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Law Statements

Edited by Markus Schrenk (Heinrich-Heine-Universität Düsseldorf)
Assistant editor: Florian Boge (University of Cologne, University of Düsseldorf)
About this topic
Summary Next to the ontological status of laws of nature, their linguistic representation can be of interest. Questions regarding law statements include which logical features are characteristic of law statements (universal quantification, conditional statements, material vs. counterfactual conditionals, modal operators… etc.), whether there even is such a thing as a general common form of such statements, whether there is always or even essentially a mathematic form, differential equations for example, what distinguishes statements of laws from accidental generalizations, and so forth.

These questions relate, in particular, to the “lawlikeness”-debate that dates back to logical empiricism, whose proponents focused on language analysis as the central method to solve philosophical problems. The guiding idea to define what a law of nature is was, for example, to split the problem into two parts: first, say what necessary and sufficient features statements, i.e., linguistic entities, must have in order to be counted as expressions of laws. Call those statements that fulfill the criteria -- like universality, containing only natural predicates, having conditional form, etc. -- "lawlike". Then, second, say that a law of nature (the ultimate target of the enquiry) is a true lawlike statement. Thus, overall, there are two separate tasks to tackle: find criteria for lawlikeness, then find out whether the respective statements are true (the latter task leads straight into conformation theory and its problems; see philpapers for confirmation). It should be said that no necessary or sufficient set of pure syntactic nor semantic criteria could ever be given.

Key works The seminal papers are Goodman 1954 and Hempel & Oppenheim 1948, see also the last chapter of Reichenbach 1980.
Introductions Psillos 2002
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  1. Joseph Agassi (1995). Blame Not the Laws of Nature. Foundations of Science 1 (1):131-154.
    1. Lies, Error and Confusion 2. Lies 3. The Demarcation of Science: Historical 4. The Demarcation of Science: Recent 5. Observed Regularities and Laws of Nature.
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  2. Christopher Belanger (2010). Marc Lange. Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature. Spontaneous Generations 4 (1):266-269.
    In Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature, Marc Lange has presented an engagingly written, tightly argued, and novel philosophical account of the laws of nature. One of the intuitions behind the notion of a law of nature is, roughly, that of the many regularities we observe in the world there are some which appear to be due to mere happen-stance (“accidental” regularities, in the philosopher’s jargon), while others, which we call “laws,” seem to be possessed of (...)
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  3. Bernard Berofsky (1968). The Regularity Theory. Noûs 2 (4):315-340.
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  4. Gerd Buchdahl (1971). The Conception of Lawlikeness in Kant's Philosophy of Science. Synthese 23 (1):24 - 46.
    A demarcation between kant's general metaphysics (transcendental principles) and his special metaphysics is attempted, through a discussion of kant's three accounts of lawlikeness, 'transcendental', 'empirical' and 'metaphysical'. the distinctions are defended via a number of 'indicators' in kant's writings, and the 'looseness of fit' between the different types of lawlikeness is discussed.
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  5. B. Carr (1978). HARRÉ, R. And MADDEN, E. H. "Causal Powers: A Theory of Natural Necessity". [REVIEW] Mind 87:305.
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  6. Martin Carrier, Evolutionary Change and Lawlikeness : Beatty on Biological Generalizations.
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  7. Wayne A. Davis (1987). Scientific Knowledge. [REVIEW] Review of Metaphysics 41 (1):136-137.
  8. A. Drewery (2011). Laws and Lawmakers: Science, Metaphysics and the Laws of Nature * by Marc Lange. Analysis 71 (3):599-601.
    Marc Lange’s new book on laws offers a restatement and development of the account he proposed in Natural Laws and Scientific Practice (Oxford University Press, 2000), henceforth NLSP, and the new material is helpfully summarized in the preface. Laws and Lawmakers presents the key idea from NLSP in a rather more reader-friendly manner – this idea being roughly that the difference between laws and accidents is that laws, unlike accidents, form a ‘stable’ set, i.e. a logically closed set of truths (...)
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  9. Alice Drewery (2005). The Logical Form of Universal Generalizations. Australasian Journal of Philosophy 83 (3):373 – 393.
    First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.
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  10. C. Z. Elgin (1980). Lawlikeness and the End of Science. Philosophy of Science 47 (1):56-68.
    Although our theories are not precisely true, scientific realists contend that we should admit their objects into our ontology. One justification--offered by Sellars and Putnam--is that current theories belong to series that converge to ideally adequate theories. I consider the way the commitment to convergence reflects on the interpretation of lawlike claims. I argue that the distinction between lawlike and accidental generalizations depends on our cognitive interests and reflects our commitment to the direction of scientific progress. If the sciences disagree (...)
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  11. Robert Farrell (1979). HARRE, R. & MADDEN, E. H., "Causal Powers: A Theory of Natural Necessity". [REVIEW] Australasian Journal of Philosophy 57:114.
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  12. James H. Fetzer (1974). The Likeness of Lawlikeness. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974:377 - 391.
    The thesis of this paper is that extensional language alone provides an essentially inadequate foundation for the logical formalization of any lawlike statement. The arguments presented are intended to demonstrate that lawlike sentences are logically general dispositional statements requiring an essentially intensional reduction sentence formulation. By introducing a non-extensional logical operator, the 'fork', the difference between universal and statistical laws emerges in a distinction between dispositional predicates of universal strength as opposed to those of merely statistical strength. While the logical (...)
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  13. Toby Friend (2016). Laws Are Conditionals. European Journal for Philosophy of Science 6 (1):123-144.
    The ubiquitous schema ‘All Fs are Gs’ dominates much philosophical discussion on laws but rarely is it shown how actual laws mentioned and used in science are supposed to fit it. After consideration of a variety of laws, including those obviously conditional and those superficially not conditional, I argue that we have good reason to support the traditional interpretation of laws as conditionals of some quantified form with a single object variable. I show how this conclusion impacts on the status (...)
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  14. Nelson Goodman (1983). Fact, Fiction, and Forecast. Harvard University Press.
    In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.
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  15. Carl G. Hempel (1968). Maximal Specificity and Lawlikeness in Probabilistic Explanation. Philosophy of Science 35 (2):116-133.
    The article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding "ambiguity" in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic explanations must be (...)
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  16. Carl G. Hempel (1968). On a Claim by Skyrms Concerning Lawlikeness and Confirmation. Philosophy of Science 35 (3):274-278.
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  17. Risto Hilpinen & Jaakko Hintikka (1971). Rules of Acceptance, Indices of Lawlikeness, and Singular Inductive Inference: Reply to a Critical Discussion. Philosophy of Science 38 (2):303-307.
  18. Jaakko Hintikka (1969). Statistics, Induction, and Lawlikeness: Comments on Dr. Vetter's Paper. Synthese 20 (1):72 - 83.
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  19. Peter Van Inwagen (1979). Laws and Counterfactuals. Noûs 13 (4):439 - 453.
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  20. Evan K. Jobe (1967). Some Recent Work on the Problem of Law. Philosophy of Science 34 (4):363-381.
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  21. John L. King (1979). Coextensiveness and Lawlikeness. Erkenntnis 14 (3):359 - 363.
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  22. Robert Kowalenko (2012). Reply to Israel on the New Riddle of Induction. Philosophia 40 (3):549-552.
    Israel 2004 claims that numerous philosophers have misinterpreted Goodman’s original ‘New Riddle of Induction’, and weakened it in the process, because they do not define ‘grue’ as referring to past observations. Both claims are false: Goodman clearly took the riddle to concern the maximally general problem of “projecting” any type of characteristic from a given realm of objects into another, and since this problem subsumes Israel’s, Goodman formulated a stronger philosophical challenge than the latter surmises.
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  23. Leonard I. Krimerman (1965). Laws and Counterfactuals. Philosophical Studies 16 (3):40 - 44.
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  24. Mark Lance & Maggie Little (2010). Lange, Marc . Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature . Oxford: Oxford University Press, 2009 . Pp. 280. $99.00 (Cloth); $24.95 (Paper). [REVIEW] Ethics 120 (2):431-437.
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  25. Marc Lange (2009). Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature. Oxford University Press.
    Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.
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  26. Marc Lange (1999). Laws, Counterfactuals, Stability, and Degrees of Lawhood. Philosophy of Science 66 (2):243-267.
    I identify the special sort of stability (invariance, resilience, etc.) that distinguishes laws from accidental truths. Although an accident can have a certain invariance under counterfactual suppositions, there is no continuum between laws and accidents here; a law's invariance is different in kind, not in degree, from an accident's. (In particular, a law's range of invariance is not "broader"--at least in the most straightforward sense.) The stability distinctive of the laws is used to explicate what it would mean for there (...)
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  27. Marc Lange (1993). Lawlikeness. Noûs 27 (1):1-21.
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  28. Chang Liu (1999). Approximation, Idealization, and Laws of Nature. Synthese 118 (2):229-256.
    Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory of (...)
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  29. Peter Long (1952). Natural Laws and So-Called Accidental General Statements. Analysis 13 (1):18 - 23.
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  30. Ludvig Lövestad (1945). The Structure of Physical Laws. Theoria 11 (1):40-70.
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  31. E. J. Lowe (1980). Sortal Terms and Natural Laws. American Philosophical Quarterly 19 (4):253-60.
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  32. Stanislaw Mazierski (1973). Criteria of Acceptation the General Statements as Natural Laws. Roczniki Filozoficzne 21 (3):42.
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  33. Sandra D. Mitchell (2000). Dimensions of Scientific Law. Philosophy of Science 67 (2):242-265.
    Biological knowledge does not fit the image of science that philosophers have developed. Many argue that biology has no laws. Here I criticize standard normative accounts of law and defend an alternative, pragmatic approach. I argue that a multidimensional conceptual framework should replace the standard dichotomous law/ accident distinction in order to display important differences in the kinds of causal structure found in nature and the corresponding scientific representations of those structures. To this end I explore the dimensions of stability, (...)
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  34. Donald Nute (1981). Causes, Laws, and Law Statements. Synthese 48 (3):347 - 369.
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  35. Juhani Pietarinen (1974). Inductive Immodesty and Lawlikeness. Philosophy of Science 41 (2):196-198.
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  36. Juhani Pietarinen (1972). Lawlikeness, Analogy and Inductive Logic. Amsterdam,North-Holland Pub. Co..
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  37. C. F. Presley (1954). Laws and Theories in the Physical Sciences. Australasian Journal of Philosophy 32 (2):79 – 103.
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  38. George L. Proctor (1959). Scientific Laws and Scientific Objects in the Tractatus. British Journal for the Philosophy of Science 10 (39):177-193.
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  39. Rosemarie Rheinwald (1993). An Epistemic Solution to Goodman's New Riddle of Induction. Synthese 95 (1):55 - 76.
    Goodman'snew riddle of induction can be characterized by the following questions: What is the difference between grue and green?; Why is the hypothesis that all emeralds are grue not lawlike?; Why is this hypothesis not confirmed by its positive instances?; and, Why is the predicate grue not projectible? I argue in favor of epistemological answers to Goodman's questions. The notions of lawlikeness, confirmation, and projectibility have to be relativized to (actual and counterfactual) epistemic situations that are determined by the available (...)
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  40. James E. Roper (1982). Models and Lawlikeness. Synthese 52 (2):313 - 323.
    Do analogical models ever play an essential role in scientific explanation and confirmation, or is their role (at most) heuristic? For many years scientists and philosophers have debated this question. I argue that such models may sometimes play an essential role. My argument is based on a proposal to augment Goodman''s theory of projection in order to make it easier for novel predicates (extensions) to acquire entrenchment. The heart of this proposal is the claim that analogical models may, under certain (...)
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  41. Jean-Jacques Rosat (2001). Schlick, Waismann, Wittgenstein et la grammaire des lois de la nature. Les Etudes Philosophiques 3 (3):317-333.
    En 1931, Schlick propose de considérer les lois de la nature non comme des propositions au sens strict mais comme des instructions ou des règles pour la formation d’assertions et de prédictions. « Je dois, ajoute-t-il, cette idée et cette terminologie à Wittgenstein. » Cette conception a été couramment considérée comme typiquement instrumentaliste . À partir d’une lecture minutieuse des textes contemporains de Wittgenstein et de Waismann, on montre que ces auteurs proposent non pas une théorie mais une analyse de (...)
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  42. Severin Schroeder (2009). Hempel's Paradox, Law-Likeness and Causal Relations. Philosophical Investigations 32 (3):244-263.
    It is widely thought that Bayesian confirmation theory has provided a solution to Hempel's Paradox (the Ravens Paradox). I discuss one well-known example of this approach, by John Mackie, and argue that it is unconvincing. I then suggest an alternative solution, which shows that the Bayesian approach is altogether mistaken. Nicod's Condition should be rejected because a generalisation is not confirmed by any of its instances if it is not law-like. And even law-like non-basic empirical generalisations, which are expressions of (...)
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  43. Gerhard Schurz (2005). Laws of Nature Versus System Laws. In Jan Faye, Paul Needham, Uwe Scheffler & Max Urchs (eds.), Nature's Principles. Springer 255--268.
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  44. R. A. Sharpe (1971). Laws, Coincidences, Counterfactuals and Counter-Identicals. Mind 80 (320):572-582.
  45. R. A. Sharpe (1964). The Logical Status of Natural Laws. Inquiry 7 (1-4):414-416.
    In this note I have presented the essentials of a view of how laws are falsified, a view which has been held by some notable philosophers but which is radically opposed to that of Professor Popper. I have not scrupled to ?improve? upon it, so the view of no one philosopher is presented. I try to show that an interesting and convincing account of scientific simplicity is implicit in the theory and I conclude by suggesting how we can bring the (...)
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  46. Elliott Sober (1988). Confirmation and Law-Likeness. Philosophical Review 97 (1):93-98.
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  47. Wolfgang Spohn (2005). Enumerative Induction and Lawlikeness. Philosophy of Science 72 (1):164-187.
    The paper is based on ranking theory, a theory of degrees of disbelief (and hence belief). On this basis, it explains enumerative induction, the confirmation of a law by its positive instances, which may indeed take various schemes. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. It proves, then, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus, it shows that de Finetti's probabilistic representation theorems may be transformed (...)
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  48. Wolfgang Spohn (2004). Laws Are Persistent Inductives Schemes. In F. Stadler (ed.), Vienna Circle Institute Yearbook. Kluwer 11--135.
    The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Hence, ranking theory with its resources of formalizing defeasible reasoning or inductive schemes seems ideally suited to explicate the idea in a formal way. This is what the paper attempts to do. Thus it will turn out that a law is simply the deterministic analogue of a sequence (...)
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  49. John R. Wallace (1966). Lawlikeness=Truth? Journal of Philosophy 63 (24):780-781.
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  50. Dieter Wandschneider (1986). Die Inkonsistenz Empiristischer Argumentation Im Zusammenhang MIT Dem Problem der Naturgesetzlichkeit. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 17 (1):131-142.
    Summary The well-knownempiristical apories of the law of nature prevent until this day an adequate philosophical interpretation ofempirical science. Clarification can only be expected through animmanent refutation of the empiristical point of view. In this sense it is proved in this paper thatHume's argumentation, paradigmatic for modern empirism, is not just one-sided, but simplyinconsistent: Anyone who claimes experience to be the basis of all knowledge (as the empirist does), and, due to this, denies that the lawlike character of nature can (...)
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