Functions in "Begriffsschrift"

[...]it implies a fundamental discontinuity between Begriffsschrift and Grundgesetze since the two calculi are related to different conceptions of a function (Geach 1967, 151; Dummett 1991, 163; Kenny 1995 17, 1012).This interpretation of Begriffsschrift is claimed to be forced on us by the single section (Frege 1879, 9) where Frege explained what a function is; there is allegedly no alternative interpretation that fits this text provided we give scrupulous attention to his referring to symbols (or expressions) and his use of quotation-marks.5 Despite some admitted inconsistencies of phrasing, he must have there used quotation-marks for the usual purpose of mentioning linguistic expressions. [...]two of the functions (concepts) that Frege abstracted here from the proposition that Cato killed Cato are not constituents of the sentence Cato killed Cato.The difficulty crops up even more acutely in his explanation of the possibility of treating properties as arguments (10:4):Since the symbol occurs at a place in the expression(A)and since we can think of it as replaced by other symbols [such as] , X which then express other functions of the argument A we can consider (A) as a function of the argument .How is this to be understood? [...]he tied his concept of a function to concept-formation, hence indirectly to his analysis of count-statements (which state properties of concepts (Frege 1884, 46)). [...]his explanations of the possibilities for carving up given judgeable-contents in different ways into functions and arguments (Frege 1879, 10; 1884, 64) cannot be faulted as incoherent except on the grounds of internal inconsistency; certainly not on288 G. P. BAKER AND P. M. S. HACKERthe grounds that every sentence of a natural language must, if unambiguous, have a single complete logical (semantic) analysis.