'
Another point of consensus among the contributors, apart from their obvious support of logical and mathematical methods in philosophy, is the belief that formalisms can easily be abused: van Benthem (2, 'boring people get even more boring when you give them formulas'), Follesdal (36, 'Formalism may be overused. It is sometimes used to present reasoning or results that can just as easily be presented without the formalism'), Hintikka (112, 'Formal methods are important only when they actually do some work instead of merely being another notation'), Segerberg (164, 'The bad examples arise when formal investigation begins too early, or if the formalism does not have enough structural richness to reward technical work'). Those passages remind us of the dangers of unjustified formalising and that all successful applications of formal methods must 'have a philosophical story at their heart' (Fitting, 29f).
The process of formalisation itself is one topic I wish the interviewees had addressed in more detail. Both Follesdal (36, 'Philosophy is, like mathematics, concerned with structures') and Williamson (210, 'Little progress is made in mathematics or philosophy without a strong capacity for abstract pattern recognition') defend a structuralist view of philosophy, on which philosophical inquiry ultimately requires formalisation. But only Spohn tries to enumerate some of the presuppositions and features of formalisation. For instance, amenability to formal methods comes in degrees and depends on the philosophical field (170), and formal methods are required at every stage of philosophical activity (180). (Hanson's article, 'Formalization in Philosophy' [Bulletin of Symbolic Logic 6, 2000], contains further information on this topic.)
Contrary to widespread prejudice, formal philosophers can also be funny: When Gaifman (63) knows that 'something wrong has happened to "metaphysics" ' in view of debates about possible worlds containing only gunk; when Glymour (67) tells us why he threw Toulmin's Philosophy of Science into a deep cavern; when Levi talks about the 'unholy marriage of game theory and evolutionary biology' (130); when Parikh laments that brilliant young set theorists are 'wasting their time inventing stronger and stronger "large cardinal" axioms' (144); and when Segerberg points to rigor as 'one reason why those of our nonformal colleagues who don't like us don't like us' (163), entertainment is guaranteed.
After Logical Empiricism's decline, proponents of logical and mathematical methods found themselves pushed from the core areas of philosophy into the less threatening positions of 'mere' logicians or of scientists working in philosophy-'related' disciplines (typically, computer science). Despite the recent renewal of interest, not every contributor to Formal Philosophy is therefore unreservedly optimistic about the future prospects of doing philosophy this way. For example, Segerberg worries that 'beginning graduate students in philosophy increasingly turn to nonformal areas of philosophy' (16). If this is so, then the editors of this volume should not just get credit for putting together a splendid set of interviews; they should also be praised for swimming against the stream. As the sequel Masses of Formal Philosophy (Automatic Press 2006) indicates, the number of salmon might be on the rise.
University of Bristol