Three topics are discussed concerning the application probability and explanation to the confirmation of theories. The first concerns the debate over prediction versus accommodation. I argue that we typically have reason to be more confident of a theory given that it was constructed independently of the knowledge of certain data than if it was designed to accommodate those data. The second concerns the puzzle of the apparent 'fine-tuning' of the universe for life. I argue that the fact that our universe (...) meets the extremely improbable yet necessary conditions for life provides no evidence for the thesis that there are, or have been, very many universes. The third chapter concerns the need to explain the existence of life. I argue that if life's existence needs an explanation at all, the place to look is in a teleological explanation. If this option is rejected, we should be content to see the origin of life as an extremely improbable fluke. (shrink)

Extreme Permissivism is the view that a body of evidence could rationally permit both the attitude of belief and disbelief towards a proposition. This paper puts forward a new argument against Extreme Permissivism, which improves on a similar style of argument due to Roger White (2005, 2014). White’s argument is built around the principle that the support relation between evidence and a hypothesis is objective: so that if evidence E makes it rational for an agent to believe a (...) hypothesis H, then E makes it rational to believe H, for all agents. In this paper, I construct a new argument against Extreme Permissivism that appeals to a logically weaker, less demanding view about evidential support, Relational Objectivity: whether a body of evidence E is more likely if H is true than if H is false is an objective matter and does not depend on how any agent interprets the relationship between E and H. Relational Objectivity is solely concerned with the conditional probabilities called likelihoods and does not put substantive constraints on an agent’s prior and posterior credences. For this reason, the presented argument avoids the standard permissivist criticism levelled against White’s argument. (shrink)

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...) state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)

In this paper we analyze the existence of joint probabilities for the Bell-type and GHZ entangled states. We then propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for the contextual hidden variables. Finally, we show that for the extreme example of no error, the GHZ state allows for the definition of a joint upper probability that is consistent with the strong correlations.

By “physical probability” I mean the empirical concept of probability in ordinary language. It can be represented as a function of an experiment type and an outcome type, which explains how non-extreme physical probabilities are compatible with determinism. Two principles, called specification and independence, put restrictions on the existence of physical probabilities, while a principle of direct inference connects physical probability with inductive probability. This account avoids a variety of weaknesses in the theories of Levi and Lewis.

Anthropomorphized, or human-like artefacts, have been used in teaching and training of medical skills for a long time. The most famous artefact used today is probably the Resusci ® Anne CPR training manikin, which is used for training of resuscitation skills. However, what has changed over the lifespan of these artefacts is the level of human-like features in them. All around the globe, highly anthropomorphized ICT artefacts are used in training of medical skills. Amongst others, the UNAM University in Mexico (...) City and Royal North Shore Hospital in New South Wales use artefacts, which are closer to human-like robots than traditional manikins in teaching. The purpose of this article is to look deeper into this phenomenon, consider its potential implications for the patient-physician relationship and quality of patient care, and to propose some practical methods for minimizing the possible risks emerging from the use of these extremely anthropomorphized artefacts. (shrink)

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are (...) known. Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence. (shrink)

The author recently claimed that Pr(P, Q), where Pr is a probability function and P and Q are two sentences of a formalized language L, qualifies as an estimate--made in the light of Q--of the truth-value of P in L. To substantiate his claim, the author establishes here that the two strategies lying at the opposite extremes of the spectrum of truth-value estimating strategies meet the first five of the six requirements (R1-R6) currently placed upon probability functions and fail to (...) meet the sixth one. He concludes from those two results that the value for P and Q of any function satisfying R1-R5 must rate "minimally satisfactory" and the value for P and Q of any function satisfying R1-R6 must rate "satisfactory" as an estimate--made in the light of Q--of the truth-value of P in L. (shrink)

This ambitious study, by a professor of rhetoric, proposes itself as "intellectual history in a traditional sense" and not as philosophical discourse. Though philosophy does not appear in its title, however, much of its content will appear to philosophers as pertaining to their discipline, and the thesis it develops surely commends itself to philosophical critique. The author's aim, at least in part, is to challenge "the commonly held view" that the scientific revolution created or intensified the modern division between the (...) humanities and the sciences. In the early Renaissance, she argues, rhetoric and philosophy were seen as "pursuing different goals by different means," with rhetoric assigned to the humanities and concerned with opinion and probability and science assigned to philosophy and concerned with truth and certainty. Such a dichotomy was broken down at the onset of the modern period, she holds, particularly in seventeenth-century England, where a sceptical approach to knowledge made for common ground between humanists and scientists. The weakening of knowledge claims in the probabilistic empiricism of the period is thus, for her, the key to understanding its intellectual life and the climate of opinion in which it flourished. To make the point she devotes successive chapters to natural philosophy and empirical science; religion; history; law; witchcraft; and language, communication, and literature. The presentation is scholarly throughout and well documented in an abundance of notes at the end of the volume. Considering the difficulty of her thesis and its extremely broad range the author argues her case well; yet there are problems with it that make one wonder whether her generalization can claim validity in anything more than a trivial sense. (shrink)

Theism is a far simpler hypothesis, and so a priori more probably true, than naturalism, understood as the hypothesis that the existence of this law-governeduniverse has no explanation. Theism postulates only one entity (God) with very simple properties, whereas naturalism has to postulate either innumerableentities all having the same properties, or one very complicated entity with the power to produce the former. If theism is true, it is moderately probable that God would create humanoid beings and so humanoid bodies; but (...) laws of nature would have to have very special properties if they are to bring about the existencne of humaoid bodies. Given laws of the present form (quantum theory with the Pauli principle and the four forces), the constants of the laws and variables of the boundary conditions of the universe would need to be extremely fine-tuned; and no simpler set of laws would allow the existence of humanoid bodies at all. So the evidence of the existence of humanoid bodies adds further to the probability of theismas against naturalism. (shrink)

The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces are strictly convex (...) smooth compact convex sets and that each such set _K_ gives rise to a quantum logic of this class with the state space _K_. The transition probabilities are symmetric iff _K_ is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics for epistemic (...) modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

Improved life sustaining technology in the neonatal intensive care unit (NICU) has resulted in an increased probability of survival in extremely premature babies. Miracle baby stories in the popular press are a regular occurrence and these reports are often the first source from which the general public learn about extremely premature babies. The research from which this paper is drawn sought to explore the care‐giving and ethical dilemmas of neonatal nurses when caring for extremely premature babies 24 weeks gestation and (...) less. This current paper aims to outline the views of neonatal nurses on miracle baby stories in the media. Data were collected via a questionnaire to 760 Australian neonatal nurses with 414 returned, representing a response rate of 54.4%. Narrative was collected from semi‐structured interviews with 24 experienced neonatal nurses in NSW, Australia. A qualitative approach utilising thematic analysis was utilised to analyse the data. The theme the myth of the miracle baby is seen as generating myths and unrealistic expectations on the part of vulnerable families and the public. Neonatal nurses, as the primary caregivers for tiny babies and their families, viewed popular media publications with suspicion, believing published reports to be incomplete, inaccurate and biased towards the positive. (shrink)

On any speedometer, there are two kinds of what might very loosely be called ‘zones of indifference’. The first kind is found between any two marked speeds. If your speed is in fact 61 mph, it probably falls in one kind of zone of indifference. A normal speedometer is simply not designed to distinguish speeds between 60 and 65 mph, and if asked, we would probably report such a speed as ‘about 60’. There is, however, another kind of zone of (...) indifference. It is the one that extends beyond the highest marked speed, and includes all speeds that are too fast for the speedometer to register them—all the speeds that are literally off the scale. The big-picture theoretical aim of this paper is to explore the possibility that natural languages work in more or less the same way, with both kinds of zones of indifference. (shrink)

In this paper we examine the thesis that the probability of the conditional is the conditional probability. Previous work by a number of authors has shown that in standard numerical probability theories, the addition of the thesis leads to triviality. We introduce very weak, comparative conditional probability structures and discuss some extremely simple constraints. We show that even in such a minimal context, if one adds the thesis that the probability of a conditional is the conditional probability, then one trivializes (...) the theory. Another way of stating the result is that the conditional of conditional probability cannot be represented in the object language on pain of trivializing the theory. (shrink)

We add texture to the conclusion of Duchon and Drake (Journal of Business Ethics, 85, 2009, 301) that extreme narcissism is associated with unethical conduct. We argue that the special features possessed by financial accounting facilitate extreme narcissism in susceptible CEOs. In particular, we propose that extremely narcissistic CEOs are key players in a recurring discourse cycle facilitated by financial accounting language and measures. Such CEOs project themselves as the corporation they lead, construct a narrative about the corporation (...) and themselves using financial accounting measures, and then reflect on how their accounting-constructed performance is perceived by stakeholders. We do not present empirical evidence about whether the use of accounting language and measures leads to unethical behaviour by extreme narcissistic CEOs — although the conclusions of Duchon and Drake (2009) suggest empirical support is probable. Rather, we focus on developing alertness to the potential for accounting, when engaged by an extremely narcissistic CEO, to be a precursor or implement of unethical behaviour. (shrink)

Itamar Pitowsky's book, published in the Springer-Verlag Lecture Notes in Physics series, brings together several extremely interesting component investigations concerning the foundations of quantum mechanics. All deal with issues of probability including, in one case, the relation of probability to logic. It is a significant contribution, offering both new, nontrivial mathematical results, and provocative philosophical remarks about their significance.

In this paper I intend to discuss social decision-making involving extreme risks. By an extreme risk, I mean a potential outcome of an act for which the probability is low, but whose negative value is high. Extreme risks are often discussed when new technologies are introduced into society. Nuclear power and genetic engineering are two well-known examples.

Proteins with nearly the same structure and function (homologous proteins) are found in increasing numbers in phylogenetically different, even very distant taxa (e.g. hemoglobins in vertebrates, in some invertebrates, and even in certain plants). In discussing the origin of those proteins biologists hardly at all consider convergent evolution because the origin of proteins is held to be a random process, at least ultimately, since selection can work only what the random process delivers as having a minimum adaptive value. The repetition (...) of a random process with the same result is considered to be extremely unlikely. The supposed (un)likelihood, however, is almost never determined quantitatively. This paper attempts such a quantitative determination. It appears that the probability for the random origin of a definite protein is greater than what one would expect in view of the enormous number of equally possible nucleotide sequences in the corresponding gene since what is equally possible is not always equally likely. The probability, however, of the convergent evolution of two proteins with approximately the same structure and function is too low to be plausible, even when all possible circumstances are present which seem to heighten the likelihood of such a convergence. If this is so, then the plausibility of a random evolution of two or more different but functionally related proteins seems hardly greater. (shrink)

A necessary criterion of Duncan Pritchard’s Anti-luck Virtue Epistemology is his safety condition. A believer cannot know p unless her belief is safe. Her belief is safe only if p could not have easily been false. But “easily” is not to be understood probabilistically. The chance that p is false might be extremely low and yet p remains unsafe. This is what happens, Pritchard argues, in lottery examples and explains why knowledge is not a function of the probabilistic strength of (...) one’s evidence. This paper argues that, contra Pritchard, modality holds no epistemic advantage over this type of “probabilistic evidentialism” that he criticizes. I begin with a review of Pritchard’s argument supporting modality over probability; second, I explain the problems with this argument, and third, I offer an alternative explanation of the lottery example. At the completion of the paper, modality and probability are on equal epistemic footing. (shrink)

Preoperative diagnosis of gastric cancer and primary gastric lymphoma is challenging and has important clinical significance. Inspired by the inductive reasoning learning of the human brain, transfer learning can improve diagnosis performance of target task by utilizing the knowledge learned from the other domains (source domain). However, most studies focus on single-source transfer learning and may lead to model performance degradation when a large domain shift exists between the single-source domain and target domain. By simulating the multi-modal information learning and (...) transfer mechanism of human brain, this study designed a multisource transfer learning feature extraction and classification framework, which can enhance the prediction performance of the target model by using multisource medical data (domain). First, this manuscript designs a feature extraction network that takes the maximum mean difference based on the Wasserstein distance as an adaptive measure of probability distribution and extracts the domain-specific invariant representations between source and target domain data. Then, aiming at the random generation of parameters bringing uncertainties to prediction accuracy and generalization ability of extreme learning machine network, the 1-norm regularization is used to implement sparse constraints of the output weight matrix and improve the robustness of the model. Finally, some experiments are carried out on the data of two medical centers. The experimental results show that the area under curves (AUCs) of the method are 0.958 and 0.929 in the two validation cohorts, respectively. The method in this manuscript can provide doctors with a better diagnostic reference, which has certain practical significance. (shrink)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 purely inductive (...) dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

According to reliabilist conceptions of knowledge, knowledge implies reliable true belief. Since reliability is an irreducibly probabilistic notion, one's view of knowledge also depends on one's view of probability. If one believes that all probability is subjective probability, knowledge becomes a relativized concept: knowledge is relative to a given body of beliefs of a given person at a given time. Since such a relativized conception of knowledge is extremely implausible and since reliabilism seems to capture at least part of the (...) truth, one should rather give up a purely subjective view of probability. -/- . (shrink)

Jon Elster reports that in 1940, and again in 1970, the U.S. draft lottery was challenged for falling short of the legally mandated ‘random selection’. On both occasions, the physical mixing of the lots appeared to be incomplete, since the birth dates were clustered in a way that would have been extremely unlikely if the lots were fully mixed. There appears to have been no suspicion on either occasion that the deficiency in the mixing was intended, known, or believed to (...) favor or disfavor any identifiable group. If the selection was non-random in the way charged, Elster asks, was it unfair? (shrink)

Skeptical hypotheses such as the brain-in-a-vat hypothesis provide extremely poor explanations for our sensory experiences. Because these scenarios accommodate virtually any possible set of evidence, the probability of any given set of evidence on the skeptical scenario is near zero; hence, on Bayesian grounds, the scenario is not well supported by the evidence. By contrast, serious theories make reasonably specific predictions about the evidence and are then well supported when these predictions are satisfied.

Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing (...) the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 387 vs. "objective" is all no doubt rather imprecise, but points toward an important truth. In fact, in the contrast between them, we can see, I believe, not merely a clash of methods, standards or styles in writing history, but, more deeply still, an instance of the general antithesis between a "formalist" and a "sympathetic" sensibility, one encountered over and over in humanistic studies.6 PLATO New in (...) this section is an essay on "Some Controversial Points of Plato Interpretation Reconsidered" (pp. 183-209). Its first two parts combat the view that Plato ever gave up the metaphysics of his "middle period," but they do so only by rehearsing familiar theses about the Idea of the Good and the "two worlds" theory. These pages afford nothing new (apart from an extremely unfortunate appeal [p. 185 and again on p. 230] to an Homeric usage of the genitive to settle a problem at Rep. 518C9). The third part (pp. 194209 ) expands upon some views about later Plato for which Mme. de Vogel is already widely known, and these are very useful indeed. They offer a welcome expansion and defense of her view that in order to "do justice" (196-197, cf. 228) to the famous phrase,o) 7r,,v,e)~r ~v,t at Soph. 248E7, we must concede that Plato came to assign "the motion of a thinking mind" (208-209) to the very being of the Ideas, i.e., came to regard "the intelligibleworld as a vo~r (p. 194). Two interesting objections to her reading are confronted at some length (pp. 200-206) and several others are more briefly dealt with, thus affording her a good chance to explain her view. Valuable as these pages are, however, their upshot is rather unsatisfactory: just what Plato's view would, on her reading of it, really come to, remains mightily obscure--an obscurity she tends to concede but to explain away as Plato's "seeming peculiar to a modern mind" though we can get some grip upon his views if we but "take the trouble to follow his lead" (pp. 201, 198; cf. pp. 228-230, etc.). Such reminders of the genuine strangeness of Plato's view can no doubt be healthy in themselves, but can also be stultifying when reiterated in the face of genuine dissatisfaction with the sense that she makes of his meaning. This situation is not helped by the fact that, at crucial junctures in her argument, she buttresses her case about Plato's meaning by appeals to Aristotle's report at de Anima 1.2, 404b18-27 (see pp. 193-194, 199-200, 208, 277-281, 384-385). As she rightly reports (pp. 280, 385), Prof. Harold Cherniss has vigorously opposed the view that Aristotle is there giving Plato's view at all; yet--despite the fact that she has dedicated this volume to Cherniss--she never makes any reference to his most extended and most powerful defense of his position on this text, and much less does she attempt to answer his argument. (See Cherniss' review of H. D. Saffrey's book--a book to which de Vogel does refer, and repeatedly--in Gnomon 31 [1959], 36-51.) This matter is crucial, not merely as a bibliographical nicety, but because she tends to argue ]rom this text, maintaining that, however peculiar and isolated the sense of Soph. 248-249 and of certain phrases in the Timaeus may, on her reading of them, seem, this text proves that Plato must be read in her way. If it is not about Plato's view at all, it of course proves no such thing. The full weight of her argument will thus be borne by her view of how best to "do justice" to the text of Soph. 248E. Though she makes a clear and reasonable case 6 See Leo Steinberg's comments on this contrast as encountered in current art criticism: Other Criteria (Oxford: Oxford University Press, 1972), Essay 3 (especially pp. 63-68). His remarks about the prescriptive or "interdictory stance" of formalism also fit an important aspect of Burkert's book--an aspect which, though not articulated by her, accounts (I suspect... (shrink)

Emilio Santos has argued (Santos, Studies in History and Philosophy of Physics http: //arxiv-org/abs/quant-ph/0410193) that to date, no experiment has provided a loophole-free refutation of Bell’s inequalities. He believes that this provides strong evidence for the principle of local realism, and argues that we should reject this principle only if we have extremely strong evidence. However, recent work by Malley and Fine (Non-commuting observables and local realism, http: //arxiv-org/abs/quant-ph/0505016) appears to suggest that experiments refuting Bell’s inequalities could at most confirm (...) that quantum mechanical quantities do not commute. They also suggest that experiments performed on a single system could refute local realism. In this paper, we develop a connection between the work of Malley and Fine and an argument by Bub from some years ago [Bub, The Interpretation of Quantum Mechanics, Chapter VI(Reidel, Dodrecht,1974)]. We also argue that the appearance of conflict between Santos on the one hand and Malley and Fine on the other is a result of differences in the way they understand local realism. (shrink)

We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these (...) constraints inform the analysis by fixing an a posteriori determinant of the probabilities, whereas, in the case of a priori reasoning, they imply certain claims which then serve as the basis for subsequent probabilistic deductions. In a given context of inquiry, the particular form which a priori or a posteriori reason may take depends, in large part, on the strength of the underlying symmetry assumed: the stronger the symmetry, the more information can be acquired a priori and the less information about the long-run behavior of the process is needed for an a posteriori assessment of the probabilities. In the context of this framework, frequency-based reasoning emerges as a limiting case of a posteriori reasoning, and reasoning about simple games of chance, as a limiting case of a priori reasoning. Between these two extremes, both a priori and a posteriori reasoning can take a variety of intermediate forms. (shrink)

Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.

Whenever a litigant needs to prove that a certain result was caused in a specific way, what could be more compelling than citing the infinitesimal probability of that result emanating from an alternative natural cause? Contrary to this intuitive position, in the present article, I argue that the contention that a result was due to a certain cause should remain unaffected by statistical evidence of the extremely low probability of an alternative cause. The only scenario in which the low probability (...) of a natural cause would be relevant to the case at hand is if it were contrasted with another piece of statistical evidence: the frequency of the criminal activity among people who are similar to the accused. However, by connecting the use of probabilistic generalisations in legal fact-finding to the issue of free will, I hold that, in Criminal Law, contrasting frequencies in this manner is objectionable—as a matter of principle—regardless of how reliable the statistical analysis is. Consequently, if the low probability of a natural cause is probative only if contrasted with another piece of statistical evidence that is objectionable, then neither piece of evidence should be admitted in criminal trials. (shrink)

Subjective Probability: The Real Thing is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability.Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7:3 to be fair odds for a bet on rain. There are two extreme (...) Bayesian positions. Strict subjectivists think that an agent can adopt whatever degrees of belief she likes, as long as they satisfy the axioms of probability. Thus your degree of belief in rain and degree of belief in no rain must sum to one but are otherwise unconstrained. At the other extreme, objectivists claim that an agent's background knowledge considerably narrows down the choice of appropriate degrees of belief. In particular, if you know only that the frequency of rain is 0.7 then you should believe it will rain to degree 0.7; if you know absolutely nothing about the weather then you should set your degree of belief in rain to be 0.5; in neither of these cases is there room for subjective choice of degree of belief. In this book, Jeffrey advocates what is sometimes called empirically-based subjectivism, a position that lies between the two extremes of strict subjectivism and objectivism. According to this position, knowledge of frequencies constrains degree of belief, but lack of knowledge does not impose any constraints, so that if you know nothing about the weather you may adopt any degree of belief in rain you like.1The aim of the book is not so much to justify this point of view as to provide a comprehensive exposition of probability theory from the …. (shrink)

A great deal of scholarship defines rational thought in terms of probability theory. An important problem with such an approach is that disasters, particularly large disasters, do not provide us with a meaningful distribution of events that would approximate a normal curve. Here, I propose that using possibilistic thinking can helpfully complement probabilistic thinking regarding risk and disaster. Possibilistic thinking highlights consequences of actions or events, while not ignoring their likelihood of occurrence. I point out the myriad ways that individuals (...) and organizations use possibilistic thinking, even if they do not recognized it as such. I propose several conceptual tools to help discipline a possibilistic approach. (shrink)

This paper contends that the first argument of Hume's "Of scepticism with regard to reason" entails that humans have no knowledge as Hume understands knowledge. In defending this claim, we also see how Hume's argument anticipates an important aspect of an extremely influential 20th century development: the collapse of the analytic/synthetic distinction.

Recent evidence suggests that people are highly efficient at detecting conflicting outputs produced by competing intuitive and analytic reasoning processes. Specifically, De Neys and Glumicic demonstrated that participants reason longer about problems that are characterized by conflict between stereotypical personality descriptions and base-rate probabilities of group membership. However, this finding comes from problems involving probabilities much more extreme than those used in traditional studies of base-rate neglect. To test the degree to which these findings depend on such (...) extreme probabilities, we varied base-rate probabilities over five experiments and compared participants’ response time for conflict problems with non-conflict problems. Longer response times for stereotypical responses to conflict versus non-conflict problems were found only in the presence of extreme probabilities. Our results suggest that humans may not be consistently efficient at detecting conflicts during reasoning. (shrink)

Some theories of practical reasons incorporate a lexical priority structure, according to which some practical reasons have infinitely greater weight than others. This includes absolute deontological theories and axiological theories that take some goods to be categorically superior to others. These theories face problems involving cases in which there is a non-extreme probability that a given reason applies. In view of such cases, lexical-priority theories are in danger of becoming irrelevant to decision-making, becoming absurdly demanding, or generating paradoxical cases (...) in which each of a pair of actions is permissible yet the pair is impermissible. (shrink)

As is well known, A. C. Haddon visited Torres Straits for the first time in the\nsummer of 1888 with the purpose of studying, as a marine biologist, the fauna\nand the structure and mode of formation of the coral reefs in Torres Straits. There\nbegan Haddon’s ’conversion’ from zoology to anthropology.’ It seems that\nHaddon felt an urgent need to collect ethnographic information on the islanders\nbecause he saw they were changing and diminishing in number very quickly, and\ntherefore their customs were vanishing.\nVery soon after (...) my arrival in the Straits I found that the natives of the\nislands had of late years been greatly reduced in number, and that, with the\nexception of but one or two individuals, none of the white residents knew\nanything about the customs of the natives, and not a single person cared\nabout them personally. When I began to question the natives I discovered\nthat the young men had a very imperfect acquaintance with the old habits\nand beliefs, and that only from the older men was reliable information to be\nobtained. So it was made clear to me that if I neglected to avail myself of the\npresent opportunity of collecting information on the ethnography of the\nislanders, it was extremely probable that that knowledge would never be\ngleaned - for if no one interested himself in the matter meanwhile, it was\nalmost certain that no trustworthy information could be collected in, say, ten years’ time. This being my opinion, I felt it my duty to fill up all the\ntime not actually employed in my zoological researches in anthropological\nstudies. (shrink)

Prominent theories of decision under risk that challenge expected utility theory model risk attitudes at least partly with transformation of probabilities. This paper shows how attributing local risk aversion to attitudes towards probabilities can produce extreme probability distortions that imply paradoxical risk aversion.

According to Nancy Cartwright, a causal law holds just when a certain probabilistic condition obtains in all test situations which in turn satisfy a set of background conditions. These background conditions are shown to be inconsistent and, on separate account, logically incoherent. I offer a corrective reformulation which also incorporates a strategy for problems like Hesslow's thrombosis case. I also show that Cartwright's recent argument for modifying the condition to appeal to singular causes fails.Proposed modifications of the theory's probabilistic condition (...) to handle effects with extreme probabilities (0 or 1) are found unsatisfactory. I propose a unified solution which also handles extreme causes. Undefined conditional probabilities give rise to three good, but non-equivalent, ways of formulating the theory. Various formulations appear in the literature. I give arguments to eliminate all but one candidate. Finally, I argue for a crucial new condition clause, and show how to extend the results beyond a simple probabilistic framework. (shrink)

When A Revision of Demand Theory was first published in 1956, the late Harry Johnson described it as "elegant in the extreme, probably the last word there is to be said on this aspect of demand theory." This landmark work by Nobel Prize winner J.R. Hicks is now available again.

Several authors have argued that non-extreme probabilities used in special sciences such as chemistry and biology can be objective chances, even if the true microphysical description of the world is deterministic. This article examines an influential version of this argument and shows that it depends on a particular methodology for defining the relationship between coarse-grained and fine-grained events. An alternative methodology for coarse-graining is proposed. This alternative methodology blocks this argument for the existence of emergent chances, and makes (...) better sense of two well-known subjects of philosophical discussion: the Miners Puzzle and Simpson’s Paradox. (shrink)

Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require rational agents (...) to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a Bayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases. (shrink)

L’articolo si propone di chiarire uno dei punti oscuri della biografia di Giordano Bruno. Nel 1571 il Capitolo generale dei Domenicani di Roma lo assegnò come studente formale allo Studio di Andria. Secondo i suoi più importanti biografi, il Nolano non ci sarebbe mai andato. Attraverso l’accurata analisi dei documenti relativi al corso di studi, e il riscontro delle citazioni contenute in alcune opere, l’ipotesi che Bruno abbia soggiornato ad Andria per circa un anno appare, invece, estremamente probabile. The article (...) tries to clarify one of the obscure points of Giordano Bruno’s biography. In 1571 the General Chapter of the Dominicans in Rome assigned him, as a formal student, to the Study of Andria. According to his most important biographers, the Nolan never went there. However, through the careful analysis of the documents relating to his course of studies, and the comparison of the quotations contained in some of his works, the hypothesis that Bruno stayed in Andria for about a year appears extremely probable. (shrink)

          The production of a number of vaccines involves the use of cell-lines originally derived from fetuses directly aborted in the 1960s and 1970s. Such cell-lines, indeed sometimes the very same ones, are important to on-going research, including at Catholic institutions. The cells currently used are removed by a number of decades and by a significant number of cellular generations from the original cells. Moreover, the original cells extracted from the bodies (...) of the aborted fetuses were transformed to produce the cell lines, since otherwise they would be incapable of the kind of culturing that is required.           It is generally acknowledged by ethicists, including many Catholic ones generally considered to be orthodox, and by the U.S. bishops, that the use of the cell-lines in connection with the production of vaccines is morally permissible. It does not appear that there is a relevant qualitative difference between the use of the cell-lines in vaccines and in research. One might argue that there is certainty of benefit from a vaccine while the benefits of research are uncertain. However, in any given case of the administration of a vaccine to an individual, it is far from certain that such administration will be of benefit to that individual. After all, the individual might never come in contact with someone infected with the disease in question, particularly if the disease is now uncommon in the individual’s locale. Yet, it is morally certain that some of the administrations of the vaccine will be beneficial. This is parallel to the fact that while any one research project might not be beneficial, the history of biomedical research makes it extremely probable, indeed morally certain, that some project involving the use of such cell-lines will be beneficial. There may, of course, be quantitative difference between the cases—the probabilities and benefits may not be equal—but the difference does not seem to be a qualitative one. Therefore, if one accepts the use of the cell-lines in vaccines, one should accept the use in research in at least some conceivable and perhaps actual circumstances.           The main argument I am interested in in favor of the use of the cell-lines proceeds by first granting that the initial abortion and extraction of cells from the deceased fetus was morally gravely illicit. However, the connection between the currently used derived cells and the abortion and original derivation is sufficiently remote that the use becomes licit. Not all fruit of a poisoned tree is poisoned: it can be morally.... (shrink)

Can we attribute individual extreme weather events to human‐induced climate change? In this chapter I will be turning a philosophical eye on this question, asking what concept (or concepts) of causation are being employed by scientists and asking which concept of causation is most appropriate. I will show that scientists, politicians, and journalists have made a number of mistakes in their thinking about the causal links between individual extreme events and climate change, and argue that scientists should be (...) less hesitant when it comes to attributing such events to climate change. (shrink)

Policies and position statements regarding decision-making for extremely premature babies exist in many countries and are often directive, focusing on parental choice and expected outcomes. These recommendations often state survival and handicap as reasons for optional intervention. The fact that such outcome statistics would not justify such approaches in other populations suggests that some other powerful factors are at work. The value of neonatal intensive care has been scrutinized far more than intensive care for older patients and suggests that neonatal (...) care is held to a higher standard of justification. The relative value placed on the life of newborns, in particular the preterm, is less than expected by any objective medical data or any prevailing moral frameworks about the value of individual lives. Why do we feel less obligated to treat the premature baby? Do we put newborns in a special and lesser moral category? We explore this question from a legal and ethical perspective and offer several hypotheses pertaining to personhood, reproductive choices, “precious children,” and probable evolutionary and anthropological factors. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)