Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift of 1879, and its relation to his view in ‘Über Sinn und Bedeutung’ of 1892 deserve careful attention. The issues involved have a wider significance than Frege’s specific views on identity in different periods, though these are important enough. They concern also the move from what I call below ‘thin’ semantics, which is exhausted in signs being assigned content, to a ‘thick’ semantics, in (...) which ‘modes of determining their content’, or Sinne are also concerned. (shrink)

Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift of 1879, and its relation to his view in ‘Über Sinn und Bedeutung’ of 1892 deserve careful attention. The issues involved have a wider significance than Frege’s specific views on identity in different periods, though these are important enough. They concern also the move from what I call below ‘thin’ semantics, which is exhausted in signs being assigned content, to a ‘thick’ semantics, in (...) which ‘modes of determining their content’, or Sinne are also concerned. (shrink)

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...) as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)