or proposition that we see not how to reconcile with some other thing that we are perswaded to be a truth The first of these three sorts of things may for brevity and distinction sake be called Incomprehensible the second Inexplicable and the third Unsociable But for fear lest the shortness I have used in my expressions may have kept them from being so clear I shall somewhat more explicitly reckon up the three sorts of things that seem to me above Reason The first consists of those whose Nature is not distinctly and adequately comprehensible by us To which sort perhaps we may refer all those intellectual Beings if it be granted that there are such as are by nature of a higher order than humane Souls To which sort some 〈◊〉 the Angels at least of the good ones may probably belong but more than probably we may refer to this Head the Divine Author of Nature and of our Souls Almighty God whose perfections are so boundless and his Nature so very singular that 't is no less weakness than presumption to imagine that such finite Beings as our Souls can frame full and adequate Idea's of them We may indeed know by the consideration of his works and particularly those parts of them that we our selves are both That he is and in a great measure What he is not but to understand throughly What he is is a task too great for any but his own infinite Intellect And therefore I think we may truly call this immense Object in the newly declared sence supra-Intellectual Euge. I suppose I may now ask what is the second sort of Things above Reason Sophr. It consists of such as though we cannot deny that they are yet we cannot clearly and satisfactorily conceive how they can be such as we acknowledge they are As how Matter can be infinitely or which is all one in our present discourse indefinitely divisible And how there should be such an incommensurableness betwixt the Side and Diagonal of a Square that no measure how small soever can adequatly measure both the one and the other That Matter is endlesly divisible is not only the assertion of Aristotle and the Schools but generally embraced by those rigid Reasoners Geometricians themselves and may be farther confirm'd by the other instance of the Side and Diagonal of a Square whose incommensurableness is believed upon no less firm a proof than a demonstration of Euclid and was so known a truth among the Ancients that Plato is said to have pronounced him rather a Beast than a Man that was a stranger to it And yet if continued quantity be not divisible without stop how can we conceive but that there may be found some determinate part of the side of a Square which being often enough repeated would exactly measure the Diagonal too But though Mathematical Demonstrations assure us that these things are so yet those that have strained their Brains have not been able clearly to conceive how it should be possible that a Line for instance of not a quarter of an inch long should be still divisible into lesser and lesser portions without ever coming to an end of those subdivisions or how among the innumerable differing partitions into aliquot parts that may be made of the side of a Square not one of those parts can be found exactly to measure so short a Line as the Diagonal may be Euge. There is yet behind Sophronius the third sort of those things which according to you surpass our Reason Sophr. I shall name that too Eugenius as soon as I have premised that some of the Reasons that moved me to refer some instances to this head do not so peculiarly belong to those instances but that they may be applicable to others which 't was thought convenient to refer to the second or first of the foregoing Heads And this being once intimated I shall proceed to tell you that the third sort of things that seem to surpass our Reason consists of those to which the Rules and Axioms and Notions whereby we judge of the truth and falshood of ordinary or other things seem not to agree This third sort being such as are incumbred with Difficulties or Objections that cannot directly and satisfactorily be removed by them that acquiesce in the received Rules of subordinate Sciences and do reason but at the common rate such Objects of Contemplation as this third sort consists of having something belonging to them that seems not reconcilable with some very manifest or at least acknowledged Truths This it may here suffice to make out by a couple of Instances the one of a Moral the other of a Mathematical Nature And first that Man has a free will in reference at least to civil matters is the general confession of Mankind All the Laws that forbid and punish Murder Adultery Theft and other Crimes being founded on a Supposition that men have a power to forbear committing them and the sense men have of their being possest of this power over their own actions is great enough to make Malefactors acknowledg their punishments to be just being no less condemned by their own Consciences than by their Judges And yet some Socinians and some few others excepted the generality of Mankind whether Christians Jews Mahometans or Heathens ascribe to God an infallible Prescience of humane Actions which is supposed by the belief of Prophecies and the recourse to Oracles by one or other of which two ways the Embracers of the several Religions newly mentioned have endeavoured and expected to receive the informations of future things and such as depend upon the Actings of men But how a certain fore-knowledg can be had of contingent things and such as depend upon the free will of man is that which many great wits that have solicitously tryed have found themselves unable clearly to comprehend nor is it much to be admired that they should be puzled to conceive how an infinitely perfect Being should want Prescience or that their will should want that liberty whereof they feel in themselves the almost perpetual exercise The other instance I promised you Euge. is afforded me by Geometricians For these you know teach the divisibility of Quantity in infinitum or without stop to be Mathematically demonstrable Give me leave then to propose to you a strait line of three foot long divided into two parts the one double to the other I suppose then that according to their doctrine a line of two foot is divisible into infinite parts or it is not If you say it is not you contradict the demonstrations of the Geometricians if you say that it is then you must confess either that the line of one foot is divisible into as many parts as the line of two foot though the one be but half the other or else that the infinite parts into which the line of one foot is granted to be divisible is exceeded in number by the parts into which the line of two foot is divisible and
have added others if I had thought it unlikely that in the progress of our Conference there may be occasions offered of mentioning them more opportunely Pyrocl. I have long thought that the wit of man was able to lay a fine varnish upon any thing that it would recommend but I have not till now found Reason set a work to degrade it self as if it were a noble exercise of its power to establish its own impotency And indeed 't is strange to me how you would have our Reason comprehend and reach things that you your selâ— confess to be above Reason which is methinks as if we were told that we may see things with our eyeâ— that are invisible Sophr. I do not think that ' tiâ— to degrade the understanding to refuse to idolize it and 't is not aâ—â— injury to Reason to think it a liâ—mited faculty but an injury to thâ— Author of it to think man's understanding infinite like his And if what I proposed be well grounded I assign Reason its most noble and genuine Exercise which is to close with discovered Truths in whose embraces the perfection of the Intellect too much consists to suffer that perfective action to be justly disparaging to it And a sincere understanding is to give or refuse its assent to propositions according as they are or are not true not according as we could or could not wish they were so and methinks it were somewhat strange that Impartiality should be made a disparagement in a Judge But Pyrocles leaving the reflection with which you usher'd in your Objection I shall now consider the Argument it self which being the weightiest that can be framed against the opinion you oppose I shall beg leave to offer some considerations wherein I shall endeavour to answer it both by proving my Opinion by experience and by shewing that experience not to be disagreeable to Reason Pyrocl. I shall very willingly listen to what you have to say on such a subject Sophr. I shall then in the first place alledge the experience of many persons and divers of them great Wits who have perplexed themselves to reconcile I say not the Grace of God but even his Prescience to the liberty of mans will even in bare moral actions And I have found partly by their Writings and by discourse with some of them that the most towring and subtle sort of Speculators Metaphysicians and Mathematicians perchance after much racking of their brains confess themselves quite baffled by the unconquerable difficulties they met with not only in such abstruse subjects as the nature of God or of the humane Soul but in the nature of what belongs in common to the most obvious Bodies in the world and even to the least portions of them You will easily guess that I have my eye on that famous controversie Whether or no a continued quantity which every body as having length bredth depth must be allowed to have be made up of Indivisibles Of the perplexing difficulties of this Controversie I might give you divers confessions or complaints made by a sort of men too much accustomed to bold assertions and subtle Arguments to be much disposed to make acknowledgments of that kind But I shall content my self with the testimony which one of the more famous modern Schoolmen gives both of himself and other learned men and which if I well remember he thus expresses Aggredimur comtinus compositionem cujus hujusque non separata difficultas omnium Doctorum male ingenia vexavit neque ullus fuit qui illam non pene insuperabilem agnoscat Hanc plerique terminorum obscuritate illorumque replicatis implicatis distinctionibus subdistinctionibus obtenebrant ne aperté capiantur desperantes rem posse alio modo tractari neque rationis lucem sustinere sed necessario confusionis tenebris obtegendum ne argumentorum evidentiâ detegatur And though he had not been thus candid in his confession yet what he says might be easily concluded by him that shall duly weigh with how great though not equal force of Arguments each of the contending parties imputes to the opinion it opposes great and intolerable absurdities as contained in it or legitimately deducible from it Eug. I have not the vanity to think that the weakness of my Reason ought to make another diffident of the strength of his But as to my self what Sophronius has been saying cannot but be confirm'd by several tryals wherein having exerted the small abilities I had to clear up to my self some of the difficulties about Infinites I perceived to my trouble that my speculations satisfied me of nothing so much as the disproportionateness of those abstruse subjects to my reason But Sophronius may it not be well objected that though the Instances you have given have not been hitherto cleared by the light of Reason yet 't is probable they may be so hereafter considering how great progress is from time to time made in the discoveries of Nature in this learned Age of ours Sophr. In answer to this question Eugenius give me leave to tell you first that you allow my past discourse to hold good for ought yet appears to the contrary Whence it will follow that your Objection is grounded upon a hope or at most a Conjecture about which I need not therefore trouble my self till some new discoveries about the things in question engage me to a new consideration of them But in the mean while give me leave to represent to you in the second place that though I am very willing to believe as well as I both desire and hope it that this inquisitive Age we live in will produce discoveries that will explicate divers of the more hidden mysteries of Nature yet I expect that these discoveries will chiefly concern those things which either we are ignorant of for want of a competent History of Nature or we mistake by reason of erroneous Prepossessions or for want of freedom and attention in our speculations But I have not the like expectations as to all Metaphysical difficulties if I may so call them wherein neither matters of Fact nor the Hypothesis of subordinate parts of Learning are wont much to avail But however it be as to other abstruse Objects I am very apt to think that there are some things relating to that infinite and most Monadical Being if I may so speak that we call God which will still remain incomprehensible even to Philosophical understandings And I can scarce allow my self to hope to see those Obstacles surmounted that proceed not from any Personal infirmity or evitable faults but from the limited nature of the Intellect And to these two considerations Eugenius I shall in answer to your question add this also That as mens inquisitiveness may hereafter extricate some of those grand difficulties that have hitherto perplexed Philosophers so it may possibly lead them to discover new difficulties more capable than the first of baffling humane understandings For even among the things
wherewith we are already conversant there are divers which we think we know only because we never with due attention tryed whether we can frame such Ideas of them as are clear and worthy for a rational seeker and lover of truth to acquiesce in This the great intricacy that considering men find in the notions commonly receiv'd of space time motion c. and the difficulties of framing perspicuous and satisfactory apprehensions even of such obvious things may render highly probable We see also that the Angle of Contact the Doctrine of Asymptotes and that of surd numbers and incommensurable Lines all which trouble not common Accomptants and Surveyors who though they deal so much in numbers and lines seldom take notice of any of them perplex the greatest Mathematicians and some of them so much that they can rather demonstrate that such affections belong to them than they can conceive how they can do so All which may render it probable that mens growing curiosity is not more likely to find the solutions of some difficulties than to take notice of other things that may prove more insuperable than they Tim. This conjecture of yours Sophronius is not a little favoured by the Rota Aristotelica for though the motion of a Cart-wheel is so obvious and seems so plain a thing that the Carman himself never looks upon it with wonder yet after Aristotle had taken notice of the difficulty that occurr'd about it this trivial Phaenomenon has perplex'd divers great Wits not only Schoolmen but Mathematicians and continues yet to do so there being some circumstances in the progressive motion and rotation of the circumference of a Wheel and its Nave or of two points assigned the one in the former and the other in the latter that have appeared too subtle and even to modern Writers so hard to be conceived and reconciled to some plain and granted Truths that some of them have given over the solution of the attending difficulties as desperate which perchance Pyrocles would not think strange if I had time to insist on the intricacies that are to be met with in a speculation that seems so easie as to be despicable Sophr. Your Instance Timotheus must be acknowledged a very pregnant one if you are certain that a better account cannot be given of the Rota Aristotelica than is wont to be in the Schools by those Peripateticks that either frankly confess the difficulties to be insoluble or less ingenuously pretend to give solutions of them that suppose things not to be proved or perhaps so much as understood as Rarefaction and Condensation strictly so called or lose the question and perhaps themselves by running up the dispute into that most obscure and perplexing Controversie de compositione continui Eugen. I am content to forbear pressing any further at present an Objection much of whose force depends on future contingents and I shall the rather dismiss the proof drawn from experience that I may the sooner put you in mind of your having promised us another Argument to the same purpose by manifesting the opinion to be agreeable to Reason Sophr. I understand your pleasure Eugenius and shall endeavour to comply with it but the difficulty and intricateness of the Subject of our discourse obliges me to do it by steps and for fear we should want time for more necessary things I will not now stay to examine whether all the things that hitherto have appeared above Reason be impenetrable to us because of an essential disability of our understandings proceeding from the imperfection and limitedness of their nature or only because of some other impediment such as may be especially the condition of the soul in this life or the infirmities resulting from its state of union with a gross and mortal body Forbearing then to discourse how this came into my mind and what thoughts I had upon it I shall proceed in my considerations and to clear the way for those that are to follow I shall in the first place observe to you that whatever be thought of the faculty in abstracto yet Reason operates according to certain Notions or Ideas and certain Axiomes and Propositions by which as by Prototypes or Models and Rules and Measures it conceives things and makes estimates and judgments of them And indeed when we say that such a thing is consonant to Reason or repugnant to it we usually mean that it is either immediately or mediately deducible from or at least consistent with or contradictory to one or other of those standard Notions or Rules And this being premis'd I consider in the next place that if these Rules and Notions be such as are abstracted only from finite things or are congruous but to them they may prove useless or deceitful to us when we go about to stretch them beyond their measure and apply them to the infinite God or to things that involve an Infiniteness either in multitude magnitude or littleness To illustrate and confirm this notion give me leave to represent in the third place that in my opinion all the things that we naturally do know or can know may be divided into these two sorts The one such as we may know without a Medium and the other such as we cannot attain to but by the intervention of a Medium or by a discursive act To the first belong such Notions as are supposed to be connate or if you please innate such as that Two contradictories cannot be both together true The whole is greater than any part of it Every entire number is either even or odd c. And also those other Truths that are assented to upon their own account without needing any medium to prove them because that as soon as by perspicuous terms or fit examples they are clearly proposed to the understanding they discover themselves to be true so manifestly by their own light that they need not be assisted by any intervening Proposition to make the Intellect acquiesce in them of which kind are some of Euclids Axioms as that If to equal things equal things be added the totals will be equal and that two right lines cannot include a space To the second sort of things knowable by us belong all that we acquire the knowledge of by Ratiocinations wherein by the help of intervening Propositions or Mediums we deduce one thing from another or conclude affirmatively or negatively one thing of another This being supposed and we being conscious to our selves if it were but upon the score of our own infirmities and imperfections that we are not Authors of our own nature for ought we know it may be true and all the experience we have hitherto had leads us to think it is true that the measures suggested to us either by sensations the results of sensible observation or the other instruments of knowledge are such as fully reach but to finite things or Beings and therefore are not safely applicable to others And divers of those very Principles that we think very
consequently that the line of two foot has a multitude of parts greater than infinite Which Reasonings may let us see that we may be reduced either to reject Inferences legitimately drawn from manifest or granted Truths or to admit conclusions that appear absurd if we will have all the common Rules whereby we judge of other things to be applicable to Infinites And now Gentlemen having acquainted you with what sorts of things seem to be above Reason I must to prevent mistakes desire you to take along with you this Advertisement That though the nobleness and difficulty of so uncultivated a Subject inclined me to offer something towards the elucidating of it by sorting those things into three kinds yet I shall not and need not in this Conference insist on them severally or lay any stress on this partition For though I have above intimated that a Proposition may speak of somewhat that is supra-intellectual or else contain somewhat which we cannot conceive how it may be true or lastly teach us somewhat for a truth that we cannot reconcile with some other thing that we are convinced is true yet if but any one of these have true Instances belonging to it That may suffice for my main purpose in this place where I need only shew in general that there may be things that surpassour Reason at least so far that they are not to be judged of by the same measures and rules by which men are wont to judge of ordinary things for which reason I shall often give them one common name calling them Priviledg'd Things Euge. Methinks that to manifest the Imperfections of our Reason in reference to what you call Priviledg'd Things you need not have recourse to the unfathomable Abysses of the Divine Nature since for ought I know Pyrocles as well as I may be non-plus'd by an instance that came into my mind de Compositione continui Timoth. Since Sophronius has not thought fit to give us any of the Arguments of the contending party's I shall be glad to know what difficulty occurr'd to you Euge. Suppose a great Circle divided into its three hundred and sixty degrees and suppose that as great a number as you please or can conceive of strait lines be drawn from the several designable parts of some one of these degrees to the Centre 't is manifest that the degrees being equal as many lines may be drawn from any and so from every one of the others as from that degree which was pitched upon Then suppose a Circular Arch equal to the assumed degree to be further bent into the circumference of a little circle having the same Centre with a great one it follows from the nature of a Circle and has been geometrically demonstrated that the semi-diameters of a Circle how many soever they be can no where touch one another but in the Centre Whence 't is evident that all the lines that are drawn from the circumference to the Centre of the greater Circle must pass by differing points of the circumference of the smaller for else they would touch one another before they arrive at the Centre and consequently that as many lines soever as can even mentally be drawn from the several points of the circumference of the great Circle to the common Centre of both Circles must all pass through different points of the little Circle and thereby divide it into as many parts proportionably smaller as the greater Circle is divided into So that here the circumference of the lesser Circle presents us with a curve line which was not possibly divisible into more parts than an Arch of one degree or the three hundred and sixtieth part of the Circumference of the greater Circle and yet without being lengthned becomes divisible into as many parts as the whole circumference of the same greater Circle And though we should suppose the circumference of the internal Circle not to exceed one inch and that of the exterior Circle to exceed the circumference of the Terrestrial Globe or even of the Firmament it self yet still the demonstration would hold and all the lines drawn from this vast Circle would find distinct points in the lesser to pass through to their common Centre Timoth. Though I will not pretend to confirm what Sophronius has been proving by adding Arguments a priori yet I shall venture to say that I think it very agreeable both to the nature of God and to that of man that what he has endeavoured to prove true should be so for we men mistake and flatter Humane Nature too much when we think our faculties of Understanding so unlimited both in point of capacity and of extent and so free and unprepossest as many Philosophers seem to suppose For whatever our self-love may incline us to imagine we are really but created and finite Beings and that probably of none of the highest orâ—ders of intellectual Creatures and we come into the world but such as it pleased the Almighty and most free Author of our Nature to make us And from this dependency and limitedness of our Natures it follows not only that we may be for I now dispute not whether we are born with certain congenit Notions and Impressions and Appetites or Tendencies of Mind but also that the means or measures which are furnished us to employ in the searching or judging of Truth are but such as are proportionable to Gods designs in creating us and therefore may probably be supposed not to be capable of reaching to all kinds or if you please of Truths many of which may be unnecessary for us to know here and some may be reserved partly to make us sensible of the imperfections of our Natures and partly to make us aspire to that condition wherein our faculties shall be much enlarged and heightned It seems not therefore unreasonable to think both that God has made our faculties so limited that in our present mortal condition there should be some Objects beyond the comprehension of our Intellects that is that some of his creatures should not be able perfectly to understand some others yet that he has given us light enough to perceive that we cannot attain to a clear and full knowledge of them Pyrocl. I think Sophronius that I now understand what you mean by Things above reason or as you not unfitly stiled them priviledged things But I presume you need not be told that to explain the sence of a Proposition and to make out the truth of it unless in common Notions or things evident by their own light are always two things and oftentimes two very distant ones Sophr. I need not scruple Pyrocles to grant the truth of what you say but I must not so easily admit your application of it for among the examples I have been proposing there are some at least that do not only declare what I mean by things above reason but are instances and consequently may be proofs that such things there are And to those I could
still some true account or other there must be of that insufficiency And as we should very thankfully receive from Pyrocles any better account than what we have propounded so if he cannot assign any better I hope he will joyn with us in looking upon this as very agreeable to our Hypothesis since hereby some things must appear to us so sublime and abstruse that not only we find we are not able to comprehend them but that we are unable to discern so much as upon what account it is that they cannot be comprehended by us Eug. I am not averse Sophronius from your Paradox about gradual notions and I am the more in clin'd to think that some of the Axioms and Rules that are reputed to be very general are not to be in differently extended to all Subject and cases whatsoever when I consider the differing apprehension that the mind may frame of the same object as well according to the vigour or if I may so call it rank of the understanding as according to the differing information 't is furnished with For if onâ— should propose to a child for inâ—stance of four or five years old the demonstration of the one huâ—â—dred and seventeenth Propositioâ— of Euclid's tenth Book wherein 〈◊〉 proves the side and Diagonal 〈◊〉 a Square to be incommensurâ—â—ble thongh possibly he may be â—â—ble to read the words that expreâ—â— the Theorem and though he haâ— eyes to see the Scheme imployâ—â— for the demonstration yet if 〈◊〉 should spend a whole year about 〈◊〉 you would never be able to make him understand it because 't is quite above the reach of a Childs capacity And if one should stay till he be grown a man yet supposing him to have never learned Geometry though he may easily know what you mean by two incommensurable lines yet all the reason he has attained to in his virile age would but indispose him to attain to that demonstration for all the experience he may have had of lines will but have suggested to him as a manifest and general truth that of any two strait lines we may by measuring find how many Feet Inches or other determinate measure the one exceeds the other And though one that has been orderly instructed in all that long train of Propositions that in Euclid's Elements precede the one hundred and seventeenth of the tenth Book will be also able to arrive at an evidence of this truth that those two Lines are incommensurable yet as Sophronius formerly noted how it should be possible that two short Lines being proposed whereof each by it self is easily measurable among those innumerable multitudes of parts into which each of them may be mentally divided there should not be any one capable of exactly measuring both is that which even a Geometrician that knows it is true is not well able to conceive But Gentlemen that you may not accuse my digression I shall urge these comparisons no further my scope in mentioning them being to observe to you that for ought wâ— know to the contrary such a diffeâ—rence of intellectual Abilities as iâ— but gradual in Children and Menâ— may be essential in differing rankâ— of Intellectual Beings And so 〈◊〉 may be that some of those Axiom that we think general may wheâ—â— we apply them to things whereoâ— they are not the true and propeâ— measures lead us into error thougâ— perhaps Intellects of an higher oâ—â—der may unriddle those difficultiâ— that confound us men which conjecture I should confirm by some things that would be readily granted me by Christians if I thought it proper to play the Divine in a discourse purely Philosophical Pyrocl. You Gentlemen have taken the liberty to make long discourses and I shall not much blame you for it because 't is a thing as more easily so more speedily done to propose difficulties than to solve them yet methinks amongst you all you have left one part of my Objection unanswer'd not to say untouch'd Sophr. I suppose Pyrocles you mean what you said about discerning invisible things with the Eye but I purposely forbore to take notice of that because I foresaw it might be more seasonably done after some other points had been clear'd Wherefore give me leave now to represent to you as a Corollary from the foregoing discourses that nothing hinders but that we may reasonably suppose that the great and free Author of humane nature God so framed the nature of Man as to have furnish'd his Intellective Faculty with a light whereby it cannot only make estimates of the power of a multitude of other things but also judge of its own nature and power and discern some at least of the limits beyond which it cannot safely exercise its act of particularly and peremptorily judging and defining And now that God who as I said is a most free Agent may have given the mind of Man such a limited nature accompanied with such a measure of light you will not I presume deny but the question is you will tell me whether he hath done so But I hope what has been formerly discoursed by these Gentlemen and me has put that almost quite out of question However I shall now invite you to observe with me that the Rational Soul does not only pass judgments about things without her but about her self and what passes within her She searches out and contemplates her own spirituality and union with the Body The Intellect judges wherein it s own nature consists and whether or no it self be a distinct faculty from the Will and to come yet closer to the point be pleased to consider that Logick and Metaphysicks are the works of the Humane Intellect which by framing those disciplines manifests that it does not only judge of Ratiocinations but of the very Principles and Laws of Reasoning and teaches what things are necessary to the obtaining of an Evidence and Certainty and what kind of Mediums they are from whence you must not expect any demonstrative Arguments concerning such or such a subject To these things it is agreeable that if we will compare the bodily Eye with the Understanding which is the Eye of the Mind we must allow this difference that the Intellect is as well a Looking-glass as a Sensory since it does not only see other things but it self too and can discern its own blemishes or bad conformation or whatever other infirmitiesit labours under Upon which consideration we may justifie the boldness of our excellent Verulam who when he sets forth the four sorts of Idols as he calls them that mislead the studiers of Philosophy makes one of them to be Idola Tribûs by which he means those Notions that tho' radicated in the very nature of mankind are yet apt to mislead us which may confirm what I was saying before that the Soul when duly excited is furnished with a light that may enable her to judge even of divers of those original Notions by which she is wont to judge of other things