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I am an Intelligence Community Postdoctoral Research Fellow in the Department of Philosophy at Carnegie Mellon University.  My current research develops methods to improve reasoning under uncertainty—especially methods that can help individuals resolve disagreements or reach greater mutual understanding.

Previously I was an Assistant Professor in the Department of Philosophy at Bilkent University.  

I received my B.S. in Physics from MIT in 2009 and my PhD in Philosophy from Stanford University in 2018. My CV can be found here.

I can be reached at dibella [at] cmu [dot] edu.

Below are some of my papers.  Comments are very welcome!

• "Cantor, Choice, and Paradox"

  • Forthcoming, The Philosophical Review.

  • Abstract. I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor’s account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory.  

• "Fair Infinite Lotteries, Qualitative Probability, and Regularity"

  • 2022. Philosophy of Science, 89(4), 824-844.

  • Abstract.  A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating Countable Additivity.   In this paper, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions.  I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous uniform distributions.  Along the way, I provide a novel argument for a weak qualitative, epistemic version of Regularity.

• "The Qualitative Paradox of Non-Conglomerability"

  • 2018.  Synthese, 195(3), 1181-1210.

  • Abstract.  A probability function is non-conglomerable just in case there is some proposition E and partition π of the space of possibilities such that the probability of E conditional on any member of π is bounded by two values yet the unconditional probability of E is not bounded by those values.  The paradox of non-conglomerability is the counterintuitive—and controversial—claim that a rational agent's subjective probability function can be non-conglomerable.  In this paper, I present a qualitative analogue of the paradox.  I show that, under antecedently plausible assumptions, an analogue of the paradox arises for rational comparative confidence.  As I show, the qualitative paradox raises its own distinctive set of philosophical issues.

• "Qualitative Probability and Infinitesimal Probability"

  • Abstract.  (Draft.)  Infinitesimal probability has long occupied a prominent niche in the philosophy of probability.  It has been employed for such purposes as defending the principle of regularity, making sense of rational belief update upon learning evidence of classical probability 0, modeling fair infinite lotteries, and applying decision theory in infinitary contexts.  In this paper, I show that many of the philosophical purposes infinitesimal probability has been enlisted to serve can be served more simply and perspicuously by appealing instead to qualitative probability—that is, the binary relation of one event's being at least as probable as another event.  I also that show that qualitative probability has comparable (if not greater) representational power than infinitesimal probability.  These considerations suggest that qualitative probability provides a superior framework to infinitesimal probability for theorizing about a variety of philosophical contexts.

• "Probabilistic Proof of an External World"

  • Abstract.  (Draft.)  I provide a novel internal critique of skepticism about the external world.  Appealing to premises that an external-world skeptic could accept, I argue that the skeptic should (by her own lights) be extraordinarily confident that an external world exists.  These premises include commitments to various forms of a priori reasoning—including commitments to classical logic, set theory, and probabilistic reasoning—as well as radical empiricism about evidence.  As I argue, these premises entail that the skeptic should, by her own lights, be at least 99.99999% confident—just shy of certain—that an external world exists.

• "The World Is (Almost Surely) a Strange Place"

  • Abstract.  (Draft.)  I argue that we should be extremely confident that the world is extraordinarily ontologically complex.  More precisely, I argue for the following thesis: for any (finite or infinite) cardinality K, we should at least 99.99999% confident that there exist more than K-many things in total as well as more than K-many kinds of things.  This thesis contrasts starkly with the widespread view in science and metaphysics that simplicity is a guide to truth.