functional analysis — news, coverage & facts — IJR

functional analysis — news, coverage & facts — IJR

Notable quotes

“In the entire history of Greek mathematics, all but the incomparable Archimedes and a few of the more heterodox sophists appear to have hated or feared the mathematical infinite. Analysis was thwarted when it might have prospered.”
— Eric Temple Bell, The Development of Mathematics (1940)
“Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.”
— Auguste Comte, The Positive Philosophy, 1853, Bk. 1, chap. 1, as cited in: in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book, (1914), p. 224
“Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.”
— Antoine Augustin Cournot. Mathematical Theory of the Principles of Wealth, [Bacon, N. T.], (New York, 1897), p. 3.
“[D]uring the last half-century, number and measurable quantity have been separated... the idea of number alone has been recognized as the foundation upon which Mathematical Analysis rests, and the theory of extensive magnitude is now regarded as a separate department in which the methods of Analysis are applicable, but as no longer forming part of the foundation upon which Analysis itself rests.”
— E. W. Hobson, Mathematics, from the points of view of the Mathematician and of the Physicist (1912) p. 8.
“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”
— John von Neumann, originally published in Works of the Mind (edited by Robert B. Heywood, 1947) and reproduced in von Neumann, Collected Works (edited by A. H. Taub, 1961), Vol. I, "The Mathematician", pp. 1–10.
“The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.”
— Bertrand Russell, Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5

Quotes via Wikiquote (CC BY-SA), each with its original source.

Overview

Functional analysis in behavioral psychology is the application of the laws of operant and respondent conditioning to establish the relationships between stimuli and responses. To establish the function of operant behavior, one typically examines the "four-term contingency": first by identifying the motivating operations (EO or AO), then identifying the antecedent or trigger of the behavior, identifying the behavior itself as it has been operationalized, and identifying the consequence of the behavior which continues to maintain it. Functional assessment in behavior analysis employs principles derived from the natural science of behavior analysis to determine the "reason", purpose, or motivation for a behavior. The most robust form of functional assessment is functional analysis, which involves the direct manipulation, using some experimental design (e.g., a multielement design or a reversal design) of various antecedent and consequent events and measurement of their effects on the behavior of interest; this is the only method of functional assessment that allows for demonstration of clear cause of behavior. Applications in clinical psychology Functional analysis and consequence analysis are commonly used in certain types of psychotherapy to better understand, and in some cases change, behavior. It is particularly common in behavioral therapies such as behavioral activation, although it is also part of Aaron Beck's cognitive therapy. In addition, functional analysis modified into a behavior chain analysis is often used in dialectical behavior therapy. There are several advantages to using functional analysis over traditional assessment methods. Firstly, behavioral observation is more reliable than traditional self-report methods. This is because observing the individual from an objective stand point in their regular environment allows the observer to observe both the antecedent and the consequence of the problem behavior. Secondly, functional analysis is advantageous as it allows for the development of behavioral interventions, either antecedent control or consequence control, specifically designed to reduce a problem behavior. Thirdly, functional analysis is advantageous for interventions for young children or developmentally delayed children with problem behaviors, who may not be able to answer self-report questions about the reasons for their actions.

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