Online research in philosophy

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

In this paper we present a new framework of idealization in biology. We characterize idealizations as a network of counterfactual conditionals that can exhibit different degrees of contingency. We use the idea of possible worlds to say that, in departing more or less from the actual world, idealizations can serve numerous epistemic, methodological or heuristic purposes within scientific research. We defend that, in part, it is this structure what helps explain why idealizations, despite being deformations of reality, are so successful in scientific practice.

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: pincock@purdue.edu.

Contemporary literature in philosophy of science has begun to emphasize the practice of modeling, which differs in important respects from other forms of representation and analysis central to standard philosophical accounts. This literature has stressed the constructed nature of models, their autonomy, and the utility of their high degrees of idealization. What this new literature about modeling lacks, however, is a comprehensive account of the models that figure in to the practice of modeling. This paper offers a new account of both concrete and mathematical models, with special emphasis on the intentions of theorists, which are necessary for evaluating the model-world relationship during the practice of modeling. Although mathematical models form the basis of most of contemporary modeling, my discussion begins with more traditional, concrete models such as the San Francisco Bay model.

In this paper, a criticism of the traditional theories of approximation and idealization is given. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model -- something analogous to Hempel's D-N model for explanation -- but to study its different guises in the praxis of science. A case study of it is then made in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels.

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it.

The book reveals different dimensions of modeling in the historical sciences.

This essay is concerned with the processes of idealization as described by Husserl in his last work, "The Crisis of European Sciences and Transcendental Phenomenology". Central as the processes of idealization are to Husserl's reflections on the origin of natural scientific knowledge and his attempt to reground that knowledge in the "forgotten meaning-fundament of natural science," they have not always been well understood. One reason for this is the lack of concrete historical examples. The main purpose of this paper is to correct this deficit. The paper is comprised of four sections. The first distinguishes two separate processes of idealization, one ascending from the life-world and the other descending and applying to it. The interaction of the two is then considered. The second section takes up Husserl's own discussion of Galileo's employment of idealization in his original mathematization of nature. The third section examines Galileo's analysis of freefall as a historical example of the processes of idealization. Here it is seen that the evidence clearly justifies Husserl's claims regarding the role of idealization in the origins of modern natural science. The conclusion employs the insights gained in the previous sections to exhibit the importance of understanding the processes of idealization as propaedeutic to the appreciation of the role and importance of the phenomenological methods of epoché and reduction to restoring lost layers of meaning by nullifying the idealizations which cover the life world.

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.

This paper considers the relationship between continuum hydrodynamics and discrete molecular dynamics in the context of explaining the behavior of breaking droplets. It is argued that the idealization of a fluid as a continuum is actually essential for a full explanation of the drop breaking phenomenon and that, therefore, the less "fundamental," emergent hydrodynamical theory plays an ineliminable role in our understanding.