Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

Many standard philosophical accounts of scientific practice fail to distinguish between modeling and other types of theory construction. This failure is unfortunate because there are important contrasts among the goals, procedures, and representations employed by modelers and other kinds of theorists. We can see some of these differences intuitively when we reflect on the methods of theorists such as Vito Volterra and Linus Pauling on the one hand, and Charles Darwin and Dimitri Mendeleev on the other. Much of Volterra's and (...) Pauling's work involved modeling; much of Darwin's and Mendeleev's did not. In order to capture this distinction, I consider two examples of theory construction in detail: Volterra's treatment of post-WWI fishery dynamics and Mendeleev's construction of the periodic system. I argue that modeling can be distinguished from other forms of theorizing by the procedures modelers use to represent and to study real-world phenomena: indirect representation and analysis. This differentiation between modelers and non-modelers is one component of the larger project of understanding the practice of modeling, its distinctive features, and the strategies of abstraction and idealization it employs. (shrink)

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

Modeling is an important scientific practice, yet it raises significant philosophical puzzles. Models are typically idealized, and they are often explored via imaginative engagement and at a certain “distance” from empirical reality. These features raise questions such as what models are and how they relate to the world. Recent years have seen a growing discussion of these issues, including a number of views that treat modeling in terms of indirect representation and analysis. Indirect views treat the model as a bona (...) fide object, specified by the modeler and used to represent and reason about some portion of the concrete empirical world. On some indirect views, model systems are abstract entities, such as mathematical structures, while on other views they are concrete hypothetical things. Here I assess these views and offer a novel account of models. I argue that regarding models as abstracta results in some significant tensions with the practice of modeling, especially in areas where non-mathematical models are common. Furthermore, viewing models as concrete hypotheticals raises difficult questions about model-world relations. The view I argue for treats models as direct, albeit simplified, representations of targets in the world. I close by suggesting a treatment of model-world relations that draws on a recent work by Stephen Yablo concerning the notion of partial truth. (shrink)

In this paper I propose an account of representation for scientific models based on Kendall Walton’s ‘make-believe’ theory of representation in art. I first set out the problem of scientific representation and respond to a recent argument due to Craig Callender and Jonathan Cohen, which aims to show that the problem may be easily dismissed. I then introduce my account of models as props in games of make-believe and show how it offers a solution to the problem. Finally, I demonstrate (...) an important advantage my account has over other theories of scientific representation. All existing theories analyse scientific representation in terms of relations, such as similarity or denotation. By contrast, my account does not take representation in modelling to be essentially relational. For this reason, it can accommodate a group of models often ignored in discussions of scientific representation, namely models which are representational but which represent no actual object. (shrink)

It is a commonplace that contemplation of an imaginary particular may have cognitive and motivational effects that differ from those evoked by an abstract description of an otherwise similar state of affairs. In his Treatise on Human Nature, Hume ([1739] 1978) writes forcefully of this.

forthcoming in R. Cameron, B. Hale and A. Hoffmann (ed.s), The Logic, Epistemology and Metaphysics of Modality, Oxford University Press. Presents a concept-grounding account of modal knowledge.

The paper offers an account of the structure of information provided by models that relevantly deviate from reality. It is argued that accounts of scientific modeling according to which a model’s epistemic and pragmatic relevance stems from the alleged fact that models give access to possibilities fail. First, it seems that there are models that do not give access to possibilities, for what they describe is impossible. Secondly, it appears that having access to a possibility is epistemically and pragmatically idle. (...) Based on these observations, an alternative is developed. (shrink)

The chapter defends an evolutionary explanation of modal knowledge from knowledge of counterfactual conditionals. Knowledge of counterfactuals is evolutionarily useful, as it enables us to learn from mistakes. Given the standard semantics for counterfactuals, there are several equivalences between modal claims and claims involving counterfactuals that can be used to explain modal knowledge. Timothy Williamson has suggested an explanation of modal knowledge that draws on the equivalence of ‘Necessarily p’ with ‘If p were false, a contradiction would be the case’. (...) He postulates a cognitive process that draws on this equivalence and that is supposed to underlie our modal judgements. The existence of this cognitive process would, however, have consequences that conflict with results from empirical psychology. The chapter argues that the equivalence of ‘Necessarily p’ with ‘For all q, if q were true then p would be true’ should instead be used to explain knowledge of necessity. This explanation requires giving an account of how we know truths of the form ‘For all q, if q were true then p would be true’. In order to provide such an account, the chapter draws on a different suggestion by Williamson about knowledge of generalizations. According to this suggestion, we come to know truths of the form ‘All Fs are G’ by imagining a generic F and judging that it is G. Applied to our case, the suggestion would be that we come to know that p is counterfactually implied by all propositions (and hence that p is necessary) by entertaining a generic proposition and judging that it counterfactually implies p. It would even suffice to entertain a generic possible proposition and judge that it counterfactually implies p, for it can be shown that the claim ‘For all possible q, if q were true then p would be true’ is equivalent to the original claim ‘For all q, if q were true then p would be true’ and hence is equivalent to ‘Necessarily p’. It might seem that, from an evolutionary perspective, probabilistic reasoning is just as useful as reasoning involving counterfactuals. The chapter argues, however, that this would not undermine the envisaged explanation of modal knowledge. The chapter concludes by suggesting avenues of empirical research that might shed light on the cognitive processes that actually underlie our evaluations of modal claims and on the relation between these processes and those involved in counterfactual reasoning. The results of such empirical research would be highly relevant epistemologically, since they will ultimately determine which (if any) equivalence between modal claims and claims involving counterfactuals should be used to explain our modal knowledge. (shrink)

I compare two prominent approaches to knowledge of metaphysical modality, the more traditional approach via conceiving viz. imagining a scenario and a more recent approach via counterfactual reasoning. In particular, Timothy Williamson has claimed that the proper context for a modal exercise of imagination is a counterfactual supposition. I critically assess this claim, arguing that a purely conceivability/imaginability-based approach has a key advantage compared to a counterfactual-based one. It can take on board Williamson’s insights about the structure of modal imagination (...) while avoiding aspects of counterfactual reasoning which are orthogonal to figuring out metaphysical modality. In assessing whether A is possible, we creatively devise test scenarios, psychologically and metaphysically apt A-scenarios, which manifest the relevant metaphysical requirements and test them for their compatibility with A. In this exercise, imagination is subject to implicit constraints as Williamson has it, but it is not bound to drawing consequences from minimally altering actuality such as to make room for A. (shrink)