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Identity in Frege's Begriffsschrift: Where Both Thau-Caplan and Heck are Wrong

From: Canadian Journal of Philosophy
Volume 36, Number 3, September 2006
pp. 355-370 | 10.1353/cjp.2006.0014

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Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift (Bs) of 1879, and its relation to his view in 'Über Sinn und Bedeutung' (SB) 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' (Bs), or Sinne (SB) are also concerned.

In 'What's Puzzling Gottlob Frege?' (2001) Michael Thau and Ben Caplan (T&C) argue that in SB Frege did not reject his earlier view of identity in Bs, and that the arguments raised there endorse those of Bs. In this, I believe they are right. However, T&C adopt and enhance a widespread view, according to which the Bs theory of identity is 'meta-linguistic.' By this they presumably mean that identity is a relation between signs and that an identity statement is about signs. This, I believe, is wrong, or at least misleading. I shall argue that the objectual vs. meta-linguistic opposition is anachronistic and may be misleading with regard to Bs, in a way that can distort its view. If, nevertheless, we insist on enforcing it on the text, the Bs view should rather be seen as objectual, not meta-linguistic in the above sense: identity, in Bs, is identity of content; and the contents of names are objects. But in order thus to talk of objects, Frege realized, we must regard identity statements as concerned also with the ways of determining these contents. So, at least, I shall argue.

T&C also argue that the meta-linguistic theory they find in Bs is never rejected or replaced by Frege in his later writings. I think this is wrong, but shall not discuss the matter here. I confine my remarks here only to some aspects of Bs and SB.

In his 'Frege on Identity and Identity Statements' (2003), Richard Heck accepts T&C's meta-linguistic construal of identity in Bs, on which, as stated above, I believe he is wrong, but rejects their view with regard to Frege's later writings. Heck insists on distinguishing the question of what identity is, from the question of what identity statements express. In Bs, according to him, Frege thought that identity is a relation between expressions; later (from the early 90s), he rejected it and thought that identity is a relation between objects. Heck seems to begin the late phase (as is customary) with 'Funktion und Begriff' (FB), from which he cites extensively. This should include SB, which was published after FB, but Heck doesn't discuss SB in detail. As to what identity statements express, Heck is less clear. He claims that in Basic Laws of Arithmetic (of 1893, BL), Frege thought that '0=1' for instance 'denote the True if and only if zero is one. The thought it expresses is thus that zero is one, not that "0'' denotes the same object as "1'" (95). This is of course right, but it may seem to underrate the main point, viz. that the thought expressed here is not just the identity of the objects, but their identity as conceived under the particular corresponding senses (of 'zero' and 'one'), which are constituents of the thought. 

I The Main Point of the Identity Section (8) in Bs and Its Relation to SB

Both T&C and Heck (as almost everybody) seem to ignore a terminological point that reflects Frege's main innovation in the identity section (8) of Bs. Frege distinguishes there between names (Namen) and signs (Zeichen). The distinction is not explicitly stated, but it is used almost consistently in section 8. In the second sentence of the section, for instance, Frege writes:

'Während sonst die Zeichen lediglich Vertreter ihres Inhaltes sind ... sobald sie durch das Zeichen der Inhaltsgleichheit verbunden werden; denn es wird dadurch der Umstand bezeichnet, dass zwei Namen derselben Inhalt haben.'

('Whereas in other contexts signs are merely representatives of their content ... they suddenly display...

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