The Logic of SINN

_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58 eviews THE LOGIC OF SINN N G Bertrand Russell Research Centre / McMaster U. Hamilton, , Canada   @. Kevin C. Klement. Frege and the Logic of Sense and Reference. London and New York: Routledge, . Pp. xiii, . .. his is, I think, the best book on Frege I have ever read. It has a narrow Tfocus, dealing only with Frege’s distinction between Sinn and Bedeutung, but it covers it exceptionally thoroughly, adding considerably to our knowledge of what might have seemed to be an overworked topic and throwing, in the process, a flood of light on a number of other Fregean topics. Klement’s book exemplifies what used to be the hallmark virtues of analytic philosophy—rigour, clarity, and attention to detail—and shows that, even on topics that have been deluged in ink, they pay off. Frege’s distinction between Sinn and Bedeutung has been widely hailed as his most important contribution to the philosophy of language, and, indeed, one of the greatest contributions to philosophy of language ever. Despite partial anticipations , notably in Mill’s distinction between connotation and denotation, Frege was the first modern philosopher to maintain that the distinction holds for all linguistic expressions and the first to distinguish sense from the psychological associations of the expression (which Frege labelled its “tone”). Despite Frege’s systematic elaboration of propositional and predicate logic, he never attempted a similarly rigorous semantic theory. Nonetheless, his remarks on the Sinn/Bedeutung distinction suggest that he would have regarded it as a feasible project. He can indeed be thought to have set the stage for such a theory, without actually supplying one. That Frege himself did not attempt a formal semantics based on the Sinn/ Bedeutung distinction hardly constitutes dereliction of duty, but, as work on formal semantics burgeoned during the twentieth century, it becomes more surprising that the project attracted so little attention, especially since the Sinn/  J. S. Mill. A System of Logic (), Bk. , Chap. . russell: the Journal of Bertrand Russell Studies n.s.  (summer ): – The Bertrand Russell Research Centre, McMaster U.  - _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58  Reviews Bedeutung distinction retains wide intuitive appeal. At least one problem with the project was pointed out by Russell in a letter to Frege of  September : since Frege admits Gedanken as the Sinne of complete sentences, an analogue of the propositional paradox which Russell presents in Appendix B of The Principles of Mathematics (PoM, §) should arise in the logic of Sinn. Frege, in the absence of a formal proof, refused to admit that this was so— and, of course, in the absence of an explicit logic for Sinn, a formal proof was not forthcoming. Though he did not intend to be historically faithful to Frege, Alonzo Church took up the project of creating a viable logic of sense and reference in the s, and it remained very much his project for the next  years. Church presented three different systems, which he called Alternatives , , and , with progressively more relaxed identity criteria for senses. On Alternative , which he favoured on account of its appropriateness for modal logic, two sentences , A and B, had the same sense if A ≡ B was a thesis of the logic. This system had little relevance for Frege, since it was part of Frege’s intention to use the notion of Sinn to capture what he called the “cognitive value” (Erkenntniswert ) of an expression; plainly A ≡ B may be a thesis even though A and B differ in cognitive value. Alternatives  and  attempt to capture a much stronger notion that Church calls synonymous isomorphism. They differ in that in Alternative  synonymous isomorphism is preserved under λ-conversion, while in Alternative  it is not; that is, in Alternative  “(λx Fx)a” and “Fa” are synonymously isomorphic while in Alternative  they are not. Unfortunately, Church developed his theories within simple type theory, the theory which Russell had found himself forced to abandon on account of the propositional paradox he had presented to Frege in September . It did not take long before Myhill proved a close relative of this paradox, usually now known as...

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