ABSTRACT
In this chapter, the attempt is made to formulate a logical calculus for the theory o f Sinn and Bedeutung that is as close as possible to the sort o f system Frege himself would have developed had he had “the occasion to do so,” given what has been concluded in the preceding chapters. Our primarily aim is not to create a feasible intensional logical calculus, but only one that reflects Frege’s views. In fact, a number o f formal difficulties will be found with the calculus formulated, and these problems reveal flaws in Frege’s semantic views that have
scarcely been discussed by philosophers. Because our aim is to develop a fully Fregean logical calculus o f Sinn and
Bedeutung, we build our system upon Frege’s own Begriffsschrift, as outlined in Chapter 2 (employing the typographical changes therein). We shall consider expansions o f both systems FC and FC+V
While some of the decisions with regard to the development o f the calculus will be made so as to improve on ways in which Church’s Logic o f Sense and Denotation fails to reflect Frege’s own views, many of the strategies and approaches taken here are borrowed from Church. Firstly, and perhaps most importantly, we adopt the method of direct discourse. Rather than transcribing ordinary language expressions with the same signs in the Begriffsschrift regardless o f the context of their occurrence, sometimes they are transcribed using signs that stand for their customary Bedeutungen, and sometimes they are transcribed using signs that stand for their customary Sinne (their indirect Bedeutungen). We then introduce new function signs, principally “Δ” , to express relationships between Sinne and the Bedeutungen they present.
