•  15
    John Stillwell.*A Concise History of Mathematics for Philosophers
    Philosophia Mathematica 28 (1): 128-131. 2020.
    StillwellJohn.* * _ A Concise History of Mathematics for Philosophers. _ Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press, 2019. Pp. 69. ISBN: 978-1-108-45623-4, 978-1-108-61012-4. doi.org/10.1017/9781108610124
  •  6
    The broadly-stated aim of this rich collection is to reevaluate and reconceptualize the mathematization thesis, which the editors take to signify “above all the transformation of scientific concepts and methods, especially those concerning the nature of matter, space, and time, through the introduction of mathematical techniques and ideas”. As a historiographical thesis, it is the thesis that “the scientific revolution, and by implication modern science as a whole, is guided by the project of ma…Read more
  •  199
    Poincaré’s Philosophy: From Conventionalism to Phenomenology (review)
    Philosophical Review 111 (4): 579-582. 2002.
    This is a book of wide-ranging scope, as the title suggests. First, it canvasses a broad selection of topics—from electromagnetism and quantum mechanics to Husserl’s phenomological constitution of logic, from Russell and Wittgenstein to Hartry Field. Second, its aims are broad. The author describes the book both as a “rational reconstruction of Poincaré’s position” and as a “treatise on modern epistemology”. The former description is somewhat misleading in that, together with Zahar’s stated aim …Read more
  •  98
    This paper is part of a larger project about the relation between mathematics and transcendental philosophy that I think is the most interesting feature of Kant’s philosophy of mathematics. This general view is that in the course of arguing independently of mathematical considerations for conditions of experience, Kant also establishes conditions of the possibility of mathematics. My broad aim in this paper is to clarify the sense in which this is an accurate description of Kant’s view of the re…Read more
  •  25
    Introduction
    Canadian Journal of Philosophy 44 (5-6): 519-523. 2014.
  • Mathematics, Metaphysics and Intuition in Kant
    Dissertation, Harvard University. 1996.
    This thesis attempts to argue against an influential interpretation of Kant's philosophy of mathematics according to which the role of pure intuition is primarily logical. Kant's appeal to pure intuition, and consequently his belief in the synthetic character of mathematics, is, on this view, a result of the limitations of the logical resources available in his time. In contrast to this, a reading is presented of the development of Kant's philosophy of mathematics which emphasises a much richer …Read more
  • There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula of Uni…Read more
  •  40
    Intuition and the Axiomatic Method (edited book)
    with Renate Huber
    Springer. 2006.
    By way of these investigations, we hope to understand better the rationale behind Kant's theory of intuition, as well as to grasp many facets of the relations ...
  •  59
    On realism in set theory
    Philosophia Mathematica 4 (1): 3-17. 1996.
    In her recent book, Realism in mathematics, Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails to explain the key issue…Read more
  •  53
    This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.A central theme of the book is that an adequate understanding of Kant's p…Read more
  • Mathematics in Kant's Critical Philosophy (edited book)
    Routledge. 2015.
    There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula of Uni…Read more
  •  106
    Kant on Intuition in Geometry
    Canadian Journal of Philosophy 27 (4). 1997.
    It's well-known that Kant believed that intuition was central to an account of mathematical knowledge. What that role is and how Kant argues for it are, however, still open to debate. There are, broadly speaking, two tendencies in interpreting Kant's account of intuition in mathematics, each emphasizing different aspects of Kant's general doctrine of intuition. On one view, most recently put forward by Michael Friedman, this central role for intuition is a direct result of the limitations of the…Read more
  •  57
    Locke’s account of certain and instructive knowledge
    British Journal for the History of Philosophy 10 (3). 2002.
    This Article does not have an abstract
  •  29
    Hintikka on Kant's mathematical method
    Revue Internationale de Philosophie 250 (4): 435-449. 2009.
  •  93
    In this paper I argue that Kant's distinction in the Inaugural Dissertation between the sensible and the intelligible arises in part out of certain open questions left open by his comparison between mathematics and metaphysics in the Prize Essay. This distinction provides a philosophical justification for his distinction between the respective methods of mathematics and metaphysics and his claim that mathematics admits of a greater degree of certainty. More generally, this illustrates the import…Read more