Branden Fitelson University of California, Berkeley
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  • Faculty, University of California, Berkeley
  • PhD, University of Wisconsin, Madison, 2001.

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  1. Branden Fitelson & Kenny Easwaran, Partial Belief, Full Belief, and Accuracy–Dominance.
    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.
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  2. James Hawthorne & Branden Fitelson, An Even Better Solution to the Paradox of the Ravens.
    Think of confirmation in the context of the Ravens Paradox this way. The likelihood ratio measure of incremental confirmation gives us, for an observed Black Raven and for an observed non-Black non-Raven, respectively, the following “full” likelihood ratios.
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  3. Branden Fitelson, Dempster-Shafer Functions as Metalinguistic Probability Functions.
    Let Ln be a sentential language with n atomic sentences {A1, . . . , An}. Let Sn = {s1, . . . , s2n} be the set of 2n state descriptions of Ln, in the following, canonical lexicographical truth-table order: State Description A1 A2 · · · An−1 An T T T T T s1 = A1 & A2 & · · · &An−1 & An T T T T F s1 = A1 & A2 & · · · (...)
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  4. Branden Fitelson, Epistemological Critiques of ‘Classical’ Logic: Two Case Studies.
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  5. Branden Fitelson, “Survey” of Formal Epistemology: Some Propaganda and an Example.
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  6. Vincenzo Crupi, Branden Fitelson, Ole Hjortland & Florian Steinberger (2013). Note of the Editors. Erkenntnis:1-1.
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  7. Branden Fitelson (2013). 3 Contrastive Bayesiansim. In Martijn Blaauw (ed.), Contrastivism in Philosophy. Routledge. 39--64.
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  8. Kenny Easwaran & Branden Fitelson (2012). An 'Evidentialist' Worry About Joyce's Argument for Probabilism. Dialetica 66 (3):425-433.
    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 (...)
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  9. Branden Fitelson (2012). Accuracy, Language Dependence, and Joyce's Argument for Probabilism. Philosophy of Science 79 (1):167-174.
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  10. Branden Fitelson (2012). Contrastive Bayesianism. In Martijn Blaauw (ed.), Contrastivism in Philosophy: New Perspectives. Routledge.
    Bayesianism provides a rich theoretical framework, which lends itself rather naturally to the explication of various “contrastive” and “non-contrastive” concepts. In this (brief) discussion, I will focus on issues involving “contrastivism”, as they arise in some of the recent philosophy of science, epistemology, and cognitive science literature surrounding Bayesian confirmation theory.
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  11. Branden Fitelson & Richard Feldman (2012). Evidence of Evidence is Not (Necessarily) Evidence. Analysis 72 (1):85-88.
    In this note, I consider various precisifications of the slogan ‘evidence of evidence is evidence’. I provide counter-examples to each of these precisifications (assuming an epistemic probabilistic relevance notion of ‘evidential support’).
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  12. Jeanne Peijnenburg, Branden Fitelson & Igor Douven (2012). Introduction to the Special Issue: Probability, Confirmation and Fallacies. Synthese 184 (1):1-1.
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  13. Jiaying Zhao, Vincenzo Crupi, Katya Tentori, Branden Fitelson & Daniel Osherson (2012). Updating: Learning Versus Supposing. Cognition 124 (3):373-378.
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  14. Branden Fitelson (2011). Favoring, Likelihoodism, and Bayesianism. [REVIEW] Philosophy and Phenomenological Research 83 (3):666-672.
    This (brief) note is about the (evidential) “favoring” relation. Pre-theoretically, favoring is a three-place (epistemic) relation, between an evidential proposition E and two hypotheses H1 and H2. Favoring relations are expressed via locutions of the form: E favors H1 over H2. Strictly speaking, favoring should really be thought of as a four-place relation, between E, H1, H2, and a corpus of background evidence K. But, for present purposes (which won't address issues involving K), I will suppress the background corpus, so (...)
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  15. Branden Fitelson & Christopher Hitchcock (2011). Probabilistic Measures of Causal Strength. In Phyllis McKay Illari Federica Russo (ed.), Causality in the Sciences. Oxford University Press. 600--627.
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  16. Branden Fitelson (2010). FEW 2009 Special Issue: Preface. [REVIEW] Journal of Philosophical Logic 39 (6):591-591.
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  17. Branden Fitelson (2010). Pollock on Probability in Epistemology. [REVIEW] Philosophical Studies 148 (3):455 - 465.
    In Thinking and Acting John Pollock offers some criticisms of Bayesian epistemology, and he defends an alternative understanding of the role of probability in epistemology. Here, I defend the Bayesian against some of Pollock's criticisms, and I discuss a potential problem for Pollock's alternative account.
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  18. Branden Fitelson (2010). Strengthening the Case for Knowledge From Falsehood. Analysis 70 (4):666-669.
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  19. Branden Fitelson (2010). The Wason Task(s) and the Paradox of Confirmation. Philosophical Perspectives 24 (1):207-241.
    The (recent, Bayesian) cognitive science literature on the Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on the Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, re-examining the (WT) with these historico-philosophical insights in mind.
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  20. Branden Fitelson & James Hawthorne (2010). How Bayesian Confirmation Theory Handles the Paradox of the Ravens. In Ellery Eells & James Fetzer (eds.), The Place of Probability in Science. Springer. 247--275.
    The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...)
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  21. Branden Fitelson & James Hawthorne (2010). Wason Task(s) and the Paradox of Confirmation. Philosophical Perspectives 24 (1):207-241.
  22. Branden Fitelson & James Hawthorne (2010). How Bayesian Confirmation Theory Handles the Paradox of the Ravens. In Ellery Eells & James Fetzer (eds.), The Place of Probability in Science. Springer. 247--275.
    The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...)
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  23. Branden Fitelson & David Jehle (2009). What is the “Equal Weight View'? Episteme 6 (3):280-293.
    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 of (EWV), but rather to (...)
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  24. Vincenzo Crupi, Branden Fitelson & Katya Tentori (2008). Probability, Confirmation, and the Conjunction Fallacy. Thinking and Reasoning 14 (2):182 – 199.
    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 to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal (...)
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  25. Branden Fitelson (2008). A Decision Procedure for Probability Calculus with Applications. Review of Symbolic Logic 1 (1):111-125.
    (new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.
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  26. Branden Fitelson (2008). Goodman's "New Riddle". Journal of Philosophical Logic 37 (6):613 - 643.
    First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed (especially, from a Bayesian inductive-logical point of view). Specifically, the analogy (...)
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  27. Branden Fitelson (2008). Teaching & Learning Guide For: The Paradox of Confirmation. Philosophy Compass 3 (5):1103-1105.
    The early twentieth century witnessed a shift in the way philosophers of science thought about traditional 'problems of induction'. Keynes championed the idea that Hume's Problem was not a problem about causation (which had been the traditional reading of Hume) but rather a problem about induction. Moreover, Keynes (and later Nicod) viewed such problems as having both logical and epistemological components. Hempel picked up where Keynes and Nicod left off, by formulating a rigorous formal theory of inductive logic. This spawned (...)
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  28. Branden Fitelson & Neil Thomason (2008). Bayesians Sometimes Cannot Ignore Even Very Implausible Theories (Even Ones That Have Not yet Been Thought Of). Australasian Journal of Logic 6:25-36.
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  29. Branden Fitelson (2007). Introduction. Studia Logica 86 (2):351-352.
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  30. Branden Fitelson (2007). Likelihoodism, Bayesianism, and Relational Confirmation. Synthese 156 (3):473 - 489.
    Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" (...)
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  31. Branden Fitelson & Andrew Waterman (2007). Comparative Bayesian Confirmation and the Quine–Duhem Problem: A Rejoinder to Strevens. British Journal for the Philosophy of Science 58 (2):332 - 338.
    By and large, we think (Strevens's [2005]) is a useful reply to our original critique (Fitelson and Waterman [2005]) of his article on the Quine-Duhem (QD) problem (Strevens [2001]). But, we remain unsatisfied with several aspects of his reply (and his original article). 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.
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  32. Branden Fitelson & Edward N. Zalta (2007). Steps Toward a Computational Metaphysics. Journal of Philosophical Logic 36 (2):227-247.
    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 PROVER9's first-order syntax, and (2) how (...)
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  33. Branden Fitelson (2006). Logical Foundations of Evidential Support. Philosophy of Science 73 (5):500-512.
    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 favor of bridging (...)
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  34. Branden Fitelson (2006). The Paradox of Confirmation. Philosophy Compass 1 (1):95–113.
    Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...)
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  35. Branden Fitelson, Alan Hajek & Ned Hall (2006). Probability. In Jessica Pfeifer & Sahotra Sarkar (eds.), The Philosophy of Science: An Encyclopedia. Routledge.
    There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...)
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  36. Laura Ruetsche, Chris Smeenk, Branden Fitelson, Patrick Maher, Martin Thomson‐Jones, Bas C. van Fraassen, Steven French, Juha Saatsi, Stathis Psillos & Katherine Brading (2006). 10. Can Philosophy Offer Help in Resolving Contemporary Biological Controversies? In Borchert (ed.), Philosophy of Science. Macmillan.
     
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  37. Laura Ruetsche, Chris Smeenk, Branden Fitelson, Patrick Maher, Martin Thomson‐Jones, Bas C. van Fraassen, Steven French, Juha Saatsi, Stathis Psillos & Katherine Brading (2006). 1. Preface Preface (Pp. I-Ii). Philosophy of Science 73 (5).
     
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  38. B. Fitelson (2005). Review: Bayesian Epistemology. [REVIEW] Mind 114 (454):394-400.
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  39. Branden Fitelson (2005). Review of Richard Jeffrey, Subjective Probability: The Real Thing. [REVIEW] Notre Dame Philosophical Reviews 2005 (10).
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  40. Branden Fitelson & Andrew Waterman (2005). Bayesian Confirmation and Auxiliary Hypotheses Revisited: A Reply to Strevens. British Journal for the Philosophy of Science 56 (2):293-302.
    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's simplifying idealization Indications that (I) oversimplifies Q–D Strevens's argument (...)
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  41. Branden Fitelson (2004). Discussion: Re-Solving Irrelevant Conjunction with Probabilistic Independence. Philosophy of Science 71 (4):505-514.
    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 overcomes the (...)
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  42. James Hawthorne & Branden Fitelson (2004). Discussion: Re‐Solving Irrelevant Conjunction with Probabilistic Independence. Philosophy of Science 71 (4):505-514.
    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 overcomes the problem of (...)
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  43. Paul Teller, Stefano Gattei, Kent W. Staley, Eric Winsberg, James Hawthorne, Branden Fitelson, Patrick Maher, Peter Achinstein & Mathias Frisch (2004). 10. Selection, Drift, and the “Forces” of Evolution Selection, Drift, and the “Forces” of Evolution (Pp. 550-570). Philosophy of Science 71 (4).
     
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  44. Darren Bradley & Branden Fitelson (2003). Monty Hall, Doomsday and Confirmation. Analysis 63 (277):23–31.
    We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.
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  45. Darren Bradley & Branden Fitelson (2003). Monty Hall, Doomsday and Confirmation. Analysis 63 (1):23-31.
  46. Branden Fitelson (2003). A Probabilistic Theory of Coherence. Analysis 63 (3):194–199.
    Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..
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  47. Branden Fitelson (2003). Hacking Ian. An Introduction to Probability and Inductive Logic. Cambridge University Press, 2000, Xvii+ 302 Pp. [REVIEW] Bulletin of Symbolic Logic 9 (4):506-508.
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  48. Branden Fitelson (2003). Review of Richard Swinburne (Ed.), Bayes's Theorem. [REVIEW] Notre Dame Philosophical Reviews 2003 (11).
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  49. Branden Fitelson (2003). Review: The Foundations of Causal Decision Theory. [REVIEW] Mind 112 (447):545-551.
  50. Branden Fitelson (2003). Review of I. Hacking, An Introduction to Probability and Inductive Logic. [REVIEW] Bulletin of Symbolic Logic 9 (4):5006-5008.
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  51. I. Hacking & Branden Fitelson (2003). REVIEWS-An Introduction to Probability and Inductive Logic. Bulletin of Symbolic Logic 9 (4):506-507.
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  52. Luc Bovens, Branden Fitelson, Stephan Hartmann & Josh Snyder (2002). Too Odd (Not) to Be True? A Reply to Olsson. British Journal for the Philosophy of Science 53 (4):539-563.
    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, whereas the witnesses in (...)
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  53. Ellery Eells & Branden Fitelson (2002). Symmetries and Asymmetries in Evidential Support. Philosophical Studies 107 (2):129 - 142.
    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.
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  54. Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos (2002). Shortest Axiomatizations of Implicational S4 and S. Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  55. Branden Fitelson (2002). Putting the Irrelevance Back Into the Problem of Irrelevant Conjunction. Philosophy of Science 69 (4):611-622.
    Naive deductive 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 utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that—according to Bayesian accounts of confirmation— E will confirm the conjunction H & X less strongly than E confirms (...)
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  56. Branden Fitelson (2002). Shortest Axiomatizations of Implicational S4 and S5. Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the strict implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  57. Branden Fitelson (2002). Too Odd (Not) to Be True? A Reply to Olsson. British Journal for the Philosophy of Science 53 (4):539 - 563.
    In '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, whereas the witnesses (...)
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  58. Stephan Hartmann, Luc Bovens, Branden Fitelson & Josh Snyder (2002). Too Odd (Not) to Be True: A Reply to Olsson. British Journal for the Philosophy of Science 53 (4):539-563.
    In ‘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, whereas the witnesses (...)
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  59. Noretta Koertge, Philip Kitcher, Helen E. Longino, Eva Jablonka, Sungsu Kim, Branden Fitelson & Gábor Hofer‐Szabó (2002). 10. Discussion Note: Distributed Cognition in Epistemic Cultures Discussion Note: Distributed Cognition in Epistemic Cultures (Pp. 637-644). [REVIEW] Philosophy of Science 69 (4).
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  60. J. C. Beall, T. Bigaj, T. Fernando, B. Fitelson, N. Foo, W. Goldfarb, D. Gregory, T. Hailperin, H. Halvorson & K. Harris (2001). Arló-Costa, H., 479 Armour-Garb, B., 593 Azzouni, J., 329 Batens, D., 267. Journal of Philosophical Logic 30 (619).
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  61. Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos (2001). A Concise Axiomatization of RM→. Bulletin of the Section of Logic 30 (4):191-194.
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  62. Branden Fitelson (2001). A Bayesian Account of Independent Evidence with Applications. Proceedings of the Philosophy of Science Association 2001 (3):S123-.
    outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.
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  63. Branden Fitelson (2001). Comments on Some Completeness Theorems of Urquhart and Méndez & Salto. Journal of Philosophical Logic 30 (1):51 - 55.
    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.
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  64. Branden Fitelson (2001). Studies in Bayesian Confirmation Theory. Dissertation, University of Wisconsin, Madison
    According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...)
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  65. Branden Fitelson & Larry Wos (2001). Finding Missing Proofs with Automated Reasoning. Studia Logica 68 (3):329-356.
    This article features long-sought proofs with intriguing properties (such as the absence of double negation and the avoidance of lemmas that appeared to be indispensable), and it features the automated methods for finding them. The theorems of concern are taken from various areas of logic that include two-valued sentential (or propositional) calculus and infinite-valued sentential calculus. Many of the proofs (in effect) answer questions that had remained open for decades, questions focusing on axiomatic proofs. The approaches we take are of (...)
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  66. Kenneth Harris & Branden Fitelson (2001). Comments on Some Completeness Theorems of Urquhart and Méndez & Salto. Journal of Philosophical Logic 30 (1):51-55.
    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.
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  67. Ellery Eells & Branden Fitelson (2000). Comments and Criticism: Measuring Confirmation and Evidence. Journal of Philosophy 97 (12):663-672.
    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: the difference measure: d(H,E) = pr(H/E) - pr(H).0 This may be called a “positive (probabilistic) relevance measure” of confirmation, since, according to it, a piece of evidence E qualitatively confirms a (...)
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  68. Ellery Eells & Branden Fitelson (2000). Measuring Confirmation and Evidence. Journal of Philosophy 97 (12):663-672.
  69. Branden Fitelson (2000). Measuring Confirmation and Evidence. Journal of Philosophy 97 (12):663 - 672.
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  70. Branden Fitelson & Larry Wos (2000). Axiomatic Proofs Through Automated Reasoning. Bulletin of the Section of Logic 29 (3):125-36.
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  71. Martin Barrett, Ellery Eells, Branden Fitelson & Elliott Sober (1999). Review: Models and Reality-A Review of Brian Skyrms's Evolution of the Social Contract. [REVIEW] Philosophy and Phenomenological Research 59 (1):237 - 241.
    Human beings are peculiar. In laboratory experiments, they often cooperate in one-shot prisoners’ dilemmas, they frequently offer 1/2 and reject low offers in the ultimatum game, and they often bid 1/2 in the game of divide-the-cake All these behaviors are puzzling from the point of view of game theory. The first two are irrational, if utility is measured in a certain way.1 The last isn’t positively irrational, but it is no more rational than other possible actions, since there are infinitely (...)
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  72. Branden Fitelson (1999). How Not to Detect Design. [REVIEW] Philosophy of Science 66 (3):472 - 488.
    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 a larger set of issues. William (...)
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  73. Branden Fitelson (1999). Review: Models and Reality-A Review of Brian Skyrms's Evolution of the Social Contract. [REVIEW] Philosophy and Phenomenological Research 59 (1):237 - 241.
    Human beings are peculiar. In laboratory experiments, they often cooperate in one-shot prisoners’ dilemmas, they frequently offer 1/2 and reject low offers in the ultimatum game, and they often bid 1/2 in the game of divide-the-cake All these behaviors are puzzling from the point of view of game theory. The first two are irrational, if utility is measured in a certain way.1 The last isn’t positively irrational, but it is no more rational than other possible actions, since there are infinitely (...)
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  74. Branden Fitelson (1999). The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity. Philosophy of Science 66 (3):378.
    Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...)
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  75. Branden Fitelson, Christopher Stephens & Elliott Sober (1999). Review: How Not to Detect Design. [REVIEW] Philosophy of Science 66 (3):472 - 488.
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  76. Branden Fitelson & Elliott Sober (1998). Plantinga's Probability Arguments Against Evolutionary Naturalism. Pacific Philosophical Quarterly 79 (2):115–129.
    In Chapter 12 of Warrant and Proper Function, Alvin Plantinga constructs two arguments against evolutionary naturalism, which he construes as a conjunction E&N .The hypothesis E says that “human cognitive faculties arose by way of the mechanisms to which contemporary evolutionary thought directs our attention (p.220).”1 With respect to proposition N , Plantinga (p. 270) says “it isn’t easy to say precisely what naturalism is,” but then adds that “crucial to metaphysical naturalism, of course, is the view that there is (...)
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  77. Branden Fitelson (1996). Wayne, Horwich, and Evidential Diversity. Philosophy of Science 63 (4):652-660.
    Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely satisfying.
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  78. Branden Fitelson, Accuracy & Coherence.
    This talk is (mainly) about the relationship two types of epistemic norms: accuracy norms and coherence norms. A simple example that everyone will be familiar with.
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  79. Branden Fitelson, Accuracy & Coherence II.
    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.
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  80. Branden Fitelson, Accuracy & Coherence III.
    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.
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  81. Branden Fitelson, A Concise Analysis of Popper's Qualitative Theory of Verisimilitude.
    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.
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  82. Branden Fitelson, A Historical Introduction to Confirmation Theory.
    Here’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.
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  83. Branden Fitelson, Bayes's Theorem.
    This is a high quality, concise collection of articles on the foundations of probability and statistics. Its editor, Richard Swinburne, has collected five papers by contemporary leaders in the field, written a pretty thorough and even-handed introductory essay, and placed a very clean and accessible version of Reverend Thomas Bayes’s famous essay (“An Essay Towards the Solving a Problem in the Doctrine of Chances”) at the end, as an Appendix (with a brief historical introduction by the noted statistician G.A. Barnard). (...)
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  84. Branden Fitelson, Comments on Presting's “Computability and Newcomb's Problem”.
    • What’s essential to Newcomb’s problem? 1. You must choose between two particular acts: A1 = you take just the opaque box; A2 = you take both boxes, where the two states of nature are: S 1 = there’s $1M in the opaque box, S2 = there’s $0 in the opaque box.
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  85. Branden Fitelson, Comparative Probability, Comparative Confirmation, and the “Conjunction Fallacy”.
    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 . Carnap begins by (...)
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  86. Branden Fitelson, Decermber 30, 2005.
    Slide #0 (Title). Before I get underway, I’d like to quickly thank a few people. First, Jonathan Vogel and John MacFarlane for working behind the scenes to make this thing happen. And, of course, David Christensen for chairing, and Patrick Maher and Jim Joyce for participating. I especially want to thank Patrick for his terrific feedback on my work this term, which has helped me to get much clearer on my project. Before we get started, does everyone have a handout? (...)
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  87. Branden Fitelson, Goodman's “Grue” Argument in Historical Perspective.
    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.
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  88. Branden Fitelson, Judgment Under Uncertainty Revisited: Probability Vs Confirmation.
    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.
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  89. Branden Fitelson, Knowledge From Falsehood.
    It is useful to note how (CC) differs from closure: (C) If S comes to believe q solely on the basis of competent deduction from p and S knows that p, then S knows that q. I won’t be discussing (C) today, but here is a useful contrast.
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  90. Branden Fitelson, Knowledge From Non-Knowledge.
    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].
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  91. Branden Fitelson, Language Dependence in Philosophy of Science and Formal Epistemology.
    Suppose 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).
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  92. Branden Fitelson, Overview of Finite Propositional Boolean Algebras I.
    of monadic or relational predicate calculus (Fa, Gb, Rab, Hcd, etc.). • The Boolean Algebra BL set-up by such a language will be such that: – BL will have 2 n states (corresponding to the state descriptions of L) – BL will contain 2 2n propositions, in total. ∗ This is because each proposition p in BL is equivalent to a disjunction of state descriptions. Thus, each subset of the set of..
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  93. Branden Fitelson, Probabilistic Coherence From a Logical Point of View.
    – Foundation: Probabilistic Confirmation (c) from a Logical POV ∗ cph, eq as a “relevant” quantitative generalization of pe  hq ∗ cph, eq, so understood, is not Prpe  hq or Prph | eq, etc. ∗ cph, eq is something akin (ordinally) to the likelihood ratio..
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  94. Branden Fitelson, Remarks on Probability and “Intelligent Design”.
    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? (...)
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  95. Branden Fitelson, Some Recent Fallacies of Approximation in Bayesian Confirmation Theory.
    • Several recent Bayesian discussions make use of “approximation” – Earman on the Quantitative Old Evidence Problem – Vranas on Quantitative Approaches to the Ravens Paradox – Dorling’s Quantitative Approach to Duhem–Quine – Strevens’s Quantitative Approach to Duhem–Quine – rThere are also examples not involving confirmation: E.g.
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  96. Branden Fitelson, Some Remarks on the Model Selection Problem.
    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.
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  97. Branden Fitelson, The Central Thesis as Involving “Inference to the Best Explanation”.
    • Two competing explanations (independence of S i favors R over CB): (CB) there is a coherence bias in a’s S -formation process.
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  98. Branden Fitelson, Two Technical Corrections to My Coherence Measure.
    Note: This is not an ad hoc change at all. It’s simply the natural thing say here – if one thinks of F as a generalization of classical logical entailment. The extra complexity I had in my original (incorrect) definition of F was there because I was foolishly trying to encode some non-classical, or “relavant” logical structure in F. I now think this is a mistake, and that I should go with the above, classical account of F. Arguments about relevance (...)
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  99. Branden Fitelson & Kenny Easwaran, Accuracy, Coherence and Evidence.
    Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.
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  100. Branden Fitelson & Daniel Osherson, Remarks on “Random Sequences”.
    We consider how to reach reasonable belief about whether a (possibly idealized) physical process is producing its output randomly. For definiteness, we’ll consider a coin-flipper C which reports a sequence of outcomes of tosses of a coin. C outputs “H” for a heads outcome and “T” for a tails outcome. By C producing its output “randomly,” we mean that the probability of C issuing an H on any given trial is the same as the probability of issuing a T, and (...)
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  101. Branden Fitelson & Daniel Osherson, The Problem: First Pass.
    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 (...)
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  102. Branden Fitelson & Andrew Waterman, A Rejoinder to Strevens.
    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.
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  103. Kenneth Harris & Branden Fitelson, Distributivity in Lℵ0 and Other Sentential Logics.
    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].
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  104. Larry Wos & Branden Fitelson, G The Automation of Sound Reasoning and Successful Proof Findin.
    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 emulate s Sherlock Holmes and Mr. (...)
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  105. Larry Wos, Dolph Ulrich & Branden Fitelson, Vanquishing the XCB Question: The Methodological Discovery of the Last Shortest Single Axiom for the Equivalential Calculus.
    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..
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  106. Branden Fitelson, Automated Reasoning in Modal Logics: A Framework with Applications.
    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.
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  107. Branden Fitelson, Comments and Criticism Measuring Confirmation and Evidence.
    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.
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  108. Branden Fitelson, Comments on Jill North's “Symmetry and Probability”.
    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 (MCD). I’ll begin by telling the “canonical” story of the MCD (as I see it). 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 (...)
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  109. Branden Fitelson, Comments on Jim Franklin's “the Representation of Context: Ideas From Artificial Intelligence”.
    To be honest, I have almost nothing critical to say about Jim’s presentation (and this is quite unusual for a cranky analytic philosopher like me!). What Jim has said is all very sensible, and his examples are very well chosen, etc. So, instead of making critical remarks, I will try to expand a little on one of the themes Jim briefly touched upon in his talk: the contextuality of probability.
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  110. Branden Fitelson, Distributivity in Lℵ0 and Other Sentential Logics.
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
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  111. Branden Fitelson, Earman on Old Evidence and Measures of Confirmation.
    In 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.
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  112. Branden Fitelson, G the Automation of Sound Reasoning and Successful Proof Findin.
    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 emulate..
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  113. Branden Fitelson, Likelihoods, Counterfactuals, and Tracking.
    Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References..
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  114. Branden Fitelson, MaGIC: Matrix Generator for Implication Connectives.
    The program MaGIC (Matrix Generator for Implication Connectives) is intended as a tool for logical research. It computes small algebras (normally with up to 14 elements) suitable for modelling certain non-classical logics. Along the way, it eliminates from the output any algebra isomorphic to one already generated, thus returning only one from each isomorphism class. Optionally, the user may specify a formula which is to be..
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  115. Branden Fitelson, Notes on Gibbard's Theorem.
    Let L be a sentential (object) language containing atoms ‘A’, ‘B’, . . . , and two logical connectives ‘&’ and ‘→’. In addition to these two logical connectives, L will also contain another binary connective ‘ ’, which is intended to be interpreted as the English indicative. In the meta-language for L , we will have two meta-linguistic operations: ‘ ’ and ‘ ’. ‘ ’ is a binary relation between individual sentences in L . It will be interpreted (...)
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  116. Branden Fitelson, Overview of Presentation.
    • What are the ends of statistical experiment, analysis, and inference? • What are the most effective means for achieving these ends? • Several paradigms for statistics have been developed — each of these presupposes answers to these key “philosophical” questions about statistics.
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  117. Branden Fitelson, Overview of Talk.
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”).
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  118. Branden Fitelson, Probabilistic Coherence From a Logical Point of View From Confirmation to Coherence I.
    ∗ C pp, qq as a “mutual confirmation” generalization of pp & qq Prpe  hq won’t work Prpp & qq won’t work ∗ C pp, qq, so understood, is not Prpp & qq or Prpq | pq, etc.
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  119. Branden Fitelson, Some Remarks on the “Intelligent Design” Controversy.
    There are various questions that arise in connection with the “intelligent design” (ID) controversy. This introductory section aims to distinguish five of these questions. Later sections are devoted to detailed discussions of each of these five questions. The first (and central) question is the one that has been discussed most frequently in the news lately: (Q1) Should ID be taught in our public schools? It is helpful to break this general “public school curriculum question” into the following two more specific (...)
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  120. Branden Fitelson, The British Journal for the Philosophy of Science.
    The British Journal for the Philosophy of Science 2002 53(4):539-563; doi:10.1093/bjps/53.4.539 © 2002 by British Society for the Philosophy of Science..
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  121. Branden Fitelson, The Jowett Society & the Philosophical Sociey.
    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..
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  122. Branden Fitelson, Using Mathematica to Understand the Computer Proof of the Robbins Conjecture.
    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 Mathematica (...)
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  123. Branden Fitelson, Vanquishing the XCB Question: The Methodological Discovery of the Last Shortest Single Axiom for the Equivalential Calculus.
    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) (...)
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  124. Branden Fitelson & Lara Buchak, Advice-Giving and Scoring-Rule-Based Arguments for Probabilism.
    Dutch Book Arguments. B is susceptibility to sure monetary loss (in a certain betting set-up), and F is the formal role played by non-Pr b’s in the DBT and the Converse DBT. Representation Theorem Arguments. B is having preferences that violate some of Savage’s axioms (and/or being unrepresentable as an expected utility maximizer), and F is the formal role played by non-Pr b’s in the RT.
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  125. Branden Fitelson & Lara Buchak, Separability Assumptions in Scoring-Rule-Based Arguments for Probabilism.
    - In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.
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  126. Branden Fitelson & Alan Hájek, Declarations of Independence.
    According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are undefined whenever their antecedents have zero unconditional probability. This has important ramifications for the notion of probabilistic independence. Traditionally, independence is defined in terms of unconditional probabilities (the factorization of the relevant joint unconditional probabilities). Various “equivalent” formulations of independence can be given using conditional probabilities. But these “equivalences” break down if conditional probabilities are permitted to have (...)
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  127. Branden Fitelson & Jim Hawthorne, The Problem of Irrelevant Conjunction — Revisited.
    E confirmsi H1 more strongly than E confirmsi H2 iff c(H1, E) > c(H2, E). [where c is some relevance measure].
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  128. Branden Fitelson, Here is a “Reductio” of Classical Deductive Logic.
    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.].
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