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)

Conceptions of acceptability-based moral or political justification take it that authoritative acceptability constitutes, or contributes to, validity, or justification. There is no agreement as to what bar for authoritativeness such justification may employ. The paper engages the issue in relation to (i) the level of idealization that a bar for authoritativeness, ψ, imparts to a standard of acceptability-based justification, S, and (ii) the degree of discursive purchase of the discursive standing that S accords to people when it builds ψ. (...) I argue that (i) and (ii) are interdependent: high idealization values entail low discursive purchase, while high degrees of purchase require low idealization values. I then distinguish between alethic conceptions of justification that prioritize ends that commit to high idealization values, and recognitive conceptions that favour high discursive purchase. On this basis, I argue for a moderately recognitivist constraint on idealization. To render the recognitive discursive minimum available to relevant people at the site of justification, S should set ψ low enough so that it is a genuine option for actual people to reject relevant views in ways that S recognizes as authoritative. (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.

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)

The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, (...) I argue that large-scale simulations require that the explanandum phenomenon is identified; otherwise, the explanatory value of such explanations is difficult to establish, and testing the model empirically by comparing its behavior with the explanandum remains practically impossible. The completeness of the explanation, and hence of the explanatory value of the explanatory model, is to be assessed vis-à-vis the explanandum phenomenon, which is not to be conflated with raw observational data and may be idealized. I argue that idealizations, which include building models of a single phenomenon displayed by multi-functional mechanisms, lumping together multiple factors in a single causal variable, simplifying the causal structure of the mechanisms, and multi-model integration, are indispensable for complex systems such as brains; otherwise, the model may be as complex as the explanandum phenomenon, which would make it prone to so-called Bonini paradox. I conclude by enumerating dimensions of empirical validation of explanatory models according to new mechanism, which are given in a form of a “checklist” for a modeler. (shrink)

This paper examines the dispute between Burge and McDowell over methodology in the philosophy of perception. Burge (2005, 2011) has argued that the disjunctivism posited by naive perceptual realists is incompatible with the results of current perceptual science, while McDowell (2010, 2013) defends his disjunctivism by claiming an autonomous field of enquiry for perceptual epistemology, one that does not employ the classificatory schemes of the science. Here it is argued that the crucial point at issue in the dispute is Burge’s (...) acceptance, and McDowell’s rejection, of the ‘Cartesian idealization’ of mind as a self-contained system. Burge’s case against disjunctivism rests on the assumption of a clearly demarcated boundary between mind and world, a picture of the mind that McDowell’s philosophy reacts against. This boundary is required for scientific, causal explanations of perceptual processing because it is a simplifying assumption that helps present scientists with a clearly demarcated object of investigation. Concurring with McDowell, I conclude that philosophers need not carve up their objects of investigation in the same way. (shrink)

Explainable AI (xAI) methods are important for establishing trust in using black-box models. However, recent criticism has mounted against current xAI methods that they disagree, are necessarily false, and can be manipulated, which has started to undermine the deployment of black-box models. Rudin (2019) goes so far as to say that we should stop using black-box models altogether in high-stakes cases because xAI explanations ‘must be wrong’. However, strict fidelity to the truth is historically not a desideratum in science. Idealizations (...) – the intentional distortions introduced to scientific theories and models – are commonplace in the natural sciences and are seen as a successful scientific tool. Thus, it is not falsehood qua falsehood that is the issue. In this paper, I outline the need for xAI research to engage in idealization evaluation. Drawing on the use of idealizations in the natural sciences and philosophy of science, I introduce a novel framework for evaluating whether xAI methods engage in successful idealizations or deceptive explanations (SIDEs). SIDEs evaluates whether the limitations of xAI methods, and the distortions that they introduce, can be part of a successful idealization or are indeed deceptive distortions as critics suggest. I discuss the role that existing research can play in idealization evaluation and where innovation is necessary. Through a qualitative analysis we find that leading feature importance methods and counterfactual explanations are subject to idealization failure and suggest remedies for ameliorating idealization failure. (shrink)

Contemporary public reason liberalism holds that coercion must be publicly justified to an idealized constituency. Coercion must be justified to all qualified points of view, not the points of view held by actual persons. Critics, in particular Nicholas Wolterstorff and David Enoch, have complained that idealization, by idealizing away what actual people accept, risks authoritarianism and disrespect by forcing people to comply with laws they in fact reject. I argue that idealization can withstand this criticism if it satisfies (...) two conditions. First, the standards of idealization, such as the norms of rationality and information, must be grounded in the present commitments of the large majority of members of the public. Second, the standards of idealization must be moderate; that is, they cannot be used to attribute reasons to citizens that stray too far from their actual commitments. (shrink)

Natalia Carrillo and Tarja Knuuttila claim that there are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of them treat idealizations as deliberate misrepresentations, however. They then argue for an artifactual account of idealization, comparing it to the traditional accounts of idealization, and exemplifying it through the Hodgkin and Huxley model (...) of the nerve impulse. From the artifactual perspective, the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to some specific parts of the model. They conclude that the artifactual approach offers a unifying view into idealization in that it is able to recover several basic philosophical insights motivating both the deficiency and epistemic benefit accounts, while being simultaneously detached from the idea of distortion by misrepresentation. (shrink)

Subjectivism about well-being holds that an object contributes to one's well-being to the extent that one has a pro-attitude toward this object under certain conditions. Most subjectivists have contended that these conditions should be ideal. One reason in favor of this idea is that when people adapt their pro-attitudes to situations of oppression, the levels of well-being they may attain is diminished. Nevertheless, I first argue that appealing to idealized conditions of autonomy or any other condition to erase or replace (...) adaptive pro-attitudes is mistaken. Second, I show that the most natural version of subjectivism that does not appeal to any such idealizing condition can explain why the well-being of people having adaptive pro-attitudes should not be restricted to the fulfillment of these pro-attitudes. In sum, the existence of adaptive preferences does not militate in favor of the introduction of conditions of idealization but against it. (shrink)

David Enoch, in his paper “Why Idealize?”, argues that theories of normative reasons that hold that normative facts are subject or response-dependent and include an idealization condition might have a problem in justifying the need for idealization. I argue that at least some response-dependence conceptions of normative reasons can justify idealization. I explore two ways of responding to Enoch’s challenge. One way involves a revisionary stance on the ontological commitments of the normative discourse about reasons. To establish (...) this point, I argue by analogy with the case of color perception. To make the analogy, it suffices to show that even if colors are response-dependent properties, it does not follow that some kind of idealization cannot be introduced to specify the truth conditions of color ascriptions. The second route involves the denial of Enoch’s contention that our normative discourse is implicitly committed to a realist ontology. I adduce reasons for thinking that our normative discourse only presupposes a possibility of misrepresentation. However, this feature of the normative discourse does not favor robustly objectivist as opposed to response-dependence accounts of normative reasons. Thus, I argue that proponents of response-dependence accounts can use this feature to answer the question of why to idealize. (shrink)

Philosophers of science increasingly recognize the importance of idealization: the intentional introduction of distortion into scientific theories. Yet this recognition has not yielded consensus about the nature of idealization. e literature of the past thirty years contains disparate characterizations and justifications, but little evidence of convergence towards a common position.

A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we (...) present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

The principal task of the book series Poznan Studies in the Philosophy of the Sciences and the Humanities is to promote those developments in philosophy that respect the tradition of great philosophical ideas, on the one hand, and the manner of philosophical thinking introduced by analytical philosophy, on the other. The aim is to contribute to practicing philosophy as deep as Marxism and as caring about justification as positivism.

Preliminary words One important feature of Poincaré's conventionalism of geometry is linked to the relation between the abstract notion of space geometry and the representations of the free mobility of our bodies. In this sense «the group of rigid motions» identified by Helmholtz and Lie as the foundation of geometries of constant curvature is, according to Poincaré, an idealization of the primitive experience that acquaints us with the properties of space in the first place. 2 Furthermore, since Poincaré thinks (...) that the only adequate candidates for physical geometry – the geometries of constant curvature – are equivalent from a mathematical point of view (they are homeomorphic), we can choose any one of these. Actually, according to Poincaré, the idealization involved in passing from our own local motions to the group of motions makes use of temporal intuition: our notion of the large-space structure of space assumes that our displacements are infinitely iterables and this assumes temporal intuition. 3 Thus, it looks as Poincaré's notion of convention assumes some kind of idealization process. Indeed, the notion of convention involved in this cases seems to assume that in relation to a target system the choice between two idealizations is determined by some kind of equivalence relation, which in our case is displayed 1. (shrink)

In 1804, when asked by the aspiring writer Clemens Brentano why she had chosen to publish her work, Karoline von Günderrode wrote that she longed “mein Leben in einer bleibenden Form auszusprechen, in einer Gestalt, die würdig sei, zu den Vortreflichsten hinzutreten, sie zu grüssen und Gemeinschaft mit ihnen zu haben.” In light of this kind of statement, it is perhaps not surprising if, despite some exceptions, much of the still relatively scant literature on Günderrode reads her works largely in (...) terms of how they articulate and manifest Günderrode’s desires, frustrations, and character, for the most part ignoring their imaginary, creative, and intellectual aspects. This interpretation of the author’s works as biography is, in Günderrode’s case, often accompanied by an interpretation of her biography, particularly her suicide, as literary work. This paper is not the first to question the conflation of Günderrode’s life, death, and writing, but it is one of only a handful that aim to address the autopoietic element of Günderrode’s work in a way that does not reduce her writings to biographical and psychological expressions, or Günderrode herself to an image – or a legend – encapsulated by her writings and her relationship to them. This paper argues that Günderrode’s own position on what the self is has been largely neglected as a result of this conflation, and that taking this position into account changes how we understand Günderrode’s articulations of self in her writings. Thus this paper has two goals: to address difficulties in articulating and even constituting oneself sincerely when one’s efforts are unrecognized, belittled, censored, and forced to conform to the conventions of a society in which one is marginalized; and to unearth a neglected and potentially rich account of the modern self. (shrink)

The focus in the literature on scientific explanation has shifted in recent years towards modelbased approaches. The idea that there are simple and true laws of nature has met with objections from philosophers such as Nancy Cartwright (1983) and Paul Teller (2001), and this has made a strictly Hempelian D-N style explanation largely irrelevant to the explanatory practices of science (Hempel & Oppenheim, 1948). Much of science does not involve subsuming particular events under laws of nature. It is increasingly recognized (...) that science across the disciplines is to some degree a patchwork of scientific models, with different methods, strategies, and with varying degrees of successful prediction and explanation. And so accounts of scientific explanation have reflected this change of perspective and model-based approaches have flourished in the explanation literature (Batterman, 2002b; Bokulich, 2008; Craver, 2006; Woodward, 2003). (shrink)

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to (...) be explanations. (shrink)

Following Heidegger’s lead, I first undertake a description of philosophical wonder. A second task emerges out of this, the task of describing the manner of experiencing time upon which this wonder is based. Here I attend specifically to Plato’s discussion thereof. In the third and final section of my considerations, I illustrate how “idealization” follows from wonder and the accordant experience of time, “idealization” being that mental operation which, according to Husserl, has determined the consequent development of European (...) culture in its scientific character from Plato and Aristotle up to the contemporary crisis. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: [email protected]. (shrink)

Discussions about abstraction are so important and so profound that this topic can hardly be neglected. It has inevitably cropped up again in various periods of philosophical enquiry. Despite these ancient roots and after the great debate that characterised the empirical and rationalistic tradition, interest in the problem has unfortunately been absent in large measure from the mainstream of mathematical logic and analytic philosophy. It seems that there is a gap between the epistemological theorization, in which it is difficult to (...) find new insights on the problem of abstraction, and the historical studies concerning the development of philosophical thought. Such studies, however, present a more fertile ground for such insights. Here the reader will find presented for the first time a collection of papers about the topic, considered from an historical point of view together with an awareness of the need for building a bridge between historical research and theoretical speculation. Accordingly the volume consists of both general overviews which sketch the signifcance and the fortunes of abstraction in science, philosophy and logic (the first part) and historical case studies which focus on abstraction in particular thinkers (the second part). This volume is of interest for both general philosophers and historians of philosophy. (shrink)

Galileo proposed what has been called a proto-inertial principle, according to which a body un horizontal motion will conserve its motion. This statement is only true in counterfactual circumstances where no impediments are present. This paper analyzes how Galileo could have been justified in ascribing definite properties to this idealized motion. This analysis is then used to better understand the relation of Galileo’s proto-inertial principle to the classical inertial principle.

The aim of this essay is to emphasize a number of important points that will provide a better understanding of the history of philosophical thought concerning scientific knowledge. The main points made are: (a) that the principal way of viewing abstraction which has dominated the history of thought and epistemology up to the present is influenced by the original Aristotelian position; (b) that with the birth of modern science a new way of conceiving abstraction came into being which is better (...) characterized by the term idealization, the name that was later, in fact, to be used by scientists to describe their scientific activity; (c) that, however, on account of the influence of empirical and inductive philosophy, scientists have often not had sufficient methodological awareness of this new way of viewing abstraction; (d) that this new concept of abstraction has frequently been expressed in the framework of philosophies that lie outside the mainstream of contemporary epistemology or even exhibit marked anti-scientific tendencies; (e) that the theme of idealization has been taken up again in the last few decades and a great contribution in this direction has been made by the so-called Pozna school of methodology. (shrink)

PurposeThe fitness centers are settings for health promotion, yet may serve as a stage for counterproductive figure idealization. Such idealization may take the form of a drive toward the thin, the muscular, or lean body figure ideal, which all hold the potential to impel an experience of body appearance pressure and body dissatisfaction. The aim of this study was to explore figure idealization, body dissatisfaction, and experience of BAP in fitness instructors.Materials and MethodsFitness instructors, 70 males and (...) 236 females, were recruited through their facility chief executive officer and social media for a digital survey on mental health. Results are presented for body appreciation, body dissatisfaction, drive for muscularity, drive for leanness, questions on BAP, symptoms of eating disorders, and history of weight regulation and eating disorders.ResultsAttempts to gain body weight were reported by 17% of females and 53% of males, whereas ∼76% of males and females, respectively, reported to have attempted weight reduction. Reasons for body weight manipulation were predominantly appearance related, and 10–20% reported disordered eating behavior. Mean BAS-2 and EDI-BD were acceptable, but 28% of females were above clinical cutoff in EDI-BD, and mean DLS were high in both sexes. In total, 8% of females were above clinical cutoff in EDE-q, which corresponded well with the self-reported ED. Approximately 90% of the sample perceived BAP to be a societal issue and reported predominantly customers and colleagues to be the cause of their personal experience of BAP. Fewer than 50% knew of any actions taken by their employer to reduce BAP. There were few differences according to profession or educational level.ConclusionFitness instructors report BAP to affect them negatively, which may put them at risk of impaired mental health. Educational level did not protect against figure idealization and BAP. To care for their employees and to optimize their position as a public health promoter, the fitness industry should target BAP in health promotion programs. (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)

The Galilean explanatory style is characterized by the search for the underlying structure of phenomena, the positing of "deep" explanatory principles, and a view of the relation between theory and data, on which the search for "crucial data" is of primary importance. In this paper, I trace the dynamics of adopting the Galilean style, focusing on the science of episodic memory. I argue that memory systems, such as episodic and semantic memory, were posited as underlying competences producing the observable phenomena (...) of memory. Considered in idealized isolation from other systems, episodic memory was taken to underlay the ability of individuals to remember events from their personal past. Yet, in reality, memory systems regularly interact, standing in many-to-many relations to actual memory tasks and experiences. Upon this backdrop, I explore a puzzle about the increasing prominence of the notion of autonoetic consciousness in Tulving's theory of episodic memory. I argue that, contrary to widespread belief, the prominence is not best explained by the purported essential link between autonoetic consciousness and episodic memory. Rather, it is explained by the fact that autonoetic consciousness, hypothesized to uniquely accompany episodic retrieval, was considered a source of crucial data, predictable only from theories positing a functionally distinct episodic memory system. However, with the emergence of a new generation of theories, positing wider memory systems for remembering and imagination, the question of the relation between episodic memory and autonoetic consciousness has been reopened. This creates a pressing need for de-idealization, triggering a new search for crucial data. (shrink)

The goal of this paper is to reconstruct Nagel’s approach to idealization in the sciences and present his views as a viable option. In a nutshell, the theory that emerges can be described as follows: There are various types of idealization, which can be found in theoretical and experimental laws, and which, according to Nagel, play various important epistemic roles. In particular, they help organize complex knowledge and allow for approximations to truth. A cognate of idealization, which (...) Nagel does not refer to under this label but describes in terms of assimilation to the familiar and in terms of analogy, is key to scientific models, whose value is primarily heuristic in nature. The fact that theories involve idealization supports an instrumentalist perspective on science, a perspective which also determines a particular scope of the account of idealization. By these lights, particular types of questions simply do not arise, for instance: questions pertaining to the alleged peculiarity of scientific representation, the truth of law statements, etc. (shrink)

This paper addresses the methodological problem of analysing what it is to explain observed behaviours of engineered computing systems, focusing on the crucial role that abstraction and idealization play in explanations of both correct and incorrect BECS. First, it is argued that an understanding of explanatory requests about observed miscomputations crucially involves reference to the rich background afforded by hierarchies of functional specifications. Second, many explanations concerning incorrect BECS are found to abstract away from descriptions of physical components and (...) processes of computing systems that one finds below the logic circuit and gate layer of functional specification hierarchies. Third, model-based explanations of both correct and incorrect BECS that are provided in the framework of formal verification methods often involve idealizations. Moreover, a distinction between restrictive and permissive idealizations is introduced and their roles in BECS explanations are analysed. (shrink)