This installment of the early-career research spotlight series looks at the work of Wesley Holliday. He is an Assistant Professor in the Philosophy Department at the University of California, Berkeley, and the recent recipient of the school’s Regents’ Junior Faculty Fellowship. He received his PhD from Stanford University in 2012 with a dissertation on the topic of Epistemic Logic. His primary research interests are philosophical logic (especially epistemic, modal, and intuitionistic logic), probability, action, epistemology, and logic and language. His work has been published in Thought: A Journal of Philosophy, Theory and Decision, and Journal of Philosophical Logic.
Nathan: In a recent paper published in Oxford Studies in Epistemology, you pose an alternative to what you term the “standard alternatives picture” found in fallibilism, which you call the “Multipath Picture of Knowledge”. Can you explain what these terms mean and why they are important?
Wesley: First of all, thanks very much for the invitation and questions!
A “fallibilist” about knowledge, as I use the term, thinks that in order to know something—for example, that the transmission in your car is broken—it’s not necessary to eliminate every alternative possibility or guard against every possible way of being wrong. If your transmission is broken, a mechanic can indeed know it’s broken even if the mechanic’s diagnostics don’t rule out the extreme possibility that the CIA has modified your car and the mechanic’s equipment to fake a transmission failure. According to the fallibilist view of Fred Dretske, for example, if as a matter of fact no one in the CIA has ever been interested in faking a transmission failure in your car or even has the capability to do so, then that possibility is an “irrelevant” possibility that the mechanic’s diagnostics don’t need to rule out (see Dretske’s discussion of the Siberian Grebe in “The Pragmatic Dimension of Knowledge”). By contrast, an “infallibilist” thinks that the mechanic’s diagnostics do need to rule out every alternative possibility, including the CIA possibility, for the mechanic to know that the transmission is broken.
I think that the general fallibilist idea is right, but the particular way it has been developed is not. According to what I call the Standard Alternatives Picture, we can think of what is required for someone to know a proposition P as follows: there is a list of alternative possibilities—imagine the list on a sheet of paper—that the person needs to rule out in order to know P. Crucially, the list doesn’t have to include every possibility in which P is false. As long as the person rules out the possibilities on the list, she can come to know P.
By contrast, according to the Multipath Picture of Knowledge that I favor, in general we should think differently about what is required for someone to know a proposition P: whereas before we had a single list of alternatives, now we may have several such lists—imagine them on separate sheets of paper. In order for someone to know P, it’s necessary and sufficient that for at least one of those lists, the person has ruled out the possibilities on that list. The easiest example of this involves propositions of a disjunctive form (A or B). If a person wants to know that (A or B) holds, one path is to try to come to know that A holds. Another path is to try to come to know that B holds. A third path is to try to come to know that the disjunction holds without knowing which disjunct holds. The key point is that if we are fallibilists, then these three paths may give us three different lists of possibilities (in particular, one is not a sublist of another), so that in order to know that (A or B), it’s enough to rule out the possibilities on one of those lists. If we were infallibilists, there would be just one list of possibilities: the list of every not-(A or B) possibility. But if we are fallibilists, then the three lists may be different. As I argued in “Fallibilism and Multiple Paths to Knowledge,” there may be multiple paths to knowing (A or B), and similar points apply to knowing existential truths and to knowing inductive generalizations.
Why is this Multipath Picture important? For one reason, because it resolves a dilemma that afflicts any theory of knowledge working within the Standard Alternatives Picture, as I argued in “Fallibilism and Multiple Paths to Knowledge.” The upshot is that the Multipath Picture of Knowledge, unlike the Standard Alternatives Picture, allows a fallibilist to combine the plausible ideas (roughly) that knowing a proposition puts one in a position to know the classical logical consequences of that proposition, and that knowing a contingent empirical proposition requires doing empirical work to rule out possibilities.
Nathan: Your work makes multiple references to David Lewis and Jaakko Hintikka as individuals who either founded or substantially developed the field of “epistemic logic.” What innovations made by these thinkers helped to establish this field, and how have you built on them?
Wesley: Jaakko Hintikka’s book Knowledge and Belief was a landmark in the development of epistemic logic as a field. One of the key ideas in the book, which is now familiar to philosophers, is the idea of representing a person’s knowledge by a set of epistemic possibilities: those possibilities compatible with the person’s knowledge. For example, if you don’t know whether or not Clinton will win the election, then in your set of epistemic possibilities, there will be some possibilities in which Clinton wins and other possibilities in which Clinton doesn’t win. Whereas if you know that Clinton will win California, then in all possibilities in your set, Clinton wins California. Hintikka applied the same idea to belief (doxastic possibilities). Today this way of thinking may seem like educated common sense, and perhaps it has been for a long time. In any case, one of Hintikka’s innovations was to use this way of thinking to give a precise semantics for a formal language of epistemic logic.
As for David Lewis, although he didn’t work much on formal epistemic logic per se, he and Robert Stalnaker followed Hintikka in representing an agent’s knowledge or belief in terms of epistemic or doxastic possibilities for the agent, and they also refined this representation. In his book Convention, Lewis also introduced an account of common knowledge that has been very influential in epistemic logic.
Like other important ideas, Hintikka’s semantics for epistemic logic arose naturally in several contexts: for example, in computer science, as in the textbook Reasoning about Knowledge by Fagin, Halpern, Moses, and Vardi, and in game theory, as in the paper “Interactive epistemology I: Knowledge” by the Nobel-prize-winning economist Robert Aumann. As this suggests, the field of epistemic logic today is quite interdisciplinary.
My work in epistemic logic, like Hintikka’s, has been at the intersection of epistemic logic and epistemology. But a lot has happened in epistemology since Hintikka’s book appeared in 1962, including the appearance of the influential “relevant alternatives” and “subjunctivist” (sensitivity, safety) theories of knowledge. My paper “Epistemic Closure and Epistemic Logic I” formalized some of these theories of knowledge as formal semantics for the language of epistemic logic. This made it possible to discover exactly which principles of epistemic closure—a topic of much debate over the last 40 years—hold according to these formalized theories. Another part of my work on epistemic logic has been on dynamic epistemic logic. This builds on the basic idea of representing a person’s acquisition of new knowledge as a shrinking of her set of epistemic possibilities, an idea at the center of Stalnaker’s book Inquiry. My recent paper “Knowledge, Time, and Paradox,” written for a forthcoming volume in honor of Hintikka, discusses two epistemological applications of dynamic epistemic logic and explores a new approach to these applications, which I call “sequential epistemic logic.”
Nathan: Much of your teaching and service seems to revolve around logic (for example, you have taught “Modal Logic” and “Intermediate Logic”, and are the co-organizer of the Berkeley-Stanford Circle in Logic and Philosophy). In your experience, what are the most important theories from the field of logic that philosophers should know, and why?
Wesley: Logic can be very beautiful, so many philosophers enjoy studying it for that reason. But it’s also a very powerful tool for philosophical analysis. Beyond the essentials covered in introductory logic courses, the parts of logic that are most important for philosophers depend on their interests. For philosophers of mathematics, developments in logic such as Gödel’s incompleteness theorems or intuitionistic logic have been of central importance. For philosophers interested in metaphysics, epistemology, or the philosophy of language, I think a course in modal logic is highly relevant, since modal logic spans reasoning about necessity, time, counterfactuals, knowledge and belief, epistemic modals and conditionals, deontic modals, and more. I also think that in order to follow the history of analytic philosophy, knowledge of logic is a big plus. Many of the most influential figures in 20th or 21st century analytic philosophy—for example, Carnap, Dummett, Fine, Frege, Hintikka, Kripke, Lewis, Barcan Marcus, Putnam, Quine, Russell, Stalnaker, and Williamson, to name a few—have done significant work on formal logic. Ideas from logic have also been historically important in the philosophy of science, for example in the axiomatic and model-theoretic views of theories. In addition to these well-known points of contact between logic and other areas of philosophy, there are some perhaps unexpected connections. For example, for those interested in social and political philosophy, logic also has much to offer in more recent applications to game theory and social choice theory.
Nathan: What applications does your work have in other philosophical areas of study and other academic fields?
Wesley: Besides applications in epistemology, working on epistemic logic and modal logic more generally has led me to some applications in the philosophy of language. My paper “Roles, Rigidity, and Quantification in Epistemic Logic” with John Perry tries to tackle some classic problems in the philosophy of language going back to Frege and Quine. My paper “Measure Semantics and Qualitative Semantics for Epistemic Modals” with Thomas Icard tries to bring a logician’s perspective to contemporary debates about the semantics of epistemic modals, and some of our work in progress continues in this vein.
I also think that one of my main current projects, on “possibility semantics” for modal logic, may have applications not only in philosophical logic and philosophy of logic, but also in metaphysics. The basic idea of that project, going back to Lloyd Humberstone’s paper “From Worlds to Possibilities,” is to start in the semantics of modal logic not with the notion of maximally specific “possible worlds” but rather with the notion of partial “possibilities” that may be more or less specific.
As for applications to other academic fields, the closest connections outside of philosophy and pure logic are in computer science. Epistemic logic is actually one of the five examples of applications of logic in “On the Unusual Effectiveness of Logic in Computer Science” by Halpern, Harper, Immerman, Kolaitis, and Vardi. My work has been more on the pure rather than applied logic side of things, but I think that the pure and applied parts of the field benefit from the existence of the other. It’s also a pleasure to have the opportunity to interact with colleagues in philosophy, computer science, and mathematics with a common interest in logic. As a member of the interdisciplinary Group in Logic and the Methodology of Science at Berkeley (logic.berkeley.edu), I feel that it’s an exciting time of progress in logic!
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