Anthony Stoner

About

I am a 6th-year PhD candidate at the University of California, Riverside, working in the history and philosophy of logic, and the history and philosophy of mathematics. I am also very interested in Marxist philosophy, political economy, and history.

I have other more specific philosophical interests in–listed historically–Spinoza, Leibniz, Kant, Hegel, Peirce, neo-Kantianism, Marx, Althusser, and Deleuze and Guattari. With respect to subject matter, I am interested in the mathematics, logic, and metaphysics of continuity, infinity, and infinitesimals; the elaboration of materialism as a philosophical worldview; autonomism and operaismo; Marxist political ecology; the conception of historical materialism in Marx’s Capital and his later works; and the critical political economy of science and academia.

My dissertation (in-progress) argues for what I call “logical naturalism”–a view in the philosophy of logic that seeks to defuse the priority given to ontological and epistemological questions in contemporary philosophy of logic. In connection with this, I argue that logical realism–the view that our logical vocabulary refer to really existing, if abstract, entities or structures–violates philosophical naturalism, that realism about purported phenomena of “validity” or “entailment” collapses, and for a kind of logical instrumentalism. I draw heavily on Lakatos’ philosophy of mathematics and Dutilh Novaes’ work on the “dialogical roots of deduction.” I see much overlap between the anti-foundationalist philosophy of logic I am pursuing and recent work being done in the philosophy of mathematics, specifically in the philosophy of mathematical practice. For instance, David Corfield’s work in Towards a Philosophy of Real Mathematics and Ralf Kroemer’s Tool and Object similarly aim to defuse the priority given in philosophy of mathematics (at least since the foundation debates of the early 1900s) to the ontology of mathematical objects, in favor of an analysis of the history and sociology of mathematical research, for Corfield in general and for Kroemer specifically concerning category theory.

I have also worked on the role of infinitesimals in Neo-Kantian philosophy of mathematics. There, I offered a reading of Hermann Cohen’s Das Prinzip der Infinitesimalmethode und seine Geschichte (1883). My interpretation is that Cohen’s concept of “infinitesimal” is primarily of the infinitesimal as a genuinely new, fundamental scientific category which provides a way of answering (to speak anachronistically) Wigner’s question about why mathematics is “unreasonabl[y] effective.” Because infinitesimals were central to the development of calculus and mechanics, they are central to transcendental logic for Cohen—and therefore are fundamental to what, from a modern scientific standpoint, makes phenomena scientific objects for us. To this end, I argue against Scott Edgar’s influential interpretation that Cohen aims to justify a specific and non-contradictory concept of “infinitesimal,” emphasizing Cohen’s historicist approach to ontological and epistemological issues in mathematics. I have further offered an interpretation of Dmitry Gawronsky’s Das Urteil der Realität (1910). Gawronsky’s elaboration of Cohen makes the infinitesimal a correlative concept to the infinitely large—which provides an alternative to the Cantorian conception of the infinitely small and large and nicely corresponds to the infinitesimalist systems being worked on at the time by Giuseppe Veronese and Paul DuBois-Reymond.

Outside my philosophical interests, I am also an avid yet mediocre player of go; a keeper of cats, rats, and lizards; an aficionado of the Mojave desert; and unlikely to be late to dinner.