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By Tolas J.

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It is not really significant, therefore, that Frege recognized distinct expressions of natural languages as carrying the same sense; this may have been merely one of their many deficiencies. The important question is whether he could have allowed that the same phenomenon might occur also in an ideal formal language, such as his own Begriffsschrift. And here, as it turns out, the matter is more complicated. There are, to begin with, conclusive reasons for thinking that Frege could not possibly have allowed expressions of different syntactic structure to share the same sense; and there are also powerful, though not quite conclusive, reasons for thinking that he would not have allowed any distinct expressions to share the same sense, even if they happened to agree in syntactic structure.

He explains, for example, how to form the concept homo as the product of the already existing concepts rationale and animal (p. 33). He illustrates the familiar way in which, if these two already-existing concepts are represented by regions in a plane, the new concept can be represented by their intersection. And then, alluding to the illustration, he describes the sterility of these Boolean techniques for the formation of new concepts: In this sort of concept formation, one must assume as given a system of concepts, or speaking metaphorically, a network of lines.

And it is in part his view of definitions that enables him both to see a connection between his characterization of analyticity and Kant's, but also to break the connection Kant sees between the analytic and the uninformative truths. For Frege, the truths of arithmetic are analytic because they can be discovered through conceptual analysis alone; but his more sophisticated definitional techniques allow us to construct concepts complex enough that their analysis is genuinely informative, extending our knowledge.

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