A close reading of Descartes’ works, particularly his Regulae ad Directionem Ingenii, calls into question the common interpretation of Peirce’s ‘Questions Concerning Certain Faculties Claimed for Man’ and ‘Some Consequences of Four Incapacities’ as being anti-Cartesian. In particular, Descartes’ conception of intuition differs from Peirce’s, and on one plausible reading of Descartes his intuitionism actually mirrors Peirce’s inferentialism in key respects. Given these similarities between Descartes and Peirce, the dogmatic status of the anti-Cartesian interpretation of Peirce becomes evident.

This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...) to mathematics and a top-down naturalisation. Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter. (shrink)