•  40
    • Two competing explanations (independence of S i favors R over CB): (CB) there is a coherence bias in a’s S -formation process.
  •  39
    Jill’s paper contains several distinct threads and arguments. I will focus only on what I see as the main theses of the paper, which involve the justification or grounding of the microcanonical probability distribution of classical statistical mechanics. I’ll begin by telling the “canonical” story of the MCD. Then I will discuss Jill’s proposal. I will describe one worry that I have regarding her proposal, and I will offer a friendly amendment which seems to allay my worry
  •  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.
  •  37
    detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XC B = e(x e(e(e( ) e( )) z)) a single axiom for the classical equivalential calculus when the rules of inference consist..
  •  37
    The principle that every truth is possibly necessary can now be shown to entail that every truth is necessary by a chain of elementary inferences in a perspicuous notation unavailable to Hegel. —Williamson [5, p.
  •  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.
  •  36
    In this talk, I will explain why only one of Miller’s two types of language-dependence-of-verisimilitude problems is a (potential) threat to the sorts of accuracy-dominance approaches to coherence that I’ve been discussing
  •  35
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0 are proved axiomatically (for the first time) with the help of the automated reasoning program Otter [16]. In addition, non -distributivity results are established for a wide variety of positive substructural logics by the use of logical matrices discovered with the automated model findingprograms Mace [15] and MaGIC [25].
  •  34
    Carnap [1] aims to provide a formal explication of an informal concept (relation) he calls “confirmation”. He clarifies “E confirms H” in various ways, including: (∗) E provides some positive evidential support for H. His formal explication of “E confirms H” (in [1]) is: (1) E confirms H iff Pr(H | E) > r, where Pr is a suitable (“logical”) probability function, and r is a threshold value
  •  34
    Harman [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.].
  •  33
    Introduction
    Studia Logica 86 (3): 351-352. 2007.
  •  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
  •  30
    With the inclusion of an e ective methodology, this article answers in detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XCB = e(x e(e(e(x y) e(z y)) z)) a single axiom for the classical equivalential calculus when the rules of inference consist of detachment (modus ponens) and substitution? Where the function e represents equivalence, this calculus can be axiomatized quite naturally with the formulas (x x), e(e(x y) e(…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
  •  29
    A Rejoinder to Strevens
    with Andrew Waterman
    By and large, we think Strevens’s [6] is a useful reply to our original critique [2] of his paper on the Quine–Duhem (QD) problem [5]. But, we remain unsatisfied with several aspects of his reply (and his original paper). 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.
  •  29
    Axiomatic proofs through automated reasoning
    with Larry Wos
    Bulletin of the Section of Logic 29 (3): 125-36. 2000.
  •  29
    Review of I. Hacking, An Introduction to Probability and Inductive Logic (review)
    Bulletin of Symbolic Logic 9 (4): 5006-5008. 2003.
  •  28
    We’ll adopt a simple framework today. Our assumptions: A model (M) is a family of hypotheses. A hypothesis (H) is a curve plus an associated error term . For simplicity, we’ll assume a common N (0, 1) Gaussian
  •  27
    The Jowett Society and the Philosophical Society of the University of Oxford provide a forum for discussion of philosophical issues for all members of the Philosophy Faculty. The Jowett society dates back to the 19th century and was named in honour of Benjamin Jowett..
  •  27
    Comparative. Let C be the full set of S’s comparative judgments over B × B. The innaccuracy of C at a world w is given by the number of incorrect judgments in C at w
  •  25
    A concise axiomatization of RM→
    with Zachary Ernst, Kenneth Harris, and Larry Wos
    Bulletin of the Section of Logic 30 (4): 191-194. 2001.
  •  22
    Review of Richard Jeffrey, Subjective Probability: The Real Thing (review)
    Notre Dame Philosophical Reviews 2005 (10). 2005.
  •  22
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
  •  21
    E confirmsi H1 more strongly than E confirmsi H2 iff c(H1, E) > c(H2, E). [where c is some relevance measure]
  •  19
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”).
  •  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.
  •  18
    The consideration of careful reasoning can be traced to Aristotle and earlier authors. The possibility of rigorous rules for drawing conclusions can certainly be traced to the Middle Ages when types o f syllogism were studied. Shortly after the introduction of computers, the audacious scientist naturally envisioned the automation of sound reasoning—reasoning in which conclusions that are drawn follow l ogically and inevitably from the given hypotheses. Did the idea spring from the intent to emul…Read more
  •  16
    Review of Richard Swinburne (ed.), Bayes's Theorem (review)
    Notre Dame Philosophical Reviews 2003 (11). 2003.