A central goal of the scientific endeavor is to explain phenomena. Scientists often attempt to explain a phenomenon by way of representing it in some manner—such as with mathematical equations, models, or theory—which allows for an explanation of the phenomenon under investigation. However, in developing scientific representations, scientists typically deploy simplifications and idealizations. As a result, scientific representations provide only partial, and often distorted, accounts of the phenomenon in question. Philosophers of science have analyzed the nature and function (...) of how scientists construct representations, deploy idealizations, and provide explanations. As such, our aim in this special issue is to bring these three pillars of research into closer contact with the contributions to it focusing on three main themes. -/- The first set of papers, Alan Baker (2021) and Marc Lange (2021), address mathematical explanations in science. Baker (2021), a proponent of mathematical Platonism, examines its capacity to evade the critique that the so-called Enhanced Indispensability Argument is circular. Lange (2021) examines distinctively mathematical explanations, arguing that neither Platonism nor representationalism are successful paths, and instead argues in favor of Aristotelian realism. A second theme emerging from the papers in this special issue is the impact that various conceptualizations of idealization have on our abilities to offer scientific explanations, to pro- duce an analysis of what explanations are or should be, and to understand scientific representation. Peter Tan (2021) suggests amending inferentialist accounts of scientific representation to account for inconsistent idealizations. Michael Strevens (2021) advocates a view wherein the introduction of idealizations into a model is legitimate so long as it pertains to non-difference-making factors, arguing for a logical reading of the notion of difference-making. Natalia Carrillo and Tarja Knuuttila (2022) offer an alternative account to the idealization-as-distortion view, emphasizing instead the holistic nature of idealization. -/- Finally, contributions by Carrillo and Knuuttila (2022), Terzian (2021), Valente (2021), and Rodriguez (2021) illustrate how issues regarding idealization, representation, and explanation are applied to specific contexts and across various sciences. Carrillo and Knuuttila (2022) examine conceptions of idealization in the context of models of the nerve impulse. Giulia Terzian (2021) extends the discussion of idealizations to the context of generative linguistics. Giovanni Valente (2021) examines how idealizations and evaluations of accurate representation impact capacities to explain phenomena in the context of statistical thermodynamics. Quentin Rodriguez (2021) examines the role of idealizations and analogies in various strategies to explain critical phenomena. -/- In what follows, we offer a brief overview of important philosophical issues connected to representation, idealization, and explanation in science. We then provide short summaries of the eight papers in this special issue. (shrink)

I argue that an adequate understanding of the practice of constructing models in physics requires a distinction between two strategies that are commonly both labeled ‘idealization’. The formal characteristic of both methods is to let a parameter in the equations for a target system go to zero. But the discussion of examples from various applications of perturbation theory shows that there is in general a difference with respect to the aims such limiting procedures are supposed to serve; and with different (...) aims comes the need to characterize the means (the interpretation of the limits) differently. I therefore suggest that we distinguish ‘idealizations’ from ‘perspectives’ or perspectival representations. (shrink)

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We (...) focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (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)

This paper examines the nomic covariationist strategy of using idealization to define representation. While the literature has focused upon the possibility of defining ideal conditions for perception, I argue that nomic covariationist appeals to idealization are pseudoscientific and contrary to a foundational and empirically well-supported methodological presupposition in cognitive science. Moreover, one major figure in this camp fails to come to grips with its role and its problems in mainstream science. Thus he forwards a false dichotomy of the sciences and (...) treats idealization as a blank check written by scientists on an unknown bank. Finally, I consider and reject alternative formulations of the nomic covariationist's idealization strategy. (shrink)

In this paper, I attempt to sketch a dialectical approach on scientific representations and their role in scientific cognition. In my understanding, scientific representations can be construed as ‘tools’ mediating scientific cognition. These ‘tools’ are products of our cognitive activity, by which we signify which features of certain objects or states of affairs should be embodied in abstractive representations of them. In such a context, I explore the merits of bringing some ideas of thinkers whose work is (...) underestimated in the relevant discussion nowadays (such as K. Marx, E.V. Ilyenkov, L.S. Vygotsky, M. Wartofsky) in dialogue with currently discussed approaches. (shrink)

This paper erects a framework for analyzing some idealized models as (what I call) inferentially veridical representations. It adopts a version of the semantic view of theories that focuses on properties, and mobilizes conceptual resources associated with properties and the way that properties are related in various ways. The outcome is an elaboration of some aspects of the analysis of Jones (2005).

In this paper, I attempt to sketch a dialectical approach on scientific representations and their role in scientific cognition. In my understanding, scientific representations can be construed as ‘tools’ mediating scientific cognition. These ‘tools’ are products of our cognitive activity, by which we signify which features of certain objects or states of affairs should be embodied in abstractive representations of them. In such a context, I explore the merits of bringing some ideas of thinkers whose work is (...) underestimated in the relevant discussion nowadays in dialogue with currently discussed approaches. (shrink)

This paper calls into question one fundamental claim at the basis of an alleged puzzle for veritistic accounts of the value of idealized models: the claim that idealized models cannot be veridical representations of the world. Catherine Elgin has argued that the value of idealized models can only be explained if we construe them as exemplars, which do not represent the world. I argue that Elgin’s proposal is problematic and cannot accommodate central cases of idealization. Nevertheless, (...) there is value in Elgin’s proposal. I rescue her notion of selectiveness in exemplification and incorporate it within a revised account of representation. I provide independent motivation in favour of a form of veritism, which motivates a revision of Elgin’s case against it. I argue that an account based on selective representation has the resources to rescue veritism from the problems raised by Elgin. In the proposal I advance, idealized models are literally veridical representations of the world. (shrink)

The problem with idealization is not just that, when idealizing, scientists ask us to suppose false things. Many people do that. No, the puzzling thing about idealizers—unlike astrologers, spodomancers, and homeopaths—is that it is worth listening to them. Supposing that populations of rabbits are in- finite is useful for a variety of ecological explanations. Yet we are not up to our necks in rabbits; the puzzle is why it should be useful to suppose that we are.

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the (...) properties of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail, the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding of certain physical phenomena cannot be obtained (...) through completely detailed, non-idealized representations. (shrink)

In this paper, I first outline the view developed in my recent book on the role of idealization in scientific understanding. I discuss how this view leads to the recognition of a number of kinds of variability among scientific representations, including variability introduced by the many different aims of scientific projects. I then argue that the role of idealization in securing understanding distances understanding from truth, but that this understanding nonetheless gives rise to scientific knowledge. This discussion will clarify (...) how my view relates to three other recent books on understanding by Henk de Regt, Catherine Elgin, and Kareem Khalifa. (shrink)

In this essay, I attempt to consider a difficult issue: the triangular relationship between the subject, the object and the visual representations of masculinity in the context of male homosexual desire. I outline contemporary circumstances of society’s interaction with popular culture in which gay men form two images of an idealized masculine body: a concept of their own body and a concept of the body they feel sexually attracted to. My concern is to theorize these two kinds of (...) desire and position them in the chaotic landscape of contesting masculinities that increasingly often besiege men via visual media. I differentiate between “straight” and “gay” masculinities as historically they have been represented and negotiated independently. What I want to reflect on is in what ways these masculinities can impact on gay men’s desires—to be a man, and to have a man. Approaching this task produces a rather puzzling picture as interpreting contemporary visual culture poses more questions than it gives answers. I argue that some of these questions are worth pursuing as an empirical inquiry. My objective is to provide a theoretical background such work could be based on. I locate elements of this theory that I find problematic or out-of-date and mention certain aspects of the problem that I believe could be addressed further. (shrink)

In this essay, I attempt to consider a difficult issue: the triangular relationship between the subject, the object and the visual representations of masculinity in the context of male homosexual desire. I outline contemporary circumstances of society’s interaction with popular culture in which gay men form two images of an idealized masculine body: a concept of their own body and a concept of the body they feel sexually attracted to. My concern is to theorize these two kinds of (...) desire and position them in the chaotic landscape of contesting masculinities that increasingly often besiege men via visual media. I differentiate between “straight” and “gay” masculinities as historically they have been represented and negotiated independently. What I want to reflect on is in what ways these masculinities can impact on gay men’s desires—to be a man, and to have a man. Approaching this task produces a rather puzzling picture as interpreting contemporary visual culture poses more questions than it gives answers. I argue that some of these questions are worth pursuing as an empirical inquiry. My objective is to provide a theoretical background such work could be based on. I locate elements of this theory that I find problematic or out-of-date and mention certain aspects of the problem that I believe could be addressed further. (shrink)

The author discusses the concept of an ideal object. The statement of O.I. Genisaretsky is quoted and problematized, stating that the obligatory feature that has been preserved for the object and the terms "object" and "ideal object" is, apparently, its representability or visibility. The author shows that ideal objects began to be created during the formation of ancient philosophy and thinking. Faced with contradictions, ancient thinkers dealt with this situation in different ways. If Protogoras recognized the right of the reasoners (...) to receive contradictions and, accordingly, to consider the world contradictory, then Parmenides considered the world consistent, arguing that the criterion for the correctness (truth) of knowledge is not a reasoning person, but this world, existence, which still needs to be reached with the help of correct thought. It was within the framework of the implementation of the Parmenides program that ideal objects began to be created, which, as the author shows, performed three main functions: they allowed us to think consistently, to know the world and its phenomena, to comprehend and interpret empirical phenomena (facts) in a different way. Based on the case of Plato's "Feast", the semiotic schemes on the basis of which Plato creates ideal objects are analyzed. It is argued that it is impossible to build ideal objects, bypassing schemes, since their inventors (creators) are people. By solving problems, they synthesize meanings belonging to different areas of consciousness. The analysis of Galileo's "Conversations" allowed the author to suggest that the construction of ideal objects is due to the historical type of philosophical or scientific thinking. The author considers it necessary, before claiming to create a modern doctrine of ideal objects, to analyze the main typical cases of the construction of these objects in philosophy and science, and such an analysis can make significant adjustments to the understanding of the nature and features of this concept. Nevertheless, he suggests, it is already clear that the construction of ideal objects is an important link in philosophical, scientific and a number of other types of thinking. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

The concept of Galilean Idealization is based on a pragmatically grounded relation between universes of so-called real and idealized entities. The concept was developed in the course of a critical discussion of different explications of the concept of idealization (e.g. by W. F. Barr, C. G. Hempel and L. Nowak), these being attempts to specify sufficient syntactic and semantic criterions for idealization. But this line of argument shall not be followed here. Instead, first the concept of Pragmatic Idealization, and (...) as its special case the Galilean one, is presented (1.) and certain aspects of the application of an idealized theory are discussed (2.). Then, working within the Strucuralist View of theories, definitions of the idealized variants of the diachronic theory-element and theory-net are presented (3.). (shrink)

Bayesian epistemology provides a popular and powerful framework for modeling rational norms on credences, including how rational agents should respond to evidence. The framework is built on the assumption that ideally rational agents have credences, or degrees of belief, that are representable by numbers that obey the axioms of probability. From there, further constraints are proposed regarding which credence assignments are rationally permissible, and how rational agents’ credences should change upon learning new evidence. While the details are hotly disputed, all (...) flavors of Bayesianism purport to give us norms of ideal rationality. This raises the question of how exactly these norms apply to you and me, since perfect compliance with those ideal norms is out of reach for human thinkers. A common response is that Bayesian norms are ideals that human reasoners are supposed to approximate – the closer they come to being ideally rational, the better. To make this claim plausible, we need to make it more precise. In what sense is it better to be closer to ideally rational, and what is an appropriate measure of such closeness? This article sketches some possible answers to these questions. (shrink)

In this paper, I first argue against various attempts to justify idealizations in scientific models that explain by showing that they are harmless and isolable distortions of irrelevant features. In response, I propose a view in which idealized models are characterized as providing holistically distorted representations of their target system. I then suggest an alternative way that idealized modeling can be justified by appealing to universality.

Idealization is a fundamental feature of human thought. We build simplified models in our scientific research and utopias in our political imaginations. Concepts like belief, desire, reason, and justice are bound up with idealizations and ideals. Life is a constant adjustment between the models we make and the realities we encounter. In idealizing, we proceed “as if” our representations were true, while knowing they are not. This is not a dangerous or distracting occupation, Kwame Anthony Appiah shows. Our best (...) chance of understanding nature, society, and ourselves is to open our minds to a plurality of imperfect depictions that together allow us to manage and interpret our world. -/- The philosopher Hans Vaihinger first delineated the “as if” impulse at the turn of the twentieth century, drawing on Kant, who argued that rational agency required us to act as if we were free. Appiah extends this strategy to examples across philosophy and the human and natural sciences. In a broad range of activities, we have some notion of the truth yet continue with theories that we recognize are, strictly speaking, false. From this vantage point, Appiah demonstrates that a picture one knows to be unreal can be a vehicle for accessing reality. -/- As If explores how strategic untruth plays a critical role in far-flung areas of inquiry: decision theory, psychology, natural science, and political philosophy. A polymath who writes with mainstream clarity, Appiah defends the centrality of the imagination not just in the arts but in science, morality, and everyday life. (shrink)

Woosuk Park’s paper “Misrepresentation in Context” is a useful plea for a theory of representation with promising interaction between cognitive science, philosophy of science, and aesthetics. In this paper, I argue that such a unified account is provided by Charles S. Peirce’s semiotics. This theory puts Park’s criticism of Nelson Goodman and Jerry Fodor in context. Some of Park’s pertinent remarks on the problem of misrepresentation can be illuminated by the account of truthlikeness and idealization developed by philosophers of science.

A distinction is made between theory-driven and phenomenological models. It is argued that phenomenological models are significant means by which theory is applied to phenomena. They act both as sources of knowledge of their target systems and are explanatory of the behaviors of the latter. A version of the shell-model of nuclear structure is analyzed and it is explained why such a model cannot be understood as being subsumed under the theory structure of Quantum Mechanics. Thus its representational capacity does (...) not stem from its close link to theory. It is shown that the shell model yields knowledge about the target and is explanatory of certain behaviors of nuclei. Aspects of the process by which the shell model acquires its representational capacity are analyzed. It is argued that these point to the conclusion that the representational status of the model is a function of its capacity to function as a source of knowledge and its capacity to postulate and explain underlying mechanisms that give rise to the observed behavior of its target. (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)

Mathematical idealizations are scientific representations that result from assumptions that are believed to be false, and where mathematics plays a crucial role. I propose a two stage account of how to rank mathematical idealizations that is largely inspired by the semantic view of scientific theories. The paper concludes by considering how this approach to idealization allows for a limited form of scientific realism. ‡I would like to thank Robert Batterman, Gabriele Contessa, Eric Hiddleston, Nicholaos Jones, and Susan Vineberg for (...) helpful discussions and encouragement. †To contact the author, please write to: Department of Philosophy, Beering Hall, Purdue University, 100 N. University Street, West Lafayette, IN 47907-2098; e-mail: [email protected]. (shrink)

Are there representations in the brain? It depends on what you mean by representations, and it depends on what you want them to do for you—both in terms of the causal role they play in the system, and in terms of their explanatory value. But ideally, we would like an account of representation that allows us to assign a representational role and content to the appropriate mechanistic precursors of behavior that in fact play that role and conversely, search (...) for the mechanistic realizers of representational roles that are posited by our models of behavior and cognition. Such an account would be methodologically valuable in neuroscience. Lately, people have started asking similar questions about deep neural networks. What representations do they learn and use, and what is the relation between those representations and the sometimes impressive capacities these networks exhibit? More philosophically puzzling, perhaps, is the question of why the internal activities or dispositions labeled as such in neuroscience and AI research should count as representations at all. I think we can give a unified answer to both sets of questions, in the form of a kind of representational pragmatism. What makes something a representation just is that we can identify and re-identify it as such, and moreover, that we can manipulate it effectively to do whatever it is that we think representations ought to do for us in that particular context. For the first condition, the idea is that so long as we have some probe that allows us to pick out the relevant causally effective candidate, we should consider that to be a candidate representation-relative-to-that-probe. The second condition can be understood as a kind of anti-gerrymandering constraint: one ought to be able to intervene on the candidate, and see effects of that intervention consistent with the functional role the representation is supposed to play. Naturally the details need to be spelled out for different contexts—and I will articulate them for a few illustrative cases—which effectively allows for a kind of pluralism about representation depending on the setting and the kinds of questions being asked. With the extra components filled in, representational pragmatism can make sense of existing practices in neuroscience and AI, as well as their relationship to naturalistic theories of representation in philosophy. (shrink)

Intelligent systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing both the needs of superordinate and basic-level categorization and of identification of specific instances of familiar categories. According to the proposed theory, a shape is represented by its similarity to a number of reference shapes, measured in a high-dimensional space of elementary features. This amounts to embedding the stimulus in a (...) low-dimensional proximal shape space. That space turns out to support representation of distal shape similarities which is veridical in the sense of Shepard's (1968) notion of second-order isomorphism (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical, as in the multidimensional scaling models (Shepard, 1980), to discrete and non-hierarchical, as in the general contrast models (Tversky, 1977; Shepard and Arabie, 1979). (shrink)

This article reviews the recent literature on idealization, specifically idealization in the course of scientific modeling. We argue that idealization is not a unified concept and that there are three different types of idealization: Galilean, minimalist, and multiple models, each with its own justification. We explore the extent to which idealization is a permanent feature of scientific representation and discuss its implications for debates about scientific realism.

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to (...) our best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

What does it take to understand a phenomenon ideally, or to the highest conceivable extent? In this paper, we answer this question by arguing for five necessary conditions for ideal understanding: (i) representational accuracy, (ii) intelligibility, (iii) truth, (iv) reasonable endorsement, and (v) fitting. Even if one disagrees that there is some form of ideal understanding, these five conditions can be regarded as sufficient conditions for a particularly deep level of understanding. We then argue that grasping, novel predictions, and transparency (...) are not reasonable conditions for ideal understanding. (shrink)

Scientific models typically contain idealizations, or assumptions that are known not to be true. Philosophers have long questioned the nature of idealizations: Are they heuristic tools that will be abandoned? Or rather fictional representations of reality? And how can we reconcile them with realism about knowledge of nature? Immanuel Kant developed an account of scientific investigation that can inspire a new approach to the contemporary debate. Kant argued that scientific investigation is possible only if guided by ideal assumptions—what he (...) calls “regulative ideas”. These ideas are not true of objects of nature, and yet they are not heuristic tools or fictional represen- tations. They are necessary rules governing the construction and assessment of scientific explanations. In this paper, I suggest that some idealizations can be interpreted as having necessary regulative value and as being compatible with scientific realism. I first analyze the puzzle of the nature of idealization and present the main approaches to this topic in the literature. Second, I reconsider the puzzle vis-a-vis a restricted, Kantian definition of idealization and a novel characterization of the relation between idealization and truth. Finally, I discuss in detail an example of idealization (the Hardy-Weinberg equilibrium) along the suggested Kantian lines. (shrink)

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to (...) our best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve (...) the false assumption that the ocean is infinitely deep. While it is true that the variable associated with depth is often taken to infinity in the representation of ocean waves, I explain how this mathematical transformation of the original equations does not require the belief that the ocean being modeled is infinitely deep. More generally, as a mathematical representation is manipulated, some of its components are decoupled from their original physical interpretation. (shrink)

The ideal world semantics of standard deontic logic identifies our obligations with how we would act in an ideal world. However, to act as if one lived in an ideal world is bad moral advice, associated with wishful thinking rather than well-considered moral deliberation. Ideal world semantics gives rise to implausible logical principles, and the metaphysical arguments that have been put forward in its favour turn out to be based on a too limited view of truth-functional representation. It is argued (...) that ideal world semantics should be given up in favour of other, more plausible uses of possible worlds for modelling normative subject-matter. (shrink)

In empirical modeling, mathematics has an important utility in transforming descriptive representations of target system into calculation devices, thus creating useful scientific models. The transformation may be considered as the action of tools. In this paper, I assume that model idealizations could be such tools. I then examine whether these idealizations have characteristic properties of tools, i.e., whether they are being adapted to the objects to which they are applied, and whether they are to some extent generic.

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum (...) mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures. (shrink)

In this article I discuss the advantages of a theory of political representation for a prag- matist theory of (global) democracy. I first outline Dewey’s disregard for political rep- resentation by analyzing the political, epistemological and aesthetic underpinnings of his criticism of the Enlightenment ideal of democracy and its trust in the power of the detached gaze. I then show that a theory of political representation is not only com- patible with a pragmatist Deweyan-pragmatist perspective on democratic politics but also (...) that Dewey’s concept of “publics”, if applied to contemporary circumstances of globalized politics, requires such a theory. I suggest a pragmatic theory of political rep- resentation that combines elements of Dewey’s aesthetics, particularly his own theory of vision, with Michael Saward’s conception of representative claim-making into the notion of aesthetic democratic representation. (shrink)

Scientific research is almost always conducted by communities of scientists of varying size and complexity. Such communities are effective, in part, because they divide their cognitive labor: not every scientist works on the same project. Philip Kitcher and Michael Strevens have pioneered efforts to understand this division of cognitive labor by proposing models of how scientists make decisions about which project to work on. For such models to be useful, they must be simple enough for us to understand their dynamics, (...) but faithful enough to reality that we can use them to analyze real scientific communities. To satisfy the first requirement, we must employ idealizations to simplify the model. The second requirement demands that these idealizations not be so extreme that we lose the ability to describe real-world phenomena. This paper investigates the status of the assumptions that Kitcher and Strevens make in their models, by first inquiring whether they are reasonable representations of reality, and then by checking the models' robustness against weakenings of these assumptions. To do this, we first argue against the reality of the assumptions, and then develop a series of agent-based simulations to systematically test their effects on model outcomes. We find that the models are not robust against weakenings of these idealizations. In fact we find that under certain conditions, this can lead to the model predicting outcomes that are qualitatively opposite of the original model outcomes. (shrink)

We explore the contribution made by oscillatory, synchronous neural activity to representation in the brain. We closely examine six prominent examples of brain function in which neural oscillations play a central role, and identify two levels of involvement that these oscillations take in the emergence of representations: enabling (when oscillations help to establish a communication channel between sender and receiver, or are causally involved in triggering a representation) and properly representational (when oscillations are a constitutive part of the representation). (...) We show that even an idealized informational sender–receiver account of representation makes the representational status of oscillations a non-trivial matter, which depends on rather minute empirical details. (shrink)

Recent discussions in the philosophy of psychology have examined the use and legitimacy of such notions as ‘representation’, ‘content’, ‘computation’, and ‘inference’ within a scientific psychology. While the resulting assessments have varied widely, ranging from outright rejection of some or all of these notions to full vindication of their use, there has been notable agreement on the considerations deemed relevant for making an assessment. The answer to the question of whether the notion of, say, representational content may be admitted into (...) a scientific psychology has often been made to hinge upon whether the notion can be squared with our ‘ordinary’ or ‘folk’ style of psychological explanation, with its alleged commitment to the idiom of beliefs and desires. The emphasis on ‘folk psychology’ in arguments concerning the status of various concepts within scientific psychology is unfortunate, because it runs afoul of the ideal that the philosophy of psychology, by analogy with the philosophy of biology and the philosophy of physics, should have at its core the discussion of ongoing psychological theories. For while it may be admitted that the status of appeals to ‘folk psychology’ in order to justify a role for the belief-desire idiom within psychology proper is a matter that is of interest in its own right, it is not at all clear that mainstream experimental psychology has adopted either the language or the conceptions of ‘belief-desire’ psychology. (shrink)

Political representation lies at the core of modern politics. Democracies, with their vast numbers of citizens, could not operate without representative institutions. Yet relations between the democratic ideal and the everyday practice of political representation have never been well defined and remain the subject of vigorous debate among historians, political theorists, lawyers, and citizens. In this volume, an eminent group of scholars move forward the debates about political representation on a number of fronts. Drawing on insights from political science, history, (...) political theory, economics, and anthropology, the authors provide much-needed clarity to some of the most vexing questions about political representation. They also reveal new and enlightening perspectives on this fundamental political practice. Topics discussed include representation before democracy, political parties, minorities, electoral competition, and ideology. This volume is essential reading for anyone interested in the ideal and the reality of political representation. (shrink)