KNO
of the Demonflration, muft alfo be exactly carried in the Mind ; and a Man muft be fare that no part is left out, which, becaufe in long Deductions, the Memory cannot cafily retain, this K nowledge becomes more imper- fect than intuitive, and Men often embrace FaUhoods for Demonftrations.
It has been generally taken for granted, that Mathe- maticks alone are capable of demonftrative Certainty ; but to have fuch an Agreement or Difagreemcnt, as may be intuitively perceived, being, as we imagine, not the Privilege of the Ideas of Number, Extenfion, and Fi- gure alone; it may pombly be the want of due Method and Application in us, and not of fufficient Evidence in Things, that Demonflration has been thought to have fo little to do in other Parts of Knowledge. For in whatever Ideas the Mind can perceive the Agreement or Difagree- ment immediately, there it is capable of intuitive Know- ledge j and where it can perceive the Agreement or Dif- agreement of any two Ideas, by the intuitive Perception of the Agreement or Difagreement they have with any intermediate Ideas, there the Mind is capable of De- monftrations, not limited to the Ideas of Figure, Num- ber, Extenfion, or their Modes. The Reafon why it has been generally fuppofed to belong to thefs only, is becaufe, in comparing their Equality or Excefs, the Modes of Numbers have every, the leal! Difference, very clear and perceivable : And in Extenfion, tho' eve- ry the Ieaft Excefs is not fo perceptible, yet the Mind has found out ways to difcover the jutt Equality of two An- gles, Extenfions, or Figures ; and both Numbers and Fi- gures can be fetdown by vifible and lading Marks. But in other fimple Ideas, whofe Modes and Differences are made, and counted by Degrees, and not Quantity, we have not fo nice and accurate a Dillinction of their Dif- ferences, as to perceive or find ways to mcafure rheir juft Equality, or their leaft Differences. For thofe other fimple Ideas being Appearances or Senfations produced in us, by the Size, Figure, Motion, i£c. of minute Cor- pufcles fingly infenfible, their different Degrees alfo de- pend on the Variation of fome, or all of thofe Caufes ; which fince it cannot be obferved by us in Particles of Matter, whereof each is too fubtile to be perceived, it is impoflible for us to have any exact. Meafuresof the dif. ferent Degrees of thefe fimple Ideas. Thus, for inftance, not knowing what Number of Particles, nor what Motion of them is fit to produce any precife Degree of Whitc- nefs, becaufe we have no certain Standard to mcafure them by, nor means to diftingui/h every, the leaft Diffe- rence ; the only help we have, is from our Senfes^ which in this Point fail us. But where the Diffe- rence is fo great as to produce in the Mind Ideas clearly diftinct, thefe Ideas of Colours as we fee in different kinds, Blue and Red (for inftance) are as capable of De- monflration, as Ideas of Number and Extenfion. What is here faid of Colours, holds true in all fecondary Qua- lities. Thefe two then, Intuition and Demonflration, are the Degrees of our Knowledge ; whatever comes Ihort of one of thefe, is but Faith, or Opinion, not Knowledge, at leaft in all general Truths. There is indeed another Perception of the Mind employed about the particular Exiftence of finite Beings without us, which going be- yond Probability, but not reaching to either of the foregoing Degrees of Certainty, pafles under the Name of Knowledge.
Nothing can be more certain, than that the Idea we receive from an external Object, is in our Minds : This is intuitive Knowledge j but whether we can thence cei tain- ly infer the Exiftence of any thing without us, corre- iponding to that Idea, is that whereof fome Men think there may be a Queftion made, becaufe Men may have fuch an Idea in their Minds, when no fuch Thing exifts, no fuch Object affects their Senfes. But it is evident, that we are invincibly confeious to ourfelves of a different Perception, when we look on the Sun in the Day, and think on it by Night ; when we actually tafle Worm- wood, or fmell a Rofe, or only think on that Savsur, or Odour : fo that we may add to the two former forts of Knowledge, this alfo of the Exiftence of particular exter- nal Objects, by that Perception and Confcioufnefs we have of the actual Entrance of Ideas from them, and allow thefe three Degrees of Knowledge, viz. intuitive, demonftrative, and fenfuive. But fince our Knowledge is -founded on and imployed about our Ideas only, will it follow thence, that it muft be conformable to our Ideas, and that where our Ideas arc clear and diftinctj ob- fcure and confufed, there our Knowledge will be fo too ? We anfwer, No: For our Knowledge confifting in the Per- ception of the Agreement or Difagreement of any two Ideas, its Clearnefs or Obfcurity confitls in the Clear- nefs or Obfcurity of that Perception, and not in the Clear- nefs or Obfcurity of the Ideas themfelves. A Man (for inftance) who hath a clear Idea of the Angles of a Tri-
t 42-1 )
KNO
angle, and of Equality to two right ones, may yet have but an obfeure Perception of their Agreement, and fo have but a very obfeure Knowledge of it ; But obfeure and confufed Ideas can never produce any clear or di- ftmct Knowledge, becaufe as far as any Ideas are ob- feure or confuted, fo far the Mind can never perceive clearly, whether they agree or difagree : Or, to exnrefa the fame thing in a way lefsapt to be underftood, he'that hath not determined Ideas to the Words he ufeth, cannot make Proportions of them, of whofe Truth he can be certain.
From all this it follows 5 (1.) That we can have no Knowledge farther than we have Ideas. (2.) That we have no Knowledge farther than we can have Perception of the Agreement or Difagreement of our Ideas, either by Intuition, Demonflration, or Senfation. (3.) We cannot have an intuitive Knowledge, that mall extend itfelf to all our Ideas, and all that we would know about them y becaufe we cannot examine and perceive all the Rela- tions they have one to another by Juxta-Pofition, or an immediate Comparifon one with another. Thuswe can- not intuitively perceive the Equality of two Extenfions, the Difference of whofe Figures makes their Parts unca- pable of an exact immediate Application. (4.) Our ra- tional Knowledge cannot reach to the whole Extent of our Ideas, becaufe between two different Ideas, which we would examine, we cannot always find fuch Proofs as we can connect one to another, with an intuitive Know- ledge in all the Parts of the Deduction. (5.) Senfitive Knowledge reaching no farther than the Exiftence* of Things, actually prefent to our Senfes, is yet much nar- rower than either of the former. (6.) From all which it is evident, that the Extent of our Knowledge comes not only /hurt of the Reality of Things, but even of the Extent of our own Ideas. We have the Ideas of a Square, a Circle, and Equality, and yet perhaps mall never be able to find a Circle equal to a Square.
The Affirmations or Negations we make concerning the Ideas we have, being reduced to the four Sorts a- bovementioned, viz. Identity, Co-exiitence, Relation, and Real Exiftence, let us enquire how farour Knowledge extends in each of thefe. (1.) As to Identity and Diver- sity, our intuitive Knozvlcdge is as far extended as our Ideas themfelves ; and there can be no Idea in the Mind, which it does not prefently, by an intuitive Knowledge, perceive to be what it is, and to be different from any other. (2.) As to the Agreement or Difagreement of our Ideas of Co-exiffccnce, our Knowledge herein is very defec- tive, tho' 'tis in this that the grea tell and moft material Parts of our Knowledge concerning Subllances confifls : For our Ideas of Subllances being nothing but certain Collec- tions of fimple Ideas, co-exifling in one Subject, (our Idea of Flame, fcr initancc, is a Body hot, luminous, and mov- ing upwards.) When we would know any thing farther concerning this or any other fort of SubKance, what do we but enquire what other Qualities or Powers thefe Subllances have or have not ? which is nothing elfe but to know what other fimple Ideas do, or do not exiir. with thofe that make up that complex Idea. The Rea- fon of this is, becaufe the fimple ideas, which makeup our complex Ideas of Subllances, have no vifible neceffa- ry Connection or Inconfiflencc with other fimple Ideas, whofe Co-exiftence with them we would inform ourfelves about. Thefe Ideas being likewife fof the moft part fe- condary Qualities, which depend upon the primary Qua- lities of their minute or infenfible Parts, or on fomething yet more remote from our Comprehcnfiop 5 it is impof- lible we fhould know which have a neceffary Union or (n- confiftence one with another, fince. we know not the Root from whence they fpring, or, the Size, Figure, and Texture of Parts on which they depend, and from which theyrefult- Befidcs this, there is no difcoverable Con- nection between any fecondary Quality, and thofe pri- mary Qualities that it depends on. We are fo far from knowing what Figure, Size, or Motion produceth, (for inftance) a yellow Colour, or fweet Tafle, or fharp Sound j that we can by no means conceive how any Size, Figure, or Motion, can poffibly produce in us the Idea of any Colour, Tafle, or Sound, whatfoever 3 there be- ing no conceivable Connection between the one and the other. Our Knowledge therefore of Co-exiftence reaches little further than Experience. Some few indeed of the primary Qualities have a neceffary Dependance, and vi- vifible Connection one with another: As Figure neceffari- ly fuppofeth Extenfion ; receiving or communicating Mo- tion bylmpulfe, fuppofeth Solidity: but Qualities co- existent in any Subject, without this Dependence and Connection, cannot certainly be known to co-exifl any farther, than Experience by our Senfes informs iis, Thus tho', upon Tryal, we find Gold ye! low^ weighty, malle- able, fufible, and fixed 3 yet becaufe none of thefe have any evident Dependance or neceffary Connection with the V p p p p other.
