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ideas be capable of representing more real beings than one, or no. One thing more I crave leave to offer about fyllogifm, before I leave it, viz. may one not upon just ground inquire whether the form fyllogifm now has, is that which in reafon it ought to have? For the medius terminus being to join the extremes, i. e. the intermediate idea by its intervention, to fhow the agreement or difagreement of the two in queftion; would not the pofition of the medius terminus be more natural, and show the agreement or difagreement of the extremes clearer and better, if it were placed in the middle between ' them? Which might be easily done by tranfpofing the propofitions, and making the medius terminus the predicate of the first, and the subject of the fecond. As thus,
"Omne corpus eft entenfum & folidum,
Nullum extenfum & folidum eft pura extenfio,
I need not trouble my reader with inftances in fyllo-
fails us for want of ideas.
§. 9. Reason, though it penetrates into the depths of the fea and earth, elevates our thoughts as high as the ftars, and leads us through the vast spaces and large rooms of this mighty fabric, yet it comes far fhort of the real extent of even corporeal being; and there are many inftances 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 ftops, 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 founds, and nothing
2. Because of obfcure and
§. 10. Secondly, our reafon is often puzzled, and at a lofs, because of the obfcurity, confufion, 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 leaft extenfion of matter, nor of infinity, we are at a lofs about the divifibility of matter; but having perfect, clear, and diftinct ideas of number, our reafon 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.
3. For want of intermediate ideas.
§. 11. Thirdly, our reafon is often at a ftand, because it perceives not thofe ideas, which could ferve to fhow the certain or
probable agreement or difagreement of any other two ideas and in this fome men's faculties far outgo others. Till algebra, that great inftrument and instance of human fagacity, was discovered, men, with amazement, looked on feveral of the demonstrations of antient mathematicians, and could fcarce forbear to think the finding several of those proofs to be fomething more than human.
4. Because of wrong principles.
§. 12. Fourthly, the mind, by proceeding upon falfe principles, is often engaged
in abfurdities and difficulties, brought into ftraits and contradictions, without knowing how to free itself; and in that cafe it is in vain to implore the help of reafon, unlefs it be to discover the falfhood and reject the influence of thofe wrong principles. Reafon is fo far from clearing the difficulties which the building upon falfe foundations brings a man into, that if he will purfue it, it entangles him the more, and engages him deeper in perplexities.
§. 13. Fifthly, as obfcure and imperfect 5. Because of ideas often involve our reafon, fo, upon the doubtful fame ground, do dubious words, and uncertain figns, often in difcourfes and arguings, when not warily attended to, puzzle men's reason, and bring them to a non-plus. But thefe two latter are our fault, and not the fault of reafon. But yet the confequences of them are nevertheless obvious; and the perplexities or errours they fill men's minds with, are every where obfervable.
Our highest degree of knowledge is intuitive, without rea
S. 14. Some of the ideas that are in the mind, are fo 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 lefs than the whole circle, as clearly as it does the idea of a circle: and this therefore, as has been faid, 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 confifts the evidence of all those maxims, which nobody has any doubt about, but every man (does not, as is faid, only affent to, but) knows to be true, as soon as ever they are proposed to his underftanding. In the discovery of, and affent to these truths, there is no ufe of the difcurfive faculty, no need of reafoning, but they are known by a fuperior and higher degree of evidence. And fuch, if I may guess at things unknown, I am apt to think, that angels have now, and the fpirits of juft men made perfect, fhall have, in a future ftate, of thousands of things, which now either wholly escape our apprehenfions, or which, our short, fighted reafon having got fome faint glimpse of, we, in the dark, grope after.
The next is
demonftration by rea
§. 15. But though we have, here and there, a little of this clear light, fome sparks of bright knowledge; yet the greatest part of our ideas are fuch, that we cannot difcern their agreement or difagreement by an immediate comS
paring them. And in all these we have need of reafoning, and muft, by discourse and inference, make our difcoveries. Now of these there are two forts, which I fhall take the liberty to mention here again.
First, those whofe agreement or difagreement, 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 difagreement of the intermediate idea, on both fides with those which we would compare, is plainly difcerned, there it amounts to a demonstration, whereby knowledge is produced; which though it be certain, yet it is not fo eafy, nor altogether fo clear as intuitive knowledge. Becaufe in that there is barely one fimple intuition, wherein there is no room for any the least mistake or doubt; the truth is feen all perfectly at once. In demonftration, 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 difagreement of the ideas must be observed and feen 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 neceffary to make up the demonftration is omitted or overlooked. This makes fome demonstrations long and perplexed, and too hard for those who have not strength of parts diftinctly to perceive, and exactly carry fo many particulars orderly in their heads. And even those, who are able to mafter fuch intricate fpeculations, are fain fometimes 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 firft and the fourth is a demonstration, and produces certain knowledge, which may be called rational knowledge, as the other is intuitive.
nefs of this,
we have no
thing but judgment upon proba ble reafoning.
§. 16. Secondly, there are other ideas, whofe agreement or difagreement can no otherwise be judged of, but by the intervention of others, which have not a certain agreement with the extremes, but an ufual or likely one and in these it is that the judgment is properly exercifed, which is the acquiefcing of the mind, that ideas do agree, by comparing them with fuch probable mediums. This, though it never amounts to knowledge, no not to that which is the lowest degree of it: yet fometimes the intermediate ideas tie the extremes fo firmly together, and the probability is fo clear and strong, that affent as neceffarily follows it, as knowledge does demonstration. The great excellency and ufe of the judgment is to obferve right, and take a true estimate of the force and weight of each probability; and then, cafting them up all right together, choose that fide which has the overbalance.
§. 17. Intuitive knowledge is the percep- Intuition, tion of the certain agreement or difagree- demonftrament of two ideas immediately compared tion, judgtogether.
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 obferved to be frequent and ufual.
ces of words,
and confequences of
§. 18. Though the deducing one propofition from another, or making inferences in words, be a great part of reason, and that which it is ufually employed about; yet the principal act of ratiocination is the finding the agreement or difagreement of two ideas one with another, by the intervention of a third. As a man, by a yard, finds two houfes to be of the fame length, which could not be brought together to meafure their equality by juxta-pofition. Words have their confequences, as