I argue for an intentional conception of representation in science that requires bringing scientific agents and their intentions into the picture. So the formula is: Agents (1) intend; (2) to use model, M; (3) to represent a part of the world, W; (4) for some purpose, P. This conception legitimates using similarity as the basic relationship between models and the world. Moreover, since just about anything can be used to represent anything else, there can be no unified ontology of models. (...) This whole approach is further supported by a brief exposition of some recent work in cognitive, or usage-based, linguistics. Finally, with all the above as background, I criticize the recently much discussed idea that claims involving scientific models are really fictions. (shrink)

In this paper, I aim to provide access to the current debate on non-causal explanations in philosophy of science. I will first present examples of non-causal explanations in the sciences. Then, I will outline three alternative approaches to non-causal explanations – that is, causal reductionism, pluralism, and monism – and, corresponding to these three approaches, different strategies for distinguishing between causal and non-causal explanation. Finally, I will raise questions for future research on non-causal explanations.

The recent discussion on scientific representation has focused on models and their relationship to the real world. It has been assumed that models give us knowledge because they represent their supposed real target systems. However, here agreement among philosophers of science has tended to end as they have presented widely different views on how representation should be understood. I will argue that the traditional representational approach is too limiting as regards the epistemic value of modelling given the focus on the (...) relationship between a single model and its supposed target system, and the neglect of the actual representational means with which scientists construct models. I therefore suggest an alternative account of models as epistemic tools. This amounts to regarding them as concrete artefacts that are built by specific representational means and are constrained by their design in such a way that they facilitate the study of certain scientific questions, and learning from them by means of construction and manipulation. (shrink)

Models such as the simple pendulum, isolated populations, and perfectly rational agents, play a central role in theorising. It is now widely acknowledged that a study of scientific representation should focus on the role of such imaginary entities in scientists’ reasoning. However, the question is most of the time cast as follows: How can fictional or abstract entities represent the phenomena? In this paper, I show that this question is not well posed. First, I clarify the notion of representation, and (...) I emphasise the importance of what I call the “format” of a representation for the inferences agents can draw from it. Then, I show that the very same model can be presented under different formats, which do not enable scientists to perform the same inferences. Assuming that the main function of a representation is to allow one to draw predictions and explanations of the phenomena by reasoning with it, I conclude that imaginary models in abstracto are not used as representations: scientists always reason with formatted representations. Therefore, the problem of scientific representation does not lie in the relationship of imaginary entities with real systems. One should rather focus on the variety of the formats that are used in scientific practice. (shrink)

We propose that scientific representation is a special case of a more general notion of representation, and that the relatively well worked-out and plausible theories of the latter are directly applicable to thc scientific special case. Construing scientific representation in this way makes the so-called “problem of scientific representation” look much less interesting than it has seerned to many, and suggests that some of the (hotly contested) debates in the literature are concerned with non-issues.

We propose that scientific representation is a special case of a more general notion of representation, and that the relatively well worked-out and plausible theories of the latter are directly applicable to the scientific special case.

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

An account of scientific representation in terms of partial structures and partial morphisms is further developed. It is argued that the account addresses a variety of difficulties and challenges that have recently been raised against such formal accounts of representation. This allows some useful parallels between representation in science and art to be drawn, particularly with regard to apparently inconsistent representations. These parallels suggest that a unitary account of scientific and artistic representation is possible, and our article can be viewed (...) as laying the groundwork for such an account—although, as we shall acknowledge, significant differences exist between these two forms of representation. (shrink)

Callender and Cohen argue that there is no need for a special account of the constitution of scientific representation. I argue that scientific representation is communal and therefore deeply tied to the practice in which it is embedded. The communal nature is accounted for by licensing, the activities of scientific practice by which scientists establish a representation. A case study of the Lotka-Volterra model reveals how licensure is a constitutive element of the representational relationship. Thus, any account of the constitution (...) of scientific representation must account for licensing, meaning that there is a special problem of scientific representation. (shrink)

This article attempts to address the problem of the applicability of mathematics in physics by considering the (narrower) question of what make the so-called special functions of mathematical physics special. It surveys a number of answers to this question and argues that neither simple pragmatic answers, nor purely mathematical classificatory schemes are sufficient. What is required is some connection between the world and the way investigators are forced to represent the world.

This article discusses minimal model explanations, which we argue are distinct from various causal, mechanical, difference-making, and so on, strategies prominent in the philosophical literature. We contend that what accounts for the explanatory power of these models is not that they have certain features in common with real systems. Rather, the models are explanatory because of a story about why a class of systems will all display the same large-scale behavior because the details that distinguish them are irrelevant. This story (...) explains patterns across extremely diverse systems and shows how minimal models can be used to understand real systems. (shrink)

The aim of this paper is to defend the structural concept of representation, as defined by homomorphisms, against its main objections, namely: logical objections, the objection from misrepresentation, theobjection from failing necessity, and the copy theory objection. The logical objections can be met by reserving the relation ‘to be homomorphic to’ for the explication of potential representation (or, of the representational content). Actual reference objects (‘targets’) of representations are determined by (intentional or causal) representational mechanisms. Appealing to the independence of (...) the dimensions of ‘content’ and ‘target’ also helps to see how the structural concept can cope with misrepresentation. Finally, I argue that homomorphic representations are not necessarily ‘copies’ of their representanda, and thus can convey scientific insight. (shrink)

The paper defends the structural concept of representation, defined by homomorphisms, against the main objections that have been raised against it: Logical objections, the objection from misrepresentation, the objection from failing necessity, and the copy theory objection. Homomorphic representations are not necessarily ‘copies’ of their representanda, and thus can convey scientific insight.

The paper defends the structural concept of representation, defined by homomorphisms, against the main objections that have been raised against it: Logical objections, the objection from misrepresentation, the objection from failing necessity, and the copy theory objection. Homomorphic representations are not necessarily ‘copies’ of their representanda, and thus can convey scientific insight.

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non-causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka–Volterra equations. There are (...) at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, and another that yields explanations that are distinctively mathematical in terms of nomological strength. In the first case, one first picks out a system or class of systems, and finds that the equations hold in a causal–explanatory way. In the second case, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non-causal explanations can complement one another. _1_. Introduction _2._ Delineating the Boundaries of Causal Explanation _2.1._ Why construe causal explanation narrowly? The land of explanation versus grain-focusing _2.2._ Reasons to narrow the scope of causal explanation _3._ Broadening the Scope of Mathematical Explanation _4._ Lotka–Volterra: Same Model, Different Explanation Types _4.1._ General biocide in the Lotka–Volterra model _4.2._ Two ways a model can hold, yielding causal versus mathematical explanations _5._ Four Complementary Relationships between Mathematical and Causal Explanation _5.1._ Slight reformulations of explananda _5.2._ Causal distortion of idealized mathematical models _5.3._ Partial explanations requiring supplementation _5.4._ Explanatory dimensionality _6._ Conclusion. (shrink)

For a long time, the accepted explanatory model of language acquisition was the so-called Principles and Parameters framework (P&P). P&P seemingly provides an elegant answer to the central puzzle of generative linguistics: How do children acquire their native language given the limited time and input resources available to them? Yet P&P tells a story that is evolutionarily implausible, and for this reason it has since been abandoned. I argue that this is an unwarranted move, and that it could and should (...) be avoided by reassessing the epistemic status of P&P. In particular, I argue that contrary to extant accounts, P&P ought to be retrospectively construed as a highly idealized (toy) model of language acquisition. The proposed reinterpretation is vindicated, I argue, insofar as it paves the way for a reconciliation of the two central explanatory challenges of modern generative linguistics. (shrink)

Inferentialists about scientific representation hold that an apparatus’s representing a target system consists in the apparatus allowing “surrogative inferences” about the target. I argue that a serious problem for inferentialism arises from the fact that many scientific theories and models contain internal inconsistencies. Inferentialism, left unamended, implies that inconsistent scientific models have unlimited representational power, since an inconsistency permits any conclusion to be inferred. I consider a number of ways that inferentialists can respond to this challenge before suggesting my own (...) solution. I develop an analogy to exploitable glitches in a game. Even though inconsistent representational apparatuses may in some sense allow for contradictions to be generated within them, doing so violates the intended function of the apparatus’s parts and hence violates representational “gameplay.”. (shrink)

Scientific representation is a currently booming topic, both in analytical philosophy and in history and philosophy of science. The analytical inquiry attempts to come to terms with the relation between theory and world; while historians and philosophers of science aim to develop an account of the practice of model building in the sciences. This article provides a review of recent work within both traditions, and ultimately argues for a practice-based account of the means employed by scientists to effectively achieve representation (...) in the modelling sciences. (shrink)

This paper defends an inferential conception of scientific representation. It approaches the notion of representation in a deflationary spirit, and minimally characterizes the concept as it appears in science by means of two necessary conditions: its essential directionality and its capacity to allow surrogate reasoning and inference. The conception is defended by showing that it successfully meets the objections that make its competitors, such as isomorphism and similarity, untenable. In addition the inferential conception captures the objectivity of the cognitive representations (...) used by science, it sheds light on their truth and completeness, and it explains the source of the analogy between scientific and artistic modes of representation. (shrink)

Every model leaves out or distorts some factors that are causally connected to its target phenomenon -- the phenomenon that it seeks to predict or explain. If we want to make predictions, and we want to base decisions on those predictions, what is it safe to omit or to simplify, and what ought a causal model to describe fully and correctly? A schematic answer: the factors that matter are those that make a difference to the target phenomenon. There are several (...) ways to understand differencemaking. This paper advances a view as to which is the most relevant to the forecaster and the decision-maker. It turns out that the right notion of differencemaking for thinking about idealization in prediction is also the right notion for thinking about idealization in explanation; this suggests a carefully circumscribed version of Hempel's famous thesis that there is a symmetry between explanation and prediction. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov–Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a middle (...) ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

In this paper I show how certain requirements must be set on any tenable account of scientific representation, such as the requirement allowing for misrepresentation. I then continue to argue that two leading accounts of scientific representation— the inferential account and the interpretational account—are flawed for they do not satisfy such requirements. Through such criticism, and drawing on an analogy from non-scientific representation, I also sketch the outline of a superior account. In particular, I propose to take epistemic representations to (...) be intentional objects that come with reference, semantic contents and a representational code, and I identify faithful representations as representations that act as guides to ontology. (shrink)

This paper discusses several distinct process theories of causality offered in recent years by Phil Dowe and me. It addresses problems concerning the explication of causal process, causal interaction, and causal transmission, whether given in terms of transmission of marks, transmission of invariant or conserved quantities, or mere possession of conserved quantities. Renouncing the mark-transmission and invariant quantity criteria, I accept a conserved quantity theory similar to Dowe's--differing basically with respect to causal transmission. This paper also responds to several fundamental (...) constructive criticisms contained in Christopher Hitchcock's discussion of both the mark-transmission and the conserved quantity theories. (shrink)

The “universality” of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions in unifying a large class of phenomena, regardless of microscopic constitution. They argue for an essential explanatory role for “commonalities” rather than that of idealizations. Building on Batterman's insight, this article aims to show that assessing the differences between the universality of critical phenomena and two paradigmatic cases of “commonality (...) strategy”—the ideal gas model and the harmonic oscillator model—is necessary to avoid the objections raised by Lange and Reutlinger. Taking these universal explanations as benchmarks for critical phenomena reveals the importance of the different roles played by analogies underlying the use of the models. A special combination of physical and formal analogies allows one to explain the epistemic autonomy of the universality of critical phenomena through an explicative loop. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

This article shows how the MISS account of models—as isolations and surrogate systems—accommodates and elaborates Sugden’s account of models as credible worlds and Hausman’s account of models as explorations. Theoretical models typically isolate by means of idealization, and they are representatives of some target system, which prompts issues of resemblance between the two to arise. Models as representations are constrained both ontologically (by their targets) and pragmatically (by the purposes and audiences of the modeller), and these relations are coordinated by (...) a model commentary. Surrogate models are often about single mechanisms. They are distinguishable from substitute models, which are examined without any concern about their connections with the target. Models as credible worlds are surrogate models that are believed to provide access to their targets on account of their credibility (of which a few senses are distinguished). (shrink)

A general account of modeling in physics is proposed. Modeling is shown to involve three components: denotation, demonstration, and interpretation. Elements of the physical world are denoted by elements of the model; the model possesses an internal dynamic that allows us to demonstrate theoretical conclusions; these in turn need to be interpreted if we are to make predictions. The DDI account can be readily extended in ways that correspond to different aspects of scientific practice.

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

Several philosophers have suggested that some scientific explanations work not by virtue of describing aspects of the world’s causal history and relations, but rather by citing mathematical facts. This paper investigates what mathematical facts could be in order for them to figure in such “distinctively mathematical” scientific explanations. For “distinctively mathematical explanations” to be explanations by constraint, mathematical language cannot operate in science as representationalism or platonism describes. It can operate as Aristotelian realism describes. That is because Aristotelian realism enables (...) mathematics to apply to the physical world without a morphism’s mediation. (shrink)

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features (...) of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs. -/- . (shrink)

Representation has been one of the main themes in the recent discussion of models. Several authors have argued for a pragmatic approach to representation that takes users and their interpretations into account. It appears to me, however, that this emphasis on representation places excessive limitations on our view of models and their epistemic value. Models should rather be thought of as epistemic artifacts through which we gain knowledge in diverse ways. Approaching models this way stresses their materiality and media-specificity. Focusing (...) on models as multi-functional artifacts loosens them from any pre-established and fixed representational relationships and leads me to argue for a two-fold approach to representation. (shrink)

This essay presents a fully inferentialist-expressivist account of scientific representation. In general, inferentialist approaches to scientific representation argue that the capacity of a model to represent a target system depends on inferences from models to target systems. Inferentialism is attractive because it makes the epistemic function of models central to their representational capacity. Prior inferentialist approaches to scientific representation, however, have depended on some representational element, such as denotation or representational force. Brandom’s Making It Explicit provides a model of how (...) to fully discharge such representational vocabulary, but it cannot be applied directly to scientific representations. Pursuing a strategy parallel to Brandom’s, this essay begins with an account of how surrogative inference is justified. Scientific representation and the denotation of model elements are then explained in terms of surrogative inference by treating scientific representation and denotation as expressive, analogous to Brandom’s account of truth. The result is a thoroughgoing inferentialism: M is a scientific representation of T if and only if M has scientifically justified surrogative consequences that are answers to questions about T. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

By contrasting three general conceptions of scientific explanation, this paper seeks to clarify the explanandum and to exhibit the fundamental philosophical issues involved in the project of explicating scientific explanation. The three conceptions--epistemic, modal, and ontic--have both historical and contemporary importance. In the context of Laplacian determinism, they do not seem importantly distinct, but in the context of irreducibly statistical explanations, the three are seen to diverge sharply. The paper argues for a causal/mechanical version of the ontic conception, and concludes (...) by exhibiting some striking consequences of this approach. (shrink)