In Algebra, (x), the absolute value of x, is x if x is real and positive, — x if x is real and negative, and + V if x is a complex number of the form a + ib, where a and b are real.
In Geometry, the absolute is the region of a projective space which becomes the points at infinity when a Euclidean or non-Euclidean space is constructed from the elements of the projective space. In a Euclidean plane, as a locus, the absolute is a line, and as an envelope a pair of points on the line. In a non-Euclidean plane it is a conic, In Ethics, absolute ethics are those that are based on a fixed standard, independent of time and of society.
In Metaphysics and Theology, the absolute is a being, often identified with God, which is (a) unrelated, (b) immediately presented to our consciousness and (c) all-inclusive. An unrelated being cannot of course be the subject of the cognitive relation, so that if known it must be known in a manner involving no re latedness. This is why the absolute is supposed to be known immediately. This conception of knowledge without relation is one which it is very difficult to maintain consistently, and al most inevitably leads the absolutist (as the adherent of the doctrine of the absolute is known), to one or the other of the many forms of mysticism. It must be supposed that the
mind in some way becomes the absolute by vir tue of its act of knowledge. Furthermore, the third property of the absolute, that of being all inclusive, follows directly from its unrelated ness. However, the desire for a finished philo sophical system which contains an all-inclusive whole is probably one of the chief motives leading to the selection of an absolutistic stand point. Consult Spinoza's 'Ethics,' Bradley's 'Logic,' or Bosanquet's 'Logic' for expres sions of the absolutistic standpoint.
Absolute Space and Time are space and time viewed apart from their contents. Absolute rest is rest which possesses some intrinsic cri terion that differentiates it from motion. The absolute position of a body is its position with reference to a set of axes at absolute rest. Ab solute motion and velocity are motion and velocity with reference to a body at absolute rest.