History of Modern Philosophy. Richard Falckenberg
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i.e., ideas or words." The object of knowledge is neither single ideas nor the relations of ideas to things, but the relations of ideas among themselves. This view was at once paradoxical and pregnant. If all cognition, as Locke suggests in objection to his own theory, consists in perceiving the agreement or disagreement of our ideas, are not the visions of the enthusiast and the reasonings of sober thinkers alike certain? are not the propositions, A fairy is not a centaur, and a centaur is a living being, just as true as that a circle is not a triangle, and that the sum of the angles of a triangle is equal to two right angles? The mind directly perceives nothing but its own ideas, but it seeks a knowledge of things! If this is possible it can only be indirect knowledge—the mind knows things through its ideas, and possesses criteria which show that its ideas agree with things.
Two cases must be clearly distinguished, for a considerable number of our ideas, viz., all complex ideas except those of substances, make no claim to represent things, and consequently cannot represent them falsely. For mathematical and moral ideas and principles, and the truth thereof, it is entirely immaterial whether things and conditions correspondent to them exist in nature or not. They are valid, even if nowhere actualized; they are "eternal truths," not in the sense that they are known from childhood, but in the sense that, as soon as known, they are immediately assented to.[1] The case is different, however, with simple ideas and the ideas of substances, which have their originals without the mind and which are to correspond with these. In regard to the former we may always be certain that they agree with real things, for since the mind can neither voluntarily originate them (e.g., cannot produce sensations of color in the dark) nor avoid having them at will, but only receive them from without, they are not creatures of the fancy, but the natural and regular productions of external things affecting us. In regard to the latter, the ideas of substances, we may be certain at least when the simple ideas which compose them have been found so connected in experience. Perception has an external cause, whose influence the mind is not able to withstand. The mutual corroboration furnished by the reports of the different senses, the painfulness of certain sensations, the clear distinction between ideas from actual perception and those from memory, the possibility of producing and predicting new sensations of an entirely definite nature in ourselves and in others, by means of changes which we effect in the external world (e.g. by writing down a word)—these give further justification for the trust which we put in the senses. No one will be so skeptical as to doubt in earnest the existence of the things which he sees and touches, and to declare his whole life to be a deceptive dream. The certitude which perception affords concerning the existence of external objects is indeed not an absolute one, but it is sufficient for the needs of life and the government of our actions; it is "as certain as our happiness or misery, beyond which we have no concernment, either of knowing or being." In regard to the past the testimony of the senses is supplemented by memory, in which certainty [in regard to the continued existence of things previously perceived] is transformed into high probability; while in regard to the existence of other finite spirits, numberless kinds of which may be conjectured to exist, though their existence is quite beyond our powers of perception, certitude sinks into mere (though well-grounded) faith.
[Footnote 1: Thus it results that knowledge, although dependent on experience for all its materials, extends beyond experience. The understanding is completely bound in the reception of simple ideas; less so in the combination of these into complex ideas; absolutely free in the act of comparison, which it can omit at will; finally, again, completely bound in its recognition of the relation in which the ideas it has chosen to compare stand to one another. There is room for choice only in the intermediate stage of the cognitive process; at the beginning (in the reception of the simple ideas of perception, a, b, c, d), and at the end (in judging how the concepts a b c and a b d stand related to each other), the understanding is completely determined.]
More certain than our sensitive knowledge of the existence of external objects, are our immediate or intuitive knowledge of our own existence and our mediate or demonstrative knowledge of the existence of God. Every idea that we have, every pain, every thought assures us of our own existence. The existence of God, however, as the infinite cause of all reality, endowed with intelligence, will, and supreme power, is inferred from the existence and constitution of the world and of ourselves. Reality exists; the real world is composed of matter in motion and thinking beings, and is harmoniously ordered. Since it is impossible for any real being to be produced by nothing, and since we obtain no satisfactory answer to the question of origin until we rise to something existent from all eternity, we must assume as the cause of that which exists an Eternal Being, which possesses in a higher degree all the perfections which it has bestowed upon the creatures. As the cause of matter and motion, and as the source of all power, this Being must be omnipotent; as the cause of beauty and order in the world, and, above all, as the creator of thinking beings, it must be omniscient. But these perfections are those which we combine in the idea of God.
Intuitive knowledge is the highest of the three degrees of knowledge. It is gained when the mind perceives the agreement or disagreement of two ideas at first sight, without hesitation, and without the intervention of any third idea. This immediate knowledge is self-evident, irresistible, and exposed to no doubt. Knowledge is demonstrative when the mind perceives the agreement (or disagreement) of two ideas, not by placing them side by side and comparing them, but through the aid of other ideas. The intermediate links are called proofs; their discovery is the work of the reason, and quickness in finding them out is termed sagacity. The greater the number of the intermediate steps, the more the clearness and distinctness of the knowledge decreases, and the more the possibility of error increases. In order for an argument (e. g., that a = d) to be conclusive, every particular step in it (a = b, b = c, c = d) must possess intuitive certainty. Mathematics is not the only example of demonstrative knowledge, but the most perfect one, since in mathematics, by the aid of visible symbols, the full equality and the least differences among ideas may be exactly measured and sharply determined.
Besides real existence Locke, unsystematically enough, enumerates three other sorts of agreement between ideas—in the perception of which he makes knowledge consist—viz., identity or diversity (blue is not yellow), relation (when equals are added to equals the results are equal), and coexistence or necessary connexion (gold is fixed). We are best off in regard to the knowledge of the first of these, "identity or diversity," for here our intuition extends as far as our ideas, since we recognize every idea, as soon as it arises, as identical with itself and different from others. We are worst off in regard to "necessary connexion." We know something, indeed, concerning the incompatibility or coexistence of certain properties (e. g., that the same object cannot have two different sizes or colors at the same time; that figure cannot exist apart from extension): but it is only in regard to a few qualities and powers of bodies that we are able to discover dependence and necessary connexion by intuitive or demonstrative thought, while in most cases we are dependent on experience, which gives us information concerning particular cases only, and affords no guarantee that things are the same beyond the sphere of our observation and experiment. Since empirical inquiry furnishes no certain and universal knowledge, and since the assumption that like bodies will in the same circumstances have like effects is only a conjecture from analogy, natural science in the strict sense does not exist. Both mathematics and ethics, however, belong in the sphere of the demonstrative knowledge of relations. The principles of ethics are as capable of exact demonstration as those of arithmetic and geometry, although their underlying ideas are more complex, more involved, hence more exposed to misunderstanding, and lacking in visible symbols; though these defects can, and should, in part be made good by careful and strictly consistent definitions. Such moral principles as "where there is no property there is no injustice," or "no government allows absolute liberty," are as certain as any proposition in Euclid.
The advantage of the mathematical and moral sciences over the physical sciences consists in the fact that, in the former, the real and nominal essences of their objects coincide, while in the latter they do not; and, further, that the real essences of substances are beyond our knowledge. The true inner constitution of bodies, the root whence all their qualities, and the coexistence of these, necessarily proceed, is completely unknown to us; so that we are unable to deduce them from it. Mathematical and moral ideas, on the other hand, and their relations, are entirely accessible, for they are the products of our own voluntary operations. They are not