Fallibilism and Multiple Paths to Knowledge (Extended Version)

This chapter argues that epistemologists should replace a “standard alternatives” picture of knowledge, assumed by many fallibilist theories of knowledge, with a new “multipath” picture of knowledge. The chapter first identifies a problem for the standard picture: fallibilists working with this picture cannot maintain even the most uncontroversial epistemic closure principles without making extreme assumptions about the ability of humans to know empirical truths without empirical investigation. The chapter then shows how the multipath picture, motivated by independent arguments, saves fallibilism from this problem. The multipath picture is based on taking seriously the idea that there can be multiple paths to knowing some propositions about the world. An overlooked consequence of fallibilism is that these multiple paths to knowledge may involve ruling out different sets of alternatives, which should be represented in a fallibilist picture of knowledge. The chapter concludes by considering inductive knowledge and strong epistemic closure from this multipath perspective

Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers

We introduce a new Condorcet consistent voting method, called Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying independence of clones and the Pareto principle. Unlike other methods in this family, Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, relative to other clone-independent Paretian methods, Split Cycle mitigates “spoiler effects” and “strong no show paradoxes.

Logics of Imprecise Comparative Probability

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures

Inquisitive Intuitionistic Logic

Inquisitive logic is a research program seeking to expand the purview of logic beyond declarative sentences to include the logic of questions. To this end, inquisitive propositional logic extends classical propositional logic for declarative sentences with principles governing a new binary connective of inquisitive disjunction, which allows the formation of questions. Recently inquisitive logicians have considered what happens if the logic of declarative sentences is assumed to be intuitionistic rather than classical. In short, what should inquisitive logic be on an intuitionistic base? In this paper, we provide an answer to this question from the perspective of nuclear semantics, an approach to classical and intuitionistic semantics pursued in our previous work. In particular, we show how Beth semantics for intuitionistic logic naturally extends to a semantics for inquisitive intuitionistic logic. In addition, we show how an explicit view of inquisitive intuitionistic logic comes via a translation into propositional lax logic, whose completeness we prove with respect to Beth semantics

Possibility Frames and Forcing for Modal Logic (June 2016)

New version: https://escholarship.org/uc/item/0tm6b30

A Note on Algebraic Semantics for S5 with Propositional Quantifiers

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. This result raises the question: for which normal modal logics L can one axiomatize the quantified propositional modal logic determined by the complete modal algebras for L

Simplifying the Surprise Exam

In this paper, I argue for a solution to the surprise exam paradox, designated student paradox, and variations theoreof, based on an analysis of the paradoxes using modal logic. The solution to the paradoxes involves distinguishing between two setups, the Inevitable Event and the Promised Event, and between the two-day and n-day cases of the paradoxes. For the Inevitable Event, the problem in the two-day case is the assumption that the student knows the teacher’s announcement; for more days, the student can know the announcement, and the base case of the student’s backward induction is correct, but there is a mistake in the induction step. For the Promised Event, even the base case is questionable. After defending this analysis, I argue that it also leads to a solution to a modified version of the surprise exam paradox, due to Ayer and Williamson, based on the idea of a conditionally expected exam

Possibility Frames and Forcing for Modal Logic

New version: https://escholarship.org/uc/item/0tm6b30