Idealization
Encyclopedia
Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false. Often these assumptions are used to make models easier to understand or solve. Many times idealizations do not harm the predictive accuracy of the model for one reason or another. Most debates surrounding the usefulness of a particular model often are about the appropriateness of different idealizations.
. 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 why motion exists. 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. This hypothesis is predicated on the assumption that there is no air resistance.
arises by the process of idealization because it, at its core, is a universe of ideal entities, forms and figures. Perfect circles, spheres
, straight lines
and angles
are the essential elements of this discipline, all which would be near impossible without idealization.
introduced the method of idealization to biology
. This assisted, in no small part, Darwin’s theory of evolution
to achieve scientific maturity.
Another 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.
utilized idealization in the social sciences
(see the works written by Leszek Nowak). Similarly, in economic models
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
, 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.
. Husserl opposed the application of idealization to the study of objects belonging to the domain of the mind because he believed that mental phenomena do not lend themselves to idealization. That is, idealization does not reveal the essential essence of mental phenomena.
Although Galileo’s
idealization method is considered one of the essential elements of modern non-Aristotelian science
, it is nonetheless the source of continued controversy in the literature of the philosophy
of science. Nancy Cartwright
suggested that Galilean idealization presupposes tendencies or capacities in nature and that this allows for extrapolation beyond what is the ideal case.
There is continued philosophical concern over whether and 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 – gas laws, Newton's laws of motion
, etc. – 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 assumed away.
Early Use
Galileo utilized the concept of idealization in order to formulate the law of free fallFree fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...
. 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 why motion exists. 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. This hypothesis is predicated on the assumption that there is no air resistance.
Mathematics
GeometryGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
arises by the process of idealization because it, at its core, is a universe of ideal entities, forms and figures. Perfect circles, spheres
SPHERES
The Synchronized Position Hold, Engage, Reorient Experimental Satellites experiment is a testbed consisting of three miniaturized satellites that can operate in a variety of environments, including inside the International Space Station...
, straight lines
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
and angles
Angles
The Angles is a modern English term for a Germanic people who took their name from the ancestral cultural region of Angeln, a district located in Schleswig-Holstein, Germany...
are the essential elements of this discipline, all which would be near impossible without idealization.
Science
Charles DarwinCharles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
introduced the method of idealization to biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
. This assisted, in no small part, Darwin’s theory of evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
to achieve scientific maturity.
Another example of the use of idealization in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
is in Boyle’s Gas Law
Boyle's law
Boyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...
:
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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, people will often solve for Newtonian systems without friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of 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 MarxKarl Marx
Karl Heinrich Marx was a German philosopher, economist, sociologist, historian, journalist, and revolutionary socialist. His ideas played a significant role in the development of social science and the socialist political movement...
utilized idealization in the social sciences
Social sciences
Social science is the field of study concerned with society. "Social science" is commonly used as an umbrella term to refer to a plurality of fields outside of the natural sciences usually exclusive of the administrative or managerial sciences...
(see the works written by Leszek Nowak). Similarly, in economic models
Model (economics)
In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using...
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
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
, idealization refers to a defence mechanism
Defence mechanism
In Freudian psychoanalytic theory, defence mechanisms are unconscious psychological strategies brought into play by various entities to cope with reality and to maintain self-image. Healthy persons normally use different defences throughout life...
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
Child custody
Child custody and guardianship are legal terms which are used to describe the legal and practical relationship between a parent and his or her child, such as the right of the parent to make decisions for the child, and the parent's duty to care for the child.Following ratification of the United...
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 fits nicely into the analysis utilized by certain scientific disciplines, it has been traditionally rejected by others. For instance, the extension of the use of idealization into the study of mental phenomena has been firmly rejected. Husserl, who was aware of, and recognized, the importance of idealization, refused to extend its use into his studies of consciousnessConsciousness
Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...
. Husserl opposed the application of idealization to the study of objects belonging to the domain of the mind because he believed that mental phenomena do not lend themselves to idealization. That is, idealization does not reveal the essential essence of mental phenomena.
Although Galileo’s
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
idealization method is considered one of the essential elements of modern non-Aristotelian science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, it is nonetheless the source of continued controversy in the literature of the philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
of science. Nancy Cartwright
Nancy Cartwright (philosopher)
Nancy Cartwright FBA is a professor of philosophy at the London School of Economics and the University of California at San Diego, and a recipient of a MacArthur Fellowship...
suggested that Galilean idealization presupposes tendencies or capacities in nature and that this allows for extrapolation beyond what is the ideal case.
There is continued philosophical concern over whether and 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 – gas laws, Newton's laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
, etc. – 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 assumed away.
Further reading
- 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.)