The understanding may be defined as the faculty of judging. The function of thought in a judgment can be brought under four heads, each with three subdivisions. 1. Quantity of judgments: Universal, particular, singular. 2. Quality: Affirmative, negative, infinite. 3. Relation: Categorical, hypothetical, disjunctive. 4. Modality: Problematical, assertory, apodictic [above contradiction]. If we examine each of these forms of judgment we discover that in every one is involved some peculiar idea which is its essential characteristic. Thus, a singular judgment, in which the subject of discourse is a single object, involves obviously the special idea of oneness, or unity. A particular judgment, relating to several objects, implies the idea of plurality, and discriminates between the several objects. Now, the whole list of these ideas will constitute the complete classification of the fundamental conceptions of the understanding, regarded as the faculty which judges, and these may be called categories. 1. Of Quantity: Unity, plurality, totality. 2. Of Quality: Reality, negation, limitation. 3. Of Relation: Substance and accident, cause and effect, action and reaction. 4. Of Modality: Possibility--impossibility, existence--non-existence, necessity--contingence. These, then, are the fundamental, primary, or native conceptions of the understanding, which flow from, or constitute the mechanism of, its nature; are inseparable from its activity; and are hence, for human thought, universal and necessary, or _a priori_. These categories are "pure" conceptions of the understanding, inasmuch as they are independent of all that is contingent in sense. TRANSCENDENTAL DIALECTIC A distinction is usually made between what is immediately known and what is only inferred. It is immediately known that in a figure bounded by three straight lines there are three angles, but that these angles together are equal to two right angles is only inferred. In every syllogism is first a fundamental proposition; secondly, another deduced from it; and, thirdly, the consequence. In the use of pure reason its concepts, or transcendental ideas, aim at unity of all conditions of thought. So all transcendental ideas may be arranged in three classes; the first containing the unity of the thinking subject; the second, the unity of the conditions of phenomena observed; the third, the unity of the objective conditions of thought. This classification becomes clear if we note that the thinking subject is the object-matter of psychology; while the system of all phenomena (the world) is the object-matter of cosmology; and the Being of all Beings (God) is the object-matter of theology.