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Probabilistic Laws

Edited by Markus Schrenk (Westfälische Wilhelms Universität, Münster)
Assistant editor: Florian Boge (University of Cologne, University of Cologne)
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 2008
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  1. John Bigelow, John Collins & Robert Pargetter (1993). The Big Bad Bug: What Are the Humean's Chances? 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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  2. David Bohm (1957/1999). Causality and Chance in Modern Physics. University of Pennsylvania Press.
    CHAPTER ONE Causality and Chance in Natural Law. INTRODUCTION IN nature nothing remains constant. Everything is in a perpetual state of transformation, ...
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  3. Randolph Clarke (2010). Are We Free to Obey the Laws? 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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  4. Adam Elga (2004). Infinitesimal Chances and the Laws of Nature. 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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  5. Danny Frederick (2013). Free Will and Probability. 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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  6. Stuart S. Glennan (1997). Probable Causes and the Distinction Between Subjective and Objective Chance. Noûs 31 (4):496-519.
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  7. John Halpin (2013). Briggs on Antirealist Accounts of Scientific Law. 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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  8. Christopher Hitchcock (1992). Urbach on the Laws of Nature. Analysis 52 (2):61 - 64.
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  9. Andreas Hüttemann & Alexander Reutlinger (forthcoming). Against the Statistical Account of Special Science Laws. 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.
    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” (Earman and Roberts 1999) 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 (...)
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  10. Frank Jackson, Graham Priest & Adam Elga (2004). Infinitesimal Chances and the Laws of Nature. 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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  11. Henry E. Kyburg (1976). Chance. Journal of Philosophical Logic 5 (3):355-393.
  12. Marc Lange (2006). Do Chances Receive Equal Treatment Under the Laws? Or: Must Chances Be Probabilities? 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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  13. Marc Lange (2006). How to Account for the Relation Between Chancy Facts and Deterministic Laws. 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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  14. Barry Loewer (2012). Two Accounts of Laws and Time. 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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  15. Barry Loewer (2007). Laws and Natural Properties. Philosophical Topics 35 (1/2):313-328.
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  16. Duncan Maclean (2012). Armstrong and van Fraassen on Probabilistic Laws of Nature. 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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  17. Christopher J. G. Meacham (2010). Contemporary Approaches to Statistical Mechanical Probabilities: A Critical Commentary - Part I: The Indifference Approach. 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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  18. Christopher J. G. Meacham (2010). Contemporary Approaches to Statistical Mechanical Probabilities: A Critical Commentary - Part II: The Regularity Approach. 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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  19. Christopher J. G. Meacham (2005). Three Proposals Regarding a Theory of Chance. 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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  20. D. H. Mellor (2004). The Matter of Chance. Cambridge University Press.
    This book deals not so much with statistical methods as with the central concept of chance, or statistical probability, which statistical theories apply to nature.
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  21. John Pollock (1992). The Theory of Nomic Probability. 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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  22. John L. Pollock (1992). The Theory of Nomic Probability. 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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  23. John L. Pollock (1984). Nomic Probability. Midwest Studies in Philosophy 9 (1):177-204.
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  24. John Roberts, Laws About Frequencies.
    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. (...)
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