Definability and Logical Structure in Frege

Abstract

I. Truth, Definability, and Structure Logical s t ructure , definability, and the Begri f f sschr i f t these all work together in Frege 's thought . This paper is an a t tempt to unders tand some of that working, in par t icular to unde r s t and logical simplicity and its relat ion to indefinabil i ty. The present section has main ly to do with the indefinability of t ruth. Section II treats the views of some of Frege's predecessors on matters of definabil i ty and logical s tructure. Section III discusses Frege's relat ions to these predecessors. Sections IV and V are abou t the effect of the doctr ine of implicit definit ion on Frege's views. Frege makes frequent and impor tan t use of the no t ion of logical simplicity, but he does not , as far as I can discover, provide an account or explication of it. Logical simplicity is a g round for indefinabil i ty: O n l y what is logically complex can be defined. What is simple can only be pointed to.~ For this reason object , concept , and the dis t inct ion of comple te from incomple te cannot be defined. 2 Tru th canno t be defined either, since any a t tempt to define it would involve vicious circularity. 3 Tru th may also be logically simple, though Frege does not say this. (He does say that it is un ique [einzigartig; Der G e d a n k e , p. 50].) Al though he does not say it, it will help us in unders tand ing logical simplicity to ask what Frege could have meant in saying that t ruth is logically simple. The reason it will help is this: We shall be able to see something that logical simplicity does not mean , and that will be of general interest.