Talks

The Genealogy of ‘‘v’’

June 22, 2021

Talk, Association for Symbolic Logic, South Bend, Indiana

Joint work with Richard Zach (University of Calgary).

The propositional logic of Principia in Coq

June 19, 2021

Talk, Bertrand Russell Society, New Britain, CT

Abstract There have been multiple reconstructions of the propositional logic of *Principia* beginning with the artificial intelligence research of Newell, Simon, and Shaw in the 1950s, including the mechanical validity-checker of Hao Wang (see ''IBM Journal of Research and Development'' 1960), and the proof reconstructions of Daniel O'Leary using Polish notations (see *Russell* 1988). To these results I have added a fully computer-checked reconstruction of the propositional logic of "Principia" following the proof sketches indicated in that work. This talk will discuss what computer-checking *Principia* proofs in `Coq` tells us about the proof sketches, and also about the development of propositional logic between *Principia* and Russell's 1906 ''The Theory of Implication.''

Any philosophical canon is practically self-undermining

April 05, 2021

Talk, Pacific APA, Portland, OR

Abstract There has recently been much-needed critical discussion of the current Anglo-American philosophical canons, but not as much consideration of their nature and purposes. I discuss what philosophical canons are and argue that they are social practices, and in particular, social practices of enforcing rules. I then consider what purposes a philosophical canon can have for various stakeholders. Building on Luca Castagnoli’s work on self-refutation in ancient philosophy, I clarify various notions of being practically self-undermining. I then argue that even on an inclusive view of what the purposes of a philosophical canon are, any philosophical canon is self-undermining. There is no plausible account of the purposes of a philosophical canon that is not undermined by having one, whatever its makeup.

A theorem of infinity for Principia Mathematica

January 07, 2019

Talk, Eastern APA, New York, NY

Abstract I prove a theorem of infnity for *Principia Mathematica*. The proof requires altering the meta-theory of *Principia*. In *Principia* we have a simple type theory with a lowest type (call this 'simple ℕ-type theory'). Our key idea is to allow for infnitely-descending types just as there are infnitely-ascending types; that is, we allow our simple type theory to be not well-founded (call this 'simple ℤ-type theory'). Given the acceptableness of *Principia*'s (well-founded) simple type theory, this adjustment is minor. This adjustment is also implicitly suggested by various remarks of Whitehead and Russell. By so-adjusting *Principia*, a core objection to Logicism--namely, that Logicism cannot recover Peano arithmetic without an axiom of infnity--dissipates.

On Russell’s ‘‘Vagueness’’

March 03, 2016

Talk, Central APA, Chicago, IL

Abstract I argue that Bertrand Russell's 1923 ''Vagueness'' has wrongly endured long-standing criticism in the secondary literature on metaphysical vagueness. I divide the most com- mon criticisms of Russell into three 'myths', as I call them. I then indicate why none of these three myths is justifed by the light of a close reading of Russell's 1923 piece. The upshot of dispelling the myths is inviting work on *representationalism*, the view that metaphysical vagueness is a feature of representations.

On ‘Vagueness’

June 04, 2015

Talk, Society for the Study of the History of Analytical Philosophy, Dublin, Ireland

Regional Conferences