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)

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)

Meaningful relationships are centrally important for human functioning. It remains unclear, however, which aspects of meaningful relationships impact wellbeing the most and whether these differ between psychiatric patients and members of the community. Information about relationship attributes and functions were collected in community members and psychiatric patients. Relationship attributes and functions were examined for differences between groups, their impact on wellbeing and symptoms, and the size of network. Community members reported fewer relationships, higher frequency of contact and less desire for (...) change when compared to the psychiatric patients. Nevertheless, both groups reported relatively high levels of fulfilled functions. Quality of the relationship and investment into the relationship was associated with both wellbeing and symptoms for both the community and the patient group. Almost all functions were associated with wellbeing and symptoms for the community group. However, for the patient group, only few functions were associated with wellbeing and no functions were associated with symptoms. Contrary to our hypotheses, the results show that psychiatric patients do not have a deficit in fulfilling relationships. Most people report a well-functioning network of meaningful, high-quality relationships. Patients benefit from meaningful, function-fulfilling relationships just as much as community members. Results are discussed with respect to how targeting relationships can be used clinically. (shrink)

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why (...) certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power. (shrink)

This chapter contains section titled: Is Biology Like Physics? Laws of Nature: The Standard Picture Why Not Laws of Biology? The Problem of Exceptions Why Not Laws of Biology? The Problem of Accidentalness A Worked Example: The “Area Law” Evolutionary Accidents as Laws of Functional Biology References Further Reading.

Sober and Huemer have independently argued that simplicity has no place in evaluating philosophical views. In particular, they have argued that the best rationales for scientists to appeal to simplicity in judging between rival theories fail to carry over to philosophers judging between rival philosophical accounts. This paper disagrees with Sober and Huemer. It argues that two rationales for scientific appeals to simplicity equally well underwrite appeals to simplicity when philosophers evaluate rival rational reconstructions of some social normative practice. These (...) two rationales are shown to apply to two philosophical appeals to simplicity: in Quine’s argument against analyticity and in an argument against pluralism in accounts of scientific explanation. Some factors are identified that influence how much weight simplicity should carry in these and other philosophical cases. Simplicity’s legitimate role in evaluating rival rational reconstructions suggests that simplicity will also turn out to be justly relevant to ontological investigations. (shrink)

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.

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.

Many philosophers argue that explanatoriness plays no special role in confirmation – that “inference to the best explanation” (IBE) incorrectly demands giving hypotheses extra credit for their potential explanatory qualities beyond the credit they already deserve for their predictive successes. This paper argues against one common strategy for responding to this thought – that is, for trying to fit IBE within a Bayesian framework. That strategy argues that a hypothesis’ explanatory quality (its “loveliness”) contributes either to its prior probability or (...) to its likelihood. This paper argues that this strategy fails because it must give different treatments to two hypotheses that are unlovely for the very same reason. The strategy therefore loses the insight into scientific reasoning that its reconstruction in terms of IBE is supposed to provide. The paper then provides a Bayesian account of the confirmatory role of explanatoriness that represents explanatory quality as having an impact in the same place for two hypotheses that are unlovely for the very same reason. This approach works by “putting explanation back into IBE” – that is, by invoking hypotheses that refer explicitly to scientific explanation and by invoking the agent's background opinions regarding the kind of explanation that the evidence is liable to have. On this approach, there is no list of “explanatory virtues” the possession of which always helps to make an explanation better. Rather, for different facts, there are different characteristics that our background knowledge of other explanations gives us some reason to expect the given fact's explanation to possess. (shrink)

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)

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)

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)

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)

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition’s truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if (...) the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. (shrink)

Hempel and Giere contend that the existence of provisos poses grave difficulties for any regularity account of physical law. However, Hempel and Giere rely upon a mistaken conception of the way in which statements acquire their content. By correcting this mistake, I remove the problem Hempel and Giere identify but reveal a different problem that provisos pose for a regularity account — indeed, for any account of physical law according to which the state of affairs described by a law-statement presupposes (...) a Humean regularity. These considerations suggest a normative analysis of law-statements. On this view, law-statements are not distinguished from accidental generalizations by the kind of Humean regularities they describe because a law-statement need not describe any Humean regularity. Rather, a law-statement says that in certain contexts, one ought to regard the assertion of a given type of claim, if made with justification, as a proper way to justify a claim of a certain other kind. (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)

This paper explores whether there is any relation between mathematical proofs that specify the grounds of the theorem being proved and mathematical proofs that explain why the theorem obtains. The paper argues that a mathematical fact’s grounds do not, simply by virtue of grounding it, thereby explain why that fact obtains. It argues that oftentimes, a proof specifying a mathematical fact’s grounds fails to explain why that fact obtains whereas any explanation of the fact does not specify its ground. The (...) paper offers several examples from mathematical practice to illustrate these points. These examples suggest several reasons why explaining and grounding tend to come apart, including that explanatory proofs need not exhibit purity, tend not to be brute force, and often unify separate cases by identifying common reasons behind them even when those cases have distinct grounds. The paper sketches an account of what makes a proof explanatory and uses that account to defend the morals drawn from the examples already given. (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)

Explanation in mathematics has recently attracted increased attention from philosophers. The central issue is taken to be how to distinguish between two types of mathematical proofs: those that explain why what they prove is true and those that merely prove theorems without explaining why they are true. This way of framing the issue neglects the possibility of mathematical explanations that are not proofs at all. This paper addresses what it would take for a non-proof to explain. The paper focuses on (...) a particular example of an explanatory non-proof: an argument that mathematicians regard as explaining why a given theorem holds regarding the derivative of an infinite sum of differentiable functions. The paper contrasts this explanatory non-proof with various non-explanatory proofs of the same theorem. The paper offers an account of what makes the given non-proof explanatory. This account is motivated by investigating the difficulties that arise when we try to extend Mark Steiner’s influential account of explanatory proofs to cover this explanatory non-proof. (shrink)

Fine and Rosen have argued that normative necessity is distinct from and weaker than metaphysical necessity. The first aim of this paper is to specify what it would take for this view to be true—that is, what normative necessity would have to be like. The author argues that in order for normative necessity to be weaker than metaphysical necessity, the metaphysical necessities must all be preserved under every counterfactual antecedent with which they are all collectively logically consistent—even when their preservation (...) requires that a normative necessity fail to be preserved. By exhibiting some examples that fail to display this pattern of counterfactual invariance, the author argues against the view that normative necessity is weaker than metaphysical necessity. To give this argument is the second aim of this paper. (shrink)

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)

A conservation law in physics can be either a constraint on the kinds of interaction there could be or a coincidence of the kinds of interactions there actually are. This is an important, unjustly neglected distinction. Only if a conservation law constrains the possible kinds of interaction can a derivation from it constitute a scientific explanation despite failing to describe the causal/mechanical details behind the result derived. This conception of the relation between “bottom-up” scientific explanations and one kind of “top-down” (...) scientific explanation is motivated by several examples from classical and modern physics. (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.

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.

Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 714-719, November 2019.

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.

In “Tense and Reality”, Kit Fine () proposed a novel way to think about realism about tense in the metaphysics of time. In particular, he explored two non-standard forms of realism about tense, arguing that they are to be preferred over standard forms of realism. In the process of defending his own preferred view, fragmentalism, he proposed a fragmentalist interpretation of the special theory of relativity, which will be our focus in this paper. After presenting Fine's position, we will raise (...) a problem for his fragmentalist interpretation of STR. We will argue that Fine's view is in tension with the proper explanation of why various facts obtain. We will then consider whether similar considerations also speak against fragmentalism in domains other than STR, notably fragmentalism about tense. (shrink)

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent (...) accounts Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations. (shrink)

This paper argues that in at least some cases, one proof of a given theorem is deeper than another by virtue of supplying a deeper explanation of the theorem — that is, a deeper account of why the theorem holds. There are cases of scientific depth that also involve a common abstract structure explaining a similarity between two otherwise unrelated phenomena, making their similarity no coincidence and purchasing depth by answering why questions that separate, dissimilar explanations of the two phenomena (...) cannot correctly answer. The connections between explanation, depth, unification, power, and coincidence in mathematics and science are compared. (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)

Several philosophers have suggested that some scientific explanations work not by virtue of describing aspects of the world’s causal history and relations, but rather by citing mathematical facts. This paper investigates what mathematical facts could be in order for them to figure in such “distinctively mathematical” scientific explanations. For “distinctively mathematical explanations” to be explanations by constraint, mathematical language cannot operate in science as representationalism or platonism describes. It can operate as Aristotelian realism describes. That is because Aristotelian realism enables (...) mathematics to apply to the physical world without a morphism’s mediation. (shrink)

Humean accounts of natural law have long been charged with being unable to account for the laws’ explanatory power in science. One form of this objection is to charge Humean accounts with explanatory circularity: a fact in the Humean mosaic helps to explain why some regularity is a law (first premise), but that law, in turn, helps to explain why that mosaic fact holds (second premise). To this objection, Humeans have replied that the explanation in the first premise is metaphysical (...) whereas the explanation in the second premise is scientific, so (since these two varieties of explanation operate very differently) the two explanations cannot be chained together to yield explanatory circularity. This paper presents a new circularity argument that avoids this objection because both explanations in the premises are metaphysical. The new circularity argument also avoids the objection that the contrasts at the point where the two explanations are chained together fail to line up properly. The upshot is to leave the Humean account of law with two unattractive options: to regard scientific explanation under natural law as not constituting genuine explanation at all or to regard the Humean account as involving a vicious explanatory circularity. (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)

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.