II. Frege as Idealist and then Realist

Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre‐1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated entities.     

Bohr as a Phenomenological Realist

There is confusion among scholars of Bohr as to whether he should be categorized as an instrumentalist (see Faye 1991) or a realist (see Folse 1985). I argue that Bohr is a realist, and that the confusion is due to the fact that he holds a very special view of realism, which did not coincide with the philosophers’ views. His approach was sometimes labelled instrumentalist and other times realist, because he was an instrumentalist on the theoretical level, but a realist on the level of models. Such a realist position is what I call phenomenological realism. In this paper, and by taking Bohr’s debate with Einstein as a paradigm, I try to prove that Bohr was such a realist.

Kuhn as Perspectival Realist

In this essay I argue that T. S. Kuhn, at least in his later works, can be regarded as a perspectival realist. This is a retrospective interpretation based mainly on the essays published posthumously under the title The Road Since Structure (Kuhn 2000). Among the strongest grounds for this interpretation is that Kuhn explicitly states that one must have a “lexicon” in place before raising questions about the truth or falsity of claims made using elements of the lexicon. This, in a linguistic framework, can be understood as an affirmation of perspectival realism. The essay concludes with an examination of Donald Davidson’s famous paper, “On The Very Idea of a Conceptual Scheme,” arguing, along lines Kuhn himself suggested, that Davidson’s presentation is no threat to his notion of a conceptual scheme, or, I would add, a theoretical perspective.     

弗协调的弗雷格(英文)

本文表明,二阶弗协调概括与弗雷格的第五公理是足道的。也表明,如果等数关系是初始符号,那么通过弗协调推理可以从第五公理可以推出休谟原则。最后表明,弗协调的休谟原则不能用作逻辑主义数学的基础。     

Ramified Frege Arithmetic

?ystein Linnebo has recently shown that the existence of successors cannot be proven in predicative Frege arithmetic, using Frege’s definitions of arithmetical notions. By contrast, it is shown here that the existence of successor can be proven in ramified predicative Frege arithmetic.     

Frege on identities

The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an identity the terms flanking the symbol for identity do not have their ordinary contents, but instead have themselves as their contents. In ‘Uber Sinn und Bedeutung’ Frege became convinced that if an identity a=bis about the signs aand b, then it expresses no proper knowledge. So, since it is evident that many such identities do express proper knowledge, Frege concluded that identities are not about their contained signs. So he became convinced that his Begriffsschrift account was incorrect. What was the error in the argument that led Frege to that account? It was thinking that the content of a sentence is a function of the contents of its constituent signs, that is, the things it is about.     

Frege and his groups

Frege's docent's dissertation Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen(1874) contains indications of a bold attempt to extend arithmetic. According to it, arithmetic means the science of magnitude, and magnitude must be understood structurally without intuitive support. The main thing is insight into the formal structure of the operation of ‘addition’. It turns out that a general ‘magnitude domain’ coincides with a (commutative) group. This is an interesting connection with simultaneous developments in abstract algebra. As his main application, Frege studies iterations of functions. He does not yet pose the question of existence proofs. Measurement of magnitudes is also connected to numbers, but the discussion is here ambiguous in a way which calls for the systematic account of numbers in Grundgesetze     

Frege on Number Properties

In the Grundlagen, Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.