Helmholtz's theory of space had significant impact on Schlick's early ?critical realist? point of view. However, it will be argued in this paper that Schlick's appropriation of Helmholtz's ideas eventually lead to a rather radical transformation of the original Helmholtzian position.

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)

This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question (...) by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed. (shrink)

This is the first reprint, complete with a new introduction by John Slater.

Excerpt from Substanzbegriff und Funktionsbegriff: Untersuchungen Uber die Grundfragen der Erkenntniskritik Die erste Anregung zu den Untersuchungen, die dieser Band enthalt, ist mir aus Studien zur Philosophie der Mathe matik erwachsen. Indem ich versuchte, von Seiten der Logik aus einen Zugang zu den Grundbegriffen der Mathematik zu gewinnen, erwies es sich vor allem als notwendig, die B e g r i f f s f u n k t i 0 n e'lhsimaher zu zergliedern und auf ihre Voraussetzungen zuruckzufuhren. Hier (...) aber machte sich alsbald eine eigentumliche Schwierigkeit geltend: die her kommliche logische Lehre vom Begriff zeigte sich in ihren bekannten Hauptzugen als unzureichend, die Probleme, zu denen die Prinzipienlehre der Mathematik hinfuhrt, auch nur vollstandig z u b e z e i c h n e n. Die exakte Wissenschaft war hier, wie sich mir immer deutlicher zu ergeben schien, zu Fragen gelangt, fur welche die Formensprache der tradi tionellen Logik kein genaues Correlat besitzt. Der sachliche Gehalt der mathematischen Erkenntnisse wies auf eine Grund form des Begriffs zuruck, die in der Logik selbst nicht zu klarer Bezeichnung und Anerkennung gekommen war. Ins besondere waren es Untersuchungen jiber den Reihenbegriff und den Grenzbegriff (deren spezielles Ergebnis in die allgemeineren Erorterungen dieses Buches nich? 3iffge nommen werden konnte), die diese Uberzeugung in mir be festigten und damit zu einer erneuten Analyse der Prinzipien der Begriffsbildung selbsfhindrangten. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of (...) logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant. (shrink)