Probabilistic Laws

Edited by Markus Schrenk (Heinrich Heine University Düsseldorf)
Assistant editor: Florian J. Boge (Bergische Universität Wuppertal)
About this topic
Summary There's hardly a theory of laws of nature that starts with probabilistic laws as its primary definiendum. Almost all accounts of what a law is try to accommodate probabilistic laws into their theory only once it has been defined what deterministic laws are. In any case, any theory of laws better has to say something about indeterministic nomological relations for one of our best current scientific theories, quantum mechanics, postulates fundamental, not further analyzable probabilistic facts (atomic decay being one instance).
Key works While there is possibly not the key work for an account of probabilistic laws (see summary) some recent attempts to define what laws of nature are begin from the outset with indeterministic, probabilistic correlations as their starting point: Loewer 2007Loewer 2012Albert 2000.
Introductions Psillos 2002Carroll 1994
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  1. Physicalism Without Supervenience.Lei Zhong - 2021 - Philosophical Studies 178 (5):1529-1544.
    It is widely accepted that supervenience is a minimal commitment of physicalism. In this article, however, I aim to argue that physicalism should be exempted from the supervenience requirement. My arguments rely on a parallel between ontological dependence and causal dependence. Since causal dependence does not require causal determination, ontological dependence should not require ontological determination either. Moreover, my approach has a significant theoretical advantage: if physicalism is not committed to supervenience, then the metaphysical possibility of zombies—which is still wide (...)
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  2. Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature.Valia Allori (ed.) - 2020 - Singapore: World Scientific.
    The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot (...)
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  3. Regression Explanation and Statistical Autonomy.Joeri Witteveen - 2019 - Biology and Philosophy 34 (5):1-20.
    The phenomenon of regression toward the mean is notoriously liable to be overlooked or misunderstood; regression fallacies are easy to commit. But even when regression phenomena are duly recognized, it remains perplexing how they can feature in explanations. This article develops a philosophical account of regression explanations as “statistically autonomous” explanations that cannot be deepened by adducing details about causal histories, even if the explananda as such are embedded in the causal structure of the world. That regression explanations have statistical (...)
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  4. God, Miracles, Creation, Evil, and Statistical Natural Laws.Rem B. Edwards - 2017 - In CONNECTING FAITH AND SCIENCE: PHILOSOPHICAL AND THEOLOGICAL INQUIRIES. Claremont, CA, USA: pp. 55-85.
    This article argues that actual entities come first; the statistical laws of nature are their effects, not their causes. Statistical laws are mentally abstracted from their habits and are only formal, not efficient, causes. They do not make anything happen or prevent anything from happening. They evolve or change as the habits of novel creatures evolve or change. They do not control or inform us about what any individual entity is doing, only about what masses of individuals on average are (...)
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  5. Armstrong on Probabilistic Laws of Nature.Jonathan D. Jacobs & Robert J. Hartman - 2017 - Philosophical Papers 46 (3):373-387.
    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 (...)
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  6. The Range Conception of Probability and the Input Problem.John Roberts - 2016 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (1):171-188.
    Abrams, Rosenthal, and Strevens have recently presented interpretations of the objective probabilities posited by some scientific theories that build on von Kries’s idea of identifying probabilities with ranges of values in a space of possible states. These interpretations face a problem, forcefully pointed out by Rosenthal, about how to determine ‘input probabilities.’ I argue here that Abrams’s and Strevens’s attempts to solve this problem do not succeed. I also argue that the problem can be solved by recognizing the possibility of (...)
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  7. Typicality, Irreversibility and the Status of Macroscopic Laws.Dustin Lazarovici & Paula Reichert - 2015 - Erkenntnis 80 (4):689-716.
    We discuss Boltzmann’s probabilistic explanation of the second law of thermodynamics providing a comprehensive presentation of what is called today the typicality account. Countering its misconception as an alternative explanation, we examine the relation between Boltzmann’s H-theorem and the general typicality argument demonstrating the conceptual continuity between the two. We then discuss the philosophical dimensions of the concept of typicality and its relevance for scientific reasoning in general, in particular for understanding the reduction of macroscopic laws to microscopic laws. Finally, (...)
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  8. The Early History of Chance in Evolution.Charles H. Pence - 2015 - Studies in History and Philosophy of Science Part A 50:48-58.
    Work throughout the history and philosophy of biology frequently employs ‘chance’, ‘unpredictability’, ‘probability’, and many similar terms. One common way of understanding how these concepts were introduced in evolution focuses on two central issues: the first use of statistical methods in evolution (Galton), and the first use of the concept of “objective chance” in evolution (Wright). I argue that while this approach has merit, it fails to fully capture interesting philosophical reflections on the role of chance expounded by two of (...)
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  9. Free Will and Probability.Danny Frederick - 2013 - Canadian Journal of Philosophy 43 (1):60-77.
    The chance objection to incompatibilist accounts of free action maintains that undetermined actions are not under the agent's control. Some attempts to circumvent this objection locate chance in events posterior to the action. Indeterministic-causation theories locate chance in events prior to the action. However, neither type of response gives an account of free action which avoids the chance objection. Chance must be located at the act of will if actions are to be both undetermined and under the agent's control. This (...)
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  10. Briggs on Antirealist Accounts of Scientific Law.John Halpin - 2013 - Synthese 190 (16):3439–3449.
    Rachel Briggs’ critique of “antirealist” accounts of scientific law— including my own perspectivalist best-system account—is part of a project meant to show that Humean conceptions of scientific law are more problematic than has been commonly realized. Indeed, her argument provides a new challenge to the Humean, a thoroughly epistemic version of David Lewis’ “big, bad bug” for Humeanism. Still, I will argue, the antirealist (perspectivalist and expressivist) accounts she criticizes have the resources to withstand the challenge and come out stronger (...)
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  11. Against the Statistical Account of Special Science Laws.Andreas Hüttemann & Alexander Reutlinger - 2013 - In Vassilios Karakostas & Dennis Dieks (eds.), Recent Progress in Philosophy of Science: Perspectives and Foundational Problems. The Third European Philosophy of Science Association Proceedings. Springer. pp. 181-192.
    John Earman and John T. Roberts advocate a challenging and radical claim regarding the semantics of laws in the special sciences: the statistical account. According to this account, a typical special science law “asserts a certain precisely defined statistical relation among well-defined variables” and this statistical relation does not require being hedged by ceteris paribus conditions. In this paper, we raise two objections against the attempt to cash out the content of special science generalizations in statistical terms.
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  12. Probabilities, Laws, and Structures.Dennis Dieks, Wenceslao Gonzalez, Hartmann J., Stöltzner Stephan, Weber Michael & Marcel (eds.) - 2012 - Springer: Netherlands.
  13. Two Accounts of Laws and Time.Barry Loewer - 2012 - Philosophical Studies 160 (1):115-137.
    Among the most important questions in the metaphysics of science are "What are the natures of fundamental laws and chances?" and "What grounds the direction of time?" My aim in this paper is to examine some connections between these questions, discuss two approaches to answering them and argue in favor of one. Along the way I will raise and comment on a number of issues concerning the relationship between physics and metaphysics and consequences for the subject matter and methodology of (...)
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  14. Armstrong and van Fraassen on Probabilistic Laws of Nature.Duncan Maclean - 2012 - Canadian Journal of Philosophy 42 (1):1-13.
    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 (...)
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  15. A Modest Proposal About Chance.Jenann Ismael - 2011 - Journal of Philosophy 108 (8):416-442.
    First para: Before the 17th century, there was not much discussion, and little uniformity in conception, of natural laws. The rise of science in 17th century, Newton’s mathematization of physics, and the provision of strict, deterministic laws that applied equally to the heavens and to the terrestrial realm had a profound impact in transforming the philosophical imagination. A philosophical conception of physical law built on the example of Newtonian Mechanics became quickly entrenched. Between the 17th and 20th centuries, there was (...)
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  16. Are We Free to Obey the Laws?Randolph Clarke - 2010 - American Philosophical Quarterly 47 (4):389-401.
    It is often said that if free will is incompatible with determinism, then free actions must be anomic, not covered by any law of nature. Here it is argued that there is no need for incompatiblists to hold this view. Even if freedom requires indeterminism, our freedom can be freedom to obey the laws.
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  17. On the Nature of Statistical Language Laws.Agnieszka Kulacka - 2010 - In Piotr Stalmaszczyk (ed.), Objects of Inquiry in Philosophy of Language and Linguistics. Ontos Verlag. pp. 151.
    This article discusses the nature of langttagc laws with particular focus on statistical language laws. We discuss the notion of law of science and describe the types of laws with regard to language laws. We also study the case of the Menzerath-Altmann law to show the contemporargtr methods of investigating language laws.
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  18. Contemporary Approaches to Statistical Mechanical Probabilities: A Critical Commentary - Part I: The Indifference Approach.Christopher J. G. Meacham - 2010 - Philosophy Compass 5 (12):1116-1126.
    This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...)
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  19. Contemporary Approaches to Statistical Mechanical Probabilities: A Critical Commentary - Part II: The Regularity Approach.Christopher J. G. Meacham - 2010 - Philosophy Compass 5 (12):1127-1136.
    This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...)
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  20. A Tale of Two Vectors.Marc Lange - 2009 - Dialectica 63 (4):397-431.
    Why do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and “transcend” the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this (...)
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  21. Laws and Natural Properties.Barry Loewer - 2007 - Philosophical Topics 35 (1/2):313-328.
  22. Do Chances Receive Equal Treatment Under the Laws? Or: Must Chances Be Probabilities?Marc Lange - 2006 - British Journal for the Philosophy of Science 57 (2):383-403.
    I offer an argument regarding chances that appears to yield a dilemma: either the chances at time t must be determined by the natural laws and the history through t of instantiations of categorical properties, or the function ch(•) assigning chances need not satisfy the axioms of probability. The dilemma's first horn might seem like a remnant of determinism. On the other hand, this horn might be inspired by our best scientific theories. In addition, it is entailed by the familiar (...)
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  23. How to Account for the Relation Between Chancy Facts and Deterministic Laws.Marc Lange - 2006 - Mind 115 (460):917--946.
    Suppose that unobtanium-346 is a rare radioactive isotope. Consider: (1) Every Un346 atom, at its creation, decays within 7 microseconds (µs). (50%) Every Un346 atom, at its creation, has a 50% chance of decaying within 7µs. (1) and (50%) can be true together, but (1) and (50%) cannot together be laws of nature. Indeed, (50%)'s mere (non-vacuous) truth logically precludes (1)'s lawhood. A satisfactory analysis of chance and lawhood should nicely account for this relation. I shall argue first that David (...)
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  24. Chance, Explanation, and Causation in Evolutionary Theory.Jean Gayon - 2005 - History and Philosophy of the Life Sciences 27 (3/4):395 - 405.
    Chance comes into plays at many levels of the explanation of the evolutionary process; but the unity of sense of this category is problematic. The purpose of this talk is to clarify the meaning of chance at various levels in evolutionary theory: mutations, genetic drift, genetic revolutions, ecosystems, macroevolution. Three main concepts of chance are found at these various levels: luck (popular concept), randomness (probabilistic concept), and contingency relative to a given theoretical system (epistemological concept). After identifying which concept(s) of (...)
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  25. The Explanatory Virtues of Probabilistic Causal Laws.Henrik Hallsten - 2005 - In Jan Faye, Paul Needham, Uwe Scheffler & Max Urchs (eds.), Nature's Principles. Springer. pp. 137--150.
  26. Three Proposals Regarding a Theory of Chance.Christopher J. G. Meacham - 2005 - Philosophical Perspectives 19 (1):281–307.
    I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...)
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  27. Infinitesimal Chances and the Laws of Nature.Adam Elga - 2004 - Australasian Journal of Philosophy 82 (1):67 – 76.
    The 'best-system' analysis of lawhood [Lewis 1994] faces the 'zero-fit problem': that many systems of laws say that the chance of history going actually as it goes--the degree to which the theory 'fits' the actual course of history--is zero. Neither an appeal to infinitesimal probabilities nor a patch using standard measure theory avoids the difficulty. But there is a way to avoid it: replace the notion of 'fit' with the notion of a world being typical with respect to a theory.
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  28. Routes, Processes, and Chance-Lowering Causes.Christopher Hitchcock - 2004 - In Phil Dowe & Paul Noordhof (eds.), Cause and Chance: Causation in an Indeterministic World. Routledge.
    Causes often influence their effects via multiple routes. Moderate alcohol consumption can raise the level of HDL ('good') cholesterol, which in tum reduces the risk of heart disease. Unfortunately, moderate alcohol consumption can also increase the level of homocysteine, which in tum increases the risk of heart disease. The net or overall effect of alcohol consumption on heart disease will depend upon both of these routes, and no doubt upon many others as well. This is a familiar fact of life (...)
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  29. Probability: A Philosophical Introduction.D. H. Mellor - 2004 - Routledge.
    _Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making makes an understanding of (...)
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  30. Chance in Biology - Using Probability to Explore Nature. [REVIEW]J. Bogaert - 2003 - Acta Biotheoretica 51 (1):55-57.
  31. Laws, Regularities and Exceptions.Alice Drewery - 2000 - Ratio 13 (1):1–12.
    Sentences of the form ‘Fs are Gs’ can express laws of nature, weaker Special Science laws, and also regularities which are not a part of any explicit science. These so-called generic sentences express nomic relationships which may have exceptions. I discuss the kinds of regularities expressed by generic sentences and argue that since they play a similar role in determining our ability to categorise and reason about the world, we should look for a unified treatment of them.
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  32. Are Statistical Laws Genuine Laws? A Concern of Poincaré and Boltzmann.Paul Weingartner - 1998 - Philosophia Scientiae 3 (2):215-236.
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  33. Probable Causes and the Distinction Between Subjective and Objective Chance.Stuart S. Glennan - 1997 - Noûs 31 (4):496-519.
    In this paper I present both a critical appraisal of Humphreys' probabilistic theory of causality and a sketch of an alternative view of the relationship between the notions of probability and of cause. Though I do not doubt that determinism is false, I claim that the examples used to motivate Humphreys' theory typically refer to subjective rather than objective chance. Additionally, I argue on a number of grounds that Humphreys' suggestion that linear regression models be used as a canonical form (...)
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  34. What Chances Could Not Be.Jenann Ismael - 1996 - British Journal for the Philosophy of Science 47 (1):79-91.
    The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned. I argue that this understanding of chances in quantum mechanics, despite being a part (...)
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  35. A Probabilistic Analysis of Causal Laws.Ansgar Alfred Augustinus Simon - 1996 - Dissertation, University of California, Los Angeles
    Probabilistic theories of causation develop the idea that a cause's presence increases the likelihood of its effect as compared to its absence. The common explication, that a cause do so in a complete background context of other causes, is shown to rely on the intuition that a cause produces the probability increase on its own. This requires that, in the background context, the relevant probabilities express non-causal probabilistic laws, i.e., are nomic. A law holds of a kind; this kind determines (...)
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  36. The Second Law of Probability Dynamics.Martin Barrett & Elliott Sober - 1994 - British Journal for the Philosophy of Science 45 (4):941-953.
    When the probability of causes, and the probability of effects, given causes, are each randomly assigned, entropy ‘usually’ increases.
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  37. The Big Bad Bug: What Are the Humean's Chances?John Bigelow, John Collins & Robert Pargetter - 1993 - British Journal for the Philosophy of Science 44 (3):443-462.
    Humean supervenience is the doctrine that there are no necessary connections in the world. David Lewis identifies one big bad bug to the programme of providing Humean analyses for apparently non-Humean features of the world. The bug is chance. We put the bug under the microscope, and conclude that chance is no special problem for the Humean.
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  38. Matters of Metaphysics.Henry E. Kyburg Jr - 1992 - Review of Metaphysics 46 (2):409-411.
    These essays are characterized by meticulous argument in the analytical tradition. The book concerns matters of metaphysics in a broad sense: philosophy of mind and the problems of subjectivity; questions concerning nomological and statistical laws of nature; and, as we would expect, chance and induction.
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  39. Urbach on the Laws of Nature.Christopher Hitchcock - 1992 - Analysis 52 (2):61 - 64.
  40. The Theory of Nomic Probability.John L. Pollock - 1992 - Synthese 90 (2):263 - 299.
    This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...)
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  41. Scientific Explanation and the Causal Structure of the World.Lansana Keita - 1990 - International Philosophical Quarterly 30 (2):264-265.
  42. Explanation, Subjunctives and Statistical Theories.Del Ratzsch - 1988 - International Studies in the Philosophy of Science 3 (1):80 – 96.
  43. Armstrong on Laws and Probabilities.Bas C. van Fraassen - 1987 - Australasian Journal of Philosophy 65 (3):243 – 260.
    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 (...)
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  44. Causal Laws and Laws of Association.Frederick S. Ellett & David P. Ericson - 1985 - Noûs 19 (4):537 - 549.
    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 (...)
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  45. Nomic Probability.John L. Pollock - 1984 - Midwest Studies in Philosophy 9 (1):177-204.
  46. The Statistical Nature of Laws of Social Development.I. A. Matsiavichius - 1983 - Russian Studies in Philosophy 22 (3):82-85.
    The laws of social development are objective in content and, in contrast to the laws of nature, are manifested and function only through the activity of human beings. The development of all spheres of human activity, in turn, cannot be conceived of as independent of the will, consciousness, moods and beliefs, propensities and preferences of human beings, nor as independent of the effectiveness of forms of social organization, etc. The social specificity of laws of social development in turn defines another (...)
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  47. Causal Necessity. [REVIEW]B. M. - 1982 - Review of Metaphysics 35 (4):913-914.
  48. SKRYMS, B., "Causal Necessity". [REVIEW]L. J. O'neill - 1981 - Australasian Journal of Philosophy 59:226.
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  49. Causal Necessity. [REVIEW]Marshall Spector - 1981 - International Studies in Philosophy 13 (2):119-120.
  50. Statistical Laws and Personal Propensities.Brian Skyrms - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:551 - 562.
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