ideas be capable of representing more real beings than one, or no. One thing more I crave leave to offer about syllogism, before I leave it, viz. may one not upon just ground inquire whether the form syllogism now has, is that which in reason it ought to have? For the medius terminus being to join the extremes, i. e. the intermediate idea by its intervention, to show the agreement or disagreement of the two in question; would not the position of the medius terminus be more natural, and show the agreement or disagreement of the extremes clearer and better, if it were placed in the middle between them? Which might be easily done by transposing the propositions, and making the medius terminus the predicate of the first, and the subject of the second. As thus, "Omne corpus est entensum & solidum, I need not trouble my reader with instances in syllogisms, whose conclusions are particular. The same reason holds for the same form in them, as well as in the general. ideas. 9. Reason, though it penetrates into 1. Reason the depths of the sea and earth, elevates our fails us for thoughts as high as the stars, and leads us want of through the vast spaces and large rooms of this mighty fabric, yet it comes far short of the real extent of even corporeal being: and there are many instances wherein it fails us: as, First, it perfectly fails us, where our ideas fail. It neither does, nor can extend itself farther than they do. And therefore wherever we have no ideas, our reasoning stops, and we are at an end of our reckoning: and if at any time we reason about words, which do not stand for any ideas, it is only about those sounds, and nothing else. 2. Because of obscure and imperfect ideas. 10. Secondly, our reason is often puzzled, and at a loss, because of the obscurity, confusion, or imperfection of the ideas it is employed about; and there we are involved in difficulties and contradictions. Thus not having any perfect idea of the least extension of matter, nor of infinity, we are at a loss about the divisibility of matter; but having perfect, clear, and distinct ideas of number, our reason meets with none of those inextricable difficulties in numbers, nor finds itself involved in any contradictions about them. Thus, we having but imperfect ideas of the operations of our minds, and of the beginning of motion, or thought, how the mind produces either of them in us, and much imperfecter yet of the operation of God; run into great difficulties about free created agents, which reason cannot well extricate itself out of. of interme diate ideas. 11. Thirdly, our reason is often at a 3. For want stand, because it perceives not those ideas, which could serve to show the certain or probable agreement or disagreement of any other two ideas and in this some men's faculties far outgo others. Till algebra, that great instrument and instance of human sagacity, was discovered, men, with amazement, looked on several of the demonstrations of ancient mathematicians, and could scarce forbear to think the finding several of those proofs to be something more than human. 4. Because of wrong principles. § 12. Fourthly, the mind, by proceeding upon false principles, is often engaged in absurdities and difficulties, brought into straits and contradictions, without knowing how to free itself; and in that case it is in vain to implore the help of reason, unless it be to discover the falsehood and reject the influence of those wrong principles. Reason is so far from clearing the difficulties which the building upon false foundations brings a man into, that if he will pursue it, it entangles him the more, and engages him deeper in perplexities. 13. Fifthly, as obscure and imperfect 5. Because ideas often involve our reason, so, upon the of doubtful same ground, do dubious words, and un- terms. certain signs, often in discourses and arguings, when not warily attended to, puzzle men's reason, and bring them to a non-plus. But these two latter are our fault, and not the fault of reason. But yet the consequences of them are nevertheless obvious; and the perplexities or errours they fill men's minds with, are every where observable. soning. $14. Some of the ideas that are in the Our highest mind, are so there, that they can be by degree of themselves immediately compared one with knowledge another and in these the mind is able to is intuitive, without reaperceive, that they agree or disagree as clearly, as that it has them. Thus the mind perceives, that an arch of a circle is less than the whole circle, as clearly as it does the idea of a circle and this therefore, as has been said, I call intuitive knowledge; which is certain, beyond all doubt, and needs no probation, nor can have any; this being the highest of all human certainty. In this consists the evidence of all those maxims, which nobody has any doubt about, but every man (does not, as is said, only assent to, but) knows to be true, as soon as ever they are proposed to his understanding. In the discovery of, and assent to these truths, there is no use of the discursive faculty, no need of reasoning, but they are known by a superior and higher degree of evidence. And such, if I may guess at things unknown, I am apt to think, that angels have now, and the spirits of just men made perfect shall have, in a future state, of thousands of things, which now either wholly escape our apprehensions, or which, our short-sighted reason having got some faint glimpse of, we, in the dark, grope after. 15. But though we have, here and The next is there, a little of this clear light, some sparks demonstraof bright knowledge; yet the greatest part tion by reaof our ideas are such, that we cannot discern soning. their agreement or disagreement by an immediate com paring them. And in all these we have need of reasoning, and must, by discourse and inference, make our discoveries. Now of these there are two sorts, which I shall take the liberty to mention here again. First, those whose agreement or disagreement, though it cannot be seen by an immediate putting them together, yet may be examined by the intervention of other ideas, which can be compared with them. In this case when the agreement or disagreement of the intermediate idea, on both sides with those which we would compare, is plainly discerned, there it amounts to a demonstration, whereby knowledge is produced; which though it be certain, yet it is not so easy, nor altogether so clear as intuitive knowledge. Because in that there is barely one simple intuition, wherein there is no room for any the least mistake or doubt; the truth is seen all perfectly at once. In demonstration, it is true, there is intuition too, but not altogether at once; for there must be a remembrance of the intuition of the agreement of the medium, or intermediate idea, with that we compared it with before, when we compare it with the other; and where there be many mediums, there the danger of the mistake is the greater. For each agreement or disagreement of the ideas must be observed and seen in each step of the whole train, and retained in the memory, just as it is; and the mind must be sure that no part of what is necessary to make up the demonstration is omitted or overlooked. This makes some demonstrations long and perplexed, and too hard for those who have not strength of parts distinctly to perceive, and exactly carry so many particulars orderly in their heads. And even those, who are able to master such intricate speculations, are fain sometimes to go over them again, and there is need of more than one review before they can arrive at certainty. But yet where the mind clearly retains the intuition it had of the agreement of any idea with another, and that with a third, and that with a fourth, &c. there the agreement of the first and the fourth is a demonstration, and produces certain knowledge, which may be called rational knowledge, as the other is intuitive. §16. Secondly, there are other ideas, To supply whose agreement or disagreement can no the narrowotherwise be judged of, but by the inter- ness of this, vention of others which have not a certain we have noagreement with the extremes, but an usual thing but judgment or likely one and in these it is that the upon proba judgment is properly exercised, which is ble reasonthe acquiescing of the mind, that any ideas ing. do agree, by comparing them with such probable mediums. This, though it never amounts to knowledge, no not to that which is the lowest degree of it: yet sometimes the intermediate ideas tie the extremes so firmly together, and the probability is so clear and strong, that assent as necessarily follows it, as knowledge does demonstration. The great excellency and use of the judgment is to observe right, and take a true estimate of the force and weight of each probability; and then casting them up all right together, choose that side which has the overbalance. § 17. Intuitive knowledge is the percep- Intuition, tion of the certain agreement or disagree- demonstrament of two ideas immediately compared tion, judgtogether. ment. Rational knowledge is the perception of the certain agreement or disagreement of any two ideas, by the intervention of one or more other ideas. Judgment is the thinking or taking two ideas to agree or disagree, by the intervention of one or more ideas, whose certain agreement or disagreement with them it does not perceive, but hath observed to be frequent and usual. ideas. 18. Though the deducing one propo- Consequensition from another, or making inferences ces of words, in words, be a great part of reason, and that and consewhich it is usually employed about; yet the quences of principal act of ratiocination is the finding the agreement or disagreement of two ideas one with another, by the intervention of a third. As a man, by a yard, finds two houses to be of the same length, which could not be brought together to measure their equality by juxtaposition. Words have their consequences, as |