## Explanation across

the disciplines

September 14-15, 2018

Middlebury College

Middlebury, VT

Middlebury College

Middlebury, VT

__Conference Home -- Program -- Abstracts__**ABSTRACTS**

__FRIDAY, SEPTEMBER 14__**Session I: Philosophy and Explanation**

**110 Storrs Avenue, Davis Family Library 201 – Watson Lecture Hall**

3:30-4:30

Kareem Khalifa “Explanation: A Guide for the Perplexed”

To get the conference started and provide a

*lingua franca*, I'll provide an overview of the major philosophical accounts of explanation.

4:40-5:30

Nina Emery “Explanatory Adequacy as a Constraint on Scientifically-Respectable Philosophical Theories”

Philosophers often pride themselves on taking their cue from scientific practice and scientific theory when constructing accounts of the nature of things on which science itself is quiet. This paper develops an argument that suggests that philosophers who think that they are being scientifically respectable in this sense at least sometimes make the following important mistake: they pay too much attention to the extent to which their theories are restricted to relatively simple and straightforward types of entities, when they should pay more attention to the extent to which their theories provide adequate explanations.

Although the argument generalizes to a number of cases, my focus in this paper is on philosophical accounts of laws of nature. In particular, I present an argument for the view that laws govern their instances, where if a governs b then a explains b in a metaphysically robust sense, where causation and grounding are paradigm instances of relations that back metaphyscially robust explanations, and where mere entailment, mere unification, and mere psychological satisfaction are paradigm instances of relations that do not back metaphysically robust explanations. The view that laws play this sort of metaphysically robust explanatory role is often taken to be intuitive or commonsensical (Beebee 2000) but ultimately misguided because it requires laws to be weird or novel—and thus not scientifically respectable—sorts of entities (Lewis 1986, Loewer 2012). I turn this standard dialectic on its head, and argue that in fact there are reasons stemming from standard scientific practice to insist on a so-called governing conception of laws.

I begin by arguing that the following principle constraints theory choice in fundamental physics.

The pattern-explanation constraint. Insofar as the only way to avoiding leaving a well-established pattern unexplained is to introduce a type of entity that is metaphysically weird or novel, we ought to introduce such entities.

I argue for this constraint by considering a series of examples of novel entities that have been introduced in fundamental physics. These include universal gravitation (in Newtonian mechanics), the electromagnetic field, the neutrino, spacetime (in general relativity), and dark energy. All of these entities were, at least at the time at which they were accepted, metaphysically weird or sui generis (or both). As such, the acceptance of these entities counted as a serious cost of the theory in which they appeared. Nonetheless, that cost was considered worth paying. I argue that the most plausible explanation of why that cost was worth paying is that without such entities well-established patterns in data would go unexplained. Thus, the pattern-explanation constraint appears to play an important role in fundamental physics. Furthermore, I argue, the relevant sense of explanation in the pattern-explanation constraint is a metaphysically robust sense. Although alternative non-metaphysically robust explanations were available in the cases above, it was still considered worthwhile to introduce the relevant entities in order to secure a metaphysically robust explanation. I close the section with a discussion of whether this constraint functions in scientific theory choice beyond fundamental physics, and to what extent that affects my argument.

I then argue that given that the pattern-explanation constraint is a constraint on theory choice in fundamental physics, and we ought to adopt an understanding of laws that satisfies that constraint as well. I consider several plausible ways of understanding the relationship between physics, on the one hand, and metaphysics, on the other, and suggest that all such ways support the application of pattern-explanation constraint across the physics-metaphysics boundary. This leads straightforwardly to a governing conception of laws. Unless we have such a conception, well-established patterns in the data throughout fundamental physics will go without metaphysically robust explanations. I work through this argument using examples involving both dynamical patterns, like the pattern that gives rise to Schrödinger's equation, and synchronic patterns, like the patterns in the fundamental constants and in the properties of and relations between fundamental entities.

In the last sections of the paper I make some suggestions about where this arguments leaves us with respect to a further understanding of the nature of laws and about how the argument generalizes to other areas of philosophical theorizing. I close by emphasizing the broader point that being scientifically-respectable in one’s philosophical theorizing is not as straightforward as it might first appear. In particular, being scientifically-respectable in one’s philosophical theorizing requires one to adopt theories that are explanatory adequate even if they are otherwise surprising or strange.

5:30-6:45

219 South Main Street, Kenyon Arena Lounge

Dinner

**Keynote I**

7:00-8:30

Michael Strevens, "Grasp"

**SATURDAY, SEPTEMBER 15****Session II: The Impact of Explanations**

**110 Storrs Avenue, Davis Family Library 201 – Watson Lecture Hall**

9:00-9:50

Jeffry Ramsey, “Explanation in the Wicked World of Environmental Problems”

We explain in order to increase “the overall understanding of the world” (Friedman 1974, 18). In the sciences (and probably in other modes of inquiry), a core sense of ‘to explain’ is to “exhibit certain kinds of structural dependencies” (Morrison 1999, 63). It is usually assumed we can exhibit such dependencies among theories, models, laws, data, and/or phenomena because the systems (in the real world or in our theoretical descriptions) we study are, to a good approximation, regular and deterministic. Once the core sense and the assumption are admitted, the race is on to provide an account that tells us which kind of structural dependency (laws, causes, unifications, counterfactual dependencies, non-causal dependencies) best increases our understanding of the world.

What do explanations look like when the structural dependencies change from one proposed problem formulation to the next? How do scientists claim they are offering an explanation in such situations? Are we comfortable saying that explanations in such situations increase our understanding? This paper pursues these questions within the realm of ‘wicked problems.’ ‘Wicked’ problems are problems that have “no definitive formulation, no stopping rule, and no test for a solution” (Ludwig 2001, 759). They are characterized by “radical uncertainty” and a “plurality of legitimate perspectives” (Funtowicz et al 1999).

Many environmental problems are wicked. Climate change, water resource management, energy production, agriculture, waste disposal, marine ecosystem protection, and biodiversity loss are all wicked (Rayner 2006). Levin et al (2012) note that these kinds of problems arise often in the environmental arena because scientists are studying complex adaptive systems, with nonlinear feedbacks, different time scales, different adaptive processes, spatial variation and dynamics, and strategic interactions and unique behaviors among the individuals in the system. Add to this the point that humans are finite cognitive agents, characterized by limited capacity, resource scarcity and ignorance (Farrell and Hooker 2013, Wimsatt 2007), and it seems that our ability to explain in these complicated, complex systems is limited indeed.

I examine questions of explanation in one small part of the wicked problem of sustainability. Geels (2011) advocates a “multi-level perspective” (“MLP”) as a way to explain ‘sustainability transitions,’ i.e. the major changes in energy, transport and agri-food systems that will be needed if we are to achieve sustainability. The approach is “multi-level” because transitions are explained as due to interacting processes within and between three levels: a niche, which is the locus for innovations; locked-in and path-dependent socio-technical regimes; and an extrinsic socio-technical landscape. The MLP “looks at events rather than causal variables” and “explain[s] outcomes as the results of temporal sequences of events and the timing and conjunctures of event-chains” (Geels and Schot 2010, 93). Researchers explain transitions by embedding these events in “causal narratives . . . guided by ‘heuristic devices’ . . . that specify a certain plot” from “recurring causal patterns” (Geels 2011, 35). The notion of a “plot” is drawn from, among other sources, Merton’s (1949) notion of a ‘middle-level theory.’ “Plots” are better suited to the non-linear, multi-scalar nature of the processes under study and are therefore more explanatory than other approaches.

The MLP has been criticized on a number of grounds (cf. Geels 2010), In particular, critics have argued that: the MLP does not conceptualize the agency of individuals and institutions fully; that it focuses on the wrong level of analysis; that it is biased towards particular types of transitions; that it is limited to heuristic suggestions rather than a complete analysis of change; that it backgrounds the socio-technical landscape and thereby misses important drivers of unsustainable behaviors; and that it is too focused on how users’ roles within existing structures and thereby misses how the structures came to be and are continued. The criticisms are all partial; they involve a claim not that the MLP is entirely unexplanatory but rather that it is not fully or completely explanatory.

I analyze these criticisms, showing that they claim that the MLP does not capture the right kinds of structural dependencies in the wicked problem of sustainability and is therefore not a complete or a good explanation. They also involve a claim that there are other, more important structural dependencies to be noticed and used. In order to find the better dependencies that are more responsive to the complex adaptive systems being studied, one has to include discussion of proper ontology and methodology. As one works out the proper philosophical base, one gets a clearer sense of what structural dependencies are informative. The analysis thus provides a specific example of Friedman’s (1974) claim that scientific understanding is not a clear notion and cannot be specified in advance of giving an account of (what passes for) explanation.

Some might object that these scientists are not offering explanations because no one is producing agreed-upon structural dependencies, much less agreeing on the ontologies that give rise to them. I believe the objection is not warranted. First, these are schematized causal accounts, and so fall into the general category of causal explanations. They are attempts to find structural dependencies, but due to the nature of the complex adaptive systems they are being applied to, they remain highly schematic, fallible, and cumulative accounts. The explanation being offered looks like Cartwright’s (1984) and Wimsatt’s (2007) accounts of how laws explain. Second, the ‘failure’ to provide a non-perspectival description and explanation of the problem utilizing accepted structural dependencies is only a failure from the perspective of the philosophical models. Real-world problem-solving strategies are inevitably complex and partial when the problems are complex. If the Inexact, imprecise, and incomplete models increase understanding, that is enough.

10:00-10:50

Piper Sledge & Collin Rice “An Epistemic Case for Diversity in Science”

The philosophy of science literature has recently focused on the relationship between explanation and understanding. Explanations are thought to produce understanding and in some cases multiple conflicting explanations contribute to the overall scientific understanding of a phenomenon. We will first argue that an account of explanation and understanding that appeals to exploration of possibility (i.e. modal) space can show how multiple conflicting explanations that involve idealizations can improve overall understanding. In addition, we contend that this account provides a novel way of thinking about the value of diversity within scientific communities.

By appealing to explanation and understanding we aim to provide an epistemic foundation for diversity in science. In this talk, we show how conceptions of diversity in terms of unique standpoints of individual researchers does not guarantee these epistemic goals are achieved. Instead we argue that in order for diversity to contribute to increasing the variety of explanations in the service of promoting more substantive understanding, we must take into account the limitations and opportunities that social structures (for which individual identities typically serve as proxies) provide.

More specifically, within scientific practice, social categories of identity such as gender and race tend to be treated as an aspect of the situated knowledge of a given researcher. Diverse standpoints in science are expected to lead to alternative ways of interpreting data and to infuse a degree of creativity in the generation of different explanations. While this has been an important project of feminist critiques of science, we argue that this understanding of the role of diversity in scientific inquiry is incomplete. Rather than focusing on the characteristics of particular researchers, we argue that investigations of diversity in scientific explanation must account for the social structure of scientific inquiry in order to effectively promote the generation and consideration of diverse sets of competing explanations. If our sociological conception of diversity places limits on creativity in science, then we must look beyond the categories that make up this diversity and attend to the specific values and social structures that promote and limit the generation of a more diverse range of scientific explanations. Doing so will enable more possibility space to be effectively explored and thus lead to improved overall understanding in science.

11:00-12:15

KEYNOTE: Tania Lombrozo

12:30-1:30

Lunch

**Session III: Mathematical Explanations**

1:40-2:30 Janet Folina “Explanation and visual information in mathematics”

When teaching we often draw images on the whiteboard. A picture or diagram certainly seems like a more direct representation than words can provide. So visual tools provide another way to explain abstract or complicated concepts to students. Even if a student follows the verbal reasoning, an image provides an extra way to solidify their understanding. So images seem a helpful tool for explanation in general.

For example, when explaining Zeno’s paradoxes we often draw a line on the board, which we proceed to cut in half; then half of the half; and so on. We may also “perform” the paradox by walking across the room, stopping at the half-way points. Both illustrations are visual – and both are very different from merely speaking, or even writing sentences on the board. Another simple example of a helpful visual tool involves a popular argument for the existence of God – the First Cause, or Cosmological, argument. A common premise in this argument is that there can be no infinite regress of causes; and an objection to this premise can be illustrated by drawing an initial sequence of negative integers 0, -1, -2, …. This shows that intelligible sequences can have no natural beginning (no first item when ordered in the natural order of less than); and this illustrates a problem with the premise of the original argument.

Although these illustrations arise in philosophy class, they appeal to mathematical facts. We “draw” mathematical facts to illustrate philosophical ideas. Of course, mathematicians also use visual tools to help explain mathematical facts and theorems. Why is this so effective; why is it that in such an abstract area as the pure mathematics of number theory, for example, visual images are effective explanatory tools? Furthermore, can we articulate some general conditions that make visual illustrations particularly helpful in explanation across disciplines?

I am interested in the role of visual tools in mathematics, science and philosophy. In my teaching I would like to better understand both the utility and the limits of visual tools in philosophical explanation. In addition, one strand of my research aims to clarify the epistemic status of diagrams and other visual tools in mathematics. There are many objections (both standard and additional) to relying on diagrams in mathematical proofs. I have come to believe, however, that diagrams and other visual images can play a proper normative, justifying, role in mathematics, rather than a merely psychological role. That is, diagrams can provide genuine evidence for mathematical claims – in particular when there is a close relationship between the elements of a visual diagram and the elements of a theorem. Thus I support an intermediary status for mathematical diagrams, one between rigorous proof and mere psychological aid.

Three standard objections to mathematical diagrams are that diagrams can be misleading, they require special interpretations, and their particularity, or singularity, means that they cannot fully justify general conclusions. Of these, perhaps the most important is the generality problem. Individual pictures and diagrams are singular objects. They are thus particulars. But mathematical theorems are typically general claims about all numbers, all sets, all triangles, etc. Though we may interpret an image as a general representative, it is in fact a particular; so it seems inescapable that a picture is logically inadequate for any general conclusion it purports to justify. Thus, if we are thinking of mathematical explanations as a subset of proofs – proofs with additional epistemic virtues – pictures seem unhelpful in explaining mathematical explanation.

But there is another way to think about explanation – one that is more pragmatic and practice-oriented. From this perspective, despite any logical gaps in “proofs” that utilize or are based on pictures, it is interesting to try to determine when images are useful, and which diagrams or representation systems are particularly cognitively effective. In addition, it may be useful to understand why. Along these lines I argue that systems and images are effective when they provide genuine insight and evidence into a mathematical issue. And this occurs when there is a clear relationship, or mapping, between aspects of the visual representation (often its “parts”) and the mathematical elements so targeted.

For example, consider the following well-known arithmetic series as well as a popular picture of it:

This “picture” is effective because it represents central structural features asserted by the theorem. (Start with the single square at the bottom right and move left; each column adds one more block to the staircase, always preserving the general “shape” properties articulated by the right-hand side of the equation.) There is thus helpful information that is portrayed in such a picture – information that not merely causes us to believe a theorem, but that also provides at least partial insight into the facts making the theorem true. An explanation that utilizes a picture such as this does not play a mere psychological-causal role. Rather, it provides a normative reason (though one that falls far short of proof) for believing the mathematical statement to be true.

2:40-3:30 Sam Cowling, Seth Chin-Parker, & May Mei, “What Makes Platonists Tick? Explanatory Preferences in Mathematical Matters”

Mathematical explanations of physical events are perhaps the most pervasive species of non-causal explanations. But, for all their familiarity, the nature of these explanations remains a controversial affair. Much of this controversy stems from internecine philosophical disputes about the nature of explanation itself, but controversy also stems from disagreement about mathematical practice and the psychological and cognitive aspects of our provision and assessment of explanations. This paper sets out some efforts to make headway on one aspect of the debate regarding mathematical explanation, drawing on work in psychology, mathematics, and philosophy. These efforts are focused, in particular, on exploring a live concern in contemporary debates regarding the existence of mathematical entities from an interdisciplinary perspective, given our respective backgrounds as a psychologist, a philosopher, and a mathematician.

Within the philosophy of mathematics, platonists affirm the existence of mind-independent, mathematical abstract objects, while nominalists deny that there are any such entities. A remarkably influential line of argument in defense of platonism is the Indispensability Argument, which holds (roughly) that ontological commitment to mathematical entities is warranted on the grounds that quantification over mathematical entities like numbers and functions is ineliminable in our best physical or scientific theories. In recent years, this argument has met with especially close scrutiny and prompted an increased focus on the explanatory role of mathematical entities within our best physics. According to the Enhanced Indispensability Argument, platonism is justified just in case mathematical entities play an ineliminable explanatory role rather than, say, merely an expressive role in our theories. On the resulting view, ontologically committal quantification is bound up with the kind of explanatory work more regularly assigned to theoretical posits like genes and electrons. So, if mathematical entities figure into our scientific explanations in the right way, this suffices to establish the truth of platonism. But, if it can be shown that mathematical facts do not play such a role, nominalists will have successfully rebutted a preeminent argument for platonism. A crucial question is, then, whether purely mathematical facts—roughly, facts concerning abstract mathematical entities—are unavoidable in the provision of our scientific explanations.

Assessing the fate of the Explanatory Indispensability Argument on philosophical grounds would require affirming a range of substantial theses about the nature of explanation—e.g., whether it is rightly assimilated to unification, whether it must be backed by laws, whether it is predominantly pragmatic in character, and so on. But is there another route to gaining insight into whether purely mathematical facts are explanatorily eliminable?

Our project aims to examine the psychological role of purely mathematical facts in broadly physical explanations. Roughly put, we’re interested in determining the role, significance, and peculiarities of purely mathematical facts in ordinary reasoning in an effort to better understand folk intuitions about mathematical explanations of broadly physical phenomena as well as the distinctive role of purely mathematical facts in explanations. Although we recognize that psychological inquiry into explanation cannot and does not purport to settle perennial philosophical questions regarding the status and variety of explanation, pursuits in the philosophy of explanation ought not proceed in ignorance of what psychology and mathematics can tell us about explanation. We therefore take interdisciplinary inquiry on this front to provide one means for getting at thorny questions about the explanatoriness of purely mathematical facts when applied to the physical domain.

In order to examine these issues, we have begun empirical study of how people incorporate mathematical expressions into explanations they generate as well as how they evaluate different forms of mathematical information in terms of how well it explains. We seek to examine how people both use and assess “platonist” explanations, involving sentences with mathematical expressions occurring as singular terms, compared to “nominalist” explanations, involving mathematical expressions as determiners (e.g., ‘seven newspapers’). Although the study is in its early stages, we have found patterns of responding that indicate that participants value both forms of mathematical expression, but other qualities of the explanations appear to affect their use.

Given our initial findings, we plan to provide insight into the status of platonist explanations, and how other considerations (e.g., simplicity) inform and constrain our explanatory practices—most notably, we hope to examine whether complexity and scope impact explanatory reasoning in mathematical and non-mathematical domains in similar ways.

Our proposed talk sets out how this research interfaces with the philosophy of mathematics and the psychology of explanation. We then present some of the familiar challenges in trying to extract substantive conclusions about mathematical explanation (e.g., study design, puzzles about explanatory priming, semantic and syntactic puzzles about mathematical expressions). After noting some of the myriad questions linked to this area of inquiry, we outline the findings of our current study. We conclude by drawing some tentative inferences about what the present study might show us regarding the explanatoriness of purely mathematical facts.

3:40-5:30

Group discussion

6:00-closing time

Dinner and Continued Discussion