•  141
    Ernst Cassirer's Neo-Kantian Philosophy of Geometry
    British Journal for the History of Philosophy 19 (4). 2011.
    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 o…Read more
  •  113
    Kant on real definitions in geometry
    Canadian Journal of Philosophy 44 (5-6): 605-630. 2014.
    This paper gives a contextualized reading of Kant's theory of real definitions in geometry. Though Leibniz, Wolff, Lambert and Kant all believe that definitions in geometry must be ‘real’, they disagree about what a real definition is. These disagreements are made vivid by looking at two of Euclid's definitions. I argue that Kant accepted Euclid's definition of circle and rejected his definition of parallel lines because his conception of mathematics placed uniquely stringent requirements on rea…Read more
  •  109
    According to Michael Friedman, Ernst Cassirer’s “outstanding contribution [to Neo-Kantianism] was to articulate, for the first time, a clear and coherent conception of formal logic within the context of the Marburg School” (Friedman 2000, p. 30). In his paper “Kant und die moderne Mathematik” (1907), Cassirer argued not only that the new relational logic of Frege1 and Russell was a major breakthrough with profound philosophical implications, but also that the logicist thesis itself was a “fact” …Read more
  •  108
    The Priority Principle from Kant to Frege
    Noûs 48 (2): 268-297. 2013.
    In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought that Frege's priority p…Read more
  •  107
    Ernst Cassirer’s Substanzbegriff und Funktionsbegriff
    Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (2): 241-70. 2014.
    Ernst Cassirer’s book Substanzbegriff und Funktionsbegriff is a difficult book for contemporary readers to understand. Its topic, the theory of concept formation, engages with debates and authors that are largely unknown today. And its “historical” style violates the philosophical standards of clarity first propounded by early analytic philosophers. Cassirer, for instance, never says explicitly what he means by “substance-concept” and “function-concept.” In this article, I answer three questions…Read more
  •  44
    Realism, functions, and the a priori: Ernst Cassirer's philosophy of science
    Studies in History and Philosophy of Science Part A 48 10-19. 2014.
  •  20
    Frege, Lotze, and Boole
    In Erich H. Reck (ed.), The Historical Turn in Analytic Philosophy, Palgrave-macmillan. 2013.
    In the ‘analytic tradition’, Hans Sluga wrote thirty years ago in his book Gottlob Frege, there has been a ‘lack of interest in historical questions — even in the question of its own roots. Anti-historicism has been the baggage of the tradition since Frege’ (Sluga, 1980, p. 2). The state of the discussion of Frege among analytic philosophers, Sluga claimed, illustrated well this indifference. Despite the numbers of pages devoted to Frege, there was still, Sluga claimed, little understanding of t…Read more
  •  14