it ought to have? For the medius terminus being to join the extremes, i. e. the intermediate ideas, by its intervention, to show the agreement or disagreement of the two in question, would not the positition 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 mediu terminus the predicate of the first, and the subject of the second. As thus, Nullum extensum et solidum est pura extensio, 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. § 9. 1. Reason fails us for want of ideas. REASON, though it penetrates into the depths of the sea and earth, elevates our thoughts as high as the stars, and leads us 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, whereever 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. § 10. 2. Because of obscure and imperfect ideas. 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 the free created agents, which reason cannot well extricate itself out of. § 11. 3. For want of intermediate ideas. THIRDLY, Our reason is often at a stand, because it perceives not those ideas, which could serve to show the certain or probable agreement or disagreement of any two other 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. 12. 4. Because of wrong principles. FOURTHLY, The mind, by proceeding upon false principles, is of ten 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. 5. Because of doubtful terms. FIFTHLY, AS obscure and imperfect ideas often involve our reason, so, upon the same ground, do dubious words, and uncertain 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 errors they fill men's minds with are every where observable. § 14. Our highest degree of knowledge is intuitive, without reasoning. SOME of the ideas that are in the mind, are so there, that they can be by themselves immediately compared one with another: and in these the mind is able to perceive, 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. The next is demonstration by reasoning. Bur though we have, here and there, a little of this clear light, some sparks of bright knowledge; yet the greatest part of our ideas are such, that we cannot discern their agreement or disagreement by an immediate comparing 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 overlook ed. 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. To supply the narrowness of this, we have nothing but judgement upon probable reasoning. SECONDLY, There are other ideas, whose agreement or disagreement can no otherwise be judged of, but by the intervention of others, which have not a certain agreement with the extremes, but an usual or likely one; and in these it is that the judgement is properly exercised, which is the acquiescing of the mind, that any ideas 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 judgement 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 over balance. § 17. Intuition, demonstration, judgement. INTUITIVE knowledge is the perception of the certain agreement or disagreement of two ideas immediately compared together. Rational knowledge is the perception of the certain agreement or disagreement of any two ideas, by the intervention of one or more other ideas. Judgement is the thinking or taking two ideas to agree or diságree, 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. 18. Consequences of words, and consequences of ideas. THOUGH the deducing one proposition from another, or making inferences in words, be a great part of reason, and that which it is usually employed about; yet the principle 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 juxta-position. Words have their consequences, as the signs of such ideas and things agree or disagree, as really they are; but we observe it only by our ideas. § 19. Four sorts of arguments. BEFORE We quit this subject, it may be worth our while a little to reflect on four sorts of arguments, that men, in their reasonings with others, do ordinarily make use of, to prevail on their assent ; or at least so to awe them, as to silence their opposition. 1. Ad Verecundiam. First, the first is, to allege the opinions of men, whose parts, learning, eminency, power, or some other cause, has gained a name, and settled their reputation in the common esteem with some kind of authority. When men are established in any kind of dignity it is thought a breach of modesty for others to derogate any way from it, and question the authority of men who are in possession of it. This is apt to be censured, as carrying with it too much of pride, when a man does not readily yield to the determination of approved authors, which is wont to be received with respect and submission by others; and it is looked upon as insolence for a man to set up, and adhere to his own opinion, against the current stream of antiquity; or to put it in the balance against that of some learned doctor, or otherwise approved writer. Whoever backs his tenets with such authorities, thinks he ought thereby to carry the cause, and is ready to style it impudence in any one who shall stand out against them. This, I think, may be called argumentum ad verecundiam. § 20. 2. Ad Ignorantiam. SECONDLY, Another way that men ordinarily use to drive others, and force them to submit their judgements, and receive the opinion in debate, is to require the adversary to admit what they allege as a proof, or to assign a better. And this I call argumentum ad ignorantiam. § 21. 3. Ad Hominem. THIRDLY, A third way is to press a man with consequences drawn from his own principles or concessions. This is already known under the name of argumentum ad hominem. |