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publications

Published in , 1900

research

talks

On Russell’s ‘‘Vagueness’’

Published:

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.

A theorem of infinity for Principia Mathematica

Published:

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.

Any philosophical canon is practically self-undermining

Published:

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.

The propositional logic of Principia in Coq

Published:

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.''

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

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Teaching experience 2

Workshop, University 1, Department, 2015

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