This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be (...) construed as putting emphasis on intentionality of human mind towards certain invariant features of the elements of initial domains of discourse that are involved in equivalence relations. Definition of terms like direction, shape, number etc. is achieved by a kind of transformation of those invariants into ideal objects that is involved in intuition. Then the paper argues that at the period of 1926 Weyl’s writings on implicit definitions, he is inclined to endorse symbolic construction as a way to explicate the objectivity of certain processes as those that are carried out in case of implicit definitions. (shrink)

Michael Friedman’s project both historically and systematically testifies to the importance of the relativized a priori. The importance of implicit definitions clearly emerges from Schlick’s General Theory of Knowledge . The main aim of this paper is to show the relationship between both and the relativized a priori through a detailed discussion of Friedman’s work. Succeeding with this will amount to a contribution to recent scholarship showing the importance of Hilbert for Logical Empiricism.

In this article I discuss a recent argument due to Dan McArthur, who suggests that the charge that Michael Friedman’s relativised a priori leads to irrationality in theory change can be avoided by adopting structural realism. I provide several arguments to show that the conjunction of Friedman’s relativised a priori with structural realism cannot make the former avoid the charge of irrationality. I also explore the extent to which Friedman’s view and structural realism are compatible, a presupposition of McArthur’s argument. (...) This compatibility is usually questioned, due to the Kantian aspect of Friedman’s view, which clashes with the metaphysical premise of scientific realism. I argue that structural realism does not necessarily depend on this premise and as a consequence can be compatible with Friedman’s view, but more importantly I question whether Friedman’s view really implies mind dependence. (shrink)

Kuhn’s account of scientific change is characterized by an internal tension between a naturalist vein, which is compatible with the revolutionary perspective on the historical development of science, and an aprioristic or Kantian vein which wants to secure that science is not an irrational enterprise. Kuhn himself never achieved to resolve the tension or even to deal with the terms of the problem. Michael Friedman, quite recently, provided an account which aspires to reconcile the revolutionary and the aprioristic elements of (...) the Kuhnian historiography by placing the latter in the neo-Kantian philosophical framework. In this paper, I suggest that Friedman manages to provide a convincing description of the structuration of scientific knowledge and, further, to present science as a rational enterprise. I argue that despite these virtues Friedman’s account faces a major problem with regard to the context of transcendental idealism which he is not willing to abandon. I also argue that discarding transcendental idealism in the way the philosophical perspective of John McDowell does, we can dispose of the flaws of Friedman’s account while retaining its virtues. (shrink)

How was Poincaré’s conventionalism connected to his relationism? How, in other words, is it the case that the basic principles of geometry and mechanics are, ultimately, freely chosen conventions and that, at the same time, science reveals to us the structure of the world? This lengthy study aims to address these questions by setting Poincaré’s philosophy within its historical context and by examining in detail Poincaré’s developing views about the status and role of conventions in science and the status and (...) role of relations in science. It is argued that Poincaré was a neither a rampant conventionalist nor a pure structuralist. But he was both a conventionalist and a relationist, aiming to delineate a position which allowed room for both freely, but not arbitrarily, chosen constitutive principles of science and the acquisition of objective, though, relational knowledge of the natural world. (shrink)