Abstract
In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.
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Notes
An anonymous referee questioned whether there is any real ontological economy here, since “it is well-known (i) that characteristic functions can play the role of sets and (ii) that functions themselves can be identified with sets of a certain sort. Given either set or function as primitive, it is trivial to define the other.” The referee correctly points out that Russell’s talk of “propositional functions” is unclear, since at times they appear to be properties and at other times to be linguistic expressions. However, one thing that is certain is that Russell’s propositional functions are intensional entities; otherwise the entire discussion of classes in the Introduction to Principia Mathematica (Whitehead and Russell 1935, vol. 1, 71–81—see also Russell 1924, 183–184, and Russell, 1956, 266–267), with its distinction between intensional and extensional functions of functions, would make no sense. Hence the referee’s argument that no real ontological economy is achieved cannot be directly applied to Russell’s own view—for both the characteristic functions with which sets might be identified, and functions constructed in the usual way as sets of ordered pairs, are merely “functions in extension,” rather than propositional functions. There is no space here to enter into debate over the nature of propositional functions, so I will just state my own view dogmatically. For Russell: (a) propositional functions are real, non-linguistic, entities; (b) that propositions are analyzable into function and argument is required to account for the unity of the proposition; (c) since it is propositions that are so analyzable, propositional functions must be intensional; (d) any understanding of classes as abstract individuals gives rise to serious ontological difficulties; hence (e) the reduction of classes to propositional functions achieves a real ontological economy since propositional functions are necessary anyway for our account of propositions and their unity.
This is clear from Our Knowledge of the External World and “The Philosophy of Logical Atomism,” the texts on which Soames bases his discussion of Russell’s program of logical construction, and his logical atomism, in Chapters 6 and 7 of The Dawn of Analysis. According to Our Knowledge, “the whole theory of physical concepts … is inspired by mathematical logic” and is based on “the principle of abstraction.” (Russell 1969, p. 51) This principle, which allows us to replace talk of a common quality of a group of things with talk of membership in the group, is illustrated by Russell’s explicit definitions of points and instants as classes. (Russell 1969, p. 119, 124, 127, 132) Russell’s claim that, by allowing such definitions, the principle of abstraction “clears away incredible accumulations of metaphysical lumber,” (Russell 1969, p. 51) only becomes fully comprehensible in the light of his discussion of the no-class theory and its consequences (Russell 1969, pp. 210–213). The dependence of Russell’s theory of logical constructions on his account of classes is even more obvious in “The Philosophy of Logical Atomism.” For example, Russell states that numbers are classes of classes of particulars, and hence “logical fictions;” similarly Picadilly, desks, tables and chairs, are said to be logical fictions, since they can be analyzed as series of classes of particulars. (Russell 1956, pp. 190–191, 270–275) Yet none of this is mentioned in chapters 6 and 7 of The Dawn of Analysis.
References
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