Consider the following explanation: (1) George took his umbrella because it was just about to rain. This is an explanation of a quite distinctive sort. It is profoundly different from the sort of explanation we might use to explain, say, the movements of a bouncing ball or the gradual rise of the tide on a beach. Unlike these other types of explanations, it explains an agent’s behavior by describing the agent’s own _reasons_ for performing that behavior. Explanations (...) that work in this way have a number of distinctive and important properties, and we will refer to them here as _reason explanations_. Looking at the use of reason explanations with a philosophical eye, one is apt to experience a certain puzzlement. One wants to know precisely what makes a given reason explanation true or false. So, for example, the explanation given above seems to be saying that George’s reason for taking his umbrella was that it was just about to rain. But what exactly makes it the case that this is George’s reason? Does he have to actually be. (shrink)

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)

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)

Offering a new approach to scientific explanation, this book focuses initially on the explaining act itself.

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)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a (...) sense an ultimate form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s (...) erotetic account are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

According to a causal model of explanation, we explain phenomena by giving their causes or, where the phenomena are themselves causal regularities, we explain them by giving a mechanism linking cause and effect. If we explain why smoking causes cancer, we do not give the cause of this causal connection, but we do give the causal mechanism that makes it. The claim that to explain is to give a cause is not only natural and plausible, but it also avoids (...) many of the objections to other accounts of explanation, such as the views that to explain is to give a reason to believe the phenomenon occurred, to somehow make the phenomenon familiar, or to give a Deductive-Nomological argument. Unlike the reason for belief account, a causal model makes a clear distinction between understanding why a phenomenon occurs and merely knowing that it does, and the model does so in a way that makes understanding unmysterious and objective. Understanding is not some sort of super-knowledge, but simply more knowledge: knowledge of the phenomenon and knowledge of its causal history. A causal model makes it clear how something can explain without itself being explained, and so avoids the regress of whys, since we can know a phenomenon's cause without knowing the cause of the cause. It also accounts for legitimate self-evidencing explanations, explanations where the phenomenon is an essential part of the evidence that the explanation is correct, so the explanation can not supply a non-circular reason for believing the phenomenon occurred. There is no barrier to knowing a cause through its effects and also knowing that it is their cause. The speed of recession of a star explains its observed red-shift, even though the shift is an essential part of the evidence for its speed of recession. The model also avoids the most serious objection to the familiarity view, which is that some phenomena are familiar yet not understood, since a phenomenon can be perfectly familiar, such as the blueness of the sky or the fact that the same side of the moon always faces the earth, even if we do not know its cause. Finally, a causal model avoids many of the objections to the Deductive-Nomological model. Ordinary explanations do not have to meet the requirements of the Deductive-Nomological model, because one does not need to give a law to give a cause, and one does not need to know a law to have good reason to believe that a cause is a cause. As for the notorious over-permissiveness of the Deductive-Nomological model, the reason recession explains red-shift but not conversely, is simply that causes explain effects but not conversely, and the reason a conjunction of laws does not explain its conjuncts is that conjunctions do not cause their conjuncts. (shrink)

Studdert-Kennedy, Gerald, Evidence and Explanation in Social Science. ... Kauffman, Stuart, "Articulation of Parts Explanation in Biology and the Rational ...

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I (...) discuss potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

In this paper I examine Chalmers and Jackson’s defence of the a priori entailment thesis, that is, the claim that microphysical truths a priori entail ordinary non-phenomenal truths such as ‘water covers 60% of the Earth surface’, which they use as a premise for an argument against the possibility of a reductive explanation of consciousness. Their argument relies on a certain view about the possession conditions of macroscopic concepts such as WATER, known as ascriptivism. In the paper I distinguish (...) two versions of ascriptivism: reductive versus non-reductive ascriptivism. According to reductive ascriptivism, competent users of a concept have the ability to infer truths involving such concept from lower-level truths, whereas according to non-reductive ascriptivism, all that is required in order to be a competent user of a concept is to be able to infer truths involving that concept from other truths, which need not be lower-level truths. I argue, first, that the a priori entailment thesis is committed to reductive ascriptivism, and secondly, that reductive ascriptivism is problematic because it trivializes the notion of a priori knowledge. Therefore, I conclude that Chalmers and Jackson have not presented a convincing case for the claim that microphysical truths entail ordinary non-phenomenal truths a priori, especially when we understand this claim in the sense that is relevant for their argument against the possibility of a reductive explanation of consciousness. (shrink)

On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual 'If it had been the case that p, then it would have been the case that q' is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the (...) paper is which weights attach to different respects of similarity. I start by considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details. (shrink)

The connection between understanding and explanation has recently been of interest to philosophers. Inglis and Mejía-Ramos (Synthese, 2019) propose that within mathematics, we should accept a functional account of explanation that characterizes explanations as those things that produce understanding. In this paper, I start with the assumption that this view of mathematical explanation is correct and consider what we can consequently learn about mathematical explanation. I argue that this view of explanation suggests that we should (...) shift the question of explanation away from why-questions and towards a “what’s going on here” question. Additionally, I argue that when we recognize the connection between understanding and explanation we naturally see how more than just proof can be explanatory. I expand this point by detailing how definitions and diagrams can be explanatory. In all, we see that when we take seriously the connection between understanding and explanation, we get a better sense of how explanation arises within mathematics. (shrink)

Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it's necessary that if the grounds and the grounded both obtain, then the grounds ground the grounded. The negative part of this essay exploits empirical and provably nonparadoxical self-reference to prove conclusively that even immediate full grounding isn't an internal relation in this sense. The positive, second part of this essay uses the notion of a “completely satisfactory explanation” to shed light (...) on the logic of ground in the presence of self-reference. This allows us to develop a satisfactory logic of ground and recover a sense in which grounding is still an internal relation. (shrink)

Craver claims that mechanistic explanation is ontic, while Bechtel claims that it is epistemic. While this distinction between ontic and epistemic explanation originates with Salmon, the ideas have changed in the modern debate on mechanistic explanation, where the frame of the debate is changing. I will explore what Bechtel and Craver’s claims mean, and argue that good mechanistic explanations must satisfy both ontic and epistemic normative constraints on what is a good explanation. I will argue for (...) ontic constraints by drawing on Craver’s work in Sect. 2.1, and argue for epistemic constraints by drawing on Bechtel’s work in Sect. 2.2. Along the way, I will argue that Bechtel and Craver actually agree with this claim. I argue that we should not take either kind of constraints to be fundamental, in Sect. 3, and close in Sect. 4 by considering what remains at stake in making a distinction between ontic and epistemic constraints on mechanistic explanation. I suggest that we should not concentrate on either kind of constraint, to the neglect of the other, arguing for the importance of seeing the relationship as one of integration. (shrink)

Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s (...) mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains. (shrink)

This article examines three candidate cases of non-causal explanation in computational neuroscience. I argue that there are instances of efficient coding explanation that are strongly analogous to examples of non-causal explanation in physics and biology, as presented by Batterman, Woodward, and Lange. By integrating Lange’s and Woodward’s accounts, I offer a new way to elucidate the distinction between causal and non-causal explanation, and to address concerns about the explanatory sufficiency of non-mechanistic models in neuroscience. I also (...) use this framework to shed light on the dispute over the interpretation of dynamical models of the brain. _1_ Introduction _1.1_ Efficient coding explanation in computational neuroscience _1.2_ Defining non-causal explanation _2_ Case I: Hybrid Computation _3_ Case II: The Gabor Model Revisited _4_ Case III: A Dynamical Model of Prefrontal Cortex _4.1_ A new explanation of context-dependent computation _4.2_ Causal or non-causal? _5_ Causal and Non-causal: Does the Difference Matter? (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses (...) on cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

This volume distinguishes between two main traditions in the philosophy of science - the aristotelian, with its stress on explanation in terms of purpose and intentionality, and the galilean, which takes causal explanation as primary. It then traces the complex history of these competing traditions as they are manifested in such movements as positivism, idealism, Marxism and contemporary linguistic analysis. Hempels's theory of scientific explanation, the claims of cybernetics the rise of an analytic philosophy of action and (...) the revival of hermenuetics are all discussed. The volume also deals with causal explanation, intentionality and teleological explanation, and explanation in history and the social sciences. The author concludes that explanation of human actions cannot be reduced to simple causality, and discusses the implications of this conclusion for the disciplines of history and sociology. (shrink)

This volume, the second in the Springer series Philosophy of Science in a European Perspective, contains selected papers from the workshops organised by the ESF Research Networking Programme PSE (The Philosophy of Science in a European Perspective) in 2009. Five general topics are addressed: 1. Formal Methods in the Philosophy of Science; 2. Philosophy of the Natural and Life Sciences; 3. Philosophy of the Cultural and Social Sciences; 4. Philosophy of the Physical Sciences; 5. History of the Philosophy of Science. (...) This volume is accordingly divided in five sections, each section containing papers coming from the meetings focussing on one of these five themes. However, these sections are not completely independent and detached from each other. For example, an important connecting thread running through a substantial number of papers in this volume is the concept of probability: probability plays a central role in present-day discussions in formal epistemology, in the philosophy of the physical sciences, and in general methodological debates---it is central in discussions concerning explanation, prediction and confirmation. The volume thus also attempts to represent the intellectual exchange between the various fields in the philosophy of science that was central in the ESF workshops. (shrink)

Philosophers of mathematics commonly distinguish between explanatory and non-explanatory proofs. An important subclass of mathematical proofs are proofs by induction. Are they explanatory? This paper addresses the question, based on general principles about explanation. First, a recent argument for a negative answer is discussed and rebutted. Second, a case is made for a qualified positive take on the issue.

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)

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

Several philosophers have attempted to identify how it is that “social structure” can explain phenomena. Some of the most prominent of these philosophers have posited that what we call “social structures” are sets of constraints acting on individuals that guide and regulate their actions, either coercing agents into making choices, raising the probability that they will make certain choices, or making those actions reasonable or rational. Others have argued that social structures are factors that “program” for social outcomes. Examining historical (...) work in quantitative sociology, I argue that both views are too narrow. I present Peter Blau’s distinction between microstructure and macrostructure, articulate their differences, and then argue that for some social scientific questions, macrostructural explanations are better positioned to supply answers. Macrostructural explanations abstract away from the relata between individuals and so do not involve constraints. Further, macrostructural explanations draw on facts about population structure, and so do not fit the form of programming explanations. I motivate this category of explanation by considering social scientific research that comports with macrostructural explanation. (shrink)

Recently, Kit Fine's (1994) view that modal truths aretrue in virtue of,grounded in, orexplained byessentialist truths has been under attack. In what follows we offer two responses to the wave of criticism against his view. While the first response is pretty straightforward, the second is based on the distinction between, what we call,Reductive Finean EssentialismandNon-Reductive Finean Essentialism. Engaging the work of Bob Hale onNon-Reductive Finean Essentialism, we aim to show that the arguments against Fine's view are unconvincing, while we acknowledge (...) the presence of a deep standoff between the two views. (shrink)

This essay analyzes and develops recent views about explanation in biology. Philosophers of biology have parted with the received deductive-nomological model of scientific explanation primarily by attempting to capture actual biological theorizing and practice. This includes an endorsement of different kinds of explanation (e.g., mathematical and causal-mechanistic), a joint study of discovery and explanation, and an abandonment of models of theory reduction in favor of accounts of explanatory reduction. Of particular current interest are philosophical accounts of (...) complex explanations that appeal to different levels of organismal organization and use contributions from different biological disciplines. The essay lays out one model that views explanatory integration across different disciplines as being structured by scientific problems. I emphasize the philosophical need to take the explanatory aims pursued by different groups of scientists into account, as explanatory aims determine whether different explanations are competing or complementary and govern the dynamics of scientific practice, including interdisciplinary research. I distinguish different kinds of pluralism that philosophers have endorsed in the context of explanation in biology, and draw several implications for science education, especially the need to teach science as an interdisciplinary and dynamic practice guided by scientific problems and explanatory aims. (shrink)

Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introduction 2Why I (...) Am Not a Proof Chauvinist 2.1Proof chauvinism and mathematical practice 2.2Proof chauvinism and philosophy 3An Example: Galois Theory and Explanatory Proof 4Conclusion. (shrink)

According to a number of recent philosophers, knowledge has an intimate relationship with rationality. Some philosophers hold, in particular, that rational agents do things for good motivating reasons, and that p can be one’s motivating reason for -ing (acting/believing/fearing/etc.) only if one knows that p. This paper argues against this view and in favor of the view that p cannot be one’s motivating reason for -ing—in the relevant sense—unless there is an appropriate explanatory connection between the fact that p and (...) one’s -ing. I argue that this view offers a better account of the cases alleged to support the knowledge view. (shrink)

This paper contributes to the recently renewed debate over methodological individualism (MI) by carefully sorting out various individualist claims and by making use of recent work on reduction and explanation outside the social sciences. My major focus is on individualist claims about reduction and explanation. I argue that reductionist versions of MI fail for much the same reasons that mental predicates cannot be reduced to physical predicates and that attempts to establish reducibility by weakening the requirements for reduction (...) also fail. I consider and reject a number of explanatory theses, among them the claims that any adequate theory must refer only to individuals and that individualist theory suffices to explain fully. The latter claim, I argue, is not entailed by the supervenience of social facts on individual facts. Lastly, I argue that there is one individualist restriction on explanation which is far more plausible and significant than one would initially suspect. (shrink)

Familiar accounts have it that one explains thoughts or actions by showing them to be rational. It is common to find that the standards of rationality presupposed in these accounts are drawn from what would be thought to be aprioristic sources. I advance an argument to show this must be mistaken. But, recent work in epistemology and on rationality takes a less aprioristic approach to such standards. Does the new (psychological or cognitive scientific) realism in accounts of rationality itself significantly (...) improve the prospects for unproblematic forms of rationalizing explanation? Do earlier misgivings about rationalizing explanation ring hollow when the rationality to be attributed is "naturalized"? Answer: while explanation in terms of naturalized rationality would be free of one fatal flaw possessed by explanation in terms of rationality understood in the traditional fashion, it would yet have parallel flaws. (shrink)

I discuss Aristotle's anomalous terminology in Physics A.1 (involving "universals" and "particulars") and its coherence with Aristotle's notion of scientific demonstration.

Analogies to machines are commonplace in the life sciences, especially in cellular and molecular biology — they shape conceptions of phenomena and expectations about how they are to be explained. This paper offers a framework for thinking about such analogies. The guiding idea is that machine-like systems are especially amenable to decompositional explanation, i.e., to analyses that tease apart underlying components and attend to their structural features and interrelations. I argue that for decomposition to succeed a system must exhibit (...) causal orderliness, which I explicate in terms of differentiation among parts and the significance of local relations. I also discuss what makes a model depict its target as machine-like, suggesting that a key issue is the degree of detail with respect to the target’s parts and their interrelations. (shrink)

D. Lewis proposed the reformed conditional analysis of disposition to handle Martin's influential counterexamples to the simple counterfactual analysis. Some philosophers, however, argue that the mere fact that the reformed conditional analysis of disposition can handle Martin's counterexamples should not be regarded as a reason to prefer the reformed conditional analysis to the simple analysis. In this paper, I argue that the reformed version should be preferred not because it can handle Martin's counterexamples but because there are other counterexamples to (...) the simple conditional analysis. (shrink)

ABSTRACT Proponents of mechanistic explanation have recently suggested that all explanation in the cognitive sciences is mechanistic, even functional explanation. This last claim is surprising, for functional explanation has traditionally been conceived as autonomous from the structural details that mechanistic explanations emphasize. I argue that functional explanation remains autonomous from mechanistic explanation, but not for reasons commonly associated with the phenomenon of multiple realizability. 1Introduction 2Mechanistic Explanation: A Quick Primer 3Functional Explanation: An (...) Example 4Autonomy as Lack of Constraint 5The Price of Autonomy 6Another Argument against Autonomy 7Conclusion: Autonomy and Multiple Realization. (shrink)

Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore (...) argue that the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness. (shrink)

PurposeIn this article, we aim to present and defend a contextual approach to mathematical explanation.MethodTo do this, we introduce an epistemic reading of mathematical explanation.ResultsThe epistemic reading not only clarifies the link between mathematical explanation and mathematical understanding, but also allows us to explicate some contextual factors governing explanation. We then show how several accounts of mathematical explanation can be read in this approach.ConclusionThe contextual approach defended here clears up the notion of explanation and (...) pushes us towards a pluralist vision on mathematical explanation. (shrink)

It is argued that once biological systems reach a certain level of complexity, mechanistic explanations provide an inadequate account of many relevant phenomena. In this article, I evaluate such claims with respect to a representative programme in systems biological research: the study of regulatory networks within single-celled organisms. I argue that these networks are amenable to mechanistic philosophy without need to appeal to some alternate form of explanation. In particular, I claim that we can understand the mathematical modelling techniques (...) of systems biologists as part of a broader practice of constructing and evaluating mechanism schemas. This argument is elaborated by considering the case of bacterial chemotactic networks, where some research has been interpreted as explaining phenomena by means of abstract design principles. (shrink)

This paper explores the practice of explanation by status, in which a truth with a certain status is supposed to be explained by its having that status. It first investigates whether such explanations are possible. Having found existing accounts of the practice wanting, it then argues for a novel account of explanation by status as empty-base explanation. The latter notion captures a certain limiting case of ordinary explanation so that according to the empty-base account, explanation (...) by status can be fruitfully understood as a corresponding limiting case of ordinary explanation. One way in which the empty-base account is argued to be superior to other treatments of explanation by status is that it allows for a principled assessment of the possibility of particular kinds of explanation by status. Thus, one result of the present discussion is that explanation by essential status and status as a law are possible, while explanation by merely necessary status is not. (shrink)

Many philosophers and non-philosophers who reflect on the causal antecedents of human action get the impression that no agent can have morally relevant freedom. Call this the ‘non-existence impression.’ The paper aims to understand the (often implicit) reasoning underlying this impression. On the most popular reconstructions, the reasoning relies on the assumption that either an action is the outcome of a chance process, or it is determined by factors that are beyond the agent’s control or which she did not bring (...) about. I argue that arguments based on this premise fail to apply to some possible agents for whom the non-existence impression arises. On the alternative reconstruction I offer, the impression rests on the assumption that free will requires being involved in the ultimate explanation of one’s actions in a novel sense in which nothing can be involved in the ultimate explanation of anything. (shrink)

Lately, philosophers of mathematics have been exploring the notion of mathematical explanation within mathematics. This project is supposed to be analogous to the search for the correct analysis of scientific explanation. I argue here that given the way philosophers have been using “ explanation,” the term is not applicable to mathematics as it is in science.

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to (...) Gauss and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)