In the general problem of verisimilitude, we try to define the distance of a statement from a target, which is an informative truth about some domain of investigation. For example, the target can be a state description, a structure description, or a constituent of a first-order language. In the problem of legisimilitude, the target is a deterministic or universal law, which can be expressed by a nomic constituent or a quantitative function involving the operators of physical necessity and possibility. The (...) special case of legisimilitude, where the target is a probabilistic law, has been discussed by Roger Rosenkrantz and Ilkka Niiniluoto. Their basic proposal is to measure the distance between two probabilistic laws by the Kullback–Leibler notion of divergence, which is a semimetric on the space of probability measures. This idea can be applied to probabilistic laws of coexistence and laws of succession, and the examples may involve discrete or continuous state spaces. In this paper, these earlier studies are elaborated in four directions. First, even though deterministic laws are limiting cases of probabilistic laws, the target-sensitivity of truthlikeness measures implies that the legisimilitude of probabilistic laws is not easily reducible to the deterministic case. Secondly, the Jensen-Shannon divergence is applied to mixed probabilistic laws which entail some universal laws. Thirdly, a new class of distance measures between probability distributions is proposed, so that their horizontal differences are taken into account in addition to vertical ones. Fourthly, a solution is given for the epistemic problem of estimating degrees of probabilistic legisimilitude on the basis of empirical evidence. (shrink)

We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and (...) provides independently motivated solutions to issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked. (shrink)

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic (...) laws are, and argue that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both). (shrink)

Truthlikeness is a property of a theory or a proposition that represents its closeness to the truth. We start by summarizing Niiniluoto’s proposal of truthlikeness for deterministic laws, which defines truthlikeness as a function of accuracy, and García-Lapeña’s expanded version, which defines truthlikeness for DL as a function of two factors, accuracy and nomicity. Then, we move to develop an appropriate definition of truthlikeness for probabilistic laws based on Niiniluoto’s suggestion to use the Kullback–Leibler divergence to define (...) the distance between a probability law X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X$$\end{document} and the true probability law T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document}. We argue that the Kullback–Leibler divergence seems to be the best of the available probability distances to measure accuracy between PL. However, as in the case of DL, we argue that accuracy represents a necessary but not sufficient condition, as two PL may be equally accurate and still one may imply more true or truthlike consequences, behaviours or true facts about the system than the other. The final proposal defines truthlikeness for PL as a function of two factors, p-accuracy and p-nomicity, in intimate connexion with García-Lapeña’s proposal for DL. (shrink)

In What is a Law of Nature? (1983) David Armstrong promotes a theory of laws according to which laws of nature are contingent relations of necessitation between universals. The metaphysics Armstrong develops uses deterministic causal laws as paradigmatic cases of laws, but he thinks his metaphysics explicates other sorts of laws too, including probabilistic laws, like that of the half-life of radium being 1602 years. Bas van Fraassen (1987) gives seven arguments for why (...) Armstrong’s theory of laws is incapable of explicating probabilistic laws. The main thrust of the arguments is that Armstrong’s metaphysical apparatus serves to drive up the initial probability values stated by probabilistic laws. Armstrong replies .. (shrink)

This Article explores the costs and benefits of one subset of continuous and discontinuous rules. These expressions are shown to be distinct from the familiar dichotomy expressed as standards versus rules, but they share the difficulty of dividing the world of law in two. Still, regulatory approaches that focus on discontinuities can often be made more continuous, and vice versa. A speed limit is discontinuous in the sense that one drives above or below (or within) the announced limit. But it (...) is often made more continuous—even with more discontinuities— as when the stated limit is different for various kinds of vehicles. This Article works around these definitional problems to show that law often discourages useful disclosures by encouraging parties with information to offer continuous information in order to avoid after-the-fact lawsuits when specific disclosures prove to have inaccuracies. For example, it is common to hear or be warned that a medical procedure poses the risk of death, when a better-informed doctor or hospital could have given the precise percentages attached to various outcomes. Similarly, a corporation is on safe ground when it follows “generally accepted accounting principles,” when investors would have learned more from information about good and bad outcomes put in probabilistic terms. The Article works toward the suggestion that law might create a safe harbor in which probabilistic disclosures are protected when they are, or are certified to be, more useful than the ready alternative of fairly general disclosures. (shrink)

This paper makes the case for a wider acceptance of a probabilistic approach to causation in negligence. This acceptance would help to remove much of the incoherence which has come to afflict the English law of personal injury law. This incoherence can also be found in other common law jurisdictions (notably those of the United States, Canada and Australia). Concentrating upon recent UK case law, the argument opposes the contention that ‘naked statistics’ can play no role in establishing causation. (...) The argument is controversial but it can be reduced to three unremarkable grounds: (1) With its acceptance (albeit in certain carefully prescribed circumstances) of liability for a negligently increased risk which has eventuated, the common law has already embraced a probabilistic conception of causation; (2) The English common law already employs a probabilistic (frequentist) approach to identifying coincidences; and (3) With the ‘balance of probabilities’ as the standard of proof in civil cases, the common law has long had a probabilistic (epistemic) concept at its core. Probabilistic approaches (at both the type and token level) are shown to be consistent with laypersons’ understanding of the concepts such as risk, chance, odds and likelihood. Moreover, a wider acceptance of a probabilistic perspective on causation would entail no major challenge to the fundamental aims of tort, viz. deterrence and corrective justice. (shrink)

Two distinct conceptions for the relation between reversible, time-reversal invariant laws of nature and the irreversible behavior of physical systems are outlined. The standard, extrinsic concept of irreversibility is based on the notion of an open system interacting with its environment. An alternative, intrinsic concept of irreversibility does not explicitly refer to any environment at all. Basic aspects of the two concepts are presented and compared with each other. The significance of the terms extrinsic and intrinsic is discussed.

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 (...) class='Hi'>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)

One of the many intriguing features of the axiomatic systems of probability investigated in Popper (1959), appendices _iv, _v, is the different status of the two arguments of the probability functor with regard to the laws of replacement and commutation. The laws for the first argument, (rep1) and (comm1), follow from much simpler axioms, whilst (rep2) and (comm2) are independent of them, and have to be incorporated only when most of the important deductions have been accomplished. It is (...) plain that, in the presence of (comm1), the principle (sub), which says that terms that are intersubstitutable in the first argument are intersubstitutable also in the second argument, implies (comm2), and in Popper’s systems the converse implication obtains. It is naturally asked what is needed in an axiomatic theory of probability in order to enforce this equivalence. Leblanc (1981) offered a rather weak set of axioms, containing (comm1) and (comm2), that suffice for the derivation of (sub). In this paper Leblanc’s result is improved in a number of different ways. Three weaker systems, one of which is incomparable with the other two, are shown to admit the same implication. DOI:10.5007/1808-1711.2011v15n2p271. (shrink)

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and (...) safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. (shrink)

In the first part of my analysis, I wish briefly to clarify the different modes of relation found in the living being, and point out the multiplicity of disciplines in which biologists use (explicitly or implicitly) the notion of laws. In the second part, I shall analyse the notion of universal laws in biology and examine successively: (1) accidental generalizations; (2) non-causal biological correlations; (3) the meaning of 'necessity' in these correlations; and (4) causal connections. Finally, in the (...) third part, I shall examine statistical laws and probabilistic laws in biology, in particular: (1) chance in biology; (2) probabilistic theories; and (3) relations between logical probability and statistical probability. (shrink)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be (...) otherwise. The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

The main aim of this paper is to provide some probabilistic notions on causality proposed to be applied to the nomic statements which intend to give account of the indeterministic processes within the domain of a scientific theory. In general, such statements are, in more or less extent, idealized statements which rest on a variety of unrealistic suppositions. I try to show how the probability distribution over the final states of an indeterministic process changes accordingly as the nomic statement (...) in question is de-idealized by means of addition of the causally relevant factors. In order to illustrate the study I take few nomic statements from population genetics. Besides, in the course, I attempt to contrast the ideas embraced here with some of the notions of Humphreys´ ontic conceptions of causality and explanation, which are contrary to the epistemic view adopted here about those subjects. (shrink)

Preface to Volumes 1 and 2 Lorenz Krüger xv Introduction to Volume 1 Lorraine J. Daston 1 I Revolution 1 What Are Scientific Revolutions? Thomas S. Kuhn 7 2 Scientific Revolutions, Revolutions in Science, and a Probabilistic Revolution 1800-1930 I. Bernard Cohen 23 3 Was There a Probabilistic Revolution 1800-1930? Ian Hacking 45 II Concepts 4 The Slow Rise of Probabilism: Philosophical Arguments in the Nineteenth Century Lorenz Krüger 59 5 The Decline of the Laplacian Theory of Probability: (...) A Study of Stumpf, von Kries, and Meinong Andreas Kamlah 91 6 Fechner’s Indeterminism: From Freedom to Laws of Chance Michael Heidelberger 117 7 The Saint Petersburg Paradox 1713-1937 Gerard Jorland 157 8 Laplace and Thereafter: The Status of Probability Calculus in the Nineteenth Century Ivo Schneider 191 9 Emile Borel as a Probabilist Eberhard Knobloch 215 III Uncertainty 10 The Domestication of Risk: Mathematical Probability and Insurance 1650-1830 237 11 The Objectification of Observation: Measurement and Statistical Methods in the Nineteenth Century Zeno G. Swijtink 261 12 The Measurement of Uncertainty in Nineteenth-Century Social Science Stephen M. Stigler 287 IV Society 13 Rational Individuals versus Laws of Society: From Probability to Statistics Lorraine J. Daston 295 14 Decrire, Compter, Calculer: The Debate over Statistics during the Napoleonic Period Marie-Noelle Bourguet 305 15 Probability in Vital and Social Statistics: Quetelet, Farr, and the Bertillons Bernard-Pierre Lécuyer 317 16 Paupers and Numbers: The Statistical Argument for Social Reform in Britain during the Period of Industrialization Karl H. Metz 337 17 Lawless Society: Social Science and the Reinterpretation of Statistics in Germany, 1850-1880 Theodore M. Porter 351 18 Prussian Numbers 1860-1882 Ian Hacking 377 19 How Do Sums Count? On the Cultural Origins of Statistical Causality M. Norton Wise 395. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, (...) e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

John Dupré (1984) has recently criticized the theory of probabilistic causality developed by, among others, Good (1961-62), Suppes (1970), Cartwright (1979), and Skyrms (1980). He argues that there is a tension or incompatibility between one of its central requirements for the presence of a causal connection, on the one hand, and a feature of the theory pointed out by Elliott Sober and me (1983), on the other. He also argues that the requirement just alluded to should be given up. (...) I defend the theory against Dupré's criticisms and conclude with comments on Dupré's appraisal of the bearing of his arguments on the nature of probabilistic causal laws. (shrink)

A formulation of probabilistic causality is given in terms of the theory of abstract dynamical systems. Causal factors are identified as invariants of motion of a system. Repetition of an experiment leads to the notion of stationarity, and causal factors yield a decomposition of the stationary probability law of the experiment into ergodic components. In these, statistical behaviour is uniform. Control of identified causal factors leads to a corresponding statistical law for the events, which is offered as a notion (...) of probabilistic causality. After a suggestion by Feller, randomization is identified as mixing, formulated in above terms. (shrink)

This paper proposes an approach to investigate norm-governed learning agents which combines a logic-based formalism with an equation-based counterpart. This dual formalism enables us to describe the reasoning of such agents and their interactions using argumentation, and, at the same time, to capture systemic features using equations. The approach is applied to norm emergence and internalisation in systems of learning agents. The logical formalism is rooted into a probabilistic defeasible logic instantiating Dung’s argumentation framework. Rules of this logic are (...) attached with probabilities to describe the agents’ minds and behaviours as well as uncertain environments. Then, the equation-based model for reinforcement learning, defined over this probability distribution, allows agents to adapt to their environment and self-organise. (shrink)

One of the many intriguing features of the axiomatic systems of probability investigated in Popper (1959), appendices _iv, _v, is the different status of the two arguments of the probability functor with regard to the laws of replacement and commutation. The laws for the first argument, (rep1) and (comm1), follow from much simpler axioms, whilst (rep2) and (comm2) are independent of them, and have to be incorporated only when most of the important deductions have been accomplished. It is (...) plain that, in the presence of (comm1), the principle (sub), which says that terms that are intersubstitutable in the first argument are intersubstitutable also in the second argument, implies (comm2), and in Popper’s systems the converse implication obtains. It is naturally asked what is needed in an axiomatic theory of probability in order to enforce this equivalence. Leblanc (1981) offered a rather weak set of axioms, containing (comm1) and (comm2), that suffice for the derivation of (sub). In this paper Leblanc’s result is improved in a number of different ways. Three weaker systems, one of which is incomparable with the other two, are shown to admit the same implication. (shrink)

In her paper entitled "Causal Laws and Effective Strategies" (1979), Cartwright sets out to establish the connection between laws of association and causal laws. In part Cartwright is trying to show the sense in which a cause increases the probability of its effect, and to explain what causal laws assert by giving an account of how causal laws are related to certain kinds of statistical laws. In section II we explicate the essential features of (...) Cartwright's for- mulation and in section III we argue that there are several reasons for believing that Cartwright's formulation is inadequate and must be rejected. Nonetheless, we believe Cartwright's formulation does contain two key insights into the nature of causation. In section IV we use these two insights to sketch out the key features of an alternative formulation that holds the certain laws of association are necessary conditions for causal laws. The alternative formu- lation, we believe, explains what it means to say a cause increases the probability of its effect. (shrink)

The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certainty-reductions to instances of the law of excluded (...) middle or the law of noncontradiction in logic or certainty-reductions to the certainties of probabilist epistemology. The author proposes special and general versions of the MERF principle and uses them to explain the examples, including the reasoning that would lead to thoroughgoing fallibilism—that is, to a state of being certain of nothing. The author responds to the main defenses of probabilism: Dutch Book arguments, Joyce’s potential accuracy defense, and the potential calibration defenses of Shimony and van Fraassen by showing that, even though they do not satisfy the probability axioms, degrees of belief that satisfy the MERF principle minimize expected inaccuracy in Joyce’s sense; they can be externally calibrated in Shimony and van Fraassen’s sense; and they can serve as a basis for rational betting, unlike probabilist degrees of belief, which, in many cases, human beings have no rational way of ascertaining. The author also uses the MERF principle to subsume the various epistemic akrasia principles in the literature. Finally, the author responds to Titelbaum’s argument that epistemic akrasia principles require that we be certain of some epistemological beliefs, if we are rational. (shrink)

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing papers coming (...) from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​. (shrink)

It has recently been remarked that the argument for physicalism from the causal closure of the physical is incomplete. It is only effective against mental causation manifested in the action of putative mental forces that lead to acceleration of particles in the nervous system. Based on consideration of anomalous, physically unaccounted-for correlations of neural events, I argue that irreducible mental causation whose nature is at least prima facie probabilistic is conceivable. The manifestation of such causation should be accompanied by (...) a local violation of the Second Law of thermodynamics. I claim that mental causation can be viewed as the disposition of mental states to alter the state probability distribution within the nervous system, with no violation of the conservation laws. If confirmed by neurophysical research, it would indicate a kind of causal homogeneity of the world. Causation would manifest probabilistically in both quantum mechanical and psychophysical systems, and the dynamics of both would be determined by the temporal evolution of the corresponding system state function. Finally, I contend that a probabilistic account of mental causation can consistently explain the character of selectional states that ensure the uniformity of causal patterns, as well as the fact that different physical realizers of a mental property cause the same physical effects in different contexts. (shrink)

James Joyce's 'Nonpragmatic Vindication of Probabilism' gives a new argument for the conclusion that a person's credences ought to satisfy the laws of probability. The premises of Joyce's argument include six axioms about what counts as an adequate measure of the distance of a credence function from the truth. This paper shows that (a) Joyce's argument for one of these axioms is invalid, (b) his argument for another axiom has a false premise, (c) neither axiom is plausible, and (d) (...) without these implausible axioms Joyce's vindication of probabilism fails. (shrink)

If the influence of libertarian free will on human behaviour is real, the frequency of certain freely chosen actions will differ from the probability of their occurrences deduced from the statistical calculations and neuroscientific observations and laws. According to D. Pereboom, contemporary science does not prove the efficacy of libertarian free will. According to P. van Inwagen, there is always a random element in free decisions, and hence the effect of the free will remains unknown. Swinburne observes that it (...) is not correct to conclude that libertarian free will has no causal effect in the physical world. One can only conclude that these choices are not neurologically real. People sometimes choose to act on abstract principles, and they can do so on a regular and long-term basis. Consequently, human behaviour can be predicted and explained in terms of personal agency and the reasons upon which the people have chosen to act. Probabilistic calculations strengthen the argument that the best way to explain and predict such rational behaviour is to affirm the efficacy of the libertarian free will, which can overcome neurophysiological motivational states of the body and which guarantees a kind of long-term rational determinism. (shrink)

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This (...) criterion is formulated and proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe. (shrink)

In what follows, I’ll discuss both the metaphysics and the epistemology of supervenience from a probabilistic point of view. The first half of this paper will explore how supervenience claims are related to other issues; these will include the thesis that physics is causally complete, the claim that there are emergent properties, the idea that mental properties are causally efficacious, and the notion that there are scientific laws about supervenient properties that generalize over systems that deploy different physical (...) realizations of the properties in question. The second half will examine the question of how observational evidence can lend support to supervenience claims. This problem turns out to raise some surprisingly deep issues about the nature of hypothesis testing in science. (shrink)

When the likelihood ratio approach is employed for evidential reasoning in law, it is often necessary to employ subjective probabilities, which are probabilities derived from the opinions and judgement of a human. At least three concerns arise from the use of subjective probabilities in legal applications. Firstly, human beliefs concerning probabilities can be vague, ambiguous and inaccurate. Secondly, the impact of this vagueness, ambiguity and inaccuracy on the outcome of a probabilistic analysis is not necessarily fully understood. Thirdly, the (...) provenance of subjective probabilities and the associated potential sources of vagueness, ambiguity and inaccuracy tend to be poorly understood, making it difficult for the outcome of probabilistic reasoning to be explained and validated, which is crucial in legal applications. The former two concerns have been addressed by a wide body of research in AI. The latter, however, has received little attention. This paper presents a novel approach to employ argumentation to reason about probability distributions in probabilistic models. It introduces a range of argumentation schemes and corresponding sets of critical questions for the construction and validation of argument models that define sets of probability distributions. By means of an extended example, the paper demonstrates how the approach, argumentation schemes and critical questions can be employed for the development of models and their validation in legal applications of the likelihood ratio approach to evidential reasoning. (shrink)

In this paper I argue that economic theories have never been able to provide a coherent explanation of the causation requirement in tort law. The economic characterization of this requirement faces insurmountable difficulties, because discourse on tort liability cannot be reduced to a cost-benefit analysis without a loss of meaning. More seriously, I try to show that by describing causation in economic terms, economic theories offer an image of the practice in which the participants incur in logical contradictions and develop (...) patterns of inference that are far from intuitive. For this reason, efficiency cannot be the fundamental principle underlying tort law. Finally, I suggest that economic analysis of law can provide a genuine explanation of certain aspects of legal practice if it relinquishes its reductionist claims. (shrink)

This paper contends that some of the recent critical appraisals of universals theories of natural laws, namely, van Fraassen's analysis of Armstrong's probabilistic laws, are largely ineffective since they fail to disclose the incompatibility of universals and any realistic natural law setting. Rather, a more profitable line of criticism is developed that contests the universalists' claim to have resolved the induction problem (i.e., the separation of natural laws from mere accidental regularities), and thereby reveals the universals' (...) philosophically inadequate concept of a physical property. (shrink)

A law about frequencies would be a law of nature that imposes a constraint on one or more (actual, global) frequencies. On any of the leading philosophical approaches to laws of nature, there could be laws about frequencies. Hypotheses that posit laws about frequencies turn out to behave very similarly to hypotheses that posit corresponding laws about probabilities or chances -- they make the same predictions, provide similar explanations, and are confirmed or disconfirmed by empirical evidence (...) in the same ways. This makes it interesting to consider the possibility of interpreting probabilistic laws from scientific theories as laws about frequencies. This is surprising proposal, but I argue that the resulting view (which I call 'nomic frequentism') is able to overcome all of the standard objections to frequentist interpretation of objective probabilities. (shrink)

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of the (...) probability as the square of the scalar product follows from Gleason's theorem. (shrink)

This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation built on the principle that the antecedent of a conditional is probabilistically independent of the conditional and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces (...) a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis|generating a rather wide consensus that it yields `unintuitive' or `wrong' probabilities for compounds |fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic `causal' interpretation alongside its usual epistemic interpretation. (shrink)

The question of David Armstrong's recent book, What Is a Law of Nature? would seem to have little point unless there really are laws of nature. However that may be, so much philosoFhical thinking has utilized this concept, that an inquiry of this sort was needed whether there are or not. The book begins with a devastating attack on so-called Regularity views of law, and then proceeds with an exposition of Armstrong's own answer to the question. I wish to (...) raise here some difficulties for Armstrong's answer, concentrating on his account of probabilistic laws where I see the severest problems. To locate myself with respect to his approach, however, I shall first enter some lesser demurrals. (shrink)

A system whose expected state changes with time cannot have both a forward-directed translationally invariant probabilistic law and a backward-directed translationally invariant law. When faced with this choice, science seems to favor the former. An asymmetry between cause and effect may help to explain why temporally oriented laws are usually forward-directed.

Formally-inclined epistemologists often theorize about ideally rational agents--agents who exemplify rational ideals, such as probabilistic coherence, that human beings could never fully realize. This approach can be defended against the well-know worry that abstracting from human cognitive imperfections deprives the approach of interest. But a different worry arises when we ask what an ideal agent should believe about her own cognitive perfection (even an agent who is in fact cognitively perfect might, it would seem, be uncertain of this fact). (...) Consideration of this question reveals an interesting feature of the structure of our epistemic ideals: for agents with limited information, our epistemic ideals turn out to conflict with one another. (shrink)

SummaryThere are two rival ways in which events in the world can be explained: the covering law way and the dispositionalist way. The covering law model, which takes the law of nature as its fundamental explanatory unit, faces a number of renown difficulties. Rather than attempt to patch up this approach, the alternative dispositionalist strategy is recommended. On this view, general facts are dependent upon particular facts about what things do, rather than vice versa. This way of viewing the world (...) is not only more intuitive but also handles some of the notorious problems faced by laws; such as those of probabilistic and unrealized facts. The dispositionalist strategy faces its own difficulties of explaining generality and contingency of behaviour. It is shown, however, that at least these difficulties should not dissuade the dispositionalist. The prospects for a convincing dispositionalist ontology to replace one based on laws of nature are thus healthy. (shrink)

And this paper is an attempt to say precisely how, thus addressing a philosophical problem which is commonly taken to be a serious one. It does so, however, in quite an idiosyncratic way. It is based on the account of inductive schemes I have given in (1988) and (1990a) and on the conception of causation I have presented in (1980), (1983), and (1990b), and it intends to fill one of many gaps which have been left by these papers. Still, I (...) have tried to make this paper self-contained. Section 1 explains the philosophical question this paper is about; in more general terms it asks what might be meant by objectifying epistemic states or features of them and to which extent epistemic states can be objectified. The next sections introduce the basis I rely on with formal precision and some explanation; section 2 deals with induction and section 3 with causation. Within these confines, section 4 attempts to give an explication of the relevant sense of objectification and section 5 investigates the extent to which various features of epistemic states are objectifiable. The two most salient results are roughly that the relation "A is a reason for B" cannot be objectified at all and that the relation "A is a cause of B" can be objectified only under substantial, though reasonable restrictions. What has all of this to do with probability? A lot. The paper trades on a pervasive duality between probabilistic and deterministic epistemology, between a probabilistic representation of epistemic states together with a theory of probabilistic causation and another representation of epistemic states which I call deterministic because it lends itself, in a perfectly parallel fashion, to a theory of deterministic causation. Here I explicitly deal only with the deterministic side, but the duality should pave the way for further conclusions concerning objective probabilities and statistical laws. This outlook is briefly expanded in the final section 6. (shrink)

Two radically different views about time are possible. According to the first, the universe is three dimensional. It has a past and a future, but that does not mean it is spread out in time as it is spread out in the three dimensions of space. This view requires that there is an unambiguous, absolute, cosmic-wide "now" at each instant. According to the second view about time, the universe is four dimensional. It is spread out in both space and time (...) - in space-time in short. Special and general relativity rule out the first view. There is, according to relativity theory, no such thing as an unambiguous, absolute cosmic-wide "now" at each instant. However, we have every reason to hold that both special and general relativity are false. Not only does the historical record tell us that physics advances from one false theory to another. Furthermore, elsewhere I have shown that we must interpret physics as having established physicalism - in so far as physics can ever establish anything theoretical. Physicalism, here, is to be interpreted as the thesis that the universe is such that some unified "theory of everything" is true. Granted physicalism, it follows immediately that any physical theory that is about a restricted range of phenomena only, cannot be true, whatever its empirical success may be. It follows that both special and general relativity are false. This does not mean of course that the implication of these two theories that there is no unambiguous cosmic-wide "now" at each instant is false. It still may be the case that the first view of time, indicated at the outset, is false. Are there grounds for holding that an unambiguous cosmic-wide "now" does exist, despite special and general relativity, both of which imply that it does not exist? There are such grounds. Elsewhere I have argued that, in order to solve the quantum wave/particle problem and make sense of the quantum domain we need to interpret quantum theory as a fundamentally probabilistic theory, a theory which specifies how quantum entities - electrons, photons, atoms - interact with one another probabilistically. It is conceivable that this is correct, and the ultimate laws of the universe are probabilistic in character. If so, probabilistic transitions could define unambiguous, absolute cosmic-wide "nows" at each instant. It is entirely unsurprising that special and general relativity have nothing to say about the matter. Both theories are pre-quantum mechanical, classical theories, and general relativity in particular is deterministic. The universe may indeed be three dimensional, with a past and a future, but not spread out in four dimensional space-time, despite the fact that relativity theories appear to rule this out. These considerations, finally, have implications for views about the arrow of time and free will. (shrink)

SummaryThere are two rival ways in which events in the world can be explained: the covering law way and the dispositionalist way. The covering law model, which takes the law of nature as its fundamental explanatory unit, faces a number of renown difficulties. Rather than attempt to patch up this approach, the alternative dispositionalist strategy is recommended. On this view, general facts are dependent upon particular facts about what things do, rather than vice versa. This way of viewing the world (...) is not only more intuitive but also handles some of the notorious problems faced by laws; such as those of probabilistic and unrealized facts. The dispositionalist strategy faces its own difficulties of explaining generality and contingency of behaviour. It is shown, however, that at least these difficulties should not dissuade the dispositionalist. The prospects for a convincing dispositionalist ontology to replace one based on laws of nature are thus healthy. (shrink)

We prove convergence laws for logics of the form equation image, where equation image is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics equation image, where equation image is a collection of generalized quantifiers and k ∈ ℕ+, under arbitrary probability measures of finite structures.