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# Idealization

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 Title: Idealization Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Idealization

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.

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.

## Contents

• Early Use 1
• Other examples of idealization 2
• Mathematics 2.1
• Science 2.2
• Social science 2.3
• Limits on use 3
• References 4

## 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.

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.

## Other examples of idealization

### 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.

### 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.

### Social science

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 who 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.

## Limits on use

While idealization is used extensively by certain scientific disciplines, it has been traditionally rejected by others. 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.[3]

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. 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.[4]

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.

## References

1. ^ About the Poznań School, see F. Coniglione, Realtà ed astrazione. Scuola polacca ed epistemologia post-positivista, Catania:CUECM 1990
2. ^ 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
3. ^ Klawiter A (2004). Why did Husserl not become the Galileo of the Science of Consciousness? Link
4. ^ Cartwright N (1994) Nature's capacities and their measurement. pp.186-191. Link

• 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.
• 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.
• William F, Barr, A Pragmatic Analysis of Idealization in Physics, Philosophy of Science, Vol. 41, No. 1, pg 48, Mar. 1974.
• Leszek Nowak, The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science, Dordrecht:Reidel 1980
• 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.
• Nancy Cartwright, How the laws of physics lie, Clarendon Press:Oxford 1983
• Craig Dilworth, The Metaphysics of Science: An Account of Modern Science in Terms of Principles, Laws and Theories, Springer:Dordrecht 2007 (2a ed.)
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