The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...) necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence (...) of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof. (shrink)

The present paper is concerned with Helmholtz’s theory of measurement. It will be argued that an adequate understanding of this theory depends on how Helmholtz’s application of the concepts of perception and coincidence is interpreted. In contrast both to conventionalist and Kantian readings of Helmholtz’s theory, a more realistic interpretation will be suggested.

According to Wittgenstein, internal relations are such that, once their terms are given, it is unthinkable that they do not hold. In his early philosophy, the concept of internal relation plays a central role in his views on meaning. The present paper addresses the question of how Wittgenstein's views about internal relations develop during his years of transition (1930-32). In particular, it investigates the connections between the concepts of internal relation, logical multiplicity, and aspect seeing in two thematic fields: (1) (...) Wittgenstein's discussion of the relation between an expectation and what fulfils it, and (2) his discussion of the relation between a sign and an action guided by it. (shrink)