Philosophical accounts of scientific explanation are broadly divided into ontic and epistemic views. This paper explores the idea that the lexical ambiguity of the verb to explain and its nominalisation supports an ontic conception of explanation (Salmon 1989; Craver 2007). I analyse one argument which challenges this strategy by criticising the claim that explanatory talk is lexically ambiguous (Wright, European Journal of Philosophy of Science 2(3), 375–394, 2012). I propose that the linguistic mechanism of transfer of meaning (Nunberg, Journal of (...) Semantics 12(2), 109–132, 1995) provides a better account of the lexical alternations that figure in the systematic polysemy of explanatory talk, and evaluate the implications of this proposal for the debate between ontic and epistemic conceptions of scientific explanation. (shrink)

We argue that artificial networks are explainable and offer a novel theory of interpretability. Two sets of conceptual questions are prominent in theoretical engagements with artificial neural networks, especially in the context of medical artificial intelligence: Are networks explainable, and if so, what does it mean to explain the output of a network? And what does it mean for a network to be interpretable? We argue that accounts of “explanation” tailored specifically to neural networks have ineffectively reinvented the wheel. In (...) response to, we show how four familiar accounts of explanation apply to neural networks as they would to any scientific phenomenon. We diagnose the confusion about explaining neural networks within the machine learning literature as an equivocation on “explainability,” “understandability” and “interpretability.” To remedy this, we distinguish between these notions, and answer by offering a theory and typology of interpretation in machine learning. Interpretation is something one does to an explanation with the aim of producing another, more understandable, explanation. As with explanation, there are various concepts and methods involved in interpretation: Total or Partial, Global or Local, and Approximative or Isomorphic. Our account of “interpretability” is consistent with uses in the machine learning literature, in keeping with the philosophy of explanation and understanding, and pays special attention to medical artificial intelligence systems. (shrink)

The logical empiricists knew that scientific theories sometimes arise out of the attempt to reconcile or unify two existing theories. They also thought that, at best, old theories would be retained as approximations to their successors. Kuhn lost both insights when he rejected the logical empiricists' formal approach in favor of an exclusively historical and psychological one. But when Putnam tried to restore such ideas he failed to provide them with the historical support they require. An account of revolutionary unifications (...) is defended as reconciling Putnam's realist ideas about methodology with Kuhn's historical approach. (shrink)

I present an argument for the view that laws ground their instances. I then outline two important consequences that follow if we accept the conclusion of this argument. First, the claim that laws ground their instances threatens to undermine a prominent recent attempt to make sense of the explanatory power of Humean laws by distinguishing between metaphysical and scientific explanation. And second, the claim that laws ground their instances gives rise to a novel argument against the view that grounding relations (...) are metaphysically necessary. (shrink)

In this critical notice of Kment's _Modality and Explanatory Reasoning_, we focus on Kment’s arguments for impossible worlds and on a key part of his discussion of the interactions between modality and explanation – the analogy that he draws between scientific and metaphysical explanation.

Models provide scientists with knowledge about target systems. An important group of models are those that are called general. However, what exactly is meant by generality in this context is somewhat unclear. The aim of this paper is to draw out a distinction between two notions of generality that has implications for scientific practice. Some models are general in the sense that they apply to many systems in the world and have many particular targets. Another sense is captured by models (...) that are aimed at understanding the fundamental or underlying dynamics of a phenomenon, as opposed to how it manifests in each particular case. They have non-specific, i.e. generic targets. While both notions of generality and genericness are legitimate and correspond to different aspects of scientific practice, they must be distinguished. Failing to do so obscures the danger of overgeneralisation faced by general models and facilitates the illegitimate use of generic models as general models. This can lead to a reduction of the explanatory and predictive power of both. (shrink)

Invasion biology is a relatively young discipline which is important, interesting and currently in turmoil. Biological invaders can threaten native ecosystems and global biodiversity; they can incur massive economic costs and even introduce diseases. Invasion biologists generally agree that being able to predict when and where an invasion will occur is essential for progress in their field. However, successful predictions of this type remain elusive. This has caused a rift, as some researchers are pessimistic and believe that invasion biology has (...) no future, whereas others are more optimistic and believe that the key to successful prediction is the creation of a general, unified theoretical framework which encompasses all invasion events. Although I agree that there is a future for invasion biology, extensive synthesis is not the way to better predictions. I argue that the causes of invasion phenomena are exceedingly complex and heterogeneous, hence it is impossible to make generalizations over particular events without sacrificing causal detail. However, this causal detail is just what is needed for the specific predictions which the scientists wish to produce. Instead, I show that a limited type of synthesis is a more useful tool for generating successful predictions. An important implication of my view is that it points to a more pluralistic approach to invasion biology, where generalization and prediction are treated as important yet distinct research goals. (shrink)

A hallmark of ecological research is dealing with complexity in the systems under investigation. One strategy is to diminish this complexity by constructing models and theories that are general. Alternatively, ecologists can constrain the scope of their generalizations to particular phenomena or types of systems. However, research employing the second strategy is often met with scathing criticism. I offer a theoretical argument in support of moderate generalizations in ecological research, based on the notions of interdependence and causal heterogeneity and their (...) effect on the trade-off between generality and realism. (shrink)

This paper argues that typical biological species are natural kinds, on a familiar realist understanding of natural kinds—classes of individuals across which certain properties cluster together, in virtue of the causal workings of the world. But the clustering is far from exceptionless. Virtually no properties, or property-combinations, characterize every last member of a typical species—unless they can also appear outside the species. This motivates some to hold that what ties together the members of a species is the ability to interbreed, (...) others that it is common descent. Yet others hold that species are scattered individuals,of which organisms are parts rather than members. But not one of these views absolves us of the need to posit a typical phenotypic profile. Vagueness is here to stay. Some seek to explain the vagueness by saying species are united by “homeostatic property clusters”; but this view collapses into the more familiar realist picture. (shrink)

The aim of the present paper is to understand what the notions of explanation and prediction in contemporary linguistics mean, and to compare various aspects that the notion of explanation encompasses in that domain. The paper is structured around an opposition between three main styles of explanation in linguistics, which I propose to call ‘grammatical’, ‘functional’, and ‘historical’. Most of this paper is a comparison between these different styles of explanations and their relations. A second, more methodological aspect this paper (...) seeks to clarify concerns the extent to which linguistic explanations can be viewed as predictive, rather than merely descriptive, and the problem of whether linguistic explanations ought to be causal, rather than noncausal. I argue that the notion of prediction is equally applicable in linguistics as in other empirical sciences. The extent to which the computational model of generative syntax can be viewed as providing a causal or psychologically realist model of language is more controversial. (shrink)

argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for selecting (...) arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework. (shrink)

Hempel and Oppenheim, in their paper 'The Logic of Explanation', have offered an analysis of the notion of scientific explanation. The present paper advances considerations in the light of which their analysis seems inadequate. In particular, several theorems are proved with roughly the following content: between almost any theory and almost any singular sentence, certain relations of explainability hold.

Various senses in which laws of nature are supposed to be "universal" are distinguished. Conditions designed to capture the content of the more important of these senses are proposed and the relations among these conditions are examined. The status of universality requirements is briefly discussed.

The perennial fear associated with the free will problem is the prospect of hard determinism being true. Unlike prevalent attempts to reject hard determinism by defending compatibilist analyses of freedom and responsibility, this article outlines a pragmatic argument to the effect that we are justified in betting that determinism is false even though we may retain the idea that free will and determinism are incompatible. The basic argument is that as long as we accept that libertarian free will is worth (...) wanting, there is a defensible rationale, given the uncertainty which remains as to whether determinism is true or false, to refrain from acting on hard determinism, and thus to bet that libertarian free will exists. The article closes by discussing two potentially decisive objections to this pragmatic argument. (shrink)

This paper aims to answer the question: what does the realism of laws of nature consist of? To achieve this, in the first part, three philosophical accounts of laws of nature are presented and examined: the universalist, the dispositionalist and the counter-factualist. The presentation and examination focuses on the answer given by each of these accounts to the question: what is a law of nature? Later, in the second part, convergences and divergences between these three accounts are shown. Finally, in (...) the third section, the points of agreement between them are put together to advance the fundamental thesis that encompasses each of these accounts as realist accounts of laws of nature. This thesis, I argue, is at the end the core of the general realist stance on laws of nature that I name “Realism of Laws of Nature”. (shrink)

By reviewing most of the neurobiology of consciousness, this article highlights some major reasons why a successful emulation of the dynamics of human consciousness by artificial intelligence is unlikely. The analysis provided leads to conclude that human consciousness is epigenetically determined and experience and context-dependent at the individual level. It is subject to changes in time that are essentially unpredictable. If cracking the code to human consciousness were possible, the result would most likely have to consist of a temporal pattern (...) code simulating long-distance signal reverberation and de-correlation of all spatial signal contents from temporal signals. In the light of the massive evidence for complex interactions between implicit (non-conscious) and explicit (conscious) contents of representation, the code would have to be capable of making implicit (non-conscious) processes explicit. It would have to be capable of a progressively less and less arbitrary selection of temporal activity patterns in a continuously developing neural network structure identical to that of the human brain, from the synaptic level to that of higher cognitive functions. The code’s activation thresholds would depend on specific temporal signal coincidence probabilities, vary considerably with time and across individual experience data, and would therefore require dynamically adaptive computations capable of emulating the properties of individual human experience. No known machine or neural network learning approach has such potential. (shrink)

It is a traditional empiricist doctrine that natural laws are universal truths. In order to overcome the obvious difficulties with this equation most empiricists qualify it by proposing to equate laws with universal truths that play a certain role, or have a certain function, within the larger scientific enterprise. This view is examined in detail and rejected; it fails to account for a variety of features that laws are acknowledged to have. An alternative view is advanced in which laws are (...) expressed by singular statements of fact describing the relationship between universal properties and magnitudes. (shrink)

Inference to the Best Explanation is usually employed in the Scientific Realism debates. As far as particular scientific theories are concerned, its most ready usage seems to be that of a theory of confirmation. There are however more uses of IBE, namely as an epistemological theory of testimony and as a means of categorising and justifying the sources of evidence. In this paper, I will present, develop and exemplify IBE as a theory of the quality of evidence - taking examples (...) from medicine and showing that IBE can thereby provide the epistemological underpinning and justify the criteria of grading quality of mechanistic evidence that have been recently provided in the Clarke et al. paper on how evidence of medical mechanisms is to be construed alongside population studies. (shrink)

Philosophy of science was once a much more socially engaged endeavor, and can be so again. After a look back at philosophy of science in the 1930s-1950s, I turn to discuss the current potential for returning to a more engaged philosophy of science. Although philosophers of science have much to offer scientists and the public, I am skeptical that much can be gained by philosophers importing off-the-shelf discussions from philosophy of science to science and society. Such efforts will likely look (...) like efforts to do applied ethics by merely applying ethical theories to particular contexts and problems. While some insight can be gained by these kinds of endeavors, the most interesting and pressing problems for the actual practitioners and users of science are rarely addressed. Instead, I recommend that philosophers of science engage seriously and regularly with scientists and/or the users of science in order to gain an understanding of the conceptual issues on the ground. From such engagement, flaws in the traditional philosophical frameworks, and how such flaws can be remedied, become apparent. Serious engagement with the contexts of science thus provides the most fruit for philosophy of science per se and for the practitioners whom the philosophers aim to assist. And if one focuses on contexts where science has its most social relevance, these efforts can help to provide the thing that philosophy of science now lacks: a full-bodied philosophy of science in society. (shrink)

Individuals are often the subject of generalizations of various special sciences. The traditional argument is that there can't be laws about such individuals, since the law statements would have to contain local predicates. Marc Lange argues that, despite local predication, there can be laws about individuals. This paper argues, on the contrary, that there can be no such laws – not because of local predication, but because the laws would discriminate among material systems on non-qualitative grounds. I rely on the (...) principle that qualitatively identical systems under one set of laws must evolve in the same manner. If there could be laws about individuals, nothing would guarantee that the principle is satisfied. My argument is illustrated by a thought experiment inspired by Strawson's massive reduplication argument. (shrink)

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws of nature. (...) On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

One of the main challenges confronting Humean accounts of natural law is that Humean laws appear to be unable to play the explanatory role of laws in scientific practice. The worry is roughly that if the laws are just regularities in the particular matters of fact (as the Humean would have it), then they cannot also explain the particular matters of fact, on pain of circularity. Loewer (2012) has defended Humeanism, arguing that this worry only arises if we fail to (...) distinguish between scientific and metaphysical explanations. However, Lange (2013, 2018) has argued that scientific and metaphysical explanations are linked by a transitivity principle, which would undercut Loewer's defense and re-ignite the circularity worry for the Humean. I argue here that the Humean has antecedent reasons to doubt that there are any systematic connections between scientific and metaphysical explanations. The reason is that the Humean should think that scientific and metaphysical explanation have disparate aims, and therefore that neither form of explanation is beholden to the other in its pronouncements about what explains what. Consequently, the Humean has every reason to doubt that Lange's transitivity principle obtains. (shrink)

Explanations in genetics have intriguing aspects to both biologists and philosophers, and there is no account that satisfactorily elucidates such explanations. The aim of this article is to analyze the kind of explanations usually given in Classical (Transmission) Genetics (CG) and to present in detail the application of an account of explanation as ampliative, specialized nomological embedding to elucidate the such explanations. First, we present explanations in CG in the classical format of inferences with the explanans as the premises and (...) the explanandum as the conclusion and compare them with explanations in other paradigmatic explanatory fields such as Classical Mechanics. Second, we summarize the main aspects discussed in the literature with regard the peculiarities of genetic explanations. Third, we introduce the account of scientific explanation as ampliative, specialized nomological embedding making use of Sneedian structuralism, in particular the notions of theory-net, fundamental law or guiding principle, specialization, and special laws. Finally, we apply this account to the case of CG and show that this analysis sheds light to the intriguing aspects of genetic explanations and remove most of their alleged oddities. (shrink)

The goal of this paper is to present and defend an empiricist, neo-Hempelian account of scientific explanation as ampliative, specialized embedding. The proposal aims to preserve what I take to be the core of Hempel’s empiricist account, by weakening it in some respects and strengthening it in others, introducing two new conditions that solve most of Hempel’s problems without abandoning his empiricist strictures. According to this proposal, to explain a phenomenon is to make it expectable by introducing new conceptual/ontological machinery (...) and using special, and non-ad hoc, non-accidental regularities. The new conditions are elaborated making essential use of two central structuralist ideas, namely T-theoreticity and specialization. I first introduce and qualify the project, then present the new account in detail and assess it vis-à-vis its rivals, and finally discuss some possible objections, concluding that the account fares better than its monistic rivals and well enough to qualify as a promising neo-Hempelian account. Even for those unpersuaded by its monistic goals, it has the merit of calling attention to two new necessary conditions not explicitly emphasized thus far and showing how they serve to answer many of the criticisms addressed against Hempel’s account. (shrink)

Despite the importance of network analysis in biological practice, dominant models of scientific explanation do not account satisfactorily for how this family of explanations gain their explanatory power in every specific application. This insufficiency is particularly salient in the study of the ecology of the microbiome. Drawing on Coyte et al. (2015) study of the ecology of the microbiome, Deulofeu et al. (2021) argue that these explanations are neither mechanistic, nor purely mathematical, yet they are substantially empirical. Building on their (...) criticisms, in the present work we make a step further elucidating this kind of explanations with a general analytical framework according to which scientific explanations are ampliative, specialized embeddings (ASE), which has recently been successfully applied to other biological subfields. We use ASE to reconstruct in detail the Coyte et al.’s case study and on its basis, we claim that network explanations of the ecology of the microbiome, and other similar explanations in ecology, gain their epistemological force in virtue of their capacity to embed biological phenomena in non-accidental generalizations that are simultaneously ampliative and specialized. (shrink)

I argue that Carl Hempel’s pioneering work on scientific explanation introduced an assumption that Hempel never motivated, namely, that explanation is an aim of science. Ever since, it has remained largely unquestioned in analytic philosophy of science. By expanding the historical scope of the debate on explanation to philosophers from the first half of the twentieth century, I show that the debate should include a critical reflection on Hempel’s assumption. This reflection includes two problems: how to motivate one’s position on (...) the aims of scientific knowledge and how to decide which examples count as expressions of those aims. (shrink)

Implicit contextual factors mean that the boundary between causal and noncausal explanation is not as neat as one might hope: as the phenomenon to be explained is given descriptions with varying degrees of granularity, the nature of the favored explanation alternates between causal and non-causal. While it is not surprising that different descriptions of the same phenomenon should favor different explanations, it is puzzling why re-describing the phenomenon should make any difference for the causal nature of the favored explanation. I (...) argue that this is a problem for the ontic framework of causal and noncausal explanation, and instead propose a pragmatic-modal account of causal and non-causal explanation. This account has the added advantage of dissolving several important disagreements concerning the status of non-causal explanation. (shrink)

Veel wetenschappers, filosofen en theologen zijn van mening dat God nooit opgevoerd mag worden als verklaring voor een verschijnsel. Eén argument dat ze hiervoor aandragen is dat het op de een of andere manier in de aard van wetenschap zit dat God er geen rol in kan spelen. In dit artikel ga ik in op een specifieke versie van dit argument. Ik vraag me af of de aard van wetenschappelijke verklaringen uitsluit dat God als verklaringsgrond wordt genoemd. Om die vraag (...) te beantwoorden ga ik na of de door wetenschapsfilosofen ontwikkelde standaardmodellen van wetenschappelijk verklaren ruimte bieden aan theïstische verklaringen. Dat blijkt inderdaad zo te zijn, enige kwalificaties daargelaten. De conclusie moet dan ook luiden dat de aard van wetenschappelijke verklaringen niet zodanig is dat theïstische verklaringen uitgesloten zijn. (shrink)

Explaining is one of the most important everyday practices in science education. In this article, we examine how scientific explanations could serve as cultural tools for members of a group of pre-service physics teachers. Specifically, we aim at their use of explanations about forces of inertia in non-inertial frames of reference. A basic assumption of our study is that explanatory tools (e.g., typical explanations learned) shape the ways we think and speak about the world. Drawing on the theory of mediated (...) action, analysis illustrates three major claims on scientific explanations: (1) explaining is an act of actively responding to explanations presented by others (and not only to evidence itself); (2) the actual experience of explaining involves the enactment of power and authority; (3) resistance (not acknowledging an explanation as one’s own) might be a constitutive part of learning how to explain (hence, teachers could approach scientific explanation in a less dogmatic way). These assertions expand the possibilities of dialogue between studies of scientific explanations and the social sciences. Implications for science teaching and research in science education are presented. (shrink)

What is scientific progress? On Alexander Bird’s epistemic account of scientific progress, an episode in science is progressive precisely when there is more scientific knowledge at the end of the episode than at the beginning. Using Bird’s epistemic account as a foil, this paper develops an alternative understanding-based account on which an episode in science is progressive precisely when scientists grasp how to correctly explain or predict more aspects of the world at the end of the episode than at the (...) beginning. This account is shown to be superior to the epistemic account by examining cases in which knowledge and understanding come apart. In these cases, it is argued that scientific progress matches increases in scientific understanding rather than accumulations of knowledge. In addition, considerations having to do with minimalist idealizations, pragmatic virtues, and epistemic value all favor this understanding-based account over its epistemic counterpart. (shrink)

In this paper we investigate ignorance in relation to our capacity to justify our beliefs. To achieve this aim we specifically address scientific misconceptions, i.e. beliefs that are considered to be false in light of accepted scientific knowledge. The hypothesis we put forward is that misconceptions are not isolated false beliefs, but rather form part of a system of inferences—an explanation—which does not match current scientific theory. We further argue that, because misconceptions are embedded in a system, they cannot be (...) rectified simply by replacing false beliefs with true ones. To address our misconceptions, we must rather act on the system of beliefs that supports them. In the first step of our analysis, we distinguish between misconceptions that are easy to dispel because they represent simple errors that occur against the background of a correct explanatory apparatus and misconceptions that are, on the contrary, very difficult to dispel because they are the product of pseudo explanations. We show that, in the latter case, misconceptions constitute an integral part of an incorrect explanation and the reasons that support such misconceptions are deeply misleading. In the second step, we discuss various approaches that have been adopted to address the problem of misconceptions. Challenging the notion that directly addressing and criticizing specific misconceptions is an effective approach, we propose that critical thinking is the most fruitful means to deal with misconceptions. We define the core competences and knowledge relevant for the practice of critical thinking and discuss how they help us avoid misconceptions that arise from accepting beliefs that form part of a mistaken explanation. (shrink)

Although many aspects of Inference to the Best Explanation have been extensively discussed, very little has so far been said about what it takes for a hypothesis to count as a rival explanatory hypothesis in the context of IBE. The primary aim of this article is to rectify this situation by arguing for a specific account of explanatory rivalry. On this account, explanatory rivals are complete explanations of a given explanandum. When explanatory rivals are conceived of in this way, I (...) argue that IBE is a more plausible and defensible rule of inference than it would otherwise be. The secondary aim of the article is to demonstrate the importance of accounts of explanatory rivalry by examining a prominent philosophical argument in which IBE is employed, viz. the so-called Ultimate Argument for scientific realism. In short, I argue that a well-known objection to the Ultimate Argument due to Arthur Fine fails in virtue of tacitly assuming an account of explanatory rivalry that we have independent reasons to reject. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

It is commonly accepted that theatrical fictional worlds could serve as a potent tool for increasing man’s understanding of his own world. This research connects insights that have been developed in such diverse areas of thought as semiotics of theater and drama, philosophical logic and ontology, epistemology, and philosophy of science, so as to establish a model that suggests an explication of this epistemic effect and thereby a new observation of the theatrical enterprise. The theory advanced in this study states (...) that fictional worlds are a kind of thought experiment through which spectators’ theories about their own world may be tested, amended or even invented. (shrink)

There appears to be a widespread belief that the social sciences during the 1950s and 1960s can be characterized by an almost unquestioned faith in a positivist philosophy of science. In contrast, the article shows that even within the narrower segment of Cold War social science, positivism was not an unquestioned doctrine blindly followed by everybody, but that quite divergent views coexisted. The article analyses two ‘techniques of prospection’, the Delphi technique and political gaming, from the perspective of a comprehensive (...) set of ideas attributed to ‘positivism’. Both techniques were developed in the early 1950s by researchers at the RAND Corporation, a Californian think tank with tight relations to the US Air Force. Despite the closeness of origin, the two techniques show considerable differences in their basic epistemologies. The article thus concludes that more important than positivism in uniting US Cold War social science was the shared sense of urgency and of the potential of social science to put decision-making in foreign policy on a rational basis. In this sense, as far as the Cold War social sciences were of a piece, they were made so by the sense of danger and urgency of action evoked by the image of the Iron Curtain. (shrink)

Although the inferring of explanations plays an important role in both our everyday lives and in the workings of science, I argue that inference to the best explanation as it is commonly conceived is often not the best way to capture this sort of reasoning. I suggest that a different form of reasoning – so-called immediate explanatory inference – is instead often much better suited to this task. This is a form of inference in which we are justified in believing (...) explanations for the evidence before us purely in virtue of this evidence, and not in virtue of the evidence plus some general principle or rule of non-deductive reasoning. I defend the idea of such a notion of inference, and argue that it plays a central role in both ordinary life and science. (shrink)

According to the traditional view, the following incompatibility holds true: in reasoning, either there is warrant (certainty) or there is novelty. If there is warrant, there is not novelty: that would be the case of deductive reasoning. If there is novelty, there is not warrant: that would be the case of inductive reasoning. Causal reasoning would belong to the second group because there is novelty and, therefore, there is not warrant in it. I argue that this is false: reasoning may (...) have novelty and, nevertheless, be a deductive one. That is precisely what happens in (some) causal reasoning. And I will develop the following line of argumentation: one thing is to warrant that some state of affairs exists and other thing is to warrant that warrant. So we may have correct deductive reasoning without having certainty of that correction, like in some cases of causal reasoning. (shrink)

This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

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)

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...) they relate to the sorts of explanation encountered in philosophy of science and metaphysics? (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Several revisions of the Hempel and Oppenheim definition of explanation have been offered in recent years, and none have gone uncriticized in the literature. In the present paper it is argued that the difficulties involved with these attempts are based upon a confusion between three types of explanation, and that Professor David Kaplan's model of S-explanation provides a uniform treatment of all three types.

The background hypothesis of this essay is that psychological phenomena are typically explained, not by subsuming them under psychological laws, but by functional analysis. Causal subsumption is an appropriate strategy for explaining changes of state, but not for explaining capacities, and it is capacities that are the central explananda of psychology. The contrast between functional analysis and causal subsumption is illustrated, and the background hypothesis supported, by a critical reassessment of the motivational psychology of Clark Hull. I argue that Hull's (...) work makes little sense construed along the subsumptivist lines he advocated himself, but emerges as both interesting and methodologically sound when construed as an exercise in the sort of functional analysis featured in contemporary cognitive science. (shrink)

A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds and to describe the possibility spaces associated with these processes. By doing this, we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in subsequently asking a (...) how-actually question. Once one has explained how-possibly, there is little left to do. (shrink)