With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...) grasp of the content of geometrical concepts plays a central role; moreover, our grasp of this content is a priori. (shrink)

The Manifestation Requirement, advanced by Dummett in his critique of semantic realism, has been criticized for being behavioristic, and the responses have been made that the critics are mistaken. However, the dispute has failed to exhibit the point of the Requirement. In this paper, I shall argue (1) that, in the light of Anscombe's theory of practical knowledge, knowledge of linguistic meaning is to be seen as the knowledge-how that forms the basis of the practical knowledge that an agent has (...) of his own intentional actions, (2) that such knowledge of linguistic meaning is to be based on mutual agreements in a community, and (3) that the Manifestation Requirement is a condition for the possibility of such mutual agreements. As a result, the Manifestation Requirement finds its basis on the idea that language and linguistic acts are tools that we use while continually improving them. (shrink)