Gregory Wheeler

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate.

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models

The structural view of rational acceptance is a commitment to developing a logical calculus to express rationally accepted propositions sufficient to represent valid argument forms constructed from rationally accepted formulas. This essay argues for this project by observing that a satisfactory solution to the lottery paradox and the paradox of the preface calls for a theory that both (i) offers the facilities to represent accepting less than certain propositions within an interpreted artificial language and (ii) provides a logical calculus of rationally accepted formulas that preserves rational acceptance under consequence. The essay explores the merit and scope of the structural view by observing that some limitations to a recent framework advanced James Hawthorne and Luc Bovens are traced to their framework satisfying the first of these two conditions but not the second.

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.

Modeling a complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

Yet, in broader terms, formal epistemology is not merely a methodological tool for epistemologists, but a discipline in its own right. On this programmatic view, formal epistemology is an interdisciplinary research program that covers work by philosophers, mathematicians, computer scientists, statisticians, psychologists, operations researchers, and economists who aim to give mathematical and sometimes computational representations of, along with sound strategies for reasoning about, knowledge, belief, judgment and decision making

C.P. Snow observed that universities are largely made up of two broad types of people, literary intellectuals and scientists, yet a typical individual of each type is barely able, if able at all, to communicate with his counterpart. Snow's observation, popularized in his 1959 lecture Two Cultures and the Scientific Revolution (reissued by Cambridge 1993), goes some way to explaining the two distinct cultures one hears referred to as "the humanities" and "the sciences." Snow's lecture is a study of these two cultures, their rules, hierarchies, and educational traditions, which raises the following question: to what degree are "the humanities" and "the sciences" a consequence of how we organize and fund modern universities? Rather than a happenstance of interests and temperament, perhaps "humanist" and "scientist" are largely bureaucratic categories