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Let us start with a wide-angle view of why we construct models of the world at all. And here I do not just mean the relatively esoteric products of professional science; I mean the internal world-models that the brain constructs in order to help us navigate a complex and changing terrain. We are the only creatures who seem to have evolved to use models as the setting for an explicit form of practical reasoning (or at least do so with anything like the power and sophistication that we do; there is evidence that mice and other creatures do a rudimentary form of map keeping, but we have full-blown models of the world on which we represent ourselves and our ends). Our behavior (or, rather, our deliberate behavior, i.e., the willfully initiated movements of our limbs) is governed by a decision process that involves explicitly representing potential actions, imaginatively tracing out their effects, and making a choice about what to do based on projected outcomes. This process is our most powerful cognitive tool, one that gives us our primary advantage over other kinds of naturally evolved cognitive systems. Models provide the setting for this deliberative process. The added layer of representational mediation between stimulus and response gives us a kind of flexibility and foresight that holds perhaps our greatest advantage over natural competitors.

Functionally, constructing models is a human strategy for behavior management. Science is an extension of this basic strategy which involves the collectivization and systematization of information, the creation of models of varying scope, specially tailored for all different kinds of purposes. We make maps of outer space and build models of atoms, cells, and ecosystems. These models all play a role in our interaction with the natural environment. In this capacity, model construction is not merely a matter of copying. It involves restructuring, reorganizing, and reconfiguring information: integrating and reformatting it in ways that prepare it for use in inference or navigation. Models are tools. Their job is to facilitate interaction between an embodied agent and an open environment. Some of the structures defined in a model have the job of representing: tracking or mirroring localized elements in the landscape. In those cases, the account of how the models are used will support the kinds of localized correspondence that most people think of as paradigmatic of representation. We expect this kind of localized extensional correspondence, for example, between first-order elements in a model of space-time and localized events (e.g., a lightning strike or the decay of a radioactive atom). But that is a quite specialized function. There are also structures defined on our models that encode information about distributed features of the world like trends and currencies, the latest fashions, the value of the dollar, or the state of the union. And there are structures whose main function is to facilitate computation. We store information about dates and locations in formats that make it easy to compute duration and distance. And, in general, information will be encoded in different formats to facilitate different kinds of function. The lesson here is that models provide embedding frameworks for phenomena that package information for useful application in situ. This re-packaging can introduce a holistic restructuring that does not in general preserve piecemeal correspondence, and (more importantly for our purposes) introduces elements that do something other than simply reflect first-order features of the landscape.

Chances are easy to understand in these terms.[1] Chance is a species of statistical probability tailored to guide credence for creatures that have no direct source of information from the future. Statistical probabilities are objective, modalized quantities grounded in relative frequencies that guide expectation in open-ended classes of systems. They do not correspond to actual frequencies because actual frequencies can be skewed in a way that would make them unsuitable for that role. If a coin falls heads half the time, but all of those head-tosses occur before the birth of Socrates and after, say, 3011 ce, it would be stupid for you and I to take even odds on heads or tails. Chances reflect facts about stable relative frequencies over the short term in a way that is quite precisely designed to allow them to play their role-guiding expectation.

The epistemic uses of models have to do with carrying information, computing, and predicting. But these are not the only uses. Models also guide our interactions with the systems they represent. In this manner, the ways in which we represent things will contain information that is useful for the purposes of intervention. The intervener does not simply need to know how things are; he needs to know how things would be if he acted on the world in various ways.[2] To think of models in purely epistemic terms is to forget about their practical role. To the embedded agent who doesn’t just observe, but also intervenes in, his environment, the world is chock-full of opportunities and affordances. The terms in which he represents the world will be designed to disclose them. Causal relations are the generic form of these opportunities and affordances. Formally, causal relations are inductive generalizations of emergent relations among networks of variables that tell us what would happen to other variables in a network if we intervene on one. These relations are captured in DAGs (Directed Acyclic Graphs) that highlight strategic routes to bringing about ends.[3]

Recognizing the practical dimension of use is what we need in order to understand alethic modalities. Epistemic modality involves the notion of how things might actually be, given what we already know. Alethic modality involves the notion of how things would be, under conditions that may or may not be actual. It is the alethic modalities that have seemed to carry metaphysical commitments that have been uncomfortable to empiricists. This is because making out the modal content of an alethic modal claim involves quantification over specifically counterfactual (i.e., non-actual) possibilities. To say that A follows B as a matter of law, is to say that A must follow B, i.e., that A could not fail to follow B. To say that the association between A and B is not merely a correlation, but a cause, also adds some counterfactual force. It supports the inference that if one were (hypothetically) to bring about A, B would follow. In both cases, the extra modal force can only be made out in counterfactual terms. The modal force captures something crucial to the content of those notions. What does the modal force add? It does not add anything new to our beliefs about what does happen. But it does add something of practical importance that makes a difference to choice. You might try to bring about an exception to a regularity, but you would not want to try to bring about an exception to a law.

It would be a waste of time, i.e., a strategic mistake. To know that the relation between A and B is a causal one does not add anything to our stock of categorical beliefs; it signals that one could use the link strategically by manipulating A to bring B about.

Philosophers have focused on the counterfactual as the most basic alethic modality, but counterfactuals are just hypothetical statements with false antecedents. And in cognitive terms, the hypothetical statement is the more basic category. The role that beliefs about hypothetical circumstances play in practical reasoning is easy to discern.[4] When I am deciding how to act, I consider a range of actions. The way that I decide is by tracing out the downstream consequences of actions considered in the hypothetical. What would happen if I accept the Queen’s Gambit or defend my knight? Should I take the beaten path or the road less traveled? The answers depend on what would happen if I did.[5] And there is no way of eliminating the modal content. Only some of the hypothetical futures I consider under the guise of potential actions will be actualized. The others are, and will remain, strictly counterfactual. One way of putting this is that epistemic modalities are to theoretical reason what alethic modalities are to practical reason. Looking back now, we can see more clearly why the attempts at reduction of laws to regularities, and chances to frequencies, failed. In both cases, the looseness of fit between the categorical facts and the structures that reside on the second-order overlay is essential to the function of those structures. Chances have the function of guiding expectation in open- ended classes of systems when we have general information about the distribution of values for some quantity in the class from which the system is drawn, but no specific information about the value the quantity takes in the case in question.[6] And the open-ended application means that chances have to range over possible, not merely actual, instances. They have to cover any system we might come across, and we have no way, in advance, of delimiting the ones we will come across from those we could. Claims about laws have specifically counterfactual implications because they have the function of guiding the kinds of purely hypothetical imaginings that are part of deliberation. To play this role, these quantities have to have implications that guide belief about hypothetical, potential futures.[7]

What do we say about these structures, then, if they do not describe what happens ? We say that they are inductions on patterns in the manifold of facts that supply us with best-guesses-under-the-circumstances for what will happen, and also about what would happen if we acted in various ways. The regularities that underwrite the modalized structures that embody these best guesses are part of the pattern of actual events. The modal force is an inductive projection of those patterns into the unknown and the purely hypothetical. Naturalistic philosophers looking for a complete, non-redundant catalogue of the basic objects, quantities, and relations of which the world is composed can look to the categorical part of physics. But science is not just about reflecting what is the case. It is also charged with providing representations that can function as a convenient user interface for creatures with our combination of limitations and needs. Overcoming the limitations that our native equipment imposes on how far we can see, and how effectively we can intervene, sets the task for science (and, indeed, for cognition more generally). Scientific models— on the local and global scale—are embodiments of our very best inductive practices. I am suggesting that the modal content of our models—the overlay of laws, dispositions, capacities, and potencies—are to be understood in terms of their role guiding prediction and decision.[8]

  • [1] Because of Lewis’s influence, the problem that chance played in his metaphysics, and the pristine clarity of hisown work on the subject, there is a very well-developed discussion of chance in the philosophical literature.These programmatic remarks about chance are supported in more precise detail in Ismael (2011b, 201). Forsome of the background on chance, see Bigelow, Collins, and Pargetter (1993) and Hall (1994).
  • [2] The case of cause parallels that of chance. Just as in the case of chance, causes can be implicitly defined by theirrole in practical reasoning. And causes relate to correlations in a manner that is quite similar to the relationship between probabilities and frequencies. See Ismael (2012; 2016, chap. 5). For background, see Pearl (2000);Spirtes, Glymour, and Scheines (2000); Woodward (2003).
  • [3] One might think of causal beliefs as encoding implicit, conditional practical imperatives whose practical consequences are drawn out in deliberative application. The practical consequences are a little more complex than“do x" They say “do x if you want y to be the case" or “do x if you want y to be the case, and one of {Zi...zn} andnone of {z*i.. .z*n} obtain as well" ... or something of this sort.
  • [4] This insight is captured succinctly in Alison Gopnik’s lovely dictum, “Counterfactuals about the past ... seemto be the price we pay for counterfactuals about the future” (2009, 23). I would change this slightly to say thatpast counterfactuals are the price we pay for future conditionals. Counterfactuals and future conditionals areboth species of hypothetical. Science deals generically with hypotheticals, and although hypotheticals give usthe logical resources to define counterfactuals, it is the future conditionals that have the most basic cognitivefunction.
  • [5] On the logic of these imaginative explorations and what distinguishes them from purely epistemic reasoning,see Joyce (2002); Anscombe (1963); Ismael (2011a).
  • [6] There are well-defined probabilities only when there are stable relative frequencies across arbitrary subselections from the class. If the class does not have the right structure, or we have specific information about theinstance in question, then chances are not relevant in the same way.
  • [7] This is not their only role. We also care about what would have happened in the past if we had acted differently,even though there is no possibility now of changing that fact, for assigning responsibility, and learning practicallessons, for example.
  • [8] And if asked what the specifically modal content represents/stands-for/corresponds to, I say either (using “represents” in a deflationary way) that it represents modal facts, or (using “represents” in a non-deflationary way)that it does not represent anything. The ambiguity between inflationary and deflationary conceptions makesthe vocabulary of representation famously fraught. I have tried to be explicit in the text where I mean it in aninflationary sense to avoid confusion. See Price (2011) and Thomasson (2015) for discussion of the deflationaryalternative. In either case, I deny that either reduction or reification is needed for realism about these structures.
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