This article has three aims. The first is to give a partial explication of the concept of unification. My explication will be partial because I confine myself to unification of particular events, because I do not consider events of a quantitative nature, and discuss only deductive cases. The second aim is to analyze how unification can be reached. My third aim is to show that unification is an intellectual benefit. Instead of being an intellectual benefit unification could be an intellectual (...) harm, i.e., a state of mind we should try to avoid by all means. By calling unification an intellectual benefit, we claim that this form of understanding has an intrinsic value for us. I argue that unification really has this alleged intrinsic value. (shrink)

In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to the views that Mark Zelcer has put forward recently. Throughout this (...) paper, we show why Zelcer’s arguments fail. (shrink)

In a recent article in this journal, Federica Russo and Jon Williamson argue that an analysis of causality in terms of probabilistic relationships does not do justice to the use of mechanistic evidence to support causal claims. I will present Ronald Giere's theory of probabilistic causation, and show that it can account for the use of mechanistic evidence (both in the health sciences—on which Russo and Williamson focus—and elsewhere). I also review some other probabilistic theories of causation (of Suppes, Eells, (...) and Humphreys) and show that they cannot account for the use of mechanistic evidence. I argue that these theories are also inferior to Giere's theory in other respects. (shrink)

In the literature on scientific explanation two types of pluralism are very common. The first concerns the distinction between explanations of singular facts and explanations of laws: there is a consensus that they have a different structure. The second concerns the distinction between causal explanations and uni.cation explanations: most people agree that both are useful and that their structure is different. In this article we argue for pluralism within the area of causal explanations: we claim that the structure of a (...) causal explanation depends on the causal structure of the relevant fragment of the world and on the interests of the explainer. (shrink)

I offer an explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that this is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories. I suggest that explanations of the sort I describe (...) reveal something important about one way in which physical theories may be related diachronically. (shrink)

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics.

This paper explores the role of physically impossible idealizations in model-based explanation. We do this by examining the explanation of gravitational waves from distant stellar objects using models that contain point-particle idealizations. Like infinite idealizations in thermodynamics, biology and economics, the point-particle idealization in general relativity is physically impossible. What makes this case interesting is that there are two very different kinds of models used for predicting the same gravitational wave phenomena, post-Newtonian models and effective field theory models. The paper (...) contends that post-Newtonian models are explanatory while effective field theory models are not, because only in the former can we eliminate the physically impossible point-particle idealization. This suggests that, in some areas of science at least, models invoking ineliminable infinite idealizations cannot have explanatory power. (shrink)

This paper explores the role of physically impossible idealizations in model-based explanation. We do this by examining the explanation of gravitational waves from distant stellar objects using models that contain point-particle idealizations. Like infinite idealizations in thermodynamics, biology and economics, the point-particle idealization in general relativity is physically impossible. What makes this case interesting is that there are two very different kinds of models used for predicting the same gravitational wave phenomena, post-Newtonian models and effective field theory models. The paper (...) contends that post-Newtonian models are explanatory while effective field theory models are not, because only in the former can we eliminate the physically impossible point-particle idealization. This suggests that, in some areas of science at least, models invoking ineliminable infinite idealizations cannot have explanatory power. (shrink)

Many explanations in physics rely on idealized models of physical systems. These explanations fail to satisfy the conditions of standard normative accounts of explanation. Recently, some philosophers have claimed that idealizations can be used to underwrite explanation nonetheless, but only when they are what have variously been called representational, Galilean, controllable or harmless idealizations. This paper argues that such a half-measure is untenable and that idealizations not of this sort can have explanatory capacities.

Many philosophers now regard causal approaches to explanation as highly promising, even in physics. This is due in large part to James Woodward's influential argument that a wide variety of scientific explanations are causal, based on his interventionist approach to causation. This article argues that some derivations describing causal relations and satisfying Woodward's criteria for causal explanation fail to be explanatory. Further, causal relations are unnecessary for a range of explanations, widespread in physics, involving highly idealized models. These constitute significant (...) limitations on the scope of causal explanation. We have good reason to doubt that causal explanation is as widespread or important in physics as Woodward and other proponents maintain. (shrink)

As machine learning has gradually entered into ever more sectors of public and private life, there has been a growing demand for algorithmic explainability. How can we make the predictions of complex statistical models more intelligible to end users? A subdiscipline of computer science known as interpretable machine learning (IML) has emerged to address this urgent question. Numerous influential methods have been proposed, from local linear approximations to rule lists and counterfactuals. In this article, I highlight three conceptual challenges that (...) are largely overlooked by authors in this area. I argue that the vast majority of IML algorithms are plagued by (1) ambiguity with respect to their true target; (2) a disregard for error rates and severe testing; and (3) an emphasis on product over process. Each point is developed at length, drawing on relevant debates in epistemology and philosophy of science. Examples and counterexamples from IML are considered, demonstrating how failure to acknowledge these problems can result in counterintuitive and potentially misleading explanations. Without greater care for the conceptual foundations of IML, future work in this area is doomed to repeat the same mistakes. (shrink)

Here I consider the relative merits of two recent models of explanation, James Woodward's interventionist-counterfactual model and the model model. According to the former, explanations are largely constituted by information about the consequences of counterfactual interventions. Problems arise for this approach because countless relevant interventions are possible in most cases and because it overlooks other kinds of equally relevant information. According the model model, explanations are largely constituted by cognitive models of actual mechanisms. On this approach, explanations tend not to (...) represent any of the aforementioned information explicitly but can instead be used to produce it on demand. The model model thus offers the more plausible account of the information of which we are aware when we have an explanation and of the ratiocinative process through which we derive many kinds of information that are relevant to the evaluation of explanations. (shrink)

A rapidly growing body of scholarship shows that we can gain new insights into theories and policies by understanding and increasing their systemic structure. This paper will present an overview of this expanding field and discuss how concepts of structure are being applied in a variety of contexts to support collaboration, decision making, learning, prediction, and results. Next, it will delve into the underlying structures of logic that may be found within those theories and policies. Here, we will go beyond (...) Toulmin’s logics of claim and proof that have not proven useful for advancing the social sciences and focus on five structures of “causal logic.” The results suggest a useful and more comprehensive approach to developing deeper understanding of our conceptual systems such as theory and policy. (shrink)

In evolutionary biology changes in population structure are explained by citing trait fitness distribution. I distinguish three interpretations of fitness explanations—the Two‐Factor Model, the Single‐Factor Model, and the Statistical Interpretation—and argue for the last of these. These interpretations differ in their degrees of causal commitment. The first two hold that trait fitness distribution causes population change. Trait fitness explanations, according to these interpretations, are causal explanations. The last maintains that trait fitness distribution correlates with population change but does not cause (...) it. My defense of the Statistical Interpretation relies on a distinctive feature of causation. Causes conform to the Sure Thing Principle. Trait fitness distributions, I argue, do not. *Received July 2009; revised October 2009. †To contact the author, please write to: Department of Philosophy/Institute for the History, Philosophy of Science and Technology, University of Toronto, Victoria College, 91 Charles Street West, Toronto, ON M5S 1K7, Canada; e‐mail: [email protected]. (shrink)

In this paper, I outline two strands of evidence for the conclusion that the dynamical approach to cognitive science both seeks and provides covering law explanations. Two of the most successful dynamical models—Kelso’s model of rhythmic finger movement and Thelen et al.’s model of infant perseverative reaching—can be seen to provide explanations which conform to the famous explanatory scheme first put forward by Hempel and Oppenheim. In addition, many prominent advocates of the dynamical approach also express the provision of this (...) kind of explanation as a goal of dynamical cognitive science. I conclude by briefly outlining two consequences. First, dynamical cognitive science’s explanatory style may strengthen its links to the so-called “situated” approach to cognition, but, secondly, it may also undermine the widespread intuition that dynamics is related to emergentism in the philosophy of mind. (shrink)

There is a current debate about the extent to which Academic Freedom should be permitted in our universities. On the one hand, we have traditionalists who maintain that Academic Freedom should be unrestricted: people who have the appropriate qualifications and accomplishments should be allowed to develop theories about how the world is, or ought to be, as they see fit. On the other hand, we have post-traditional philosophers who argue against this degree of Academic Freedom. I consider a conservative version (...) of post-traditional philosophy that permits restrictions on Academic Freedom only if the following conditions are met, Condition 1: The dissemination of the results of a given research project R must cause significant harm to some people, especially to people from oppressed groups. Condition 2: Condition 1 must possess strong empirical support, and which accepts the following assumptions: (1) there is a world of objective facts that is, in principle, discoverable, (2) rational means are the means of discovering it and, (3) rational means requires strong empirical support. I define strong empirical support for an hypothesis h on evidence e in probabilistic terms, as a ratio of posterior to prior probabilities substantially exceeding 1. I now argue in favour of a research policy that accepts unrestricted Academic Freedom. My argument is that there is a formal and general quandary that arises within the standard theory of probability when we apply this account of empirical support to a set of possible causal hypotheses framed in such a way that the “reverse probabilities”, pr(e/h) are 1. I consider various possible ways to escape this quandary, none of which are without difficulties, concluding that a research policy allowing for unrestricted Academic Freedom is probably the best that we can hope for. (shrink)

Recent years have seen renewed interest in the emergence issue. The contemporary debate, in contrast with that of past times, has to do not so much with the mind–body problem as with the relationship between the physical and other domains; mostly with the biological domain. One of the main sources of this renewed interest is the study of complex and, in general, far-from-equilibrium self-preserving systems, which seem to fulfil one of the necessary conditions for an entity to be emergent; namely, (...) that its causal powers are not predictable from the causal powers of basic physical properties. However, I argue that much of the current emergentism debate has misfired by focusing on the interpretation of self-maintaining systems. In contrast, I claim that if we want to find emergent properties, we should look not at complex systems, but at selection (natural selection, in particular). I argue that selection processes make the causal world ‘exuberant’ by making non-physical functional and relational properties enter the causal web of the world. (shrink)

According to an increasing number of authors, the best, if not the only, argument in favour of physicalism is the so-called 'overdetermination argument'. This argument, if sound, establishes that all the entities that enter into causal interactions with the physical world are physical. One key premise in the overdetermination argument is the principle of the causal closure of the physical world, said to be supported by contemporary physics. In this paper, I examine various ways in which physics may support the (...) principle, either as a methodological guide or as depending on some other laws and principles of physics. (shrink)

Physicalism is the claim that that there is nothing in the world but the physical. Philosophers who defend physicalism have to confront a well-known dilemma, known as Hempel’s dilemma, concerning the definition of ‘the physical’: if ‘the physical’ is whatever current physics says there is, then physicalism is most probably false; but if ‘the physical’ is whatever the true theory of physics would say that there is, we have that physicalism is vacuous and runs the risk of becoming trivial. This (...) article has two parts. The first, negative, part is devoted to developing a criticism of the so-called via negativa response to Hempel’s dilemma. In the second, more substantial, part, I propose to take the first horn of Hempel’s dilemma. However, I argue for a broad construal of ‘current physics’ and characterize ‘the physical’ accordingly. The virtues of the broad characterization of ‘the physical’ are: first, it makes physicalism less likely to be false; and second, it ties our understanding of ‘the physical’ to the reasons we have for believing in physicalism. That is, it fulfills the desideratum of construing our theses according to the reasons we have to believe in them. (shrink)

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly explanation (...) which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding. (shrink)

The story of how Perrin’s experimental work established the reality of atoms and molecules has been a staple in (realist) philosophy of science writings (Wesley Salmon, Clark Glymour, Peter Achinstein, Penelope Maddy, …). I’ll argue that how this story is told distorts both what the work was and its significance, and draw morals for the understanding of how theories can be or fail to be empirically grounded.

In debates about the nature of scientific explanation, one theme repeatedly arises: that explanation is about providing understanding. However, the concept of understanding has only recently been explored in any depth, and this paper attempts to introduce a useful concept of understanding to that literature and explore it. Understanding is a higher level cognition, the recognition of connections between various pieces of knowledge. This conception can be brought to bear on the conceptual issues that have thus far been unclear in (...) the literature. Though this notion of understanding is broad, explaining various concepts of explanation, it is robust enough to underwrite an objective and useful notion of explanation. (shrink)

Pluralism with respect to the structure of explanations of facts is not uncommon. Wesley Salmon, for instance, distinguished two types of explanation: causal explanations (which provide insight in the causes of the fact we want to explain) and unification explanations (which fit the explanandum into a unified world view). The pluralism which Salmon and others have defended is compatible with several positions about the exact relation between these two types of explanations. We distinguish four such positions, and argue in favour (...) of one of them. We also compare our results with the views of some authors who have recently written on this subject. (shrink)

In this paper I show that a novel ontic reading of explanation, intending to capture the de re essential features of individuals, can support the qualitative view of individual essences. It is argued further that the putative harmful consequences of the Leibniz Principle and its converse for the qualitative view can be avoided, provided that individual essences are not construed in the style of the naïve bundle theory with set-theoretical identity- conditions. Adopting either the more sophisticated two-tier BT or, alternatively, (...) the neo-Aristotelian position of taking essences as natures in the Aristotelian sense, can help to evade these main charges against the qualitative view. The functional parallels with the alternative haecceitistic view of individuation and individual essence will also be considered. (shrink)

I consider the problem of extending Reichenbach's principle of the common cause to more than two events, vis-a-vis an example posed by Bernstein. It is argued that the only reasonable extension of Reichenbach's principle stands in conflict with a recent proposal due to Horwich. I also discuss prospects of the principle of the common cause in the light of these and other difficulties known in the literature and argue that a more viable version of the principle is the one provided (...) by Penrose and Percival (1962). (shrink)

Proponents of the dispositional theory of properties typically claim that their view is not one that offers a realist, governing conception of laws. My first aim is to show that, contrary to this claim, if one commits to dispositionalism then one does not automatically give up on a robust, realist theory of laws. This is because dispositionalism can readily be developed within a Platonic framework of universals. Second, I argue that there are good reasons for realist dispositionalists to favour a (...) Platonic view. This is because the alternative Aristotelian version of dispositionalism, on which universals are immanent entities, is unstable for various reasons. My final aim is to address a common criticism facing Platonic theories of laws, which is the problem of how external entities can play an explanatory role where the world’s law-like patterns of behaviour are concerned. I argue that the Platonists’ response to the one over many problem can help to shed light on this matter, and a possible solution is sketched, one which makes use of the notions of essence, constitution and ontological dependence. (shrink)

My aim is to question an assumption that is often made in the philosophical literature on dispositions. This is the assumption that, generally, the stimulation (or ‘triggering’) of a disposition temporally precedes the manifesting of that disposition. I will begin by examining precisely what the trigging of a disposition may be thought to consist in, and will identify two plausible views. I will then argue that on either of these views about triggering, a case can be made against the view (...) that the triggering of a disposition always occurs before the manifesting of that disposition. More precisely, if the first view about triggering is accepted, and certain plausible assumptions about dispositions are put into place, a metaphysical argument can be formulated for the claim that the stimulation of a disposition never occurs before that disposition manifests. If the second view about triggering is accepted, the question concerning simultaneity becomes an empirical one. There are, however, examples of dispositional interaction which, on the second view about triggering, clearly seem to involve simultaneity.1. (shrink)

In the 1960s and 1970s, Hilary Putnam articulated a notion of relativized apriority that was motivated to address the problem of scientific change. This paper examines Putnam’s account in its historical context and in relation to contemporary views. I begin by locating Putnam’s analysis in the historical context of Quine’s rejection of apriority, presenting Putnam as a sympathetic commentator on Quine. Subsequently, I explicate Putnam’s positive account of apriority, focusing on his analysis of the history of physics and geometry. In (...) the remainder of the paper, I explore connections between Putnam’s account of relativized a priori principles and contemporary views. In particular, I situate Putnam’s account in relation to analyses advanced by Michael Friedman, David Stump, and William Wimsatt. From this comparison, I address issues concerning whether a priori scientific principles are appropriately characterized as “constitutive” or “entrenched”. I argue that these two features need to be clearly distinguished, and that only the constitutive function is essential to apriority. By way of conclusion, I explore the relationship between the constitutive function of a priori principles and entrenchment. (shrink)

I provide a brief history of pragmatics as it relates to explanation, highlighting the great neglect of pragmatics and pragmatic considerations in regard to explanation during the mid-twentieth century. In order to understand pragmatic considerations regarding explanation, I utilize the work of Bas C. van Fraassen, Peter Achinstein, and Jan Faye. These thinkers provide crucial tools for understanding pragmatics, especially with regard to concepts such as context and exigence. The work of these thinkers provides the platform from which I compose (...) a definition of pragmatic considerations. (shrink)

John Dewey provided a robust and thorough conception of scientific explanation within his philosophical writing. I provide an exegesis of Dewey's concept of scientific explanation and argue that this concept is important to contemporary philosophy of science for at least two reasons. First, Dewey's conception of scientific explanation avoids the reification of science as an entity separated from practical experience. Second, Dewey supplants the realist-antirealist debate within the philosophical literature concerning explanation, thus moving us beyond the current stalemate within philosophy (...) of science. (shrink)

Optimality models are widely used in different parts of biology. Two important questions that have been asked about such models are: are they explanatory and, if so, what type of explanations do they offer? My concern in this paper is with the approach of Rice (2012, 2015) and Irvine (2015), who claim that these models provide non-causal explanations. I argue that there are serious problems with this approach and with the accounts of explanation it is intended to justify. The idea (...) behind this undertaking is to draw attention to an important issue associated with the recent pluralist stance on explanation: the rampant proliferation of theories of explanation. This proliferation supports a pluralist perspective on explanation, and pluralism encourages such a proliferation. But, if we are not careful about how we arrive at and how we justify new accounts of explanation — i.e., if we do not try to avoid the sort of problems discussed in this paper — we may end up trivializing the concept of explanation. (shrink)

Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider that (...) the above question can have an affirmative answer? My main aim here is to give an account that takes mathematics, in some of the cases discussed in the literature, as contributing to our understanding of physical phenomena despite not being explanatory. (shrink)

What exactly do we need in order to enjoy the cognitive benefit that is supposed to be provided by an explanation? Some philosophers :15–37, 2012, Episteme 10:1–17, 2013, Eur J Philos Sci 5:377–385, 2015, Understanding, explanation, and scientific knowledge, Cambridge University Press, Cambridge, 2017) would say that all that we need is to know the explanation. Others :1–26, 2012; Strevens in Stud Hist Philos Sci Part A 44:510–515, 2013) would say that achieving understanding with the help of an explanation requires (...) more than that, that it requires a grasping or an understanding of the explanation. My aim in this paper is to come up with a new answer to this problem by exploring the shortcomings of the received view of understanding. In my view, besides having testimonial knowledge of an explanation, obtaining explanatory understanding requires full cognitive access to the explanation. (shrink)

Philosophers agree that scientific explanations aim to produce understanding, and that good ones succeed in this aim. But few seriously consider what understanding is, or what the cues are when we have it. If it is a psychological state or process, describing its specific nature is the job of psychological theorizing. This article examines the role of understanding in scientific explanation. It warns that the seductive, phenomenological sense of understanding is often, but mistakenly, viewed as a cue of genuine understanding. (...) The article closes with a discussion of several new paths of research that tie the psychology of scientific explanation to cognate notions of learning, testimony, and understanding. (shrink)

Characterization of a form of explanation involving grounding on the model of mechanistic causal explanation.

In this paper, I critique two conceptions of mechanisms, namely those put forth by Stuart Glennan (Erkenntnis 44:49–71, 1996; Philosophy of Science 69:S342–S353, 2002) and Machamer et al. (Philosophy of Science 67:1–25, 2000). Glennan’s conception, I argue, cannot account for mechanisms involving negative causation because of its interactionist posture. MDC’s view encounters the same problem due to its reificatory conception of activities—this conception, I argue, entails an onerous commitment to ontological dualism. In the place of Glennan and MDC, I propose (...) a “modified conception” of mechanisms, which (a) obviates the problem of negative causation by reinterpreting MDC’s activities according to a “descriptivist” account, and (b) avoids MDC’s problem by postulating a monistic ontology of entities. Thus, by solving these problems, my modified conception offers a cogent, more adequate alternative to Glennan’s and MDC’s conceptions of mechanisms. (shrink)

It is widely thought that there is an important argument to be made that starts with premises taken from the science of physics and ends with the conclusion of physicalism. The standard view is that this argument takes the form of a causal argument for physicalism. Roughly, physics tells us that the physical realm is causally complete, and so minds (among other entities) must be physical if they are to interact with the world as we think they do. In what (...) follows, I raise problems for this view. After an initial review of the causal argument, I begin my case by showing that the totality of physical truths do not deductively entail the causal completeness of the physical realm, using a double-prevention scenario and causation by omission to show that nonphysical causes of physical effects would not need to violate physical conservation laws. I then move on to raise problems for an inductive argument for causal completeness by drawing on the neo-Russellian view that there is no causation in fundamental physics, and so causation must itself be a realized or derived entity. I conclude by suggesting that the underlying problem is that the causal argument has fallen out of touch with the sophisticated understanding that philosophers have developed of the role of causation within physics. (shrink)