Redressing Frege's Failure to Develop a Logical Calculus for the Theory of Sinn and Bedeutung

Dissertation, The University of Iowa (2000)

Kevin Klement
University of Massachusetts, Amherst
Gottlob Frege's theories of meaning, and, in particular, his distinction between sense and denotation were developed as part and parcel of his views in logic and the philosophy of arithmetic. Nevertheless, the logical calculus developed in his Grundgesetze der Arithmetik does not fully reflect his semantic views. It provides no method for transcribing the so-called "oblique" contexts of ordinary language, and does not reflect his metaphysical commitment to the "third realm" of sense. The dissertation highlights ways in which Frege's views cannot be fully evaluated until this gap in his logical language is filled. It then fills this gap by presenting a expansion of Frege's logical system in line with his mature views in the philosophy of language. Along the way, a number of exegetical issues with regard to Frege's understanding of both logic and semantics are discussed, and a new interpretation of the nature of senses emerges. Previous attempts at developing the logic of sense and denotation, such as those of Church and others, are discussed but are concluded to reflect inadequately the views of the historical Frege. ;However, once an accurate account of the logic of sense and denotation is in place, new and hitherto unnoticed problems with Frege's philosophical position are revealed. For example, it is shown that contradictions stemming from certain new semantical and Cantorian antinomies are demonstrable in the expanded system, and that some of them are independent of the inconsistent class theory already present in the extant system. Through a comparison with philosophers whose semantic views are in some ways similar, the source of the difficulties in the logic of sense and denotation is traced to a set of mutually untenable metaphysical commitments in Frege's philosophy of language. A number of possible revisions to Frege's semantic theories are considered, and it is concluded that while it may be possible to salvage a broadly Fregean theory of meaning and incorporate it within a logical calculus, the theory must abandon at least some of the core elements within Frege's robust ontology of abstract objects
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