1 Stegmüller Wolfgang, The Structuralist View of Theories: A Possible Analogue of the Bourbaki Programme in Natural Science (Berlin: Springer-Verlag, 1979). Stegmüller asks what would have happened if Bourbaki had used first-order logic and set theory: “The Bourbaki volumes would then look like, for example, the last chapter of Shoenfield's Mathematical Logic. I really fear that the Bourbaki volumes would not exist, at least not yet, since instead of having published more than 20 volumes, Bourbaki would still have been working on his first volume” (p. 5). To anybody who did any work in logic-related areas in the sixties or early seventies these are refreshing sentiments indeed: did philosophers really have so little to occupy them in those days that they had to spend their days and nights trying to live up to Harvard views on first-order rigour?
2 I refer to Mary Williams's formalization of the theory of natural selection, which Thompson quotes on p. 57–58. This is because of Axiom 4 of this formalization: “[If] … D 2 is superior in fitness to the rest of D for sufficiently many generations, then the proportion of D2 in D will increase” (my italics). How is the italicized clause to be spelt out? The claim, presumably, is that the superior fitness of D2 will lead to its proportional increase in a finite number of generations, but since we are dealing with a probabilistic effect, there can be no fixed finite upper bound on the number of generations required for this to occur. But this cannot be expressed in first-order logic, since it is a consequence of the compactness theorem that if a first-order theory can be true in an arbitrarily large finite model, then it has an infinite model.
3 Putnam Hilary, “The Meaning of ‘Meaning,’” in Language, Mind, and Knowledge, edited by Gunderson K., Minnesota Studies in Philosophy of Science, No. VII (Minneapolis: University of Minnesota Press, 1975).
4 Suppes Patrick, “The Desirability of Formalization in Science,” Journal of Philosophy, 65 (1968): 651–54.
5 Thompson seems in fact to contradict himself on the question of mathematical power, for he implies on p. 75 that set theory provides us with a more powerful tool for formalizing a theory than mathematical logic, but then asserts on p. 76 that the “models of a theory T axiomatized by defining a set-theoretical predicate are exactly the same as models of T axiomatized in mathematical logic.” The second claim is true only if we are restricted to first-order set theory, but on this restriction the first claim is false.
6 A synoptic account of Aristotle's theory of science will be found in “The Structure of Aristotelian Science,” the Introduction to Aristotle Today: Essays on Aristotle's Ideal of Science, edited by Matthen Mohan (Edmonton: Academic Printing and Publishing, 1987).
7 Salmon Wesley C., Scientific Explanation and the Causal Structure of the World (Princeton: Princeton University Press, 1984).
8 I refer to developments of the idea, first explicitly floated by Donald Campbell, that the evolution of culture proceeds by “blind variation and selective retention”: see his “Evolutionary Epistemology,” in The Philosophy of Karl Popper, edited by Schilpp P. A. (LaSalle IL: Open Court, 1974), Vol. 1, p. 412–63.
9 For a classic critique of this tendency, see Bromberger Sylvain “Why-Questions,” in Mind and Cosmos, edited by Colodny R. G. (Pittsburgh: University of Pittsburgh Press, 1966), p. 86–111.
10 Sober Elliott, “Fact, Fiction, and Fitness: A Reply to Rosenberg,” Journal of Philosophy, 81 (1984): 372–84, see especially p. 379–80.
11 Ruse Michael, Taking Darwin Seriously: A Naturalistic Approach to Philosophy (Oxford: Blackwell, 1986), chaps. 4 and 5.
12 Berlin B. and Kay P., Basic Color Terms: Their Universality and Evolution (Berkeley: University of California Press, 1969). See Ruse, Taking Darwin Seriously, p. 143–45.
13 Ibid., p. 110. My emphasis.
14 Thompson Paul, “Tempo and Mode in Evolution: Punctuated Equilibria and the Modern Synthetic Theory,” Philosophy of Science, 50 (1983): 432–52.
15 Mayr Ernst, Toward a New Philosophy of Biology (Cambridge: Harvard University Press, 1988), p. 149.
17 Stidd Benton M., “Are Punctuationists Wrong About the Modern Synthesis?” Philosophy of Science, 52 (1985): 98–109; extract from p.105.
19 Ibid., p. 139. My emphasis.
20 Here it should be said that a number of formalists, like Sneed and Stegmüller, have said that their articulation of scientific theories is capable of accommodating the insights of Kuhn. The insights they have in mind have to do with the incommensurability of meaning across theories — ironically a topic in connection with which Kuhn was most influenced by the formalist theory of meaning put forward by Carnap and the positivists. Kuhn's very important idea that science is governed by paradigms, not theories, by psychological associations and preferences, not entailments and consistency, is completely ignored by Sneed et al.