Transcendental equation
(gcide) | Transcendental \Tran`scen*den"tal\, a. [Cf. F. transcendantal,
G. transcendental.]
1. Supereminent; surpassing others; as, transcendental being
or qualities.
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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.
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3. Vaguely and ambitiously extravagant in speculation,
imagery, or diction.
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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.
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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.
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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.
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