Abstract mathematics
(gcide) | Abstract \Ab"stract`\ (#; 277), a. [L. abstractus, p. p. of
abstrahere to draw from, separate; ab, abs + trahere to draw.
See Trace.]
1. Withdraw; separate. [Obs.]
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The more abstract . . . we are from the body.
--Norris.
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2. Considered apart from any application to a particular
object; separated from matter; existing in the mind only;
as, abstract truth, abstract numbers. Hence: ideal;
abstruse; difficult.
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3. (Logic)
(a) Expressing a particular property of an object viewed
apart from the other properties which constitute it;
-- opposed to concrete; as, honesty is an abstract
word. --J. S. Mill.
(b) Resulting from the mental faculty of abstraction;
general as opposed to particular; as, "reptile" is an
abstract or general name. --Locke.
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A concrete name is a name which stands for a
thing; an abstract name which stands for an
attribute of a thing. A practice has grown up in
more modern times, which, if not introduced by
Locke, has gained currency from his example, of
applying the expression "abstract name" to all
names which are the result of abstraction and
generalization, and consequently to all general
names, instead of confining it to the names of
attributes. --J. S. Mill.
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4. Abstracted; absent in mind. "Abstract, as in a trance."
--Milton.
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An abstract idea (Metaph.), an idea separated from a
complex object, or from other ideas which naturally
accompany it; as the solidity of marble when contemplated
apart from its color or figure.
Abstract terms, those which express abstract ideas, as
beauty, whiteness, roundness, without regarding any object
in which they exist; or abstract terms are the names of
orders, genera or species of things, in which there is a
combination of similar qualities.
Abstract numbers (Math.), numbers used without application
to things, as 6, 8, 10; but when applied to any thing, as
6 feet, 10 men, they become concrete.
Abstract mathematics or Pure mathematics. See
Mathematics.
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