Chap. III.

I. We have hitherto shewed, that there are many Ideas of the Mind, which, though the Cogitations of them be often occasionally invited from the Motion or Appulse of Sensible Objects without made upon our Bodies; yet notwithstanding the Ideas themselves could not possibly be stamped or Impressed upon the Soul from them, because Sense takes no Cognizance at all of any such Things in those Corporeal Objects, and therefore they must needs arise from the Innate Vigour and Activity of the Mind it self. Such as are, First, the Relative Ideas of the several Scheses or Respects <189> which are betwixt Corporeal Things themselves compared with one another. Which Relative Ideas being not Comprehended by Sense, and yet notwithstanding, the Natures of all Compounded Corporeal Things, whether Artificial or Natural, that is, whether made by the Artifice of Men or Nature, Consisting of them, We have demonstratively proved from thence, that the Natures of no Compounded Corporeal Things can possibly be Known or Comprehended by Sense. And again, the Ideas of Cogitative Beings, and the several Modes of them, together with all such Notions as involve some Respect or Relation to them. For although these also be often occasionally invited and Elicited by the Objects of Sense, when the Mind, in the Contemplation of them by its own Active Strength, perceives the Signatures of Art, Counsels, Contrivance, Wisdom, nay, and Goodness also, (all which are Modes of Cogitative Beings) printed upon them; yet they cannot owe their Being or Efficiency to the Activity of those Outward Objects, but meerly to the Activity of the Mind it self.

I Should now proceed to shew, that Even those simple Corporeal Things themselves, which by Sense we have a Passive Per <190> ception of, in Individual Bodies without us, are also known and understood by the Active Power of the Mind Exerting its own Intelligible Ideas upon them.

2. That Sensation is not Knowledge of those Corporeal Things that we sensibly perceive, we have before largely shewed; and indeed it sufficiently appears from hence, because upon the Seeing of Light and Colours, though never so clearly, the Feeling of Heat and Cold smartly, the Hearing of loud Sounds and Noises, we naturally enquire further, What this Light and Colours, Heat and Cold, and Sounds are, which is an undoubted Acknowledgement that we have not a Clear and Satisfactory Comprehension of those Things which make so strong a Stroke and Impression upon our Senses; and therefore the Mind desires to Master and Conquer them by its Own Active Strength and Power, and to Comprehend them by some Ideas of its own, which are not Foreign, but Native, Domestick and Intrinsical to it.

Now if Sense it self be not Knowledge, much less can any Secondary or Derivative Result from Sense be Knowledge; for this would be a more Obscure, Shadowy and Evanid Thing than Sense it self is. As when <191> the Image of a Man’s Face, received in a Mirror or Looking-glass, is reflected from thence into a Second Mirror, and so forward into a Third; still further it goes, the more Obscure, Confused and imperfect it grows, till at last it becomes altogether imperceptible. Or as in the Circlings and Undulations of Water, caused by the falling of a Stone into it, that are successively propagated from one to another; the further and wider they go, the Waves are still the less, slower and weaker, till at length they become quite undiscernible. Or as a Secondary Echo, that is, the Echo of an Echo, falls as much short of the Primary Echo in Proportion, as that doth of the Original Voice. Or, Lastly, If we could suppose a Shadow to cast a Shadow, this Secondary Shadow, or Projection of a Shadow, would fall as much short of the Primary Shadow, as that did of the Substance it self. So if the knowledge of Corporeal Things were but a Secondary and Derivative Result from Sense, (though it cannot be conceived that the Passion of Sense should ray upon the Intellect, so as to beget a Secondary Passion there, any more than one Shadow should cast another) then Knowledge would be a much weaker Perception of them than Sense it self <192> is, and nothing but as it were the Secondary Reflection of an Image, or the Remote Circlings and Undulations of the fluid Water, or the meer Echo of the Echo of an Original Voice: Or, Lastly, nothing but the Shadow of the Shadow of a Substance. Whereas it is a far more real, substantial and satisfactory, more penetrative and comprehensive Perception than Sense is, reaching to the Very Inward Essence of the Things perceived. And therefore it must of Necessity proceed from the Active Power of the Mind it self, exerting its own Intelligible Ideas upon that which is Passively perceived, and so comprehending it by something of its own that is Native and Domestick to it. So that besides the ^[1]Sensations or ^[2]Phantasms, the Sensible Ideas of Corporeal Things passively impressed from us from without, there must be also ^[3]Conceptions, or Intelligible Ideas of them Actively Exerted from the Mind it self; or otherwise they could never be Understood.

3. Wherefore, that we may the better illustrate this Business, let us suppose some Individual Body; as for Example, a White <193> or Black Triangular Superficies, or a Solid ^[4]Four-Square included all within a Triangular Superficies, exposed first to the View of Sense or a Living Eye; and then afterward considered by the Intellect, that we may see the Difference betwixt the Passive Perception of it by Sense, and the Active Comprehension of it by the Understanding. Now Sense, that is a Living Eye or Mirror, as soon as ever it is Converted toward this Object, will here Passively perceive an Appearance of an Individual Thing, as existing without it, White and Triangular, without any Distinction Concretely and Confusedly together; and it will perceive no more than this, though it dwell never so long upon this Object; for it perceives no more than is impressed upon it; and here the Passion of Sense ends and goes no further. But the Mind or Intellect residing in the same Soul that hath a Power of Sensation also, then beginning to make a Judgment upon that which is thus Passively perceived, Exerts its own Innate Vigour and Activity, and displays it self gradually after this manner. For, First, with its subtle Divisive Power, it will Analyse and resolve this Con <194> crete Phantasmatical ^[5]Whole, and take Notice of several distinct Intellectual Objects in it. For Considering that every White or Black Thing is not necessarily Triangular, nor every Triangular Thing White or Black, it finds here two distinct Intellectual Objects; the one White, the other Triangular: And then again, because that which is Nothing can have no Affections, it concludes, that here is something as a Common ^[6]Subject to both these Affections or Modifications, which it calls a Corporeal Substance; which being one and the same Thing, is here both White and Triangular. Wherefore it finds at least three distinct Objects of Intellectual Cogitation, Corporeal Substance, White, and Triangular, all Individual. But then reflecting again upon these several Objects, and that it may further enquire into the Natures and Essences of them, it now bids adieu to Sense and Singularity; and taking a higher Flight, considers them all Universally and abstractly from Individuating Circumstances and Matter. That is, it no more seeks the Knowledge and Comprehension of these Things without it self, from whence it hath already passively per <195> ceived them by Sense; but revolving within it self upon its own Inward Notions and Active Anticipations (which must needs be universal) it looks for some Domestick Ideas of its own to understand these General Natures by, that so from thence with a Descending View it may comprehend under them those Individuals that now affect the Sense.

4. First therefore, for Corporeal Substance in general, which is the ^[7]Subject both of Colour and Figure, not to pursue any long and tedious Processes, it quickly concludes the Essence of it to be this; A Thing Extended Impenetrably, or which hath impenetrable Longitude, Latitude and Profundity: And because it is not here Considered meerly as a Notion or Objective Cogitation, but as a Thing actually existing without the Mind, therefore it exerts another ^[8]Notion of Existence or Singularity also; which added to the former, makes it up a Thing that hath Impenetrable Extension Existing. Now none of these Ideas, neither of Essence nor Existence, nor Thing, nor Substance, nor Something nor Nothing; nor Impenetrability nor Extension, nor Longitude, Latitude and Profundity, <196> were Impressed or stamped upon the Mind, either from this Individual, or any other sensible Object; for they can be neither seen nor perceived by any Corporeal Sense; but are meerly excited from the Innate Activity of the Mind it self, that same Power by which the Mind is enabled to Conceive of ^[9]Nothing as well as ^[10]Something; And certain it is that the Idea of Nothing was never impressed from any Thing. And if the Essence of Body, or Corporeal Substance it self, be only comprehended and understood by the Active Ideas of the Mind, (for Sense here perceived no such Thing, but only was affected from the Exteriour Induments thereof, Colour and Figure) then the several Modes of it, such as Whiteness and Triangularity, which are but certain Modes of an Extended Substance, must needs be Understood in like manner, not by Passive Ideas and Phantasms, but the Noematical or Intelligible Ideas of the Mind.

5. Wherefore in the next place, as for White Colour or Whiteness, here is a Plain and Palpable Difference betwixt Sense and Intellection; betwixt the ^[11]Phantasm and ^[12]Con <197> ception, betwixt a Sensible and Intelligible Idea; For the Sense or Phantasm of White, that we have from the Individual Object, is no clear Comprehension of any Essence or Intelligible ^[13]Notion; but only a Passion or Affection in the Soul, Caused by some Local Motions communicated to the Brain from the Object without, that is, a Drowsy, Confused and imperfect Perceptive Cogitation; But now the awakened Mind or Intellect revolving its own Inward Ideas, and being not able to Comprehend any such Mode or Quality in extended Substance, as this Sensible Idea of White is, formally considered; for this very Reason, boldly and confidently concludes that this is no Real Quality in that Body it self absolutely considered, because no such Thing is Intelligible by it; in which Opinion, it is confirmed by Sense it self, in that the lower Ends of the Rainbow that reach to the Earth do not Stain or Dye any Thing with the several Colours of it; and that the same Drops of Dew or Rain to Eyes at several Distances, have all those several Colours of the Rainbow in them, and none at all: And by other Experiments it appears that these Things are only Passions or Affections in the Sentient it self, <198> Caused by some Peculiar Modification of the Superficies of that Material Object in respect of the Figure, Site and Disposition of its Insensible Parts, whereby the Light or Intermediate ^[14]Globulous Particles, are in a Peculiar manner reflected upon the Eye, and that probably the Difference betwixt a White and a Black Object consists in this, that in one the small Particles are Polite and Solid, and therefore vividly reflect the Lighter ^[15]Globulous Particles; but in the other being differently disposed, the Light, as a Ball flung against an Heap of Sand, is not so smartly reflected from it, but as it were sinks into it, and its Motion is stifled and smothered in the Caverns of it. Wherefore the Intelligible Idea of a White Colour is this, that it is a certain Passion or Sense in the Soul, Caused by a Peculiar Modification of the Object without, in respect of the Disposition of its insensible Parts, whereby the Light or ^[16]Globulous Particles are more smartly and vividly reflected upon the Eye; Which is another kind of Comprehension of it, than the Sensible Idea or Phantasm of White is, which is no Intelligible Idea, but a Cogita <199> tive Passion, that is, another Species of Cogitation, or an half awakened Perception. Neither are these Intelligible Ideas of Passion and Sense Impressed upon the Soul from the Sensible Objects without; for the Eye sees neither Passion nor Sense, but they are actively exerted from the Mind it self, and therefore Mastered and Conquered, and Comprehended by it.

6. I now proceed to the last Intellectual Object Comprehended in this Individual Body, which is Triangularity, or some one Particular Species of a Triangle; as for Example, an Equilateral, or a Rectangular Triangle; For there can be no Individual Triangle but must be of one Determinate Species or another.

Now because the Phantasm of such a Triangle doth not only bear a Resemblance of the Outward Material Object, which the Phantasms of Colours and the like do not, but also of the True Intelligible Idea of a Triangle it self; and because when Men think never so abstractly and Mathematically of a Triangle, they have Commonly some rude Phantasm or Picture of it before them in their Imagination, Therefore many confidently perswade themselves, that there is no other Idea of a Triangle or other Figure, be <200> side the bare Phantasm or Sensible Idea impressed upon the Soul from some Individual Object without; that is, No active Noematical Idea inwardly exerted from the Mind it self. Which indeed is all one as to say, that there is no Intellection or Knowledge of a Triangle at all; for as much as neither Sense nor Fancy, which are but Superficial, imperfect and Incomplete Perceptive Cogitations, reach to the Comprehension of the ^[17]Notion or Essence of any Thing. Wherefore now to make the Contrary appear, we will again view this Material Triangle, or ^[18]Four-Square before our Eyes, making a nearer Approach to it; and upon this second Contemplation of it, we plainly observe much Inequality in the Superficies, Unevenness and Inequality in the Lines, and Bluntness in the Angles. From whence it evidently appears that that Idea that we had in our Minds of a Perfect Triangle, as a Plain Superficies terminated by three straight Lines joyned together in three Angles, ending in so many Points, was not impressed upon our Soul from this Individual Object, it being different from it, and far more Exact and Perfect than that is. And there <201> fore it must needs be granted that it was but occasionally or accidentally invited and drawn forth from the Mind, upon the Sight of it, just in the same manner as when a Man looks upon Certain Lines drawn with Ink upon a piece of Paper something resembling the Face of a Man, his Mind doth not fix and stay it self in the Consideration of those Inky Lines; but presently upon this occasion excites within it self the Idea of a Man’s Face. Or when a Man walking in a Gallery where there are divers Pictures hung upon the Wall, chances amongst them to espy the Picture of a Friend or Acquaintance of his, which, though perhaps far from an exact Resemblance, yet notwithstanding makes him presently to excite the Idea of his Friend in his Imagination. Neither of which Things could possibly be, if there had not been a Previous and præ-existent Idea of a Man’s Face, or such a Certain Friend in his Mind before; for otherwise a Man in this Case could think of nothing but just that that was impressed upon him by Sense, The Figures of those Inky Delineations, and those several Strokes and Shadows of the Pictures. In like manner, when we look upon the Rude, Imperfect and Irregular Figures of some Corporeal Things, the Mind <202> upon this Occasion excites from within it self the Ideas of a Perfect Triangle, Square, Circle, Pyramid, Cube, Sphere, and the like, Whose Essences are so indivisible, that they are not Capable of the least Additions, Detraction or Variation without the Destruction of them, because there was some Rude and Bungling Resemblance of these Regular Figures in those Material Objects that we look upon, of which probably the Maker had the Ideas in his Mind. And the Mind Naturally delights more to think of Simple and Regular, than of Compounded and Irregular Figures.

7. But if any one should here object and say, that it doth not follow from hence, that that more Perfect Idea which Now I have of a Triangle in my Mind, the Accuracy whereof this present Visible Idea before my Eyes doth not reach unto, was actively excited from the Mind it self; because it might be some time formerly impressed, from some other Individual Triangle which I had elsewhere seen; just in the same manner as when I looked upon a Picture, that Idea of a Man’s Face in general, or of that particular Friend, that was occasionally excited thereby, was not any Innate Idea, or an Idea that sprung <203> wholly from the Activity of the Mind, but was formerly impressed upon the Soul, from Individual Sensible Objects now remembered or called to Mind: I say, that this cannot possibly be true, because there never was any Material or Sensible straight Line, Triangle, Circle, that we saw in all our Lives, that was Mathematically exact, but even Sense it self, at least by the Help of Microscopes, might plainly discover much Unevenness, Ruggedness, Flexuosity, Angulosity, Irregularity and Deformity in them, as will appear to any one that shall make a Triangle upon the most accurate Lines that Wit or Art of Man can make; and therefore no Material Line could stamp or Impress upon the Soul in a meer Passive Way those exact Ideas that we now have of a Triangle or of a straight Line, which is the shortest possible between two Points, or a Circle that is every where Equidistant from an Individual Center, &c. And if it should be again replied, that notwithstanding there being many such Lines and Circles as Common Sense cannot discern the least Irregularity in them, howsoever they would be in the mean time really irregular to a Perfect and Lyncean Sight; yet, according to their Appearance, <204> might impress those Ideas that we have of a straight Line or Circle; I answer, that this cannot be neither, there being a Vast Difference betwixt the Confused Indistinction of Sense and Fancy, by reason of their Bluntness and Imperfection, and the Express Accuracy, Preciseness and Indivisibility of those Intelligible Ideas that we have of a straight Line, Circle, Triangle, ^[19]Four-Square, and other Geometrical Figures; and therefore that imperfect, Confused Indistinction of Sense, could never impress any such accurate Ideas upon the Mind, but only occasion the Mind Actively to exert them from within it self.

8. Nay, though it should be granted, that there were Material Lines Mathematically Exact, Perfect Triangles, Squares, Pyramids, Cubes, Spheres, and the like, such as Geometry supposes, as no doubt but the Divine Power can make such in fitting Matter; yet Sense could not at all reach to the discerning of the Mathematical Accuracy of these Things, no more than it doth to the Absolute Equality of any Quantities; as of Lines, Superficies, Bodies, Angles, which is <205> found and determined only by the Understanding, in that ^[20]Intelligible Matter which Geometry is conversant about. So that Sense could not be able to determine, what Triangle and what ^[21]Four-Square was Mathematically exact, and what not. From whence it is demonstrably Evident, that neither the ^[22]Notion of Perfect Equality, nor the Perfect Mathematical Ideas of Figures, Triangle, Square, Circle, Pyramid, Cube, Sphere, &c. were impressed upon the Soul from without by Sense; Sense not at all reaching to the Discernment of them.

9. But, Lastly, if there were Material Lines, Triangles, Pyramids, perfectly and Mechanically Exact; yet that which made them such, and thereby to differ from other Irregular Lines, imperfect Triangles and Cubes, could be nothing but a Conformity to an antecedent Intellectual Idea in the Mind, as the Rule and Exemplar of them; for Otherwise an Irregular Line and an Imperfect Triangle, Pyramid, Cube, are as perfectly that that they are, as the other is; only they are not agreeable to those anticipated and pre-conceived Ideas of Regular Lines and Figures actively <206> exerted in the Mind or Intellect, which the Mind Naturally formeth to it self, and delighteth to Exercise it self upon them, as the Proper Object of Art and Science, which the other Irregular Figures are not. Wherefore whenever a Man looking upon Material Objects judges of the Figures of them, and says this is a straight Line, this is a Perfect Triangle, that a Perfect Circle, but those are neither Perfect Triangles nor Circles; it is plain that here are two several Ideas of these Lines and Figures; The one outwardly impressed from those Individual Material Objects from without upon the Sense of the Beholder; the other Actively Exerted from his Inward Mind or Intellect. Which Latter busy Anticipation of it is the Rule, Pattern and Exemplar, whereby he judges of those Sensible Ideas or Phantasms. For otherwise, if there were no inward Anticipations or Mental Ideas, the Spectator would not judge at all, but only Suffer; and every Irregular and Imperfect Triangle being as perfectly that which it is, as the most perfect Triangle, the Mind now having no inward Pattern of its own before it, to distinguish and put a Difference, would not say one of them was more imperfect than another; but only comparing them with one <207> another, would say that this Individual Figure was not perfectly like to that; upon which Account the Perfect Triangle would be as Imperfectly the Imperfect Triangle, as the Imperfect was the Perfect.

10. Wherefore, as I said before, this is just in the same Manner, as when a Man looks upon the Picture of an absent Friend or Familiar Acquaintance, and presently judges of it, he hath plainly two several Ideas in his Mind at the same Time; One Outwardly impressed from the present Picture, the other Pre-existent in his Mind before; by one of which, as the Pattern or Exemplar, he makes a Judgment upon the other, and finds many Faults in it; saving, that here both the Ideas were Foreign and adventitious, the Pre-existent Idea having been some time formerly impressed from an outward Material Object, and thence retained in the Memory or Fancy; but in the other Case, when a Man looking upon a Material Triangle, Square, Circle, Cube, Sphere, in which there are some palpable Irregularities; which he judges of by comparing them with some inward pre-existent Ideas that he hath in his Mind of a perfect Individual Triangle, Square, Circle, Cube; and also conceives some Dis <208> like and Displeasure at the Disconformity of the one to the other: The Pre-existent Ideas here were no foreign or adventitious Things, but native and domestick to him, nor at any Time formerly passively received from any Material Objects without, but actively exerted from the Mind it self. And I think there is no doubt to be made but if a perfect adult Man, that was immediately framed out of the Earth, having a newly Created Soul infused, as the Protoplast had, should look upon two several Kinds of Objects at the same time, whereof one was a Perfect Circle or Sphere, Equilateral Triangle, ^[23]Four-Square, Square or Cube; the other having some Resemblances of the same, had notwithstanding apparent Irregularity in some Parts of them; but that at first Sight, he would be more pleased with the one than with the other; which could not be, unless he had some Native or Active Idea of his own within himself, to compare them both with, to which one was more conformable than the other. For there could be no such Thing as Pulcritude and Deformity in Material Objects, if there were no Active Power in the Soul of Framing <209> Ideas of Regular, Proportionate and Symmetrical Figures within it self, by which it might put a Difference between outward Objects, and make a Judgement of them; but that it only received Stamps and Impressions from without, for then it must needs be equally or indifferently affected with all alike, and not more pleased or displeased with one than with another. Now the Judgement that Men have of Pulchritude and Deformity in Sensible Things, is not meerly Artificial, from Institution or Instruction, or of taught Things, but such as Springs originally from Nature it self.

11. But that there is an Intelligible Idea of a Triangle inwardly exerted from the Mind it self, distinct from the Phantasm or Sensible Idea that is outwardly impressed from the Material Object, will yet further appear from that which follows; for the Mind reflecting further upon that Idea which it hath of a Triangle, considers first the Generical Nature of it, that it is a Plain Figure, and that a Plain Figure is the Termination of a Plain Superficies; which Superficies is nothing else but meer Latitude without Profundity: For plain Figures are no otherwise conceived by Geometricians. Now, it is certain that this Idea of <210> a Superficies, which Geometricians have, was never imprinted upon their Minds by Sense from any Material Objects; there being no such Thing any where existing without the Mind, as Latitude without Profundity. And therefore it must needs arise from the Activity of the Mind it self. And the Idea of a Plain Superficies, that is, such a Superficies as to all whose Parts a straight Line may be accommodated, as well as the Idea of a straight Line, must needs be actively excited from the Mind also. Again, it Considers the Difference betwixt a Triangle and other Plain Figures, that it is included in and Terminated by three straight Lines joined together in three Points; which Straight Lines being the Extremities of a Superficies, are meer Longitude without either Profundity or Latitude; and which Points being the Extremities of those Lines, have neither Longitude, Latitude nor Profundity in them. Which Mathematical Ideas, in like manner, of a Line without Latitude and Profundity, and a Point without Longitude, Latitude and Profundity, were never impressed upon Euclid, or any other Geometrician from without, as is evident without further Proof. Moreover, this Intelligible Idea of a Triangle, as it includes some Nu <211> merical Considerations in it, which Sense hath no Idea of, perceiving only One and One and One; so therein Sides and Angles are relatively considered also to one another; Nay, the very Notion of an Angle, and the Quantity thereof, is a Relative Thing, as Proclus hath observed, and therefore not impressed by Sense.

Again, the Mind considering the Idea of its own, as it can find out the several Properties of a Triangle by meer Cogitation, without any Thing of Sense; as that the Greater Side always Subtends the Greater Angle, nay, and that the three Angles are always equal to two Right Angles (as we shall shew afterwards) so it also, by its own Strength, is able to find out all the Species that are Possible in a Plain Triangle, in respect of the Differences both of Sides and Angles. As in respect of the Sides, that it is either Æquilateral or ^[24]Even-legged, or ^[25]Having Unequal Sides; of the Angles, that it is a ^[26]Straight Cornered, or ^[27]Blunt Cornered, or ^[28]Sharp Cornered Triangle, and that there can be no Individual Triangle but must of Necessity belong to one of the three Species of either Sort. So that <212> this is not gathered from Sense, but exerted from the Active Power of the Mind.

12. The Mind can clearly understand a Triangle in General, without determining its Thought to any particular Species, and yet there can be no Distinct Phantasm of any such Thing; for Every distinct Phantasm or Sensible Picture of a Triangle must of Necessity be either Equilateral or Equicrural, or Inequilateral, ^[29]Uneven-legged. And so as we can in like manner clearly understand in our Minds, ^[30]a Thing with a Thousand Corners, or ^[31]One with Ten thousand Corners, though we cannot possibly have a distinct Phantasm of either of them. But for those Particular Species of Triangles which we may have Distinct Phantasms of, this doth not at all hinder but that we have, notwithstanding, Intelligible Ideas of the same besides, actively exerted from the Mind it self. And so there is a ^[32]Phantasm and a ^[33]Conception at the same time Concurring together, an Active and a Passive Cogitation. The ^[34]Conception or Intelligible Idea being as it were Embodied in the Phantasm, which alone in it self is but <213> an Incomplete Perceptive Cogitation of the Soul half awakened, and doth not comprehend the Indivisible and Immutable ^[35]Notion or Essence of any Thing.

Which Thing to those that cannot better Understand it by what we have already declared, might be illustrated in this manner; When an Astronomer, thinking of the Sun, demonstrates that it is 160 times bigger than the Globe of the Earth, he hath all the while a Phantasm or Imagination of the Sun in his Mind, but as ^[36]a Circle of a Foot Diameter; nay, he cannot for his Life have a true Phantasm of any such Magnitude which contains the Bigness of the Earth so many times, nor indeed Fancy the Earth a hundredth Part so big as it is. Now, as the Astronomer hath an Intelligible Idea of the Magnitude of the Sun very different from the Phantasm of the same, so in like manner have we Intelligible Ideas of Corporeal Things, when we understand them, besides the Phantasms of them. The Phantasm being as it were ^[37]the Crasser Indument, or Corporeal Vehicle of the ^[38]Intelligible Idea of the Mind.

13. Hitherto, by the Instance of an Individual and Material Triangle, we have shewed, how the Soul, in Understanding Corporeal Things, doth not meerly suffer from without from the Body, but Actively Exert Intelligible Ideas of its own, and from within it self. Now I observe that it is so far from being true, that all our Objective Cogitations or Ideas are Corporeal Effluxes or Radiations from Corporeal Things without, or impressed upon the Soul from them in a gross Corporeal Manner, as a Signature or Stamp is imprinted by a Seal upon a piece of Wax or Clay; that (as I have before hinted) this is not true sometimes of the Sensible Ideas themselves. For all Perception whatsoever is a Vital Energy, and not a Meer Dead Passion; and as the Atomical Philosophy instructs us, there is nothing Communicated in Sensation from the Material Objects without, but only Certain Local Motions, that are propagated from them by the Nerves into the Brain; which Motions cannot propagate themselves Corporeally upon the Soul also, because it penetrates and runs through all the Parts of its own Body. But the Soul, by reason of that Vital and Magical Union which is between it and the Body, sympathizing with the several <215> Motions of it in the Brain, doth thereupon exert Sensible Ideas or Phantasms within it self, whereby it perceives or takes Notice of Objects Distant from the Brain, either with or without the Body. Many of which Sentiments and Phantasms have no Similitude at all, either with those Local Motions made in the Brain, or with the Objects without; such as are the Sentiments of Pain, Pleasure, and Titillation, Hunger, Thirst, Heat and Cold, Sweet and Bitter, Light and Colours, &c. Wherefore the Truth is, that Sense, if we well consider it, is but a kind of ^[39]Speech, (if I may so call it) Nature as it were talking to us in the Sensible Objects Without, by certain Motions as Signs from thence Communicated to the Brain. For, as in Speech, when Men talk to one another, they do but make Certain Motions upon the Air, which cannot Impress their Thoughts upon one another in a Passive manner; but it being first consented to and agreed upon, that such certain Sounds shall signify such Ideas and Cogitations, he that hears those Sounds in Discourse, doth not fix his Thoughts upon the Sounds themselves, but presently Exerts from within him <216> self such Ideas and Cogitations as those Sounds by Consent signify, though there be no Similitude at all betwixt those Sounds and Thoughts. Just in the same manner Nature doth as it were talk to us in the Outward Objects of Sense, and import Various Sentiments, Ideas, Phantasms, and Cogitations, not by stamping or impressing them passively upon the Soul from without, but only by certain Local Motions from them, as it were dumb Signs made in the Brain; It having been first Constituted and Appointed by Nature’s Law, that such Local Motions shall signify such Sensible Ideas and Phantasms, though there be no Similitude at all betwixt them; for what Similitude can there be betwixt any Local Motions and the Senses of Pain or Hunger, and the like, as there is no Similitude betwixt many Words and Sounds, and the Thoughts which they signify. But the Soul, as by a certain secret Instinct, ^[40]and as it were by Compact, understanding Nature’s Language, as soon as these Local Motions are made in the Brain, doth not fix its Attention immediately upon those Motions themselves, as we do not use to do in Discourse upon meer Sounds, but presently <217> exerts such Sensible Ideas, Phantasms and Cogitations, as Nature hath made them to be Signs of, whereby it perceives and takes Cognizance of many other Things both in its own Body, and without it, at a Distance from it, In order to the Good and Conservation of it. Wherefore there are two kinds of Perceptive Powers in the Soul, one below another; The first is that which belongs to the Inferiour Part of the Soul, whereby it sympathizes with the Body, which is determined by the several Motions and Pressures that are made upon that from Corporeal Things without to several Sensitive and Phantastical Energies, whereby it hath a Slight and Superficial Perception of Individual Corporeal Things, and as it were of the Outsides of them, but doth not reach to the Comprehension of the Essence or Indivisible and Immutable ^[40]Notion of any thing. The Second Perceptive Power is that of the Soul it self, or that Superiour, Interiour Noetical Part of it which is ^[40]free from Passion or Sympathy, free and disentangled from all that Magical Sympathy with the Body. Which acting alone by it self, Exerts from within the In <218> telligible Ideas of Things, Virtually Contained in its own Cognoscitive Power, that are Universal and Abstract ^[41]Notions, from which, ^[42]as it were looking downward it comprehends Individual Things. Now because these latter, which are pure Active Energies of the Soul, are many times exerted upon occasion of those other Passive or Sympathetical Perceptions of Individual Things anteceding; it is therefore conceived by many, that they are nothing else but thin and Evanid Images of those Sensible Ideas, and therefore that all Intellection and Knowledge ascends from Sense, and Intellection is nothing but the Improvement or Result of Sense. Yet notwithstanding it is most certainly true, that they proceed from a quite different Power of the Soul, whereby it actively protrudes its own Immediate Objects from within it self, and Comprehends Individuals without it, not Passively or consequentially, but as it were Proleptically, and not with an Ascending, but with a Descending Perception; whereby the Mind first reflecting upon it self, and its own Ideas, virtually contained in its own Omniform Cognoscitive Power, and thence de <219> scending downward, comprehends Individual Things under them. So that Knowledge doth not begin in Individuals, but end in them. And therefore they are but the Secondary Objects of Intellection, the Soul taking its first Rise from within it self, and so by its own inward Cognoscitive Power comprehending Things without it. Else how should God have Knowledge? And if we know as God knows, then do we know or gain Knowledge by Universals. In which Sense (though not in that other of Protagoras) the Soul may be truly said to be the Measure of all Things.

Now I say, if the very Sensible Ideas and Phantasms themselves, be not meer Stamps or Impressions from Individual Things without in a Corporeal Manner impressed upon the Soul, but Active, though Sympathetical Energies of the Soul it self: It is much more impossible that the Universal and abstract Intelligible Ideas of the Mind, or Essences of Things, should be meer Stamps or Signatures impressed upon the Soul, as upon a Dead Thing in a gross Corporeal manner.

14. Wherefore here is a Double Errour committed by Vulgar Philosophers; First, That they make the Sensible Ideas and Phantasms to be totally impressed from without in <220> a gross corporeal Manner upon the Soul, as it were upon a dead Thing; and, Secondly, That then they suppose the Intelligible Ideas, the Abstract and Universal Notions of the Mind, to be made out of these Sensible Ideas and Phantasms thus impressed from without in a Corporeal Manner likewise by Abstraction or Separation of the Individuating Circumstances, as it were by the hewing off certain Chips from them, or by hammering, beating or anvelling of them out into thin Intelligible Ideas; as if Solid and Massy Gold should be beaten out into thin Leaf-Gold. To which Purpose they have ingeniously contrived and set up an ^[43]Active Understanding, like a Smith or Carpenter, with his Shop or Forge in the Brain, furnished with all necessary Tools and Instruments for such a Work. Where I would only demand of these Philosophers, Whether this their so expert ^[44]Smith or Architect, ^[45]the Active Understanding, when he goes about his Work, doth know what he is to do with these Phantasms before-hand, what he is to make of them, and unto what Shape to bring them? If he do not, he must needs <221> be a bungling Workman; but if he do, he is prevented in his Design and Undertaking, his Work being done already to his Hand; for he must needs have the Intelligible Idea of that which he knows or Understands already within himself; and therefore now to what Purpose should he use his Tools, and go about to hew and hammer and anvil out these Phantasms into thin and subtle Intelligible Ideas, meerly to make that which he hath already, and which was Native and Domestick to him?

But this Opinion is founded in no less a Mistake of Aristotle’s Text concerning the ^[46]Active Understanding, who never dreamt of any such as these Men imagine, if we may believe the Greek Scholiasts, that best understood him; than it is of the Text of Nature; as if not only those Phantasms, but also the Intelligible Ideas themselves, were gross and corporeal Things impressed from Matter; whereas even the first of these are Passive Energies of the Soul it self, fatally united to some Local Motions in the Body, and Concurrently produced with them, by reason of that Magical Union betwixt the <222> Soul and Body; but the other are Pure Active Energies of the Mind it self, as free from Corporeal Sympathy. Neither can these Latter be made out of the Former by any Abstraction or Separation, no nor by any Depinxation or Chymical Distillation or Sublimation neither; for it is a Thing utterly impossible that Vigour, Activity and awakened Energy, as Intellections are, should be raised out of Dull, Sluggish and Drowsy Passion or Sympathy. And this Opinion is but like that other of the same Philosopher’s, Concerning the Eduction or Raising of Substantial and Immaterial Forms out of the Passive Matter, Both of them proceeding from one and the same Sottishness of Mind that induces them to think that Dull, Stupid and Senseless Matter, is the first Original Source of all Activity and Perfection, all Form and Pulchritude, all Wisdom and Knowledge in the World.

And Things being rightly considered, this Opinion doth in Truth and Reality, attribute as much Activity to the Soul, that saith it hath a Power of raising or educing of Intelligible Ideas or Universal and Abstract ^[47]Notions out of Phantasms, as that other that af <223> firms it hath a Power of exerting them from it self; as it would attribute as much Activity to the Sun to say that he had a Power of raising or educing Light or the Day out of Night and Darkness, as to say that he had a Power of exerting it out of his own Body.

15. Wherefore others of this Kind of Philosophers, that will not acknowledge any Immaterial Substance, that hath any Active Power of its own in it, or any thing in the Soul besides Impression from Corporeal Objects Without, Have found out another Device, and that is this, Plainly to deny that there are any Universal Notions, Ideas or ^[48]Reasons in the Mind at all; But that those Things which are called Universal, are nothing else but Names applied to several Individuals. Which Opinion, as it was formerly held by those that were therefore called ^[49]Nominalists; so it hath been lately revived and taken up by some of these Strenuous Impugners of Immaterial and Incorporeal Substances. There is nothing in the World (saith a late Author) Universal, but Names; for the Things Named are Every one of them Individual and Singular. Now indeed this <224> is true, and no Body denies it, of Things existing without the Mind; but this Author’s Meaning herein is to deny all Universal ^[50]Conceptions and ^[51]Reasonings of the Mind, as appears by his larger Explication of the same Opinion elsewhere. ^[52]This Universal is the Name, not of any Thing Existing in the Nature of Things, nor of any Idea or Phantasm formed in the Mind, but always the Name of some Word or Name; so that when an Animal or a Stone, or a Spectre, or any thing else is said to be Universal, it is to be understood only that those Words Animal, Stone, are universal Names, that is, Names Common to more Things; and the Conceptions answering to them in the Mind, are the Images and Phantasms of Singular Ani <225> mals or other Things. And therefore to understand the Meaning of an Universal, there is no need of any other Faculty than that of the Imagination, whereby we are minded that Words of that sort have sometimes excited one Thing, sometimes another in our Mind. That is, there are no other Ideas in the Mind but only Phantasms of Individual Corporeal Things: Only there are Universal Names, which are applied in Common to more Individuals than one; but there is no other Object of the Mind or Cogitation but only Singular and Individual Things existing without the Soul. Wherefore this Author Consentaneously hereunto defines Understanding to be nothing else but Conception Caused by Speech; and therefore if Speech be peculiar to Man, then is Understanding Peculiar to him also. This Mysterious Notion is insisted upon and explained likewise by the Third Objector against Cartesius’s Metaphysicks, after this Manner. ^[53]Now what do we say, if <226> perhaps Reasoning be nothing else but the Coupling and Chaining together of Names or Appellations, by these Words, It Is. Whence we gather nothing at all by Reason concerning the Nature of Things, but concerning their Appellations; to wit, whether we Joyn the Names of Things according to Agreements or not. If this be so, as it may be, Reasoning will depend upon Names, Names upon the Imagination, and the Imagination upon the Motion of the Bodily Organs; and so the Mind will be nothing else but a Motion in some Parts of the Body. According to which Philosophy, Reason and Science do not superadd any Thing to Sense, or reach any further in the Knowledge of the Nature of Things, but only in making use of Common Names to express several Individuals by at once.

16. Wherefore, although there be already enough said to prove, that in the Understanding of Individual Corporeal Things, beside Sense and the Sensible Phantasms from them, there are also Intelligible Ideas and <227> Universal ^[54]Notions exerted from the Mind it self, by which alone they are Comprehended; yet still to make this Business clearer, and also to demonstrate, that the Knowledge of Universal Axiomatical Truth, and Scientifical Theorems is a Thing which doth not passively Result from Sense, but from the Actual Strength and Vigour of the Intellect it self Comprehending its own Intelligible Ideas, we will here Propose that one Geometrical Theorem Concerning a Triangle; That it hath three Angles Equal to two Right Angles; and Consider what the Subject of it is, ^[55]Scientifically comprehended.

First therefore, if there be no Other Object of the Mind in Knowledge but Sensible Individuals Existing without us, Then the Subject of this Theorem, when Euclid wrought it, was only Some Individual Bodies by him Compared together. Nay, Euclid himself did not Carry this Knowledge about with him in his Mind, neither was he Master of it any Longer than he held those Individual Bodies in his Hands, or looked upon them with his Eyes; and if so, it could not signify any <228> thing at all, to any other Person which either then or now had not the same Individual Bodies to compare, that Euclid had. Whereas it is plain, that the Subject of this Theorem, whatsoever it be, is such a Thing as Every Geometrician, though in never such distant Places and Times, hath the very same always ready at his Hand, without the least Imaginable Difference. And they all pronounce Concerning the same thing. Which could not possibly otherwise be, unless it were some Universal ^[56]Notion and Intelligible Idea of the Mind.

17. Again, Secondly, No Individual or Material Thing is the Subject of this Theorem, as Sense takes Cognizance of it, that is, the Matter, and Colour, and Figure and Magnitude, all Concretely together. For the same Individual Matter may presently be made Quadrangular or Circular, but only precisely in respect of the Figure; and of that also no otherwise than as it is Conformable to the Indivisible and Immutable ^[57]Notion or Idea of a Triangle, Comprehended in the Mind as the Exemplar of it. Now, as we have shewed already, there is no Material Triangle any <229> where to be found that is Mathematically Exact and Accurate, Neither is the Individual Form of a Material Triangle immutable. And if there were any Mathematically Exact, our Sense could be no ^[58]Criterion or Rule to Judge of it, nor discern when any thing were Indivisibly such, nor judge of the Absolute and Mathematical Equality of the three Material Angles of it, with two other Angular Superficies. Wherefore the Subjects of this Geometrical Theorem are no Sensible Individual Bodies, but the ^[59]Notions and ^[60]Ideas of the Mind it self, in which alone Mathematical Accuracy is to be found, and the Exact Equality of one Thing to another certainly and infallibly Known.

18. Nay, if we should suppose that there were some Individual Material Triangles and Angles, absolutely and Mathematically Exact; And that our Sense did infallibly perceive the Indivisible Points of them; or that we had an Infallible Pair of Compasses, whose ^[61]Tops were Mathematical Points, whereby we could Measure the several Angles of the Triangle and Right Angle in a perfect Circle, accu <230> rately divided into Infinite Parts; or else Cutting off those several Angles of the Triangle, and laying them together upon an Absolute Plane, we should thus Mechanically find them Equal to the two Material Right Angles; This would not amount to the Knowledge of this Truth, that a Triangle, as such, hath of Necessity three Angles equal to two Right Angles; we thus Considering them only as Material Individuals, and Things Existing without the Mind by Corporeal Sense. For though we had now found that these Individual Material Triangles were Equal to those two Individual Material Right Angles; yet looking no further than Sense determined to Individuals, we could not tell certainly that it was so with all Individual Triangles, much less Understand any Necessity of its being so, or attain to any thing of the ^[62]Reason of it, in which alone true Science consisteth. And this Aristotle hath observed very pertinently to our Purpose, Post. Anal. Lib. I. cap. 25. ^[63]Neither is it Necessary to understand by Sense, <231> but to Perceive; but this regards a Particular Thing and Manner, and the Present Time. But it is Impossible to Perceive by Sense what relates to Every Thing, and in all Respects: For This and Now relate not to an Universal; For of an Universal we say, that it is Always and Every Where. Since then Demonstrations are of an Universal, it is Plain that there is no Knowledge of the Universal Theorems of Geometry by Sense. For it is manifest, that if we could Perceive by Sense that the three Angles of a Triangle were Equal to two Right Angles, yet should we not rest satisfied in this, as having therefore a sufficient Knowledge of it (as some say;) but would seek further after a Demonstration hereof: Sense reaching only to Singulars, but Knowledge to Universals. The Mind would not be satisfied herewith, but would still further require a Demonstration of it; which Demonstrations are not of Individuals perceived by Sense, but only of the Universal ^[64]Notions comprehended in the <232> Mind; Knowledge, as I said before, being a Descending Comprehension of a Thing from the Universal Ideas of the Mind, and not an Ascending Perception of them from Individuals by Sense.

19. Wherefore the Apodictical Knowledge of this Truth is no otherwise to be attained than by the Mind’s ascending above Sense, and Elevating it self from Individuals to the Comprehension of the Universal ^[65]Notions and Ideas of Things within it self, making the Object of its Enquiry and Contemplation, not this nor that Material Individual Triangle without it self, but the Indivisible and Immutable Notion of a Triangle. And thus it finds several Ways that a Triangle, as such, must of Necessity have its three Angles Equal to two Right Angles.

For, First, if one will Consider any Triangle, as made out of a Parallelogram (though this be the more Compounded Figure) divided by a Diagonal Line into two equal Triangles, it is Plain in every Parallelogram there are four Angles Equal to four Right Angles, because when a straight Line Cuts two Parallel Lines, the two Interiour Angles <233> must of Necessity be Equivalent to two Right Angles, one of them being the Complement of the other to a Semicircle. But when the Parallelogram is divided into two Equal Triangles by a Diagonal Line, the Quantity of the three Angles in each must of Necessity be half the Quantity of the Four Angles in the Parallelogram.

Or, if a Man will Consider the ^[66]Formation of a Plain Triangle in this Manner; First, by a straight Line Cutting two Parallel Lines, and then one of these Parallels moving upon its Centre in the Straight Line out of its Parallelism, and inclining towards the other Line, if it move never so little out of its Parallelism towards the other Parallel, <234> the Continuation of it must needs cut the other Line, and make a Triangle.

And so much as the Interiour Angle, which with the other opposite, made up two Right Angles, so much is the third Angle; and therefore all three make up two Right Angles.

20. Now here is a gross Errour of the Vulgar to imagine, because Geometricians demonstrating such Theorems, Commonly make use of such Sensible Schemes or Diagrams, that therefore the Knowledge of this Truth doth Result from Sense, or that the Geometricians themselves have no other Ideas in their Minds of straight Lines, Parallels, <235> Right, Acute and Obtuse Angles, Triangles, Equality of Angles, than what are impressed upon their Fancy from these Schemes. Whereas these are only made use of to entertain the Fancy in the mean time, whilst the Mind being intent upon the Demonstration, actively exerts other intelligible Ideas of these Things from within it self, and from thence Comprehends the Apodictical Necessity of the Theorem. Neither is the true and proper Knowledge of one Theorem or Universal and Necessary Truth, either in Geometry or Metaphysicks, passively impressed upon the Soul from Individuals Existing without, or the Result of Meer Sense, but it proceeds from the Active Strength and Vigour of the Mind, Comprehending the Intelligible Ideas and Universal ^[67]Notions of Things within it self.

21. Wherefore we Conclude, that the Immediate Objects of Geometrical Science, properly so called, are not Individual Bodies or Superficies, but the Intelligible and Universal Ideas of a Triangle, Square, Circle, Pyramid, Cube, Sphere, actively exerted from the Mind, and Comprehended in it. <236> For the Mind doth not seek its Objects of Knowledge abroad without it self, but must needs actively Comprehend them within it self: Which also, as we shall show in the following Chapter, are Immutable Things, and always the same.