What then is a proposition? Simply stated, it is the assertion of relation between two terms; or more abstractly, it is the reference of an individual to its species--the assertion of a classification. We find here the same duality which we noticed above. If we give prominence to the individual notion, we consider the proposition in extension; if we turn our attention to the specific notion we consider the proposition in intention: in the one case referring to the individuals composing the class, in the other to the attributes composing the class-type. The first corresponds to induction, the second to deduction. When we study individuals we study physics; when we study the attributes composing the class-type, we study metaphysics. The Law of Thinking as educed from a study of the proposition is the law of classification. The proposition, considered affirmatively, asserts explicitly agreement between certain attributes of two terms; that is, it asserts a classification. The aim of science is to reach this proposition, to discover and assert the principle of classification--in other words, to formulate metaphysically what nature has presented physically. We must find, then, the first or fundamental law of thinking in this _integration_ or classification. This fundamental law may be subdivided into two species, according to the two terms of the proposition; of which the first may be stated thus: "Every possible object of thought is to a certain extent identical with every other"; and as the proposition implicitly states disagreement, the second may be stated thus: "Every possible object of thought is to a certain extent diverse from every other." The first gives the positive (subjective) condition of the proposition, the second the negative (objective) condition: both together constitute the conditions of thinking. The proposition is thus the assertion of the same in the different. The proposition also asserts, implicitly, the _tertium quid_, or the basis of classification--the class-type, to which both terms are referred--that is, the proposition secondarily asserts an analysis. According to the first condition we have the inductive process; according to the second we have the deductive process. A complete movement of idea from its purely physical symbolization to its metaphysical interpretation, must involve both these processes.