Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a prediction based on that ideal case.
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then using different types of models for different aims, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, and graphical models to visualize the subject.
If an approximation is accurate, the model will have high predictive accuracy; for example, it is not usually necessary to account for air resistance when determining the acceleration of a falling bowling ball, and doing so would be more complicated. In this case, air resistance is idealized to be zero. Although this is not strictly true, it is a good approximation because its effect is negligible compared to that of gravity.
Idealizations may allow predictions to be made when none otherwise could be. For example, the approximation of air resistance as zero was the only option before the formulation of Stokes' law allowed the calculation of drag forces. Many debates surrounding the usefulness of a particular model are about the appropriateness of different idealizations.
In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.
Early use
Galileo utilized the concept of idealization in order to formulate the law of free fall. Galileo, in his study of bodies in motion, set up experiments that assumed frictionless surfaces and spheres of perfect roundness. The crudity of ordinary objects has the potential to obscure their mathematical essence, and idealization is used to combat this tendency.
In Newtonian physics, free fall is any motion of a body where gravity is the only acceleration acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
The most well-known example of idealization in Galileo's experiments is in his analysis of motion. Galileo predicted that if a perfectly round and smooth ball were rolled along a perfectly smooth horizontal plane, there would be nothing to stop the ball (in fact, it would slide instead of roll, because rolling requires friction). This hypothesis is predicated on the assumption that there is no air resistance.
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
Other examples
Mathematics
Geometry involves the process of idealization because it studies ideal entities, forms and figures. Perfect circles, spheres, straight lines and angles are abstractions that help us think about and investigate the world.
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined as the "[…] first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points."
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.
Science
An example of the use of idealization in physics is in Boyle's Gas Law: Given any x and any y, if all the molecules in y are perfectly elastic and spherical, possess equal masses and volumes, have negligible size, and exert no forces on one another except during collisions, then if x is a gas and y is a given mass of x which is trapped in a vessel of variable size and the temperature of y is kept constant, then any decrease of the volume of y increases the pressure of y proportionally, and vice versa.
In physics, people will often solve for Newtonian systems without friction. While we know that friction is present in actual systems, solving the model without friction can provide insights to the behavior of actual systems where the force of friction is negligible.
It has been argued by the "Poznań School" (in Poland) that Karl Marx utilized idealization in the social sciences (see the works written by Leszek Nowak).[1] Similarly, in economic models individuals are assumed to make maximally rational choices.[2] This assumption, although known to be violated by actual humans, can often lead to insights about the behavior of human populations.
In psychology, idealization refers to a defence mechanism in which a person perceives another to be better (or have more desirable attributes) than would actually be supported by the evidence. This sometimes occurs in child custody conflicts. The child of a single parent frequently may imagine ("idealize") the (ideal) absent parent to have those characteristics of a perfect parent. However, the child may find imagination is favorable to reality. Upon meeting that parent, the child may be happy for a while, but disappointed later when learning that the parent does not actually nurture, support and protect as the former caretaker parent had.
A notable proponent of idealization in both the natural sciences and the social sciences was the economist Milton Friedman. In his view, the standard by which we should assess any empirical theory is the accuracy of the predictions that a theory makes. This amounts to an instrumentalist conception of science, including social science. Consistently with this conception, he then argues against the criticism that we should reject an empirical theory if we find that the assumptions of that theory are not realistic, in the sense of being imperfect descriptions of reality. This criticism is wrongheaded, Friedman claims, because the assumptions of any empirical theory are necessarily unrealistic, since such a theory must abstract from the particular details of each instance of the phenomenon that the theory seeks to explain. This leads him to the conclusion that “[t]ruly important and significant hypotheses will be found to have ‘assumptions’ that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense).”[3] In this light, he makes the case for seeing the assumptions of neoclassical positive economics as not importantly different from the idealizations that are employed in natural science, drawing a comparison between treating a falling body as if it were falling in a vacuum and viewing firms as if they were rational actors seeking to maximize expected returns.[4]
Against this instrumentalist conception, which judges empirical theories on the basis of their predictive success, the social theorist Jon Elster has argued that an explanation in the social sciences is more convincing when it ‘opens the black box’ — that is to say, when the explanation specifies a chain of events leading from the independent variable to the dependent variable. The more detailed this chain, argues Elster, the less likely the explanation specifying that chain is neglecting a hidden variable that could account for both the independent variable and the dependent variable.[5] Relatedly, he also contends that social-scientific explanations should be formulated in terms of causal mechanisms, which he defines as “frequently occurring and easily recognizable causal patterns that are triggered under generally unknown conditions or with indeterminate consequences.”[6] All this informs Elster's disagreement with rational-choice theory in general and Friedman in particular. On Elster's analysis, Friedman is right to argue that criticizing the assumptions of an empirical theory as unrealistic is misguided, but he is mistaken to defend on this basis the value of rational-choice theory in social science (especially economics). Elster presents two reasons for why this is the case: first, because rational-choice theory does not illuminate “a mechanism that brings about non-intentionally the same outcome that a superrational agent could have calculated intentionally”, a mechanism “that would simulate rationality”; and second, because explanations drawing on rational-choice theory do not provide pinpoint predictions, which in certain cases (for instance, he claims, quantum mechanics) would be sufficient to convince one that the theory making these predictions is likely to be true.[7] Accordingly, Elster wonders whether the as-if assumptions of rational-choice theory help explain any social or political phenomenon.[7]
Michael Weisberg has examined these and related questions from the vantage of philosophical reflection on models and idealization. By his lights, we can develop a classification of scientific idealization that picks out three kinds: Galilean idealization, minimalist idealization, and multiple-models idealization. Galilean idealization, in his account, consists in “introducing distortions into models with the goal of simplifying, in order to make them more mathematically or computationally tractable”, whereas minimalist idealization “is the practice of constructing and studying models that include only the core causal factors which give rise to a phenomenon.”[8] Somewhat similar to minimalist idealization is multiple-models idealization, which Weisberg defines as “the practice of building multiple related but incompatible models, each of which makes distinct claims about the nature and causal structure giving rise to a phenomenon.”[9] Further, these kinds of idealization can be differentiated in terms of ‘representational ideals’, which Weisberg sees as “regulat[ing] which factors are to be included in models, set[ting] up the standards theorists use to evaluate their models, and guid[ing] the direction of theoretical inquiry.”[10] Relevant to the debate between Friedman and Elster is the representational ideal of ‘maxout’, according to which the model-builder aims only at maximal predictive accuracy; only this ideal, Weisberg claims, “sanctions black-box models”[11] Moreover, in his view, and contrary to what Friedman's discussion of the law of falling bodies suggests, Galilean idealization has as its aim not ‘maxout’ but, rather, ‘completeness’[12]— viz., providing a complete description of a given phenomenon.[13] Relatedly, Weisberg also finds unsatisfying the ideal of ‘maxout’ as a principle for guiding scientific research, inasmuch as this ideal counsels only the development of predictions, thereby neglecting what Weisberg sees as a central part of the scientific enterprise: “[w]hile scientists want to know how a system will behave in the future, they also want an explanation of why it behaves the way that it does.”[11]
The philosopher Kwame Anthony Appiah has defended the value of as-if idealization more broadly, across the sciences as well as the humanities and for ends other than prediction. In short, he argues that such idealization can aid our understanding of a given phenomenon even when that idealization involves claims about that phenomenon that are false.[14] In support of this contention he draws on the thought of Daniel Dennett,in particular his notion, elaborated in The Intentional Stance, that viewing a system as if it were an intentional agent can better our predictions of that system's behaviour and, moreover, bring to our attention patterns in its behaviour that we would otherwise not notice.[15] But Appiah goes further than this, contending that as-if idealization is an essential feature of several modes of thought. Here, his principal intellectual guide is Hans Vaihinger, whose philosophy he describes in the following way: “[his thought] regards questions concerning our everyday thinking about the world as continuous with our scientific thinking: [b]oth aim, he says, at controlling reality, and both can leave things out in order to make it practicable to represent the world we want to control.”[16] To illustrate his own claims, Appiah describes how the schematic McCulloch-Pitts neuron yielded insights regarding neurophysiology as well as computer science: “a highly idealized model of the brain acquir[ed] independent utility because its simplifying idealizations ended up providing techniques for mimicking the functions rather than the material substrate of the mind.”[17] With respect to social science in particular, Appiah analyses the conception of rationality within rational-choice theory and arrives at the conclusion that this conception assumes perfect computational ability — that is, the ability to process information without error — but is not for that reason useless or inapplicable to the study of human phenomena. In his words:
No actual agents are computationally perfect, but the states that determine their actual behavior can still be characterized by how they would manifest themselves, given computational perfection. Analogously, the actual velocities of real gas molecules, which explain their less-than-ideal actual behavior, may nevertheless be characterized as the velocities that would, if only gas molecules were perfectly inelastic point masses, produce the ideal gas laws predicted by the simplest version of the kinetic theory of gases. (pp.84-85)
Limits on use
While idealization is used extensively by certain scientific disciplines, it has been rejected by others.[18] For instance, Edmund Husserl recognized the importance of idealization but opposed its application to the study of the mind, holding that mental phenomena do not lend themselves to idealization.[19]
Although idealization is considered one of the essential elements of modern science, it is nonetheless the source of continued controversy in the literature of the philosophy of science.[18] For example, Nancy Cartwright suggested that Galilean idealization presupposes tendencies or capacities in nature and that this allows for extrapolation beyond what is the ideal case.[20]
There is continued philosophical concern over how Galileo's idealization method assists in the description of the behavior of individuals or objects in the real world. Since the laws created through idealization (such as the ideal gas law) describe only the behavior of ideal bodies, these laws can only be used to predict the behavior of real bodies when a considerable number of factors have been physically eliminated (e.g. through shielding conditions) or ignored. Laws that account for these factors are usually more complicated and in some cases have not yet been developed.
Related Research Articles
Herbert Alexander Simon was an American economist, political scientist and cognitive psychologist, whose primary research interest was decision-making within organizations and is best known for the theories of "bounded rationality" and "satisficing". He received the Nobel Prize in Economics in 1978 and the Turing Award in 1975. His research was noted for its interdisciplinary nature and spanned across the fields of cognitive science, computer science, public administration, management, and political science. He was at Carnegie Mellon University for most of his career, from 1949 to 2001.
Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. The basic premise of rational choice theory is that aggregate social behavior results from the behavior of individual actors, each of whom is making their individual decisions. The theory also focuses on the determinants of the individual choices. Rational choice theory then assumes that an individual has preferences among the available choice alternatives that allow them to state which option they prefer. These preferences are assumed to be complete and transitive. The rational agent is assumed to take account of available information, probabilities of events, and potential costs and benefits in determining preferences, and to act consistently in choosing the self-determined best choice of action.
Rationality is the quality or state of being rational – that is, being based on or agreeable to reason. Rationality implies the conformity of one's beliefs with one's reasons to believe, and of one's actions with one's reasons for action. "Rationality" has different specialized meanings in philosophy, economics, sociology, psychology, evolutionary biology, game theory and political science.
A heuristic technique, often called simply a heuristic, is any approach to problem solving or self-discovery that employs a practical method, not guaranteed to be optimal, perfect, or rational, but instead sufficient for reaching an immediate goal. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using a rule of thumb, an educated guess, an intuitive judgment, a guesstimate, profiling, or common sense.
Bounded rationality is the idea that rationality is limited when individuals make decisions: by the tractability of the decision problem, the cognitive limitations of the mind, and the time available to make the decision. Decision-makers, in this view, act as satisficers, seeking a satisfactory solution rather than an optimal one.
The term homo economicus, or economic man, is the portrayal of humans as agents who are consistently rational, narrowly self-interested, and who pursue their subjectively-defined ends optimally. It is a word play on Homo sapiens, used in some economic theories and in pedagogy.
A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.
Social simulation is a research field that applies computational methods to study issues in the social sciences. The issues explored include problems in computational law, psychology, organizational behavior, sociology, political science, economics, anthropology, geography, engineering, archaeology and linguistics.
Decision theory is the study of an agent's choices. Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do.
Ideal type, also known as pure type, is a typological term most closely associated with sociologist Max Weber (1864–1920). For Weber, the conduct of social science depends upon the construction of abstract, hypothetical concepts. The "ideal type" is therefore a subjective element in social theory and research, and one of the subjective elements distinguishing sociology from natural science.
Kwame Akroma-Ampim Kusi Anthony Appiah is a British-Ghanaian philosopher, cultural theorist, and novelist whose interests include political and moral theory, the philosophy of language and mind, and African intellectual history. Appiah was the Laurance S. Rockefeller University Professor of Philosophy at Princeton University, before moving to New York University (NYU) in 2014. He currently holds an appointment at the NYU Department of Philosophy and NYU's School of Law.
In sociology, social action, also known as Weberian social action, refers to an act which takes into the account of actions and reactions of individuals. According to Max Weber, "an Action is 'social' if the acting individual takes account of the behavior of others and is thereby oriented in its course".
Jon Elster is a Norwegian social and political theorist who has authored works in the philosophy of social science and rational choice theory. He is also a notable proponent of analytical Marxism, and a critic of neoclassical economics and public choice theory, largely on behavioral and psychological grounds.
In ecology, an ideal free distribution is a way in which animals distribute themselves among several patches of resources. The theory states that the number of individual animals that will aggregate in various patches is proportional to the amount of resources available in each. For example, if patch A contains twice as many resources as patch B, there will be twice as many individuals foraging in patch A as in patch B. The ideal free distribution (IFD) theory predicts that the distribution of animals among patches will minimize resource competition and maximize fitness.
Cristina Bicchieri is an Italian–American philosopher. She is the S.J.P. Harvie Professor of Social Thought and Comparative Ethics in the Philosophy and Psychology Departments at the University of Pennsylvania, professor of Legal Studies in the Wharton School, and director of the Philosophy, Politics and Economics program. She has worked on problems in the philosophy of social science, rational choice and game theory. More recently, her work has focused on the nature and evolution of social norms, and the design of behavioral experiments to test under which conditions norms will be followed. She is a leader in the field of behavioral ethics and is the director of the Behavioral Ethics Lab at the University of Pennsylvania.
Neo-classical economics has come under critique on the basis of its core ideologies, assumptions, and other matters.
Agent-based social simulation consists of social simulations that are based on agent-based modeling, and implemented using artificial agent technologies. Agent-based social simulation is scientific discipline concerned with simulation of social phenomena, using computer-based multiagent models. In these simulations, persons or group of persons are represented by agents. MABSS is combination of social science, multiagent simulation and computer simulation.
Analytical sociology is a strategy for understanding the social world. It is concerned with explaining important macro-level facts such as the diffusion of various social practices, patterns of segregation, network structures, typical beliefs, and common ways of acting. It explains such facts not merely by relating them to other macro-level facts, but by detailing in clear and precise ways the mechanisms through which they were brought about. This is accomplished by a detailed focus on individuals’ actions and interactions, and the use of state-of-the-art simulation techniques to derive the macro-level outcomes that such actions and interactions are likely to bring about. Analytical sociology can be seen as contemporary incarnation of Robert K. Merton's well-known notion of middle-range theory.
Analytical Marxism is an approach to Marxist theory that was prominent amongst English-speaking philosophers and social scientists during the 1980s. It was mainly associated with the September Group of academics, so called because of their biennial September meetings to discuss common interests. Self-described as "Non-Bullshit Marxism", the group was characterized, in the words of David Miller, by "clear and rigorous thinking about questions that are usually blanketed by ideological fog." Members of this school seek to apply the techniques of analytic philosophy, along with tools of modern social science such as rational choice theory to the elucidation of the theories of Karl Marx and his successors.
References
↑ About the Poznań School, see F. Coniglione, Realtà ed astrazione. Scuola polacca ed epistemologia post-positivista, Catania:CUECM 1990
↑ B. Hamminga, N.B. De Marchi (Eds.), Idealization VI: Idealization in Economics, Poznań Studies in the Philosophy of the Sciences and the Humanities, Vol. 38, Rodopi:Atlanta-Amsterdam 1994
↑ Friedman, Milton (1953). "The Methodology of Positive Economics". Essays in Positive Economics. Chicago: University of Chicago Press. p.14.
↑ Friedman, Milton (1953). "The Methodology of Positive Economics". Essays in Positive Economics. Chicago: University of Chicago Press. pp.18, 21–22.
↑ Elster, Jon (2015). Explaining Social Behavior: More Nuts and Bolts for the Social Sciences. Cambridge: Cambridge University Press. pp.23–25.
↑ Elster, Jon (2015). Explaining Social Behavior: More Nuts and Bolts for the Social Sciences. Cambridge: Cambridge University Press. p.26.
1 2 Elster, Jon (2015). Explaining Social Behavior: More Nuts and Bolts for the Social Sciences. Cambridge: Cambridge University Press. p.18.
↑ Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. pp.99–100.
↑ Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. p.103.
↑ Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. p.105.
1 2 Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. p.109.
↑ Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. p.111.
↑ Weisberg, Michael (2012). Simulation and Similarity: Using models to understand the world. Oxford: Oxford University Press. p.106.
↑ Appiah, Kwame Anthony (2017). As If: Idealization and Ideals. Cambridge, MA: Harvard University Press. pp.passim.
↑ Appiah, Kwame Anthony (2017). As If: Idealization and Ideals. Cambridge, MA: Harvard University Press. pp.34–43.
↑ Appiah, Kwame Anthony (2017). As If: Idealization and Ideals. Cambridge, MA: Harvard University Press. p.22.
↑ Appiah, Kwame Anthony (2017). As If: Idealization and Ideals. Cambridge, MA: Harvard University Press. p.34.
William F, Barr, A Pragmatic Analysis of Idealization in Physics, Philosophy of Science, Vol. 41, No. 1, pg 48, Mar. 1974.
Krzysztof Brzechczyn, (ed.), Idealization XIII: Modeling in History, Amsterdam-New York: Rodopi, 2009.
Nancy Cartwright, How the Laws of Physics Lie, Clarendon Press:Oxford 1983
Francesco Coniglione, Between Abstraction and Idealization: Scientific Practice and Philosophical Awareness, in F. Coniglione, R. Poli and R. Rollinger (Eds.), Idealization XI: Historical Studies on Abstraction, Atlanta-Amsterdam:Rodopi 2004, pp.59–110.
Craig Dilworth, The Metaphysics of Science: An Account of Modern Science in Terms of Principles, Laws and Theories, Springer:Dordrecht 2007 (2a ed.)
Andrzej Klawiter, Why Did Husserl Not Become the Galileo of the Science of Consciousness?, in F. Coniglione, R. Poli and R. Rollinger, (Eds.), Idealization XI: Historical Studies on Abstraction, Poznań Studies in the Philosophy of the Sciences and the Humanities, Vol. 82, Rodopi:Atlanta-Amsterdam 2004, pp.253–271.
Mansoor Niaz, The Role of Idealization in Science and Its Implications for Science Education, Journal of Science Education and Technology, Vol. 8, No. 2, 1999, pp.145–150.
Leszek Nowak, The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science, Dordrecht:Reidel 1980
Leszek Nowak and Izabella Nowakowa, Idealization X: The Richness of Idealization, Amsterdam / Atlanta: Rodopi 2000.
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