Idealization and modeling

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, nonidealized representations.     

Idealization in unitarian metaphysics

The aim of the paper is to propose an understanding of idealization in terms of Nowak’s unitarian metaphysics. Two natural interpretations of the procedure are critically discussed and rejected as inadequate. The first account of idealization is unable to explain why idealized factors cease to exert influence on the investigated magnitude. The second account of idealization solves this problem but does so at the cost of blurring the distinction between idealization and abstruction. Moreover, it faces the consequence that the process of idealization instead of leading to a sharper understanding of phenomena will normally result in making the picture more and more probabilistic. I propose a third account of idealization in unitarian terms that solves all three problems.     

Idealization and psychoanalytic learning

Idealization is an intrinsic part of psychological maturation, but it is also a potential barrier to psychoanalytic learning, and must to some degree be outgrown if an analyst is to develop a natural authority and individual style. Unrecognized idealizations stifle analysts' engagement in the transferences of their patients, and so compromise the ability to freely experience and analyze them. Attention to real life and the lessons it teaches counterbalances the tendency to idealize and encourages lifelong psychoanalytic growth.     

Idealization and abstraction in scientific modeling

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention.

     

Idealization in Applied First-Order Logic

Applying first-order logic to derive the consequences of laws that are only approximately true of empirical phenomena involves idealization of a kind that is akin to applying arithmetic to calculate the area of a rectangular surface from approximate measures of the lengths of its sides. Errors in the data, in the exactness of the lengths in one case and in the exactness of the laws in the other, are in some measure transmitted to the consequences deduced from them, and the aim of a theory of idealization is to describe this process. The present paper makes a start on this in the case of applied first-order logic, and relates it to Plato's picture of a world or model of 'appearances' in which laws are only approximately true, but which to some extent resembles an ideal world or model in which they are exactly true. This revised version was published online in June 2006 with corrections to the Cover Date.     

Laws and Models in a Theory of Idealization

I first give a brief summary of a critique of the traditional theories of approximation and idealization; and after identifying one of the major roles of idealization as detaching component processes or systems from their joints, a detailed analysis is given of idealized laws – which are discoverable and/or applicable – in such processes and systems (i.e., idealized model systems). Then, I argue that dispositional properties should be regarded as admissible properties for laws and that such an inclusion supplies the much needed connection between idealized models and the laws they `produce' or `accommodate'. And I then argue that idealized law-statements so produced or accommodated in the models may be either true simpliciter or true approximately, but the latter is not because of the idealizations involved. I argue that the kind of limiting-case idealizations that produce approximate truth is best regarded as approximation; and finally I compare my theory with some existing theories of laws of nature.We seem to trace [in KingLear] ... the tendency of imagination toanalyse and abstract, to decomposehuman nature into its constituentfactors, and then to construct beings in whomone or more of these factors isabsent or atrophied or only incipient     

Cartwright On Explanation And Idealization

Nancy Cartwright (1983, 1999) argues that (1) the fundamental laws of physics are true when and only when appropriate ceteris paribus modifiers are attached and that (2) ceteris paribus modifiers describe conditions that are almost never satisfied. She concludes that when the fundamental laws of physics are true, they don't apply in the real world, but only in highly idealized counterfactual situations. In this paper, we argue that (1) and (2) together with an assumption about contraposition entail the opposite conclusion — that the fundamental laws of physics do apply in the real world. Cartwright extracts from her thesis about the inapplicability of fundamental laws the conclusion that they cannot figure in covering-law explanations. We construct a different argument for a related conclusion — that forward-directed idealized dynamical laws cannot provide covering-law explanations that are causal. This argument is neutral on whether the assumption about contraposition is true. We then discuss Cartwright's simulacrum account of explanation, which seeks to describe how idealized laws can be explanatory. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Justification,Idealization, and Discursive Purchase

Philosophia - Conceptions of acceptability-based moral or political justification take it that authoritative acceptability constitutes validity, or justification. There is no agreement as to what...     

Approximation,Idealization, and Laws of Nature

Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory of idealization force us to sever its close tie to approximation. This leads to an appreciation of lawlikeness as a measure of closeness to laws, which I argue is the real measure of idealization whose main purpose is to carve nature at its joints. This revised version was published online in June 2006 with corrections to the Cover Date.     

Idealization and mourning in love relationships: normal and pathological spectra

Prior to the last two decades, psychoanalytic literature focused on the psychopathology of sexual life, rather than on an integrated overview of love relationships. Only in the last twenty-five years has its scope been expanded to include the psychodynamics and phenomenology of love relationships per se. Nevertheless, a selective, critical review of the literature indicates that little attention has been paid to a) the interrelation of narcissism, self-esteem, and love relationships; b) the role of the ego-ideal and idealizations in the capacity for falling in love and sustaining love relationships; and c) the faculty for, and/or impediments to, transcending intrapsychic self-boundaries in mature love relationships. In this paper, a brief exposition of the ego-ideal developmental sequences and their integration into the superego as a differentiated structure serves as an introduction to the proposal of a developmental continuum of mechanisms of idealization and their respective nodal transmutations throughout the life cycle. This developmental continuum may contribute to the ongoing elucidation of the aforementioned problems. This referential frame is ultimately applied to the exploration of categorical and dimensional pathological variations of idealization and mourning in love relationships and in different levels of personality organization: neurotic, borderline, and narcissistic structures. A clinical vignette illustrates some of the correspondence criteria between this frame of reference and its clinical applications.     

Idealization,Splitting, and the Challenge of Homophobia

How can we account for the persistence of homophobia? What makes homophobia so resistant to change? In this paper we discuss the psychic and discursive persistence of homophobia by problematizing the political unconscious. Focusing on Freud's psychic defense mechanisms, idealization and splitting, we show how these forces can be thought of as the psychic work of discourse. To this end we interviewed fathers of homosexual sons who had initially reacted with panic, but eventually came to “accept” their sons' homosexuality. We discuss the paradox that the fathers' narratives raise: their love and adoration of their (masculine) homosexual sons, and on the other hand their hatred and denunciation of homosexuality. We argue that idealization and splitting in this case operate as regulatory psychic mechanisms in the service of social discourse. This psychic power of discourse reappropriates masculinity (as a fetish) and reinstates the naturalization of heterosexuality and the masculine/feminine binary. The notion of the political unconscious is brought up by concluding that in order to change sexual prejudices we need to understand why we fail to change and how psychic mechanisms work in the service of social and cultural discourse.