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

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

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.

. A typical textbook explanation of a rocket’s motion when its engine is fired appeals to momentum conservation: the rocket accelerates forward because its exhaust accelerates rearward and the system’s momentum must be conserved. This paper examines how this explanation works, considering three challenges it faces. First, the explanation does not proceed by describing the forces causing the rocket’s motion. Second, the rocket’s motion has a causal-mechanical explanation involving those forces. Third, if momentum conservation and the rearward motion of the (...) rocket’s exhaust explain why the rocket accelerates forward, then presumably momentum conservation and the rocket’s forward motion likewise explain why the rocket emits exhaust rearward. Explanatory circularity threatens to follow from this pair of explanations. This paper examines how the conservation-law explanation works and how it is compatible with the causal-mechanical explanation. The paper argues that these two explanations do not explain precisely the same fact relative to the same contrast class. The paper interprets the two conservation-law explanations as non-causal and argues that they yield no explanatory circularity. (shrink)

Sober 2011 argues that, contrary to Hume, some causal statements can be known a priori to be true—notably, some ‘would promote’ statements figuring in causal models of natural selection. We find Sober's argument unconvincing. We regard the Humean thesis as denying that causal explanations contain any a priori knowable statements specifying certain features of events to be causally relevant. We argue that not every ‘would promote’ statement is genuinely causal, and we suggest that Sober has not shown that his examples (...) of ‘would promote’ statements manage to achieve a priori status without sacrificing their causal character. (shrink)

After reviewing several failed arguments that laws cannot change, I use the laws' special relation to counterfactuals to show how temporary laws would have to differ from eternal but time-dependent laws. Then I argue that temporary laws are impossible and that neither Lewis's nor Armstrong's analyses of law nicely accounts for the laws' immutability. *Received September 2006; revised September 2007. ‡Many thanks to John Roberts and John Carroll for valuable comments on earlier drafts, as well as to several anonymous referees (...) for their good suggestions. †To contact the author, please write to: Department of Philosophy, University of North Carolina, CB #3125, Caldwell Hall, Chapel Hill, NC 27599-3125; e-mail: [email protected]. (shrink)

In a notable article entitled “What is the Theory of Relativity?” written at the request of The Times and published in its November 28, 1919 edition, Albert Einstein famously distinguished “theories of principle” from “constructive theories.” Einstein placed relativity theory among the principle theories. His distinction has recently received increased attention, especially as it relates to scientific explanation. In particular, there has been considerable discussion of how to explain why there obtain the Lorentz transformations as well as of how to (...) account for the Lorentz covariance of the dynamical laws. Some .. (shrink)

Roche and Sober have offered a new argument for the view that a hypothesis H is not confirmed by its capacity to explain some observation O. Their argument purports to work by showing that O screens H off from the fact that H would explain O. This paper offers several objections to this argument. Firstly, the screening-off test cannot identify whatever evidential contribution Hs explanatoriness may make. Secondly, that H would explain O may be logically necessary, eluding the screening-off test. (...) Thirdly, the test cannot detect an important difference that Hs explanatoriness often makes to Hs confirmation. (shrink)

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the counterfactual conditionals (...) in an unfamiliar foundational role. (shrink)

Myrvold (2003) has proposed an attractive Bayesian account of why theories that unify phenomena tend to derive greater epistemic support from those phenomena than do theories that fail to unify them. It is argued, however, that "unification" in Myrvold's sense is both too easy and too difficult for theories to achieve. Myrvold's account fails to capture what it is that makes unification sometimes count in a theory's favor.

Why should science be so interested in discovering whether p is a law over and above whether p is true? The answer may involve the laws' relation to counterfactuals: p is a law iff p would still have obtained under any counterfactual supposition that is consistent with the laws. But unless we already understand why science is especially concerned with the laws, we cannot explain why science is especially interested in what would have happened under those counterfactual suppositions consistent with (...) the laws. It is argued that the laws form the only non-trivially "stable" set, where "stability" is invariance under a certain range of counterfactual suppositions not itself defined by reference to the laws. It is then explained why science should be so interested in identifying a non-trivially "stable" set: because of stability's relation to the best set of "inductive strategies". (shrink)

The merits of David Lewis’s Best System Account of natural law are frequently debated. But to my knowledge, the prospects for extending the BSA to cover meta-laws have never been examined. I shall identify two obstacles facing the most natural way of extending the BSA to cover meta-laws. The BSA’s fans should consider how these obstacles are to be overcome. Meta-laws are laws about laws. For example, Einstein’s special theory of relativity incorporates a meta-law: The content of the [special] relativity (...) theory can … be summarized in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations. [The special theory of relativity] is not a theory in the usual sense but is better regarded as a second-level theory, or a theory of theories that constrains first-level theories. The principle of relativity is an example of a symmetry principle: a principle requiring that the first-order laws be unchanged under a given transformation. Long before Einstein proposed the principle of relativity, other spacetime symmetries were widely believed to be meta-laws: that the first-order laws are covariant under arbitrary spatial displacements, temporal displacements and spatial rotations. These spacetime symmetries require the laws to treat all spatial locations and directions alike and all moments alike. For instance, symmetry under temporal displacements rules out a fundamental force law specifying that a given force declines with the inverse-square of the distance before a given moment but with the inverse-cube of the distance at and after that moment. Wigner characterizes such a symmetry principle as ‘a superprinciple which is in …. (shrink)

Wilson derives various broad philosophical morals from the scientific role played by the Principle of Virtual Work. He argues roughly that PVW conditionals cannot be understood in terms of things as large as possible worlds; that PVW conditionals are peculiar and so cannot be accommodated by general accounts of counterfactuals, thereby reflecting the piecemeal character of scientific practice and standing at odds with the one-size-fits-all approach of “analytic metaphysicians”; and that PVW counterfactuals are not made true partly by natural laws. (...) I distinguish, elaborate and critically examine various arguments for these morals suggested by the PVW and Wilson’s text, looking especially at what makes a displacement “virtual” and the operation of the conditionals that the PVW takes to express necessary and sufficient conditions for equilibrium. Ultimately, I do not find the PVW to be especially well suited to support Wilson’s morals; some of these arguments fail, whereas others arise from general considerations rather than having to appeal to anything like the PVW. (shrink)

Scientific realism is the view that one can be justified in believing, of some theory about unobservable entities, that the entities it posits are real and accurately described by the theory, in the same sense as one can be justified in believing that the theory’s empirical predictions are accurate, and that so to believe is what it means for a scientist to “accept” that theory, because the goal of science is to describe reality, even its unobservable features. The first part (...) is an epistemic claim, whereas the second concerns the rational reconstruction of scientific practice. Together they suggest that evidence justifying scientific acceptance of a theory justifies belief that the unobservable entities it posits are real and as the theory purports them to be. Anti-realism denies ; it holds that claims about unobservables are either unjustified or justified in a different sense from predictions of observations. It also denies ; it maintains that in her scientific work, as rationally reconstructed, a scientist who accepts a claim about unobservables believes that it yields accurate predictions of observables, not that it describes unobservables. (shrink)

A widespread perspective describes emotions as distinct categories bridged by fuzzy boundaries, indicating that emotions are distinct and dimensional at the same time. Theoretical and methodological approaches to this perspective still need further development. We conceptualize emotions as overlapping networks of causal relationships between emotion components—networks representing distinct emotions share components with and relate to each other. To investigate this conceptualization, we introduce network analysis to emotion research and apply it to the reanalysis of a data set on multiple positive (...) emotions. Specifically, we describe the estimation of networks from data, and the detection of overlapping communities of nodes in these networks. The network perspective has implications for the understanding of distinct emotions, their co-occurrence, and their measurement. (shrink)

Glymour, Scheines, Spirtes, and Kelly argue for ‘Spearman's Principle’: one should (ceteris paribus) favour the theory whose ‘free parameters’ need assume no particular values for the theory to save the ‘constraints’ holding of the phenomena. I argue that the rationale they give for Spearman's Principle fails, but that (contra Cartwright) Spearman's Principle cannot be made to favour either of two theories depending on how they are expressed. I examine how one must motivate the demand for a scientific explanation of a (...) parameter's value and how one justifies believing that a constraint should be explained independent of any parameter's particular value. (shrink)

We say a countable model ������ has a 0-basis if the types realized in ������ are uniformly computable. We say ������ has a (d-)decidable copy if there exists a model ������ ≅ ������ such that the elementary diagram of ������ is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model ������ with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0' be any low₂ degree. We show that there exists a homogeneous (...) model ������ with a 0-basis but no d-decidable copy. A degree d is 0-basis homogeneous bounding if any homogenous ������ with a 0-basis has a d-decidable copy. In previous work, we showed that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding $\Delta _{2}^{0}$ degrees. (shrink)

Precise measurements of well-being would be of profound societal importance. Yet, the sceptical worry that we cannot use social science instruments and tests to measure well-being is widely discussed by philosophers and scientists. A recent and interesting philosophical argument has pointed to the psychometric procedures of construct validation to address this sceptical worry. The argument has proposed that these procedures could warrant confidence in our ability to measure well-being. The present paper evaluates whether this type of argument succeeds. The answer (...) is that it depends on which methodological background assumptions are motivating the sceptical worry to begin with. We show this by doing two things. First, we clarify (a) the different types of well-being theories involved in the science of well-being, and (b) the general methodological dimensions of well-being theorising. Second, we apply these distinctions and argue that construct validation is an unsuccessful response to measurement scepticism if this scepticism is motivated by a form of methodological non-naturalism. In the light of this, the overall point of the paper is that philosophers and scientists, when discussing measurement of well-being, should explicate their deeper methodological commitments. We further suggest that making such explicit commitments might present philosophers with a dilemma. (shrink)

Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 739-748, November 2019.

Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such that the elementary (...) diagram of B is d-computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous A with a 0-basis but no decidable copy. We prove that any homogeneous A with a 0'-basis has a low decidable copy. This implies Csima's analogous result for prime models. In the case where all types of the theory T are computable and A is a homogeneous model with a 0-basis, we show A has copies decidable in every nonzero degree. A degree d is 0-homogeneous bounding if any automorphically nontrivial homogeneous A with a 0-basis has a d-decidable copy. We show that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-homogeneous bounding. (shrink)

Supporting children to successfully transition from primary to secondary school is of utmost importance for several reasons, including to prevent future emotional and behavioural problems. Level Up is a novel, UK-based intervention consisting of five online group sessions, straddling the summer holidays, and providing at-risk children and their parents/carers with skills to manage their behaviour, emotions, and relationships to support their transition to secondary school. A prior evaluation of Level Up reported a need to better describe the mechanisms of change. (...) This study therefore evaluated the experiences of children and their parents/carers regarding the facilitators and barriers to engagement and change, and the perceived impact. Fourteen children and 17 parents/carers were interviewed. Identified barriers and facilitators were: (1) Having a safe, supportive, and fun space, (2) Learning through connection, (3) A family approach, (4) Problematic group dynamics, and (5) Connecting through video calls. Perceived impact was described as: (1) Empowering children, (2) Supporting children socially, (3) Supporting parents and carers in their parenting role, and (4) Supporting a successful transition to secondary school. Another theme (5) describes some families’ experiences of limited impact. These findings can be used to better understand how to support children in their school transition. (shrink)