ART I. -- NATURE OF PRINCIPLES OF KNOWLEDGE.
58. A principle of knowledge is that by which something is known. -- A principle, in general, is that from which something proceeds. Principles are of three kinds: metaphysical principles, physical principles, and logical principles. The last named include all those principles which when known lead to the knowledge of something else. In a more restricted sense, first principles of knowledge, or simply first principles, are those propositions which are so clear and evident, that they do not require proof. Hence they are also called axioms or self-evident truths.
59. After the perception of essences, the intellect immediately perceives first principles. -- The intellect proceeding gradually in the act of knowing, first perceives what is most elementary, viz., essences. This imperfect knowledge it immediately develops in observing the relations, properties, and accidents of essences, thus calling judgment and reason into action. Of the judgments which it pronounces, some are formed immediately and others mediately. The former are called first principles.
ART II. -- THE PRINCIPLE OF CONTRADICTION.
60. The first principle known by the intellect is: It is impossible for the same thing to be and not be at the same time. This is called the principle of contradiction. -- As in the simple perception of essences there exists a first universal idea, viz., the idea of being, which precedes all others and serves as their basis; so there must be a first principle, on which all reasoning rests, and to which the intellect must assent under penalty of being unable to accept any other truth whatever. This first truth is the principle of contradiction, and is formulated thus: "It is impossible for the same thing to be and not to be at the same time and in the same respect;" or, a more didactic form, "Being is incompatible with non-being." Evidently this is the first principle which the intellect knows. For, in perceiving being, it cannot but perceive the negation of being, or non-being. In comparing these two concepts, therefore, it compares its two primary concepts; and in discovering and affirming their absolute incompatibility, it affirms the principle which in the order of knowledge precedes all others. This principle is so evident that it is immediately known by every intellect, and cannot rationlly be denied.{1}
61. The principle of contradiction is implicitly contained in all other princjples, even in those which are self-evident; it may be used to explain them or render them more evident, but can itself be proved by no other principle. -- Besides the principle of contradiction, there are many other self-evident principles; but, though the mind arrives at these by the simple perception of essence, and is not obliged to recur to a higher principle, yet in formulating them it must adhere, at least implicitly, to the principle of contradiction. Thus it is with the principle of identity, "Every being has its own essence;" with the principle of excluded middle, "A thing either is or is not;" with the principle of causality, "There is no effect without a cause; " with the principle of sufficient reason, "There is nothing without a sufficient reason." So, too, is it with all the axioms; as, "The whole is greater than any of its parts," "Two things equal to a third are equal to each other," etc. Although these principles do not require demonstration, still they are made more evident by means of the principle of contradiction. Thus, for example, we demonstrate that the whole is greater than any of its parts, from the fact that otherwise the whole would and would not be the whole.
ART. III. -- THE PRINCIPLE OF CAUSALITY.
62. The intellect forms the idea of cause in general when it ascends by abstraction from the knowledge of a particular effect and a particular cause to the idea of effect and cause in general. -- In the act of sensation, of intellection, or of volition, we necessarily distinguish two things: the sensitive, intellective, or volitive act, and the agent which produces the act; this is nothing but the cognition of a particular effect produced by a particular cause. But from this particular cognition the intellect can by abstraction form the idea of effect and of cause in general, that is, the idea, first, of some thing which exists only in virtue of the action of an agent, and the idea, secondly, of an agent by the action of which this thing is produced. Hence the idea of cause comprehends two elements the perception of an agent as producing an effect by its action, and the perception of an effect as produced by this action.
63. When the intellect has the idea of cause and effect, it immediately perceives the principle of causality, which is expressed in the formula: There is no effect without a cause. -- This principle expresses nothing more than the essential dependence of every effect on some cause. But this dependence is known from the very idea of effect; for an effect is something that begins to be, or that has a being that it had not. It must, then, have received its being from itself or from another. But it could not receive its being from itself, since in that supposition it would both exist in order to give being, and not exist in order to receive being. It must then have received its being from another, on which, therefore, it depends, and which is called a cause. The intellect, therefore, analyzing the idea of effect, immediately perceives its dependence on a cause; it expresses this dependence in the proposition: "There is no effect without a cause."{2}
64. To the principle of causality is referred the princple of sufficient reason, which may be thus formulated: Whatever is, must have a sufficient reason why it is what it is. -- This principle is only an extension of the principle of causality, but it has a more general application; while the principle of causality properly applies only to things which are effects or had a beginning, that of sufficient reason is applicable to the First Cause who had no beginning. The principle of sufficient reason has this limit, however, that with regard to free will, it is not true if taken objectively only; for not the object but the election made by the will is the reason why the will determines itself to the exercise of its act.
65. The principle of causality is analytical, and not synthetical, as Kant maintains. -- A judgment is synthetical when the idea of the predicate is not contained in that of the subject; as, "This wood is green." A judgment is analytical, when the analysis of the subject enables us to find the predicate in it. Hence the mere analysis of the idea of effect suffices to give the idea of dependence on a cause.
66. The principle of causality has an objective value, notwithstanding the assertion to the contrary of many philosophers among others Kant and Hume. -- Many philosophers, recognizing that to destroy the principle of causality is to destroy all science, accept the principle, but deny its objective or real value, and give it only a subjective or ideal value. It is evident, however, that the quality of dependence on a cause, which the effect possesses, results from its nature as effect, and, consequently, is as real as the effect itself.
{1} Kant denies to the principle of contradiction all objective reality and puts forth his doctrine of Antinomies, or the principle that contradictories may exist side by side. The repugnance of the mind to assent to such a principle is due, he asserts, to the Limited circle of our experience, within which contradictories exclude each other. But in the nature of things, he maintains, there is no reason why two and two should not make five,
{2} The word cause here means efficient cause, and is marked by two characteristics, "immediate influence and active influence." Mr. Mill ignores these marks when he defines cause as an invariable, unconditional antecedent. When, too, he tries to establish, by means of the principle of causality, the Uniformity of Nature as the fundamental principle of his Experimental school, he implies the existence of this very uniformity, and thus falls into a vicious circle.