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 copied from things, but are archetypal for reality and need no confirmation from experience. The connexion constituted by our understanding between the ideas crime and punishment (e. g., the proposition: crime deserves punishment) is valid, even though no crime had ever been committed, and none ever punished. Existence is not at all involved in universal propositions; "general knowledge lies only in our own thoughts, and consists barely in the contemplation of our own abstract ideas" and their relations. The truths of mathematics and ethics are both universal and certain, while in natural science single observations and experiments are certain, but not general, and general propositions are only more or less probable. Both the particular experiments and the general conclusions are of great value under certain circumstances, but they do not meet the requirements of comprehensive and certain knowledge.
The extent of our knowledge is very limited—much less, in fact, than that of our ignorance. For our knowledge reaches no further than our ideas, and the possibility of perceiving their agreements. Many things exist of which we have no ideas—chiefly because of the fewness of our senses and their lack of acuteness—and just as many of which our ideas are only imperfect. Moreover, we are often able neither to command the ideas which we really possess, or at least might attain, nor to perceive their connexions. The ideas which are lacking, those which are undiscoverable, those which are not combined, are the causes of the narrow limits of human knowledge.
There are two ways by which knowledge may be extended: by experience, on the one hand, and, on the other, by the elevation of our ideas to a state of clearness and distinctness, together with the discovery and systematic arrangement of those intermediate ideas which exhibit the relation of other ideas, in themselves not immediately comparable. The syllogism, as an artificial form, is of little value in the perception of the agreements between these intermediate and final terms, and of none whatever in the discovery of the former. Analytical and identical propositions which merely explicate the conception of the subject, but express nothing not already known, are, in spite of their indefeasible certitude, valueless for the extension of knowledge, and when taken for more than verbal explanations, mere absurdities. Even those most general propositions, those "principles" which are so much talked of in the schools, lack the utility which is so commonly ascribed to them. Maxims are, it is true, fit instruments for the communication of knowledge already acquired, and in learned disputations may perform indispensable service in silencing opponents, or in bringing the dispute to a conclusion; but they are of little or no use in the discovery of new truth. It is a mistake to believe that special cases (as 5 = 2 + 3, or 5 = 1 + 4) are dependent on the truth of the abstract rule (the whole is equal to the sum of its parts), that they are confirmed by it and must be derived from it. The particular and concrete is not only as clear and certain as the general maxim, but better known than this, as well as earlier and more easily perceived. Nay, further, in cases where ideas are confused and the meanings of words doubtful, the use of axioms is dangerous, since they may easily lend the appearance of proved truth to assertions which are really contradictory.
Between the clear daylight of certain knowledge and the dark night of absolute ignorance comes the twilight of probability. We find ourselves dependent on opinion and presumption, or judgment based upon probability, when experience and demonstration leave us in the lurch and we are, nevertheless, challenged to a decision by vital needs which brook no delay. The judge and the historian must convince themselves from the reports of witnesses concerning events which they have not themselves observed; and everyone is compelled by the interests of life, of duty, and of eternal salvation to form conclusions concerning things which lie beyond the limits of his own perception and reflective thought, nay, which transcend all human experience and rigorous demonstration whatever. To delay decision and action until absolute certainty had been attained, would scarcely allow us to lift a single finger. In cases concerning events in the past, the future, or at a distance, we rely on the testimony of others (testing their reports by considering their credibility as witnesses and the conformity of the evidence to general experience in like cases); in regard to questions concerning that which is absolutely beyond experience, e.g., higher orders of spirits, or the ultimate causes of natural phenomena, analogy is the only help we have. If the witnesses conflict among themselves, or with the usual course of nature, the grounds pro and con must be carefully balanced; frequently, however, the degree of probability attained is so great that our assent is almost equivalent to complete certainty. No one doubts,—although it is impossible for him to "know,"—that Caesar conquered Pompey, that gold is ductile in Australia as elsewhere, that iron will sink to-morrow as well as to-day. Thus opinion supplements the lack of certain knowledge, and serves as a guide for belief and action, wherever the general lot of mankind or individual circumstances prevent absolute certitude.
Although in this twilight region of opinion demonstrative proofs are replaced merely by an "occasion" for "taking" a given fact or idea "as true rather than false," yet assent is by no means an act of choice, as the Cartesians had erroneously maintained, for in knowledge it is determined by clearly discerned reasons, and in the sphere of opinion, by the balance of probability. The understanding is free only in combining ideas, not in its judgment concerning the agreement or the repugnancy of the ideas compared; it lies within its own power to decide whether it will judge at all, and what ideas it will compare, but it has no control over the result of the comparison; it is impossible for it to refuse its assent to a demonstrated truth or a preponderant probability.
In this recognition of objective and universally valid relations existing among ideas, which the thinking subject, through comparisons voluntarily instituted, discovers valid or finds given, but which it can neither alter nor demur to, Locke abandons empirical ground (cf. p. 155) and approaches the idealists of the Platonizing type. His inquiry divides into two very dissimilar parts (a psychological description of the origin of ideas and a logical determination of the possibility and the extent of knowledge), the latter of which is, in Locke's opinion, compatible with the former, but which could never have been developed from it. The rationalistic edifice contradicts the sensationalistic foundation. Locke had hoped to show the value and the limits of knowledge by an inquiry into the origin of ideas, but his estimate of this value and these limits cannot be proved from the a posteriori origin of ideas—it can only be maintained in despite of this, and stands in need of support from some (rationalistic) principle elsewhere obtained. Thinkers who trace back all simple ideas to outer and inner perception we expect to reject every attempt to extend knowledge beyond the sphere of experience, to declare the combinations of ideas which have their origin in sensation trustworthy, and those which are formed without regard to perception, illusory; or else, with Protagoras, to limit knowledge to the individual perceiving subject, with a consequent complete denial of its general validity. But exactly the opposite of all these is found in Locke. The remarkable spectacle is presented of a philosopher who admits no other sources of ideas than perception and the voluntary combination of perceptions, transcending the limits of experience with proofs of the divine existence, viewing with suspicion the ideas of substance formed at the instance of experience, and reducing natural science to the sphere of mere opinion; while, on the other hand, he ascribes reality and eternal validity to the combinations of ideas formed independently of perception, which are employed by mathematics and ethics, and completely abandons the individualistic position in his naïve faith in the impregnable validity of the relations of ideas, which is evident to all who turn their attention to them. The ground for the universal validity of the relations among ideas as well as of our knowledge of them, naturally lies not in their empirical origin (for my experience gives information to me alone, and that only concerning the particular case in question), but in the uniformity of man's rational constitution. If two men really have the same ideas—not merely think they have because they use similar language—it is impossible, according to Locke, that they should hold different opinions concerning the relation of their ideas. With this conviction, that the universal validity of knowledge is rooted in the uniformity of man's rational constitution, and the further one, that we attain certain knowledge only when things conform to our ideas, Locke closely approaches Kant; while his assumption of a fixed order of relations among ideas, which the individual understanding cannot refuse to recognize, and the typical character assigned to mathematics, associate him with Malebranche and Spinoza. In view of these points of contact with the rationalistic school and his manifold dependence on its founder, we may venture the paradox, that Locke may not only be termed a Baconian with Cartesian leanings, but (almost) a Cartesian influenced by Bacon. The possibility must not be forgotten, however, that rationalistic suggestions came to him also from Galileo, Hobbes, and Newton.[1]
[Footnote 1: Cf. the article by Benno Erdmann cited p. 156, note.]
Intermediate between knowledge and opinion stands faith as a form of assent which is based on testimony rather than on deductions of the reason, but whose certitude is not inferior to that of knowledge, since it is a communication from God, who can neither deceive nor be deceived. Faith and the certainty thereof depend on reason, in so far as reason alone can determine whether a divine revelation has really been made and the meaning of the words in which the revelation has come down to us. In determining the boundaries of faith and reason Locke makes use of the distinction—which has become famous—between things above reason, according to reason, and contrary to reason. Our conviction that God exists is according to reason; the belief that there are more gods than one, or that a body can be in two different places at the same time, contrary to reason; the former is a truth which can be demonstrated on rational grounds, the latter an assumption incompatible with our clear and distinct ideas. In the one case revelation confirms a proposition of which we were already certain; in the other an alleged revelation is incapable of depriving our certain knowledge of its force. Above reason are those principles whose probability and truth cannot be shown by the natural use of our faculties, as that the dead shall rise again and the account of the fall of part of the angels. Among the things which are not contrary to reason belong miracles, for they contradict opinion based on the usual course of nature, it is true, but not our certain knowledge; in spite of their supernatural character they deserve willing acceptance, and receive it, when they are well attested, whereas principles contrary to reason must be unconditionally rejected as a revelation from God. Locke's demand for the subjection of faith to rational criticism assures him an honorable place in the history of English deism. He enriched the philosophy of religion by two treatises of his own: The Reasonableness of Christianity, 1695, and three Letters on Tolerance, 1689-1692. The former transfers the center of gravity of the Christian religion from history to the doctrine of redemption; the Letters demand religious freedom, mutual tolerance among the different sects, and the separation of Church and State. Those sects alone are to receive no tolerance which themselves exercise none, and which endanger the well-being of society; together with atheists, who are incapable of taking oaths. In other respects it is the duty of the state to protect all confessions and to favor none.