Cassirer and the Arithmetization of Physics

Drawing an explicit parallel with Felix Klein’s account of the arithmetization of 19th-century mathematics, Cassirer maintains that 19th-century physics likewise underwent a process of arithmetization that culminated in the 20th century. This paper argues that this constitutes an original insight and a unifying thread running through Cassirer’s philosophy of physics over several decades, one that has yet to receive adequate scholarly attention. In contrast to his fellow Marburg neo-Kantians, Cohen and Natorp, who regarded the continuum as central to modern scientific knowledge, Cassirer treated number-formation as the prototype of scientific concept-formation in general. The number-sequence combines the structuralist view that each individual number has no intrinsic identity apart from its reciprocal ‘relation’ to all other numbers with the constructivist view that such a relation is a ‘productive relation’, generating ordered sequences of all possible numbers. The paper concludes that, for this reason, Cassirer may be said to have defended a form of ‘structural constructivism’ rather than ‘structural realism’, as is often claimed.