Transcendental function

Transcendental function
Transcendental Tran`scen*den"tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster]

2. (Philos.) In the Kantian system, of or pertaining to that which can be determined a priori in regard to the fundamental principles of all human knowledge. What is transcendental, therefore, transcends empiricism; but is does not transcend all human knowledge, or become transcendent. It simply signifies the a priori or necessary conditions of experience which, though affording the conditions of experience, transcend the sphere of that contingent knowledge which is acquired by experience. [1913 Webster]

3. Vaguely and ambitiously extravagant in speculation, imagery, or diction. [1913 Webster]

Note: In mathematics, a quantity is said to be transcendental relative to another quantity when it is expressed as a transcendental function of the latter; thus, a^{x}, 10^{2x}, log x, sin x, tan x, etc., are transcendental relative to x. [1913 Webster]

{Transcendental curve} (Math.), a curve in which one ordinate is a transcendental function of the other.

{Transcendental equation} (Math.), an equation into which a transcendental function of one of the unknown or variable quantities enters.

{Transcendental function}. (Math.) See under {Function}. [1913 Webster]

Syn: {Transcendental}, {Empirical}.

Usage: These terms, with the corresponding nouns, transcendentalism and empiricism, are of comparatively recent origin. Empirical refers to knowledge which is gained by the experience of actual phenomena, without reference to the principles or laws to which they are to be referred, or by which they are to be explained. Transcendental has reference to those beliefs or principles which are not derived from experience, and yet are absolutely necessary to make experience possible or useful. Such, in the better sense of the term, is the transcendental philosophy, or transcendentalism. Each of these words is also used in a bad sense, empiricism applying to that one-sided view of knowledge which neglects or loses sight of the truths or principles referred to above, and trusts to experience alone; transcendentalism, to the opposite extreme, which, in its deprecation of experience, loses sight of the relations which facts and phenomena sustain to principles, and hence to a kind of philosophy, or a use of language, which is vague, obscure, fantastic, or extravagant. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • transcendental function — Math. a function that is not an algebraic function. [1875 80] * * * In mathematics, a function not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and… …   Universalium

  • transcendental function — noun a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials …   Wiktionary

  • Transcendental — Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be determined a… …   The Collaborative International Dictionary of English

  • Transcendental curve — Transcendental Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be… …   The Collaborative International Dictionary of English

  • Transcendental equation — Transcendental Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be… …   The Collaborative International Dictionary of English

  • Transcendental functions — Function Func tion, n. [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.] 1. The act of executing or performing any duty, office, or calling; performance. In the function of… …   The Collaborative International Dictionary of English

  • Function — Func tion, n. [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.] 1. The act of executing or performing any duty, office, or calling; performance. In the function of his public …   The Collaborative International Dictionary of English

  • Transcendental — can refer to:In mathematics: * Transcendental number, a class of irrational numbers * Transcendental function, a class of functionsIn philosophy and religion: * Transcendence (philosophy) * Transcendental idealism, a philosophical doctrine… …   Wikipedia

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