Transcendental function

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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