Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.

Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.

Humean accounts of natural lawhood have often been criticized as unable to account for the laws’ characteristic explanatory power in science. Loewer has replied that these criticisms fail to distinguish grounding explanations from scientific explanations. Lange has replied by arguing that grounding explanations and scientific explanations are linked by a transitivity principle, which can be used to argue that Humean accounts of natural law violate the prohibition on self-explanation. Lange’s argument has been sharply criticized by Hicks and van (...) Elswyk, Marshall, and Miller. This paper shows how Lange’s argument can withstand these criticisms once the transitivity principle and the prohibition on self-explanation are properly refined. The transitivity principle should be refined to accommodate contrasts in the explanans and explanandum. The prohibition on self-explanation should be refined so that it precludes a given fact p from helping to explain why some other fact q helps to explain why p. In this way, the transitivity principle avoids having counterintuitive consequences in cases involving macrostates having multiple possible microrealizations. The transitivity principle is perfectly compatible with the irreducibility of macroexplanations to microexplanations and with the diversity of the relations that can underwrite scientific explanations. (shrink)

It is often presumed that the laws of nature have special significance for scientific reasoning. But the laws' distinctive roles have proven notoriously difficult to identify--leading some philosophers to question if they hold such roles at all. This study offers original accounts of the roles that natural laws play in connection with counterfactual conditionals, inductive projections, and scientific explanations, and of what the laws must be in order for them to be capable of playing these roles. Particular attention is given (...) to laws of special sciences, levels of scientific explanation, natural kinds, ceteris-paribus clauses, and physically necessary non-laws. (shrink)

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

This book combines physics, history, and philosophy in a radical new approach to introducing the philosophy of physics.

It has often been argued that Humean accounts of natural law cannot account for the role played by laws in scientific explanations. Loewer (Philosophical Studies 2012) has offered a new reply to this argument on behalf of Humean accounts—a reply that distinguishes between grounding (which Loewer portrays as underwriting a kind of metaphysical explanation) and scientific explanation. I will argue that Loewer’s reply fails because it cannot accommodate the relation between metaphysical and scientific explanation. This relation also resolves a puzzle (...) about scientific explanation that Hempel and Oppenheim (Philosophy of Science 15:135–75, 1948) encountered. (shrink)

Buch 1. Geschichte des Materialismus bis auf Kant.--Buch 2. Geschichte des Materialismus seit Kant.

Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations, there are few examples that have become widely accepted as exhibiting the distinction between mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds. This essay offers some examples of proofs that mathematicians have considered explanatory, and it argues that these examples suggest a (...) particular account of explanation in mathematics. The essay compares its account to Steiner's and Kitcher's. Among the topics that arise are proofs that exploit symmetries, mathematical coincidences, brute-force proofs, simplicity in mathematics, merely clever proofs, and proofs that unify what other proofs treat as separate cases. (shrink)

Ceteris-paribus clauses are nothing to worry about; aceteris-paribus qualifier is not poisonously indeterminate in meaning. Ceteris-paribus laws teach us that a law need not be associated straightforwardly with a regularity in the manner demanded by regularity analyses of law and analyses of laws as relations among universals. This lesson enables us to understand the sense in which the laws of nature would have been no different under various counterfactual suppositions — a feature even of those laws that involve no ceteris-paribus (...) qualification and are actually associated with exceptionless regularities. Ceteris-paribus generalizations of an‘inexact science’ qualify as laws of that science in virtue of their distinctive relation to counterfactuals: they form a set that is stable for the purposes of that field. (Though an accident may possess tremendous resilience under counterfactual suppositions, the laws are sharply distinguished from the accidents in that the laws are collectively as resilient as they could logically possibly be.) The stability of an inexact science's laws may involve their remaining reliable even under certain counterfactual suppositions violating fundamental laws of physics. The ceteris-paribus laws of an inexact science may thus possess a kind of necessity lacking in the fundamental laws of physics. A nomological explanation supplied by an inexact science would then be irreducible to an explanation of the same phenomenon at the level of fundamental physics. Island biogeography is used to illustrate how a special science could be autonomous in this manner. (shrink)

Symmetry principles are commonly said to explain conservation laws—and were so employed even by Lagrange and Hamilton, long before Noether's theorem. But within a Hamiltonian framework, the conservation laws likewise entail the symmetries. Why, then, are symmetries explanatorily prior to conservation laws? I explain how the relation between ordinary (i.e., first-order) laws and the facts they govern (a relation involving counterfactuals) may be reproduced one level higher: as a relation between symmetries and the ordinary laws they govern. In that event, (...) symmetries are meta-laws; they are not mere byproducts of the dynamical and force laws. Symmetries then explain conservation laws whereas conservation laws lack the modal status to explain symmetries. I elaborate the variety of natural necessity that meta-laws would possess. Proposed metaphysical accounts of natural law should aim to accommodate the distinction between meta-laws and mere byproducts of the laws just as they must accommodate the distinction between laws and accidents. (shrink)

Counterfactuals all the way down? Content Type Journal Article DOI 10.1007/s11016-010-9437-9 Authors Jim Woodward, History and Philosophy of Science, 1017 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260, USA Barry Loewer, Department of Philosophy, Rutgers University, New Brunswick, NJ 08901, USA John W. Carroll, Department of Philosophy and Religious Studies, North Carolina State University, Raleigh, NC 27695-8103, USA Marc Lange, Department of Philosophy, University of North Carolina at Chapel Hill, CB#3125—Caldwell Hall, Chapel Hill, NC 27599-3125, USA Journal Metascience (...) Online ISSN 1467-9981 Print ISSN 0815-0796 Journal Volume Volume 20 Journal Issue Volume 20, Number 1. (shrink)

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

Several foundational documents of bioethics mention the special obligation researchers have to vulnerable research participants. However, the treatment of vulnerability offered by these documents often relies on enumeration of vulnerable groups rather than an analysis of the features that make such groups vulnerable. Recent attempts in the scholarly literature to lend philosophical weight to the concept of vulnerability are offered by Luna and Hurst. Luna suggests that vulnerability is irreducibly contextual and that Institutional Review Boards (Research Ethics Committees) can only (...) identify vulnerable participants by carefully examining the details of the proposed research. Hurst, in contrast, defines the vulnerable as those especially at risk of incurring the wrongs to which all research ethics participants are exposed. We offer a more substantive conception of vulnerability than Luna but one that gives rise to a different rubric of responsibilities from Hurst's. While we understand vulnerability to be an ontological condition of human existence, in the context of research ethics, we take the vulnerable to be research subjects who are especially prone to harm or exploitation. Our analysis rests on developing a typology of sources of vulnerability and showing how distinct sources generate distinct obligations on the part of the researcher. Our account emphasizes that the researcher's first obligation is not to make the research participant even more vulnerable than they already are. To illustrate our framework, we consider two cases: that of a vulnerable population involved in international research and that of a domestic population of people with diminished capacity. (shrink)

Batterman and Rice offer an account of “minimal model explanations” and argue against “common features accounts” of those explanations. This paper offers some objections to their proposals and arguments. It argues that their proposal cannot account for the apparent explanatory asymmetry of minimal model explanations. It argues that their account threatens ultimately to collapse into a “common features account.” Finally, it argues against their motivation for thinking that an explanation appealing to “common features” would have to explain the common features’ (...) own prevalence. (shrink)

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

Among the niftiest arguments for scientific anti-realism is the ‘pessimistic induction’ (also sometimes called ‘the disastrous historical meta-induction’). Although various versions of this argument differ in their details (see, for example, Poincare 1952: 160, Putnam 1978: 25, and Laudan 1981), the argument generally begins by recalling the many scientific theories that posit unobservable entities and that at one time or another were widely accepted. The anti-realist then argues that when these old theories were accepted, the evidence for them was quite (...) persuasive – roughly as compelling as our current evidence is for our best scientific theories positing various unobservable entities. Nevertheless, the anti-realist argues, most of these old theories turned out to be incorrect in the unobservables they posited. Therefore, the anti-realist concludes that with regard to the theories we currently accept, we should believe that probably, most of them are likewise incorrect in the unobservable entities they posit. (This argument appeals to what our best current theories say about unobservables in order to show that the entities posited by some earlier theory are not real. So the argument takes the form of a reductio of the view that the apparent success of some scientific theory justifies our believing in its accuracy regarding unobservables.) Of course, this argument has been criticized on many grounds. Some have argued, for instance, that the scientific theories we currently accept are much better supported than were earlier scientific theories at the time they were accepted. In addition, some have argued that many scientific theories accepted justly in the past were in fact accurate.. (shrink)

What is the origin of the concept of a law of nature? How much does it owe to theology and metaphysics? To what extent do the laws of nature permit contingency? Are there exceptions to the laws of nature? Is it possible to give a reductive analysis of lawhood, or is it a primitive? -/- Twelve brand-new essays by an international team of leading philosophers take up these and other central questions on the laws of nature, whilst also examining some (...) of the most important intuitions and assumptions that have guided the debate over laws of nature since the concept's invention in the seventeenth century. -/- Laws of Nature spans the history of philosophy and of science, contemporary metaphysics, and contemporary philosophy of science. Contents: 1. Intuitions and Assumptions in the Debate over Laws of Nature, Walter Ott and Lydia Patton 2. Early Modern Roots of the Philosophical Concept of a Law of Nature, Helen Hattab 3. Laws of Nature and the Divine Order of Things: Descartes and Newton on Truth in Natural Philosophy, Mary Domski 4. Leges sive natura: Bacon, Spinoza, and a Forgotten Concept of Law, Walter Ott 5. Laws and Powers in the Frame of Nature, Stathis Psillos 6. Laws and Ideal Unity, Angela Breitenbach 7. Becoming Humean, John W. Carroll 8. A Perspectivalist Better Best System Account of Lawhood, Michela Massimi 9. Laws: An Invariance Based Account, James Woodward 10. How the Explanations of Natural Laws Make Some Reducible Physical Properties Natural and Explanatorily Powerful, Marc Lange 11. Laws and their Exceptions, Stephen Mumford 12. Are laws of nature consistent with contingency?, Nancy Cartwright and Pedro Merlussi. (shrink)

Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would be.

Many philosophers have believed that the laws of nature differ from the accidental truths in their invariance under counterfactual perturbations. Roughly speaking, the laws would still have held had q been the case, for any q that is consistent with the laws. (Trivially, no accident would still have held under every such counterfactual supposition.) The main problem with this slogan (even if it is true) is that it uses the laws themselves to delimit qs range. I present a means of (...) distinguishing the laws (and their logical consequences) from the accidents, in terms of their range of invariance under counterfactual antecedents, that does not appeal to physical modalities (or any cognate notion) in delimiting the relevant range of counterfactual perturbations. I then argue that this approach explicates the sense in which the laws possess a kind of necessity. (shrink)

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

Scientific essentialism aims to account for the natural laws' special capacity to support counterfactuals. I argue that scientific essentialism can do so only by resorting to devices that are just as ad hoc as those that essentialists accuse Humean regularity theories of employing. I conclude by offering an account of the laws' distinctive relation to counterfactuals that portrays laws as contingent but nevertheless distinct from accidents by virtue of possessing a genuine variety of necessity.

I here settle a recent dispute between two rival theories in distributive ethics: Restricted Prioritarianism and the Competing Claims View. Both views mandate that the distribution of benefits and burdens between individuals should be justifiable to each affected party in a way that depends on the strength of each individual’s separately assessed claim to receive a benefit. However, they disagree about what elements constitute the strength of those individuals’ claims. According to restricted prioritarianism, the strength of a claim is determined (...) in ‘prioritarian’ fashion by both what she stands to gain and her absolute level of well-being, while, according to the competing claims view, the strength of a claim is also partly determined by her level of well-being relative to others with conflicting interests. I argue that, suitably modified, the competing claims view is more plausible than restricted prioritarianism. (shrink)

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 (...) to be multiple grades (or degrees) of physical necessity. Whether there are is for science to discover. (shrink)

Rosenberg has recently argued that explanations supplied by (what he calls) functional biology are mere promissory notes for macromolecular adaptive explanations. Rosenberg's arguments currently constitute one of the most substantial challenges to the autonomy, irreducibility, and indispensability of the explanations supplied by functional biology. My responses to Rosenberg's arguments will generate a novel account of the autonomy of functional biology. This account will turn on the relations between counterfactuals, scientific explanations, and natural laws. Crucially, in their treatment of the laws' (...) relation to counterfactuals, Rosenberg's arguments beg the question against the autonomy of functional biology. This relation is considerably more subtle than is suggested by familiar slogans such as Laws support counterfactuals; accidents don't. (shrink)

In this paper I assess the adequacy of no-conspiracy conditions employed in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these cannot be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are reinterpreted as mere common cause-measurement independence conditions. In the right circumstances then, violations of measurement independence need (...) not entail any kind of conspiracy (nor backwards in time causation). To the contrary, if measurement operations in the EPR context are taken to be causally relevant in a specific way to the experiment outcomes, their explicit causal role provides the grounds for a common cause explanation of the corresponding correlations. (shrink)

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 (...) controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws that helps us to understand what this dispute was all about. (shrink)

has offered a lovely example to motivate the intuition that a successful prediction has a kind of confirmatory significance that an accommodation lacks. This paper scrutinizes Maher's example. It argues that once the example is tweaked, the intuitive difference there between prediction and accommodation disappears. This suggests that the apparent superiority of prediction to accommodation is actually a side effect of an important difference between the hypotheses that tend to arise in each case.

Recently, biologists and computer scientists who advocate the "strong thesis of artificial life" have argued that the distinction between life and nonlife is important and that certain computer software entities could be alive in the same sense as biological entities. These arguments have been challenged by Sober (1991). I address some of the questions about the rational reconstruction of biology that are suggested by these arguments: What is the relation between life and the "signs of life"? What work (if any) (...) might the concept of "life" (over and above the "signs of life") perform in biology? What turns on scientific disputes over the utility of this concept? To defend my answers to these questions, I compare "life" to certain other concepts used in science, and I examine historical episodes in which an entity's vitality was invoked to explain certain phenomena. I try to understand how these explanations could be illuminating even though they are not accompanied by any reductive definition of "life.". (shrink)

In Educations in Ethnic Violence, Matthew Lange explores the effects education has on ethnic violence. Lange contradicts the widely held belief that education promotes peace and tolerance. Rather, Lange finds that education commonly contributes to aggression, especially in environments with ethnic divisions, limited resources and ineffective political institutions. He describes four ways in which organized learning spurs ethnic conflicts. Socialization in school shapes students' identities and the norms governing intercommunal relations. Education can also increase students' frustration and (...) aggression when their expectations are not met. Sometimes, the competitive atmosphere gives students an incentive to participate in violence. Finally, education provides students with superior abilities to mobilize violent ethnic movements. Lange employs a cross-national statistical analysis with case studies of Sri Lanka, Cyprus, the Palestinian territories, India, sub-Saharan Africa, Canada and Germany. (shrink)

While quick to question the claims to knowledge that others make, philosophers have not so readily submitted their own affirmations to the same scrutiny. In fact, it seems to be the common conviction of philosophers that the assertions they make are cognitive, are true or false, and that philosophical disagreement is genuine disagreement. In this stimulating essay Professor Lange confronts this assumption, presents his own view of philosophy as proposal, and then seeks a solution to the paradox that his (...) view poses for philosophy. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)