On the Transposition of the Substantial into the Functional: Bringing Cassirer's Philosophy of Quantum Mechanics into the Twenty-First Century

Cassirer's neo-Kantian philosophy of scientific knowledge has been the subject of renewed interest recently, in particular with regard to the interpretation of General Relativity. However, Cassirer's analysis of Quantum Mechanics, found in Determinism and Indeterminism in Modern Physics, has not received the attention it deserves. Our aim in this paper is to sketch out the central themes of this work and illustrate its relevance for contemporary discussions of structuralism in the quantum context. Cassirer's general philosophy of physics is outlined before presenting the analysis of the nature and role of the causality principle. We place particular emphasis on the hierarchical view of scientific laws and principles which set causality at the apex and expressed it in abstract functional terms. Through such notions, transcendental philosophy can accommodate statistical laws and hence it can render harmless the apprent threat of quantum indeterminism. It is also shown that the uncertainty principle, quantum holism and the implications of quantum statistics are the grounds for Cassirer's conclusion that the true import of quantum mechanics was the reconceptualisation of our notion of object. Such reconceptualisation is structural, with point particles understood as ‘intersections of relations’. A brief comparison of Cassirer's neo-Kantian structuralism with some modern forms concludes our analysis.