Berntson

I'm a postdoc at Rutgers working on metaphysics, logic, and the philosophy of science. My PhD is from Princeton and I have a masters from Brown. When not doing philosophy, I'm generally either spending time with my family or out running somewhere.

Modalists like Putnam (1967) and Hellman (1989) say that mathematical practice requires only the possible existence of certain structures, not the actual existence of mathematical objects. This view, though, has has been thought to face a decisive objection: While it may be able to account for pure mathematics, it cannot account for the application of mathematics to the physical world. This paper shows how the objection can be met. [coming soon]

This paper proves completeness for a logic of conditionals that is strictly intermeidate in strength between the minimal system descrived by Burgess (1981) and the weakest system considered by Lewis (1973). Unlike the first, it validates a plausible principle that I call disjunction distribuiton. Unlike the second, it invalidates rational monotonicity, and so avoids what I have elsewhere called the paradox of counterfactual tolerance. The system is also natural from a model theoretic perspective. In terms of accessibility, it corresponds to accepting connectedness and denying transitivity. [draft]

Hanas Leitgeb (2014) proposes a new lottery paradox for counterfactuals that does does not rely on agglomeration. His parpadox suffers from various difficulties that are descried in this paper. Perhaps most notably, his paradox relies on an axiom called rational monotonicity that we have good reason to doubt for entirely differnt reasons. His basic paradox, though, can be not only rehabilitated, but strengthened by appealing to a different plausible principle. This paper shows how that can be done. [draft]

We ordinarily think that counterfactuals are both tolerant and bounded. But if so, we can prove a flat contraidiction using natural rules of inference. Something has to go then. But what? [down for repairs]

This paper shows how to prove completeness for an important class of multi-dimensional quantified modal logics. Those resuts provides a kind technical background for my other papers on relational possiblied and applied modal mathematics. [down for repairs]

Relational possibilities compare or otherwise relate how things could have been with how things are. We might say, for example, that Socrates could have been taller than he is or that the Athenians could have been happier than they are. Such comparisons have generally been thought to require quantification over things like properties, worlds, or spacetime points. But this view has certain surprising conseqneces: It would seem to entail, for example, that doing science inevitably requires quantifying over more than just particles. This paper argues for a view on which no such quantification is required. The relevant modal facts can be taken as basic, which gives us a powerful tool for doing science with minimal ontological commitment. [down for repairs]

How should the opinion of a group be related to the opinions of the group members? In this article, we defend a package of four norms – coherence, locality, anonymity and unanimity. Existing results show that there is no tenable procedure for aggregating outright beliefs or for aggregating credences that meet these criteria. In response, we consider the prospects for aggregating credal pairs – pairs of prior probabilities and evidence. We show that there is a method of aggregating credal pairs that possesses all four virtues.

[Episteme, PhilPapers]

PHI265, Rutgers University, Fall 2020. [course website]

Coming soon.

Coming soon.

Coming soon.