Kobe Colloquium on Logic, Statistics and Informatics

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Date: 2015/11/19 (Thu) 1.30pm - 5.00pm Place: Room 421 Speaker: Matthias Schirn (Munich)

Time: 1.30pm - 3.00pm Title: Second-ordert abstraction before and after Russell's paradox

Abstract: In this talk, I analyze several aspects of Frege’s paradigms of second-order abstraction: Axiom V and Hume’s Principle. The issues dealt with include self-evidence and epistemic (non-)triviality with particular emphasis on Axiom V, Frege’s attitude towards Axiom V before and after Russell’s discovery of the contradiction, as well as the possible role and the status of Hume’s Principle in the face of Russell’s paradox. In the central part, I pursue a threefold aim: (a) to shed new light on the connection between Frege’s way of introducing the primitive function-names of his logical system and the requisite self-evidence of his axioms in whose expression such a function-name occurs; (b) to analyze the semantic nature of the formal linguistic expression of Axiom V, and (c) to examine the conflict between the requirements of self-evidence and real epistemic value or genuine knowledge arising inevitably and invariably from Fregean abstraction principles, if they are singled out as axioms of a theory T. If time allows, I conclude by making some critical remarks on Frege’s reactions to Russell’s paradox in the period 1902-1906.

Time: 3:30pm - 5.00pm Title: Truth and judgement

Abstract: What the German logician and philosopher Gottlob Frege has bequeathed to us regarding the concept of truth is not a homogeneous, coherent and systematically worked out conception. It is rather an agglomeration of remarks, scattered throughout several of his writings, on the nature of judgement and assertion, the conception of the two truth-values the True and the False as the references of assertoric sentences (as objects), the relation of a (true) thought to the True, the role and the purportedly unique sense of the word “true” and its alleged redundancy on the level of both sense and assertion, the characterization of logic as the science of the most general laws of truth, the “truth-conditional“ approach concerning the semantics of his formal language — to mention some issues, but not all.

The core of my lecture will be a critical examination of what Frege says in some key passages about truth, the True and “is true”. Where it seems useful and enlightening, aspects of the current discussion of the concept of truth (for example, the role of this concept in minimalism about truth) will be taken into account. I shall argue (a) that Frege’s reflections on the relation of a (true) thought to the True are incoherent; (b) that he fails to offer a convincing argument for rejecting the view according to which a sentence of the form “The thought that p is true” expresses the subsumtion of a thought (qua object) under the concept is true; (c) that Frege seems to overlook the fact that in such a sentence, even if it is interpreted as expressing a subsumtion of this kind, we still have the relation of sense to reference, of a thought to a truth- value; (d) that he falls short of providing a cogent argument for the purported synonymy of “p” and “The thought that p is true” and thus for the alleged redundancy of “is true” on the semantic level; (e) that, contrary to what he says, he has to concede that the word “true” makes an essential contribution to the thought expressed by “The thought that p is true”; (f) that there are indispensable uses of the truth-predicate anyway, not only in sentences such as „Everything Peter says is true“ but also, for example, in informal “metalogical” discourse; (g) that, contrary to what Frege appears to claim, he is committed to acknowledging that true is a property (of true thoughts); (h) that it remains unclear what truth qua that which is acknowledged (not predicated) in a judgement is supposed to be if it is neither the True nor the concept is true.

交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/guid/access/rokko/rokkodai-dai2.html

連絡先：菊池誠　[email protected]