CHAP. I. BOOK IV. tability of the same relations between the same immutable things is now the idea that shows him, that if the three angles of a triangle were once equal to two right ones, they will always be equal to two right ones. And hence he comes to be certain, that what was once true in the case, is always true; what ideas once agreed will always agree; and consequently what he once knew to be true, he will always know to be true; as long as he can remember that he once knew it. Upon this ground it is, that particular demonstrations in mathematics afford general knowledge. If then the perception, that the same ideas will eternally have the same habitudes and relations 3, be not a sufficient ground of knowledge, there could be no knowledge of general propositions in mathematics; for no mathematical demonstration would be any other than particular: and when a man had demonstrated any proposition concerning one triangle or circle, his knowledge would not reach beyond that particular diagram. If he would extend it further, he must renew his demonstration in another instance, before he could know it to be true in another like triangle, and so on: by which means one could never come to the knowledge of any general propositions. Nobody, I think, can deny, that Mr. Newton certainly knows any proposition that he now at any time reads in his book to be true; though he has not in actual 5 1 The ground of this assumption of 'immutability' in mathematical relations is not considered. 2 This is the 'revival' through memory of the mental fact that we formerly did perceive the uncondi tional certainty of the proposition, that 'the three angles of a triangle are equal to two right angles'; but without revival of the perception itself. The two are not equivalent. To remember a conclusion, without an intellectual vision of its proof, is not the same as seeing the conclusion in its proof; it is only seeing it in our memory. 3 • Rational insight of the demonstration of an 'eternally' necessary truth is again insufficiently distinguished from the remembrance that we for merly had the rational insight, and now only mechanically remember the result. The difference between direct intuition and demonstration turns partly upon the intervention of memory in the latter, as Locke himself acknowledges in the sequel, when he says that ' demonstrative knowledge is less clear' than intuition. It is not then by comparison of instances, and tentative generalisation, that we reach what is eternally' and unconditionally true, in mathematics or other abstract science. 5 Newton's Principia, which appeared in 1687-three years before the Essay. Cf. Epistle to the Reader,' p. 14. 14 CHAP. I. view that admirable chain of intermediate ideas whereby he BOOK IV. at first discovered it to be true. Such a memory as that, able to retain such a train of particulars, may be well thought beyond the reach of human faculties1, when the very discovery, perception, and laying together that wonderful connexion of ideas, is found to surpass most readers' comprehension. But yet it is evident the author himself knows the proposition to be true, remembering he once saw the connexion of those ideas; as certainly as he knows such a man wounded another, remembering that he saw him run him through. But because the memory is not always so clear as actual perception, and does in all men more or less decay in length of time, this, amongst other differences, is one which shows that demonstrative knowledge is much. more imperfect than intuitive, as we shall see in the following chapter". ✓ 1 Cf. Bk. II. ch. x. § 9. 2 Dugald Stewart thus writes of the Book which opens in this chapter with an account of the four possible sorts of mental proposition in which there can be either certainty of knowledge or assent to probability: 'It is curious to observe that it is the Fourth Book of the Essay alone which bears directly on the author's principal object [as set forth in the "Epistle to the Reader," and the "Introduction."] In this Book, it is further remarkable, there are few, if any, references to preceding parts of the Essay; so that it might have been published separately without being less intelligible than it is. Hence it seems not unreasonable to conjecture that it was the first part of the work in the order of composition, and that it contains the leading and fundamental thoughts which first offered themselves to the author's mind, when he began to reflect on the friendly conversation which gave rise to his philosophical researches. The inquiries in the First and Second Books, which are of a much CHAPTER II. OF THE DEGREES OF OUR KNOWLEDGE. BOOK IV. 14 CHAP. II. Of the 1. ALL our knowledge consisting, as I have said, in the view the mind has of its own ideas, which is the utmost light and greatest certainty we, with our faculties, and in degrees, or our way of knowledge, are capable of, it may not be in clear- amiss to consider a little the degrees of its evidence2. The ness, of our different clearness of our knowledge seems to me to lie in ledge: the different way of perception the mind has of the agree differences Know I. Intui tive. ment or disagreement of any of its ideas. <For if we will reflect on our own ways of thinking, we will find, that sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other: and this I think we may call intuitive knowledge. For in this the mind is at no pains of proving 1 My knowledge, in short, is dependent on, or relative to myself; for I cannot transform myself into another self, with other ideas or phenomena of existence than those presented in my sense-perception and self-consciousness. It is not knowledge in the abstract that Locke is concerned with, but the actual living knowledge for which man has opportunity and capacity. 2 the degrees of its evidence.' Locke's 'knowledge,' being an unconditional certainty that is intellectually visible, does not in one sense admit of 'degrees.' But what he means is explained to be, the varied 'clearness' with which this unconditional certainty can become visible in a human under standing. It may show itself directly and involuntarily, like the light of day; or we may have to go in quest of it through demonstrations; or it may be obscured by the mists of sense. These three ways of perceiving absolute certainty are the subject-matter of this chapter. 3 Intuition originally meant ocular vision, or visual sense-perception. Locke's intuitive knowledge,' or immediate intellectual perception of unconditional certainty in mental propositions, is analogous to this. It must not be confounded with intuitive as opposed to symbolical thought, a use of the term that is foreign to Locke. or examining, but perceives the truth as the eye doth ligh., only by being directed towards it. Thus the mind perceives that white is not black, that a circle is not a triangle, that three are more than two and equal to one and two. Such kinds of truths the mind perceives at the first sight of the ideas together, by bare intuition; without the intervention of any other idea: and this kind of knowledge is the clearest and most certain that human frailty is capable of. This part of knowledge is irresistible, and, like bright sunshine1, forces itself immediately to be perceived, as soon as ever the mind turns its view that way; and 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 knowledge2 which certainty every one finds to be so great, that he cannot imagine, and therefore not require a greater: for a man cannot conceive himself capable of a greater certainty than to know that any idea in his mind is such as he per ''bright sunshine,' and 'the candle of the Lord' (Introd. § 5; Bk. IV. ch. iii. § 20), are metaphors used to signify the 'perception' which gives us knowledge or absolute certainty. The 'candle of the Lord' suggests Locke's favourite preacher, Whichcote, by whom this metaphor was employed with a like purpose; also by Culverwell in his Light of Nature. 2 Locke thus rests human knowledge on intuitive or self-evident perception of agreement or disagreement between the ideas which it interprets. While he rejects innateness (as he understands it), he recognises the need for a direct discernment of what is self-evident, as indispensable to unconditional certainty of every kind. The important statement in the text should be compared with Bk. II. ch. i. § 2, supposed to contradict it,-that a human mind has all the materials of reasoning and knowledge from experience, in which all our knowledge is founded, and from which it all ultimately derives VOL. II. N itself.' The ultimate dependence of CHAP. II. BOOK IV. ceives 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. Certainty depends so wholly on this intuition, that, in the next degree of knowledge which I call demonstrative, this intuition is necessary in all the connexions of the intermediate ideas, without which we cannot attain knowledge and certainty. II. Demonstrative. 2. The next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately. Though wherever the mind perceives the agreement or disagreement of any of its ideas, there be certain knowledge; yet it does not always happen, that the mind sees that agreement or disagreement, which there is between them, even where it is discoverable; and in that case remains in ignorance, and at most gets no further than a probable conjecture. The reason why the mind cannot always perceive presently1 the agreement or disagreement of two ideas, is, because those ideas, concerning whose agreement or disagreement the inquiry is made, cannot by the mind be so put together as to show it In this case then, when the mind cannot so bring its ideas together as by their immediate comparison, and as it were juxta-position or application one to another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more, as it happens) to discover the agreement or disagreement which it searches; and this is that which we call reasoning. Thus, the mind being willing to know the agreement or disagreement ''presently'-immediately,—'in the bright sunshine of its self-evidence.' 2 'reasoning' here means demonstration; and 'demonstration' is, as it were, indirect intuition, in which the conclusion is self-evidently contained, either in self-evident, or in already demonstrated truth, from which it is evolved in reasoning. So understood, it is available, according to Locke, only in reasonings about abstract ideas, conceived without regard to any actual beings, as in abstract mathematics and ethics;-with this exception only, that the real existence of God, or Eternal Mind, is held by him to be 'demonstrable like any abstract conclusion in our mathematical knowledge.' |