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$ 9. Reason, though it penetrates into 1. Reason fails us for the depths of the sea and earth, elevates want of our thoughts as high as the stars, and ideas.

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 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 § 10. Secondly, our reason is often of obscure puzzled and at a loss, because of the oband imper- scurity, confusion, or imperfection of the fect ideas.

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.

§ 11. Thirdly, our reason is often at a 3. For want

stand, because it perceives not those ideas diate 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,

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terms.

This

with amazement, looked on several of the demonstra-
tions of ancient mathematicians, and could scarce for-
bear to think the finding several of those proofs to be
something more than human.
$ 12. Fourthly, the mind, by proceed-

4. Because ing upon false principles, is often engaged

of in absurdities and difficulties, brought into principles.

wrong 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

of doubtful 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 nonplus. 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. 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

soning. 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

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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. The next is

§ 15. But though we have, here and demonstra- there, a little of this clear light, some tion by rea- sparks of bright knowledge; yet the soning.

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 in-,

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termediate 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 spe-
culations 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 know-
ledge, 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
otherwise be judged of but by the inter- ness of this,
vention of others, which have not a cer-

we have no
tain agreement with the extremes, but an

thing but

judgment usual or likely one: and in these it is that upon prothe judgment is properly exercised, which bable reais the acquiescing of the mind, that

soning.

any
ideas do agree, by comparing them with such pro-
bable 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 excel-
lency and use of the judgment is to observe right, and
take a true estimate of the force and weight of each

verty!

the narrow

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ment.

conse

probability; and then, casting them up all right together, choose that side which has the overbalance.

$ 17. Intuitive knowledge is the perIntuition,

ception of the certain agreement or distion, judg- agreement of two ideas immediately com

pared 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.

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.

§ 18. Though the deducing one propoConse

sition from another, or making inferences quences of words, and in words, be a great part of reason, and

that which it is usually employed about;

yet the principal act of ratiocination is ideas.

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 the signs of such ideas: and things agree or disagree, as really they are; but we observe it only by our ideas. Four sorts of

§ 19. Before we quit this subject, it arguments. 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,

First, the first is to allege the opinions 1. Ad verecundiam.

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

quences of

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