philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...

, idealization is the process by which

scientific models 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 ...

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 An approximation is anything that is intentionally similar but not exactly equality (mathematics), equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very ...

is accurate, the model will have high

predictive power The concept of predictive power, the power of a scientific theory to generate testable predictions, differs from '' explanatory power'' and ''descriptive power'' (where phenomena that are already known are retrospectively explained or describe ...

; for example, it is not usually necessary to account for

air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...

when determining the

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

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.

Early use

Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

used the concept of idealization in order to formulate the law of

free fall In Newtonian physics, free fall is any motion of a body where gravity is the only force 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 ...

, 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.

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 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: *Dry friction is a force that opposes the relative lateral motion of t ...

). This hypothesis is predicated on the assumption that there is no air resistance.

Other examples

Mathematics

Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

involves the process of idealization because it studies ideal entities, forms and figures. Perfect

circles A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

spheres The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for the ...

, straight

lines Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts ...

and

angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...

s are

abstraction Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstr ...

s that help us think about and investigate the world.

Science

An example of the use of idealization in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

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

, people will often solve for Newtonian systems without

. 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 In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

of friction is negligible.

Social science

It has been argued by the "Poznań School" (in Poland) that

Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher, economist, historian, sociologist, political theorist, journalist, critic of political economy, and socialist revolutionary. His best-known titles are the 1848 ...

used idealization in the

social sciences Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soci ...

(see the works written by Leszek Nowak). Similarly, in

economic models In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework design ...

individuals are assumed to make maximally rational choices. This assumption, although known to be violated by actual humans, can often lead to insights about the behavior of human populations. In

psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...

, idealization refers to a

defence mechanism In psychoanalytic theory, a defence mechanism (American English: defense mechanism), is an unconscious psychological operation that functions to protect a person from anxiety-producing thoughts and feelings related to internal conflicts and o ...

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 Child custody is a legal term regarding '' guardianship'' which is used to describe the legal and practical relationship between a parent or guardian and a child in that person's care. Child custody consists of ''legal custody'', which is the righ ...

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 Milton Friedman (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the ...

. In his view, the standard by which we should assess an empirical theory is the accuracy of the predictions that that theory makes. This amounts to an

instrumentalist A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who pl ...

conception of science, including social science. He also 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 “ uly 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).” Consistently with this, 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. Against this instrumentalist conception, which judges empirical theories on the basis of their predictive success, the social theorist

Jon Elster Jon Elster (; born 22 February 1940, Oslo) is a Norwegian philosopher and political theorist who holds the Robert K. Merton professorship of Social Science at Columbia University. He received his PhD in social science from the École Normale Su ...

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 it is that the explanation specifying that chain is neglecting a hidden variable that could account for both the independent variable and the dependent variable. 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.” 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 rational-choice explanations do not provide precise, pinpoint predictions, comparable to those of quantum mechanics. When a theory can predict outcomes that precisely, then, Elster contends, we have reason to believe that theory is true. Accordingly, Elster wonders whether the as-if assumptions of rational-choice theory help explain any social or political phenomenon.

Limits on use

While idealization is used extensively by certain scientific disciplines, it has been rejected by others. For instance,

Edmund Husserl , thesis1_title = Beiträge zur Variationsrechnung (Contributions to the Calculus of Variations) , thesis1_url = https://fedora.phaidra.univie.ac.at/fedora/get/o:58535/bdef:Book/view , thesis1_year = 1883 , thesis2_title ...

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. Although idealization is considered one of the essential elements of modern

science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

, it is nonetheless the source of continued controversy in the literature of the

. For example,

Nancy Cartwright Nancy Cartwright (born October 25, 1957) is an American actress. She is the long-time voice of Bart Simpson on the animated television series ''The Simpsons'', for which she has received a Primetime Emmy Award for Outstanding Voice-Over Perform ...

suggested that Galilean idealization presupposes tendencies or capacities in nature and that this allows for generalization beyond what is the ideal case.Cartwright N (1994
''Nature's capacities and their measurement.''
pp. 186–191. 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 The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...

) 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.

Early use

Other examples

Mathematics

Science

Social science

Limits on use

See also

References

Further reading