フレーゲ:論理の普遍性とメタ体系的観点

抄録

Today everyone admits that Frege is one of the founders of modern logic. However, there is a wide divergence of views on whether metatheory was possible for Frege. Some insist that Frege had virtually everything that was needed to consider metasystematic questions (consistency, independence, completeness); others urge that it was impossible for Frege to raise those questions in the first place. Our aim in this paper is to reexamine the place of metatheoretical considerations in Frege's thought. We argue that usual model-theoretic techniques could not be accepted by Frege because of his distinctive "logic of judgement." But this doesn't mean that Frege was precluded from metatheory in toto. On the contrary, he planned a different kind of metatheory, namely "Neues Gebiet" resting on the permutation invariance method. We point out further two problems concerning this new conception of metatheory.