•  18
    Remarks on Ángel Pinillos’s Why We Doubt
    International Journal for the Study of Skepticism 1-9. forthcoming.
    In these brief remarks, I describe the author’s Bayesian explication of the narrow function of the meta-cognitive, heuristic algorithm (pbs) that is at the heart of his psychological explanation of why we entertain skeptical doubts. I provide some critical remarks, and an alternative Bayesian approach that is (to my mind) somewhat more elegant than the author’s.
  • Closure, Counter-Closure, and Inferential Knowledge
    In Rodrigo Borges, Claudio de Almeida & Peter David Klein (eds.), Explaining Knowledge: New Essays on the Gettier Problem, Oxford University Press. pp. 312-324. 2017.
    The chapter begins with some general remarks about closure and counter-closure, and is followed with a discussion of the following: I (a) review some (alleged) counterexamples to counter-closure, I then continue by (b) discussing a popular strategy for responding to such counterexamples to counter-closure, and finally I (c) pose a dilemma for this popular strategy. Once I have discussed these three points I conclude the chapter by proposing that we reject counter-closure, but at the same time th…Read more
  •  751
    Deference Done Better
    with Kevin Dorst, Benjamin A. Levinstein, Bernhard Salow, and Brooke E. Husic
    Philosophical Perspectives 35 (1): 99-150. 2021.
    There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring…Read more
  • Part IV. Collective entities and formal epistemology. Individual coherence and group coherence
    with Fabrizio Cariani Rachael Briggs and When to Defer to Supermajority Testimony
    In Jennifer Lackey (ed.), Essays in Collective Epistemology, Oxford University Press. 2014.
  •  77
    Remarks on staffel on full belief
    Philosophical Studies 180 (2): 385-393. 2022.
  •  61
    A Problem for Confirmation Measure Z
    Philosophy of Science 88 (4): 726-730. 2021.
    In this article, I present a serious problem for confirmation measure Z.
  •  6
    Introduction
    Studia Logica 86 (2): 147-148. 2007.
  •  1050
    Four Approaches to Supposition
    Ergo: An Open Access Journal of Philosophy 8 (26): 58-98. 2022.
    Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematica…Read more
  •  182
    Two Approaches to Belief Revision
    with Ted Shear
    Erkenntnis 84 (3): 487-518. 2019.
    In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior.…Read more
  •  36
    Confirmation, causation, and Simpson's paradox
    Episteme 14 (3): 297-309. 2017.
    ABSTRACTIn this paper, I review some recent treatments of Simpson's Paradox, and I propose a new rationalizing explanation of its paradoxicality.
  • Introduction
    with Cherie Braden
    In Cherie Braden, Rodrigo Borges & Branden Fitelson (eds.), Themes From Klein, Springer Verlag. 2019.
  •  278
    As every philosopher knows, “the design argument” concludes that God exists from premisses that cite the adaptive complexity of organisms or the lawfulness and orderliness of the whole universe. Since 1859, it has formed the intellectual heart of creationist opposition to the Darwinian hypothesis that organisms evolved their adaptive features by the mindless process of natural selection. Although the design argument developed as a defense of theism, the logic of the argument in fact encompasses …Read more
  •  137
    Measuring Confirmation and Evidence
    with Ellery Elles
    Journal of Philosophy 97 (12): 663-672. 2000.
  •  33
    Introduction
    Studia Logica 86 (3): 351-352. 2007.
  •  78
    Probability, confirmation, and the conjunction fallacy
    Thinking and Reasoning 14 (2): 182-199. 2008.
    The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here, we elaborate the suggestion (first discussed by Sides et al., 2001) that in standard conjunction problems the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation relations, meant in terms of…Read more
  •  260
    Logical Foundations of Evidential Support
    Philosophy of Science 73 (5): 500-512. 2006.
    Carnap's inductive logic (or confirmation) project is revisited from an "increase in firmness" (or probabilistic relevance) point of view. It is argued that Carnap's main desiderata can be satisfied in this setting, without the need for a theory of "logical probability." The emphasis here will be on explaining how Carnap's epistemological desiderata for inductive logic will need to be modified in this new setting. The key move is to abandon Carnap's goal of bridging confirmation and credence, in…Read more
  •  54
    In the first edition of LFP, Carnap [2] undertakes a precise probabilistic explication of the concept of confirmation. This is where modern confirmation theory was born (in sin). Carnap was interested mainly in quantitative confirmation (which he took to be fundamental). But, he also gave (derivative) qualitative and comparative explications: • Qualitative. E inductively supports H. • Comparative. E supports H more strongly than E supports H . • Quantitative. E inductively supports H to degree r . C…Read more
  •  30
    There are various non-contrastive questions that one can ask about a single hypothesis H and a body of evidence E: What is the probability of H, given E [Pr(H | E)]? What is the likelihood of H on E [Pr(E | H)]? Does E support/counter-support H? Should we accept/reject H in light of E? There are also contrastive questions concerning pairs of alternative hypotheses H1 vs H2 and a body of evidence E: Is H1 more probable than H2, given E? Is the likelihood of H1 greater than that of H2 on E? Does E…Read more
  •  626
    To the extent that we have reasons to avoid these “bad B -properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear whether the DBA pinpoi…Read more
  •  108
    Comments on some completeness theorems of Urquhart and méndez & Salto
    with Kenneth Harris
    Journal of Philosophical Logic 30 (1): 51-55. 2001.
    Urquhart and Méndez and Salto claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do the following three things: (1) provide a counterexample to all of these alleged completeness theorems, (2) attempt to diagnose the mistakes in the reported completeness proofs, and (3) provide complete axiomatizations of the desired systems
  •  190
    Arguments for probabilism aim to undergird/motivate a synchronic probabilistic coherence norm for partial beliefs. Standard arguments for probabilism are all of the form: An agent S has a non-probabilistic partial belief function b iff (⇐⇒) S has some “bad” property B (in virtue of the fact that their p.b.f. b has a certain kind of formal property F). These arguments rest on Theorems (⇒) and Converse Theorems (⇐): b is non-Pr ⇐⇒ b has formal property F.
  •  107
    mathematicians for over 60 years. Amazingly, the Argonne team's automated theorem-proving program EQP took only 8 days to find a proof of it. Unfortunately, the proof found by EQP is quite complex and difficult to follow. Some of the steps of the EQP proof require highly complex and unintuitive substitution strategies. As a result, it is nearly impossible to reconstruct or verify the computer proof of the Robbins conjecture entirely by hand. This is where the unique symbolic capabilities of Math…Read more
  •  38
    Bayesian epistemology suggests various ways of measuring the support that a piece of evidence provides a hypothesis. Such measures are defined in terms of a subjective probability assignment, pr, over propositions entertained by an agent. The most standard measure (where “H” stands for “hypothesis” and “E” stands for “evidence”) is.
  •  94
    The Naive View (TNV) of Inferential Knowledge (slogan): (TNV) Inferential knowledge requires known relevant premises. One key aspect of (TNV) is “counter-closure” [9, 10].
  •  31
    The Problem: First Pass
    with Daniel Osherson
    Intuitively, it seems that S 1 is “more random” or “less regular” than S 2. In other words, it seems more plausible (in some sense) that S 1 (as opposed to S 2) was generated by a random process ( e.g. , by tossing a fair coin eight times, and recording an H for a heads outcome and a T for a tails outcome). We will use the notation x σ 1 ą σ 2y to express the claim that xstring σ 1 is more random than string σ 2y. And, we take it to be intuitively clear that — on any plausible definition of such…Read more
  •  50
  •  83
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”). I’ll begin with Harman’s defense of classical deductive logic against certain (epistemological) “relevantist” arguments
  •  164
    Steps Toward a Computational Metaphysics
    Journal of Philosophical Logic 36 (2): 227-247. 2007.
    In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PRO…Read more
  •  125
    Popper [3] offers a qualitative definition of the relation “p q” = “p is (strictly) closer to the truth than (i.e., strictly more verisimilar than) q”, using the notions of truth (in the actual world) and classical logical consequence ( ), as follows.