Trăn'sçend-ĕnt'al1, a.
a. [Fr. transcendental, Sp. transcendental, trascendental, It. transcendentale, trascendentale.]
Sense 1. Supereminent; surpassing others; as, transcendental being or qualities.
Sense 2. (Kantian Philos.) 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 it does not transcend all human knowledge, or become transcendent. Murdoch.
Transcendental anatomy, that department of anatomy which treats of the type or plan of structure, rather than the mere details.—Transcendental curve (Math.), a curve defined by a transcendental equation.—Transcendental equation, an equation into which a transcendental quantity enters.—Transcendental function, a function in which the relation between the function and variable is expressed by a transcendental equation. Math. Dict.—Transcendental line, a line whose equation is transcendental. Math. Dict.—Transcendental quantity, a quantity which can not be represented by an algebraic expression of a finite number of terms.
☞ Transcendental quantities are of three kinds: logarithmic, or expressed in terms of logarithms; as, a log. x, &c.; exponential, or expressed by variable exponents; as, aˣ, b aˣ, cʸ, &c.; and trigonometrical, or expressed by trigonometrical functions; as, sin. x, tan. √(2 − x²), &c.
Synonyms—TRANSCENDENTAL, EMPIRICAL. 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 has also been used in a bad sense. Empiricism, in this case, is applied 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 has been applied to the opposite extreme, which, in its depreciation of experience, loses sight of the relation which facts and phenomena sustain to principles. Hence the term has been applied to a kind of investigation, or a use of language, which is vague, obscure, fantastic, or extravagant.