There are associations of ideas which are natural and necessary, as well as arbitrary, false, and unnatural combinations. The danger of the last is vividly pointed out, which often arise from our having seen objects connected together by chance. Hence the association, which was originally purely accidental, is invariably connected in tho imagination, which consequently biasses the judgment. Hence too a number of errors, not only of opinion but of sentiment, giving rise to unnatural sympathies and antipathies which not unfrequently closely verge upon madness. This gives occasion to a variety of judicious observations on the right conduct of education, the means of guarding against the formation of such unnatural combinations of ideas, and tho method of correcting them when once formed, and of restoring the regular and due associations which have their ground iu the very nature of the human mind and its ideas. What however are tho leading laws of association, Locke has not attempted to determine.
Before passing from this deduction of ideas to the examination of the nature and extent of the knowledge which is acquired by means of them, Locke devotes the third book of his 'Essay' to the investiga tion of language and signs, which it is not important for our purpose to state.
Locke then proceeds to determine the nature, validity, and limits of the human understanding. All knowledge, strictly defined, is the perception of the agreement or disagreement of ideas, and is conse quently limited to them. It extends therefore only so far as we are able to perceive the validity of the combinations and relations of our ideas, that is, so far as we are enabled to discover them by intuition, demonstration, and sensation. Intuition, which Locke calls an imme diate perception of relation, does not apply to all ideas ; many must be proved by means of some intermediate ideas. This is the province of demonstration, every step of which however is an act of intuition. Demonstration again does not apply to the proof of all ideas, since in the case of many no middle ideas can be found by means of which the comparison may be made. Sensation is still more limited, being con fined to what is actually passing in each sense. Generally, all know ledge directs itself to identity or diversity, coexistence, relation, and the real existence of things. Identity and diversity are perceived by intuition, and we cannot have an idea without perceiving at the same time that it is different from all others. With regard to co-existence our knowledge is unlimited; for our ideas of substances are mere col lections or aggregates of certain single ideas in one subject; and from the nature of these single ideas it is impossible to see how far they are or are not combinable with others. Hence we cannot determine what qualities any object may possess in addition to those already known to us. As to the actual existence of things, we have no intui tive knowledge thereof, except in the case of our existence; that of God is demonstrative, but of all other objects we only sensuously know that they exist, that is, we perceive mediately by sensation their exist ence or presence.
Locke next passes to an examination of propositions, axioms, and definitions. The utility of axioms is denied on the ground that they are not the only self-evident propositions, and because equal if not greater certainty is contained in all particular identical propositions and limited cases. Moreover they do not serve to facilitate knowledge, for all particular propositions will find a more ready assent ; as, for instance, the proposition, twice two are four, will be more easily admitted than that the whole Is equal to Its parts. Moreover axioms are not useful for the proof of all lower propositions involved in them: they cannot consequently form the basis of any science. For example, no science has ever been raised on the basis of the principle of contra diction. They do not even contribute to the enlargement of know ledge ; the false as well as the true may be proved by them, and oousequently they serve at best but for endless dispute. Among those barren and unprofitable propositions, Locke reckons not merely those that are Identical, but analytical also, or those In which a property contained In a complex idea is predicated of it. For example : every man is an animal. By such judgments or propositions we learn in fact nothing, and our knowledge is not increased in the least degree. Knowledge can only be extended by such judgments as predicate of a aubjewt some quality or property which Is not already involved in the idea of it. Synthetical propositions therefore are alone of value. In the next place be examines certain metaphysical problems, and con cludes of most of them that they do not admit of nuy precise solution, while others might easily be set at rest if men would only come to the investigation of them free from all prejudices. Some very valuable remarks are added upon the sources of error, and on enthusiasm and faith, the due limits of which are pointed out, and the important truth repeatedly insisted upon, that reason is the ultimate test of revelation. Tho work concludes with a division of the object-matter of science or knowledge, which he makes to be three-fold:—l. Natural philosophy, or physics, which is the knowledge of things both corpo real and spiritual. The end of this is speculative truth, 2. Ethics, or practice, which is the skill of rightly applying our powers and actions for the attainment of things good and useful, the end of it being not bare speculation, but right, and a conduct suitable to it. 3. The doctrine of signs (crtwe(orrorb), the business of which is to oon eider the nature of the signs which the mind makes use of for the understanding of things or the conveying of its ideas to others. This is the most general as well as the most natural division of tho objects of the understanding. For mau can employ his thoughts about nothing but either the oontemplation of things for the discovery of truth, or about the things in his own power, which are his own actions for the attainment of his ends ; or the signs which the mind makes use of in both, and the right ordering of them for its information.