•  2
    Making a French Connection: Darwin, Brown-Séquard and the Epilepsy Studies
    Journal of the History of Biology 1-27. forthcoming.
    While French biologists were turning a cold shoulder to On the Origin of Species in the 1860s, Charles Darwin was earnestly pursuing a professional connection with one French physiologist in particular: Charles Brown-Séquard. Darwin had been closely following Brown-Séquard’s startling experiments on guinea pigs, which demonstrated that experimentally induced epilepsy could pass from parent to offspring. In Darwin’s mind, Brown-Séquard had produced the most convincing evidence to date that acquir…Read more
  •  14
    Natural formalization: Deriving the Cantor-Bernstein theorem in zf
    Review of Symbolic Logic 1-44. forthcoming.
    Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and…Read more
  •  186
    Categorical harmony and path induction
    Review of Symbolic Logic 10 (2): 301-321. 2017.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent concep…Read more