to the abstract ideas of the Essay, in the Introduction to the Principles of Human Knowledge. Abstract notions, as such, cannot be 'particular ideas,' and cannot be presented in sense, or represented in imagination. What Locke seems to mean is, that the concept, e. g. of a triangle, may be individualised, or exemplified as a particular idea, in any one of many possible applications-oblique, equilateral, &c.—all of which it is potentially, but none of them actually, save when it is exemplified in that one. Only thus can 'abstract ideas' be presented in sense, or represented in imagination. ideism. According to his account of 'ideas' and their particu- Locke's larity, and apart from their office as factors in knowledge, Locke is more properly an ideist or phenomenalist than an Idealist, our ideas being with him originally the particular phenomena in which real existences immediately present themselves in human experience. III. CONNEXION OR REPUGNANCY OF IDEAS, to us. A SECOND ELEMENT IN KNOWLEDGE. Knowledge, according to Locke, is concerned with the Knowideas, or particular manifestations, which existence presents implies ledge Now to get knowledge out of ideas implies that the interideas are related to one another, and so are interpretable; ideas. pretability for knowledge is mental assertion or denial, and this presupposes relations of 'connexion and agreement, or disagreement or repugnancy' as the foundation of assertion or denial. In short, an implied copula is distinctive of all proposition, mental or verbal, spontaneous or reflective. Locke, accordingly, proceeds to inquire what sorts of Four sorts knowable relations there are amongst ideas; whether these between all come within the range of human knowledge; and if ideas. not, why not? He finds that the 'connexions or agreements and disagreements or repugnancies' between the ideas or phenomena of existence, which constitute our real and our imaginary worlds, are of four sorts. As thus1:-'To 1 Bk. IV. ch. i. § 3. See also ch. iii. passim. of relations Identity sity as knowable relations of ideas. ་ understand wherein this agreement or disagreement consists, I think we may reduce it all to these four sorts:— (1) Identity or diversity. (2) Relation. (3) Coexistence, or necessary connexion. (4) Real existence.' He adds that though identity and coexistence are truly nothing but relations, yet they are such peculiar ways of agreement or disagreement of our ideas that they deserve to be considered as distinct heads, and not under relation in general'-the second sort. This seems to imply that perception of 'real existence' in and through means of our ideas the fourth sort of connexion-is other than perception of relation between ideas, in the way the other three preceding sorts are;-although knowledge of 'real existence,' like the other sorts of knowledge, takes the form of proposition, with implied 'connexion' between two ideas-'real existence' being therein predicated of the subject, which is thereby brought within the sphere of reality, in the mind's regard. Look a little at each sort. Take first Identity and Diversity. It is impossible to and diver have any ideas at all without perceiving that an idea is what it is, and that one idea is not another idea. This is the fundamental relation of all ideas, which in its ultimate form of abstraction appears, in logic, as the two correlative principles of identity and non-contradiction. It is so universally necessary that without a perception of it there could be no knowledge of any sort; so that, in having any ideas, this relation, at any rate, is implied, ideas 'being' universally and eternally known to be not the same, and so being' universally and constantly denied of one another. And this negative relation, the one in which knowledge is fully coextensive with ideas, opens the way to positive knowledge; because unless it is presupposed ideas are uninterpretable, there being no ideas to interpret. Abstract relations Again, there are innumerable positive relations of ideas, particular and universal, which arise when ideas are considered in abstraction from the contingencies of time and ideas, e. g. change. Those abstract relations belong to them as such, in general between in pure mathematics. and Locke accordingly regards them as relations proper. Pure mathematics and abstract ethics exemplify this second category of the knowable. coexist ence of the same as a know able Further, there are innumerable positive relations of Necessary ideas that arise out of their simultaneous and successive appearances, in the constant flux of which the sensible world simple and our own minds are the scenes. This third sort of ideas in knowable relation among ideas is described in the Essay substance, as that of their 'co-existence or non-existence in the same subject.' It implies that they are supposed to be complex relation. ideas in particular substances, material or spiritual, and not, as in the preceding case, abstracted from conditions of time. Lastly, there is the agreement or repugnance of ideas Agreewith the 'real existence' of the particular substance which they then manifest to us. This is illustrated in all propositions, mental and verbal, spontaneous and reflective, in ment or repugnance of ideas with the idea of real existence. Examples of each of the four sorts of which real existence' is affirmed or denied. Within these four sorts of agreement or disagreement of ideas, according to the Essay, lies all the knowledge we have, or are capable of. For all assertions that can be made concerning any idea presented in experience are-that it knowable is, or is not the same with some other idea; that it has relation. this or that abstract, e. g. mathematical or moral, relation with some other idea; that it does or does not always coexist with some other idea in the same individual substance; or that it has real existence, independent of any momentary perception. Thus 'blue is not yellow' is an example of the relation of diversity; 'two triangles upon equal bases between two parallels are equal' is an example of abstract relation; 'iron is susceptible of magnetical impressions' illustrates coexistence of ideas; 'Iexist,' 'things around me exist,' 'God exists,' are assertions of real existence. Pure logic reflects scientifically the first of these sorts of 'connexion and disagreement,' in their ultimate abstraction, as applicable to all ideas. The abstract sciences of mathematics and ethics, and also reasonings that deal only with arbitrary definitions of words, exemplify the second sort. Experiential inquiries into the laws of natural ideas or phenomena, under the presuppositions of physical causality, aim at the discovery of relations of the third sort. The fundamental propositions which affirm the ultimate realities of existence, constitute the fourth sort of connexion or repugnance of ideas. Know ledge distinguished from judgment of probability. Knowledge proper is intuitive, or selfevident, according to the Essay. IV. PERCEPTION, A THIRD ELEMENT IN KNOWLEDGE. In the views which the mind finds itself obliged or able to take of the connexions and repugnances amongst ideas, or of the interpretation to be put upon them, Locke finds a difference. There is the perceived absolute certainty which is essential to knowledge, and the presumption, or judgment of probability, on which after all human life turns. In knowledge or science proper we 'certainly perceive, and are undoubtedly satisfied of the agreement or disagreement of any ideas.' In judgments of probability, which are often practically certain, we affirm or deny ideas of one another, when their unconditionally certain agreement or disagreement is not perceived, but only presumed. Our knowledge extends only as far as we are conscious of an intellectual insight of necessary relation between the subject and the predicate of the mental proposition in which the knowledge rises into consciousness. This 'perception' or insight Locke describes as fundamentally intuitive; the relation is perceived 'at once, as essentially the eye perceives light, only by being directed to it.' The unconditional certainty we have that 'white is not black'; that a circle is not a triangle'; that 'three are more than two, or equal to one and two,' are examples of this intuitive perception. It does not need the medium of reasoning, and it is the utmost certainty that human understanding is capable of, or that one can even suppose possible in any intelligent being. Intuitive knowledge, according to the Essay, is irresistible,' and, like bright sunshine, forces itself immediately to be perceived as soon as ever the mind turns its view that way: it leaves no room for hesitation, doubt, or examination, but the mind is presently filled with the clear light of it. It is on this intuition that depends all the certainty and evidence of all our knowledge; which certainty every one finds to be so great, that he cannot imagine, and therefore cannot require, a greater: for a man cannot conceive himself capable of a greater certainty that to know [i.e. perceive intuitively] that any idea in his mind is such as he perceives it to be; and that two ideas, wherein he perceives a difference, are different, and not precisely the same. He that demands a greater certainty than this, demands he knows not what, and shows only that he has a mind to be a sceptic without being able to be so.' (Bk. IV. ch. ii. § 1.) Thus, while Locke, in treating of ideas per se, in the Second Book, makes human knowledge depend upon our getting particular ideas of things, through external and internal experience, without the aid of any ideas that are 'innate' or prior to all experience,'-in the Fourth Book he represents intuition, or self-evidence, as not less essential than experience; for on it, he says, 'depends all the certainty and evidence of all our knowledge.' In this recognition of the second of these two cardinal constituents of knowledge, Locke agrees with his favourite Hooker, who says that 'to make nothing evident of itself unto man's understanding were to take away the possibility of knowing anything'; and that 'herein that of Theophrastus is true-they that seek a reason of all things do utterly overthrow reason.' involves But while human knowledge is fundamentally intuitive, Demonaccording to the Essay, the percipient act in it is not in stration all instances a direct intuition. In the finite human understanding the range of direct intuition is narrow. In many human acts of knowing, the known relation between the two ideas is not perceived 'at first sight.' It needs intermediate ideas, or the chain of intuited relations which constitutes demonstration. Thus, while the axioms of geometry are known by a direct intuition, the great body of geometrical truths has to be demonstrated: it is reached in the form of intellectually necessary conclusions, not of truths that are evident at once. In a demonstrated conclusion the absolute certainty of knowledge is not immediately forced upon the understanding: it is reached gradually, in a series of steps, adapted to that weakness which obliges man to have recourse to reasoning. But all reasoning that is properly demonstrative is, as it were, saturated with intuition; each step is taken in the light of intuition; and we march towards the conclusion in a series of self-evident steps. Demonstration is intuition |