Dr Benjamin Marschall is a Junior Research Fellow working on the history of analytic philosophy, metaphysics, and the philosophy of language. In his recently completed PhD thesis he tackled these issues by investigating the philosophy of mathematics of the Vienna Circle philosopher Rudolf Carnap. Carnap put forward a radical and iconoclastic position, according to which much of the philosophical work done on the foundations of mathematics is based on misguided assumptions. Unsurprisingly this has led to a divisive reception.

In this talk Benjamin will argue that Carnap’s position is indeed too radical to be viable. Everyone needs to make sense of facts about syntax: if certain axioms and inference rules are accepted, then it is fixed whether a sentence is derivable from these or not. Drawing on an underappreciated argument by the Dutch logician E. W. Beth, we will see that Carnap struggles to meet this important demand.