-
24Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
-
21Remarks on "Random Sequences"Australasian Journal of Logic 12 (1). 2015.We show that standard statistical tests for randomness of finite sequences are language-dependent in an inductively pernicious way.
-
178Symmetries and asymmetries in evidential supportPhilosophical Studies 107 (2). 2002.Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.
-
147Discussion: Re‐solving irrelevant conjunction with probabilistic independencePhilosophy of Science 71 (4): 505-514. 2004.Naive deductivist accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H·X, for any X—even if X is completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that over…Read more
-
147Comparative Bayesian Confirmation and the Quine–Duhem Problem: A Rejoinder to StrevensBritish Journal for the Philosophy of Science 58 (2): 333-338. 2007.By and large, we think is a useful reply to our original critique of his article on the Quine–Duhem problem. But, we remain unsatisfied with several aspects of his reply. Ultimately, we do not think he properly addresses our most important worries. In this brief rejoinder, we explain our remaining worries, and we issue a revised challenge for Strevens's approach to QD.
-
216Probabilistic measures of causal strengthIn Phyllis McKay Illari Federica Russo (ed.), Causality in the Sciences, Oxford University Press. pp. 600--627. 2011.
-
209Too Odd (Not) to Be True? A Reply to OlssonBritish Journal for the Philosophy of Science 53 (4): 539-563. 2002.Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses…Read more
-
439What is the “Equal Weight View'?Episteme 6 (3): 280-293. 2009.In this paper, we investigate various possible (Bayesian) precisifications of the (somewhat vague) statements of “the equal weight view” (EWV) that have appeared in the recent literature on disagreement. We will show that the renditions of (EWV) that immediately suggest themselves are untenable from a Bayesian point of view. In the end, we will propose some tenable (but not necessarily desirable) interpretations of (EWV). Our aim here will not be to defend any particular Bayesian precisification…Read more
-
48Suppose we have two false hypotheses H1 and H2. Sometimes, we would like to be able to say that H1 is closer to the truth than H2 (e.g., Newton’s hypothesis vs. Ptolemy’s).
-
21E confirmsi H1 more strongly than E confirmsi H2 iff c(H1, E) > c(H2, E). [where c is some relevance measure]
-
280Bayesian confirmation and auxiliary hypotheses revisited: A reply to StrevensBritish Journal for the Philosophy of Science 56 (2): 293-302. 2005.has proposed an interesting and novel Bayesian analysis of the Quine-Duhem (Q–D) problem (i.e., the problem of auxiliary hypotheses). Strevens's analysis involves the use of a simplifying idealization concerning the original Q–D problem. We will show that this idealization is far stronger than it might appear. Indeed, we argue that Strevens's idealization oversimplifies the Q–D problem, and we propose a diagnosis of the source(s) of the oversimplification. Some background on Quine–Duhem Strevens…Read more
-
35Harman [8] would concede that (1)–(3) are inconsistent, and (as a result) that something is wrong with premises (1)–(3). But, he would reject the relevantists’ diagnosis that (1) must be rejected. I take it he’d say it’s (2) that is to blame here. (2) is a bridge principle [12] linking entailment and inference. (2) is correct only for consistent B’s. [Even if B is consistent, the correct response may rather be to reject some Bi’s in B.].
-
31Review of I. Hacking, An Introduction to Probability and Inductive Logic (review)Bulletin of Symbolic Logic 9 (4): 5006-5008. 2003.
-
47Here’s what Nicod [23] said about instantial confirmation: Consider the formula or the law: A entails B. How can a particular proposition, or more briefly, a fact, affect its probability? If this fact consists of the presence of B in a case of A, it is favourable to the law . . . on the contrary, if it consists of the absence of B in a case of A, it is unfavourable to this law.
-
48The Automation of Sound Reasoning and Successful Proof FindingIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.This chapter contains sections titled: The Cutting Edge Automated Reasoning, Principles and Elements Significant Successes Myths, Mechanization, and Mystique.
-
70In Bayes or Bust? John Earman quickly dismisses a possible resolution (or avoidance) of the problem of old evidence. In this note, I argue that his dismissal is premature, and that the proposed resolution (when charitably reconstructed) is reasonable.
-
45A Bayesian Account of Independent Evidence with ApplicationsPhilosophy of Science 68 (S3). 2001.A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closin…Read more
-
56In 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
-
32There 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
-
631An 'evidentialist' worry about Joyce's argument for ProbabilismDialetica 66 (3): 425-433. 2012.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
-
110Comments on some completeness theorems of Urquhart and méndez & SaltoJournal 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
-
39Bayesian 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.
-
195Arguments 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.
-
112mathematicians 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
-
99The Naive View (TNV) of Inferential Knowledge (slogan): (TNV) Inferential knowledge requires known relevant premises. One key aspect of (TNV) is “counter-closure” [9, 10].
-
31Intuitively, 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
-
84The 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
-
171Steps Toward a Computational MetaphysicsJournal 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
Boston, MA, United States of America
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Formal Epistemology |