Background: Empirical studies in Muslim communities on organ donation and blood transfusion show that Muslim counsellors play an important role in the decision process. Despite the emerging importance of online English Sunni fatwas, these fatwas on organ donation and blood transfusion have hardly been studied, thus creating a gap in our knowledge of contemporary Islamic views on the subject. Method: We analysed 70 English Sunni e-fatwas and subjected them to an in-depth text analysis in order to reveal the key concepts (...) in the Islamic ethical framework regarding organ donation and blood transfusion. Results: All 70 fatwas allow for organ donation and blood transfusion. Autotransplantation is no problem at all if done for medical reasons. Allotransplantation, both from a living and a dead donor, appears to be possible though only in quite restricted ways. Xenotransplantation is less often mentioned but can be allowed in case of necessity. Transplantation in general is seen as an ongoing form of charity. Nearly half of the fatwas allowing blood transfusion do so without mentioning any restriction or problem whatsoever. The other half of the fatwas on transfusion contain the same conditional approval as found in the arguments pro organ transplantation. Conclusion: Our findings are very much in line with the international literature on the subject. We found two new elements: debates on the definition of the moment of death are hardly mentioned in the English Sunni fatwas and organ donation and blood transfusion are presented as an ongoing form of charity. (shrink)
The Art of Living Consciously Is an Operating Manual for Our Basic Tool of Survival In The Art of Living Consciously, Dr. Nathaniel Branden, our foremost authority on self-esteem, takes us into new territory, exploring the actions of our minds when they are operating as our life and well-being require -- and also when they are not. No other book illuminates so clearly what true mindfulness means: * In the workplace * In the arena of romantic love * In (...) child-rearing * In the pursuit of personal development Today we are exposed to an unprecedented amount of information and an unprecedented number of opinions about every conceivable aspect of life. We are thrown on our own resources as never before -- and we have nothing to protect us but the clarity of our thinking. In The Art of Living Consciously, Branden gives us the tools with which to draw out the best within us. (shrink)
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 (...) a new branch of philosophy of science called confirmation theory. Hempel's theory of confirmation was based on a few very simple (and seemingly plausible) assumptions about (instantial) 'inductive-logical support'. However, as Hempel himself was keenly aware, even such simple and seemingly plausible assumptions give rise to various puzzles and paradoxes. The two most famous paradoxes of confirmation were discovered by Hempel and Goodman. This article discusses Hempel's paradox (which is known as 'the' paradox of confirmation, since it was discovered first). However, many of the historical developments surrounding Hempel's paradox (also known as the 'raven paradox') are also crucial for understanding Goodman's later ('grue') paradox. Author Recommends: Branden Fitelson, 'The Paradox of Confirmation', Philosophy Compass 1/1 (2006): 95–113, doi: [DOI link]. In this article, I explain how the inconsistency between Hempel's intuitive resolution and his official theory of confirmation affects the historical dialectic about the paradox and how it illuminates the nature of confirmation. After the survey, I argue that Hempel's intuitions about the paradox of confirmation were basically correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. C. G. Hempel, 'Studies in the Logic of Confirmation' (I and II), Mind 54 (1945): 1–26, 97–121, dois: [DOI link]; [DOI link]. This is the locus classicus of traditional (instantial) confirmation theory. It is here that original motivations for, traditional approaches to, and paradoxes of confirmation are discussed in depth for the first time, under the rubric 'confirmation theory'. Hempel's discussion (which picks up where Keynes and Nicod left off) is chock full of crucial historical, logical, and epistemological insights. J. M. Keynes, A Treatise on Probability (London: Macmillan, 1921). Keynes does not get enough credit in this context. But, basically, chapters 18 to 23 of this classic book planted the seeds for almost all of modern confirmation theory. Nicod and Hempel (as well as Hosiasson-Lindenbaum, Carnap, and others) were, basically, just picking-up where Keynes left off. J. Nicod, The Logical Problem of Induction (1923), reprinted in Foundations of Geometry and Induction (London: Routledge, 2000). Nicod's essay expands upon Keynes's work. Nicod is the first to use the term 'confirmation', in connection with a relation of 'inductive-logical support'. Nicod endorses several key confirmation-theoretic principles (which were already advanced by Keynes). In the hands of Hempel, Nicod's work later becomes an important historical foil. J. Hosiasson–Lindenbaum, 'On Confirmation', Journal of Symbolic Logic 5 (1940): 133–48. This essay contains most (if not all) of the basic ingredients of the 'Bayesian' approaches to the paradox of confirmation that appeared later. It also sheds much light on an important dispute between Keynes and Nicod concerning one of the claims Keynes makes (in his Treatise) about 'long-run convergence' in certain (instantial) confirmation-theoretic problems. This paper also contains one of the earliest rigorous axiomatizations of conditional (subjective or logical) probability. R. Carnap, Logical Foundations of Probability (Chicago, IL: University of Chicago, 1950). This is Carnap's encyclopaedic work on inductive logic and probability. There is a tremendous amount of wisdom in here. For present purposes, the sections on Hempel's theory of confirmation (in contrast to probabilistic approaches to confirmation, such as Hosiasson–Lindenbaum's and Carnap's) are probably most important and salient (see §§87–8). I. J. Good, 'The Paradox of Confirmation', British Journal for the Philosophy of Science 11 (1960): 145–9. C. Chihara, 'Quine and the Confirmational Paradoxes', in Midwest Studies in Philosophy. Vol. 6: The Foundations of Analytic Philosophy, eds. Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein (Minneapolis, MN: University of Minnesota Press, 1981), 425–52. J. Earman, Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory (Cambridge, MA: MIT Press, 1992), specifically: pp. 63–73. R. M. Royall, Statistical Evidence: A Likelihood Paradigm (New York, NY: Chapman & Hall, 1997), specifically: the Appendix on 'The Paradox of the Ravens'. C. McKenzie and L. Mikkelsen, 'The Psychological Side of Hempel's Paradox of Confirmation', Psychonomic Bulletin & Review 7 (2000): 360–6. P. Maher, 'Probability Captures the Logic of Scientific Confirmation', in Contemporary Debates in the Philosophy of Science, ed. Christopher Hitchcock (Oxford: Blackwell, 2004), 69–93. P. Vranas, 'Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution', British Journal for the Philosophy of Science 55 (2004): 545–60. This is a list of seven of my favourite papers on the paradox of confirmation, since 1950 (listed in chronological order). Most of these are coming from a broadly 'Bayesian' perspective. In particular, I recommend Vranas as a good starting point here. Online Materials: http://fitelson.org/probability/ Probability & Induction (PHIL 148, UC-Berkeley, Spring 2008) This is the Web site for an undergraduate course on probability and induction that I taught at UC-Berkeley in Spring 2008. Much of the course focuses on confirmation theory (including the paradoxes of confirmation). There are many links there to lecture notes, papers, books and other salient online resources. http://fitelson.org/confirmation/ Confirmation (graduate seminar, UC-Berkeley, Fall 2007) This is the Web site for a graduate seminar on confirmation that I taught at UC-Berkeley in Fall 2007. This seminar is a historical trace of induction/confirmation, from Aristotle to Goodman (mostly, focusing on the 20th century and the paradoxes of confirmation). Sample Syllabus: See the online syllabi for Confirmation and/or Probability & Induction (above). Note: those online syllabi contain electronic copies of many of the salient readings. (shrink)
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 (...) raise awareness about some of the difficulties inherent in formulating such precisifications. (shrink)
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’).
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 (...) reveals an intimate connection between Goodman’s problem, and the “problem of old evidence”. Several other novel aspects of Goodman’s argument are also discussed (mainly, from a Bayesian perspective). (shrink)
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 (...) the historical dialectic about the paradox and how it illuminates the nature of confirmation. In the end, we will argue that Hempel’s intuitions about the paradox of confirmation were (basically) correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. (shrink)
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 (...) that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)
A number of theories of causation posit that causes raise the probability of their effects. In this paper, we survey a number of proposals for analyzing causal strength in terms of probabilities. We attempt to characterize just what each one measures, discuss the relationships between the measures, and discuss a number of properties of each measure.
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 (...) conditions with zero unconditional probability. We reconsider probabilistic independence in this more general setting. We argue that a less orthodox but more general (Popperian) theory of conditional probability should be used, and that much of the conventional wisdom about probabilistic independence needs to be rethought. (shrink)
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 pinpoints any epistemic defect of incoherent agents. The same can be said for Representation Theorem arguments, since they involve the structure of an agent’s preferences. (shrink)
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.
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 (...) result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)
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 (...) to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens. (shrink)
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.
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.
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 (...) no such person as the God of traditional theism.” Plantinga tries to cast doubt on the conjunction E&N in two ways.His “preliminary argument” aims to show that the conjunction is probably false, given the fact (R) that our psychological mechanisms for forming beliefs about the world are generally reliable.His “main argument” aims to show that the conjunction E&N is self-defeating — if you believe E&N , then you should stop believing that conjunction.Plantinga further develops the main argument in his unpublished paper “Naturalism Defeated” (Plantinga 1994).We will try to show that both arguments contain serious errors. (shrink)
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.
- 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.
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.
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.
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.
In sum, then, Chalmers’s attempt to argue against physicalism based on the conceivability of zombies misses the mark. His version of conceivability does indeed imply possibility, but at the cost of making it unclear whether zombies are indeed conceivable.
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 (...) to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens. (shrink)
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.
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 (...) Paley saw clearly that we sometimes have an excellent reason to postulate the existence of an intelligent designer. If we find a watch on the heath, we reasonably infer that it was produced by an intelligent watchmaker. This design argument makes perfect sense. Why is it any different to claim that the eye was produced by an intelligent designer? Both critics and defenders of the design argument need to understand what the ground rules are for inferring that an intelligent designer is the unseen cause of an observed effect. (shrink)
I. Introduction Sex has been thought to reveal the most profound truths about individuals, laying bare their deepest desires and fears to their partners and themselves. In ‘Carnal Knowledge,’ Wendy Doniger states that this view is to be found in the texts of ancient India, in the Hebrew Bible, in Renaissance England and Europe, as well as in contemporary culture, including Hollywood films.1 Indeed, according to Josef Pieper, the original, Hebrew, meaning of ‘carnal knowledge’ was ‘immediate togetherness, intimate presence.’ [i] (...) But equally prevalent in both ancient and contemporary culture is the view that sex generates the deepest illusions, hiding people’s true selves behind layers of blindness, deception, or self-deception.2 There is, however, no contradiction in holding both that sexual deception and blindness are widespread, and that sex reveals some profound truths about us. Indeed, if deception or blindness about our desires and fantasies is widespread, one likely explanation is surely that many of us implicitly or explicitly believe that our desires and fantasies say something important about us – or at least that we believe that others believe that they do. There is little reason to hide from ourselves or others that which we regard as unimportant. But while such blindness to or pretence about one’s own or partner’s sexual needs and desires saves one from embarrassment or from the effort to understand and satisfy one’s partner or oneself, it also subverts a central value of any fulfilling personal relationship: ‘mutual visibility,’ that is, mutual perceptiveness and responsiveness (Branden, 1980). In sex such blindness means that both parties feel ‘unseen’ as sexual beings. Deception or self-deception in sexual relationships can also be about one’s intentions towards or feelings for one’s partner, forms of deception that are well illustrated by Valmont in his relationship to Madame Tourvel in Dangerous Liaisons (1988). All these forms of carnal deception and illusion show a failure of what I shall call ‘carnal wisdom,’ understood as an aspect of practical wisdom.. (shrink)
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 (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (shrink)
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 (...) 3 come in handy. With the help of Mathematica, it is relatively easy to work out and explain each step of the dense EQP proof in detail. In this paper, I use Mathematica to provide a detailed, step-by-step reconstruction of the highly complex EQP proof of the Robbins conjecture. (shrink)
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 (...) as to simplify our discussion. Moreover, the favoring relation is meant to be a propositional epistemic relation, as opposed to a doxastic epistemic relation. That is, the favoring relation is not meant to be restricted to bodies of evidence that are possessed (as evidence) by some actual agent(s), or to hypotheses that are (in fact) entertained by some actual agent(s). In this sense, favoring is analogous to the relation of propositional justification — as opposed to doxastic justification (Conee 1980). In order to facilitate a comparison of Likelihoodist vs Bayesian explications of favoring, I will presuppose the following bridge principle, linking favoring and evidential support: • E favors H1 over H2 iff E supports H1 more strongly than E supports H2.1 Finally, I will only be discussing instances of the favoring relation involving contingent, empirical claims. So, it is to be understood that “favoring” will not apply if any of E, H1, or H2 are non-contingent (and/or non-empirical). With this background in place, we're ready to begin. (shrink)
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" (...) between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the "Monty Hall" problem. (shrink)
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.
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 (...) confirmation and evidential support. (shrink)
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 (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (shrink)
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.
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 (...) prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. (shrink)
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.
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). (...) I will briefly discuss each of the five papers in the volume, with an emphasis on certain issues arising from the use of probability as a tool for thinking about evidence. (shrink)
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.
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 (...) many other Nash equilibria besides the one in which both players bid 1/2. At the same time, these behaviors seem to indicate that people are sometimes inclined to be cooperative, fair, and just. In his stimulating new book, Brian Skyrms sets himself the task of showing why these inclinations evolved, or how they might have evolved, under the pressure of natural selection. The goal is not to justify our ethical intuitions, but to explain why we have them.2.. (shrink)
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 & · · · (...) &An−1 & ¬An T T T F T s3 = A1 & A2 & · · · & ¬An−1 & An T T T F F s4 = A1 & A2 & · · · & ¬An−1 & ¬An.. (shrink)
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..
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.
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 (...) many other Nash equilibria besides the one in which both players bid 1/2. At the same time, these behaviors seem to indicate that people are sometimes inclined to be cooperative, fair, and just. In his stimulating new book, Brian Skyrms sets himself the task of showing why these inclinations evolved, or how they might have evolved, under the pressure of natural selection. The goal is not to justify our ethical intuitions, but to explain why we have them.2.. (shrink)
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 a relation — we should have S 1 ą S 2. (shrink)
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.
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].
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.
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.
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 (...) H (again, in the case of deductive evidence). I argue that existing Bayesian “resolutions” of this problem are inadequate in several important respects. In the end, I suggest a new‐and‐improved Bayesian account (and understanding) of the problem of irrelevant conjunction. (shrink)
Synthese 156 (3) (2007). Special issue ed. with Luc Bovens. With contributions by Max Albert, Branden Fitelson, Dennis Dieks, Igor Douven and Wouter Meijs, Alan Hájek, Colin Howson, James Joyce, and Patrick Suppes.
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 (...) hypothesis H if and only if pr(H/E) > pr(H), where qualitative disconfirmation is characterized by replacing “>” with “ “ with “=”. Other more or less standard positive relevance measures that have been proposed are: the log-ratio measure: r(H,E) = log[pr(H/E)/pr(H)] and the log-likelihood-ratio measure: l(H,E) = log[pr(E/H)/pr(E/~H)]. (shrink)
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-.
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 irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson’s solution. (shrink)
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 (...) sub-questions: (Q1.1) Should ID be included in the science curriculum of our public schools? (Q1.2) Should ID be included in some part of our public school curriculum? Of course, these public school curriculum questions should be distinguished from other (perhaps related, but distinct) questions that are often asked about ID. Here is another question that is very frequently discussed, not only in the debate about (Q1), but in the ID controversy generally: (Q2) What is ID? In other words, is ID a scientific theory, a religious doctrine, an.. (shrink)
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 (...) for the legitimacy of (I). (shrink)
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 favor H1 over H2 (or vice versa)? (shrink)
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 (...) Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. 1 Claim (C) examined for Olsson's characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion. (shrink)
they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at (...) least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied. (shrink)
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.
• 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.
∗ 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.
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 (...) irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson's solution. (shrink)
Background: Empirical studies in Muslim communities on organ donation and blood transfusion show that Muslim counsellors play an important role in the decision process. Despite the emerging importance of online English Sunni fatwas, these fatwas on organ donation and blood transfusion have hardly been studied, thus creating a gap in our knowledge of contemporary Islamic views on the subject.Method: We analysed 70 English Sunni e-fatwas and subjected them to an in-depth text analysis in order to reveal the key concepts in (...) the Islamic ethical framework regarding organ donation and blood transfusion.Results: All 70 fatwas allow for organ donation and blood transfusion. Autotransplantation is no problem at all if done for medical reasons. Allotransplantation, both from a living and a dead donor, appears to be possible though only in quite restricted ways. Xenotransplantation is less often mentioned but can be allowed in case of necessity. Transplantation in general is seen as an ongoing form of charity. Nearly half of the fatwas allowing blood transfusion do so without mentioning any restriction or problem whatsoever. The other half of the fatwas on transfusion contain the same conditional approval as found in the arguments pro organ transplantation.Conclusion: Our findings are very much in line with the international literature on the subject. We found two new elements: debates on the definition of the moment of death are hardly mentioned in the English Sunni fatwas and organ donation and blood transfusion are presented as an ongoing form of charity. (shrink)
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.
– 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..
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 (...) each trial is independent of the others. Thus, C produces its output “randomly” just in case C’s trials are independent and unbiased. If C produces its output randomly (in the above sense), then we’ll say that C is a random device. (shrink)
• 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.
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 (...) clarifying the explicandum (the informal “inductive support” concept) in various ways, including. (shrink)
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..
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.
Gödel, Tarski, Church, and the Liar , by György Serény, pages 3–25. From foundations to ludics , by Jean-Yves Girard, pages 131 -- 168. Symmetry and interactivity in programming , by P.-L. Curien, pages 169 -- 180. Two spaces looking for a geometer , by Giorgio Parisi, pages 181 -- 196. Model theory: Geometrical and set-theoretic aspects and prospects , by Angus Macintyre, pages 197 -- 212. Foundations and applications: axiomatization and education , by F. William Lawvere, pages 213 -- (...) 224. Differential calculus and nilpotent real numbers , by Anders Kock, pages 225 -- 230. The empty set, the singleton, and the ordered pair , by Akihiro Kanamori, pages 273 -- 298. Computable and continuous partial homomorphisms on metric partial algebras , by Viggo Stoltenberg-Hansen and John V. Tucker, pages 299 -- 334. Survey of the Steinhaus tiling problem , by Steve Jackson and R. Daniel Mauldin, pages 335 -- 361. A universal approach to self-referential paradoxes, incompleteness and fixed points , by Noson S. Yanofsky, pages 362 -- 386. On the philosophical development of Kurt Gödel , by Mark van Atten and Juliette Kennedy, pages 425 — 476. Identity of proofs based on normalization and generality , by Kosta Došen, pages 477 — 503. (shrink)
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.
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 (...) allay my worry. (shrink)
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.].
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 (...) as “single premise entailment” (or “single premise deducibility in L ”). ‘ ’ is a monadic predicate on sentences of L . It will be interpreted as “logical truth of the logic of L ” (or “theorem of the logic of L ”). We will not presuppose anything about the relationship between ‘ ’ and ‘ ’. Rather, we will state explicitly all assumptions about these meta-theoretic relations that will be required for Gibbard’s Theorem. (shrink)
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 (...) in Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, 'a grain of truth' to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. (shrink)
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.
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.
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 (...) in Olsson’s model are not independent in the standard sense. We argue that there is much more than, in Olsson’s words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen’s characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson’s argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson’s model is applicable. (shrink)
