Eugenius.
Give me leave, Gentlemen, to say on this occasion, that I have several times observed, that men judge some things to be irreconcileable, not only when they are both of them represented to the understanding in the form of Propositions; but when one of them is but a notion, or a current difinition. For divers of these notions do contain in them a Proposition, or are equivalent to it; As when a Circle is defin’d to be a Figure contain’d in a Line, all whose parts are equally distant from the middle-most Point or Center, this definition contains an affirmation of the essential property of a Circle; and by the generality of Geometricians is therefore discriminated from that Conick Section which they call an Ellipsis, tho that be also a Figure terminated by one curve Line.
And because you are versed in Mathematicks, I shall on this occasion shew you by a Geometrical Instance, that if a man have not genuine and adequate notions of the things he judges of, he may confidently, and even upon very probable grounds, judge things to be inconsistent, that in reality, are not so. For if an ordinary Cultivater of Mathematical Disciplines should hear one man say, that such a Figure is an Ellipsis, and another affirm it to be a Circle, he would think their assertions to be inconsistent, having his mind prepossessed with an Ellipsis’s, being a Conical Section, whose properties must therefore (he supposes) be very differing from those of a Circle; whereas such wary Geometricians as the Learned Doctor Wallis1 will tell him, that the vulgar notions of Conick Sections are not adequate to the Figures producible by them: For when a right Cone is cut quite through by an inclining Plane, the figure produced by the Section agrees well with the received notion of an Ellipsis, in which the Diameters are of unequal length; yet if the Plane cut the Cone parallel to the Basis, that Conick Section will be a true Circle, having all its Diameters equal.
‘Tis indeed an uncommon and unheeded account, but such an one upon which I have observed not only Logicians, but Philosophers themselves to err about judging things reconcileable or inconsistent; that if a man be not sufficiently acquainted with the nature of any of the two things under consideration (and much more if he be ignorant of, or mistaken about both) he may think there is a contradiction between things, wherein a Superior or more piercing Intellect may discern a consistency; for taking it for granted, that he knows one thing to be a truth, if some other thing be affirm’d to be so, which he has not understanding or skill enough to see how to reconcile to it, ‘tis no wonder, that how well soever this may be evinced, he should as little know how to admit, as how to reject it. This may be partly illustrated, and partly prov’d by instances drawn from the Mathematicks themselves: For a Novice in Arithmetick, for example, finding That, according to his Rules, there is not one mean proportional number between 4 and 32, will scarce be able to reconcile that Proposition to this other, That there are two mean proportionals between the mentioned numbers; For he may with great appearance of Reason ask, how, if there be not so much as one mean proportional, there can be two? Whereas those that are acquainted with the nature of Ranks or Series of numbers proceeding in Geometrical Proportion, will easily discern that between those two recited, both the number 8, and the number 16; are mean proportionals.
Timotheus.
Tho I disallow not your Instance, Eugenius, yet I shall be willing to hear one or two others of a less abstracted Nature.
Eug.
To obey you, Timotheus, I shall add, that if an old School-Philosopher, or a Mathematician not acquainted with the later Discoveries made by Telescopes, should hear one man say, that the Moon is the most enlightned, when she appears full to us, and another affirm that she is more inlightned at the New Moon than at the Full, he would readily conclude, upon the supposition (which he makes no doubt of) that the Moon receives all her light immediately from the Sun, that the affirmation of the later (Astronomer) cannot be true; which yet he would not conclude, if he knew (what is discovered by Telescopes) that the Moon is as well inlightned by the Earth, as the Earth by the Moon; upon which score, whereas at the Full she receives but those Beams that come to her directly, from the Sun, at the Change she receives both them in that part of her Body that is obverted to him, and those other Beams of his that are reflected from the Terrestrial Globe to that part of the Moon that is nearest to us.
And to the foregoing Instance, I shall add one more, that seems apposite enough to Arnobius’s Purpose, and ‘tis, that before Pythagoras, not only the vulgar of the Greeks, but their Philosophers and Mathematicians too, observing oftentimes that a bright Star preceded the Rising Sun, and that frequently also (on other days) after Sun-set, another Star appear’d, that was none of the fix’d ones; they confidently concluded from the so distant times of Apparition, that the Sun was attended by two differing Stars, to which accordingly they gave two differing names: But Pythagoras, who was a far better Astronomer (as may be guessed, among other things, by his maintaining in those early times the motion of the earth about the Sun) undertook to disabuse them, and effected it. Now if one that had observed Venus only in the mornings, should have affirm’d, that besides the six known Planets, there was but a seventh (namely the Phosphorus) which preceded the Rising Sun; and another, (that had taken notice notice of her only in the Evenings) should assert, that besides the same six known ones, the only seventh was that called Hesperus, which sometimes appear’d after his Setting; a By-stander would presently have concluded, that their Assertions were not reconcileable, either to one another, or to the truth; which (in his judgment) was, that there must be no less than eight visible Planets; and yet Pythagoras, who had more skill, and more piercing wit, did, (as was lately noted) discern and teach, that these two Phaenomena were produc’d by one and the same Planet Venus, determined by its peculiar motion (about the Sun) to shew it self near our Horizon, sometimes before he ascends it, and sometimes after he had left it. Such instances as these, tho offered but as illustrations, may perswade us from being too forward to reject every proposition, that we see not how to reconcile to what we take for a truth; provided the distrusted proposition be such as we would acquiesce in, if we could reconcile it to that supposed Truth.
Timotheus.
From this Discourse, Eugenius, and that of Arnobius, which preceded it, I think one may gather, that according to you two, when two Propositions are laid down, whereof one is made evident to us by Experience, or by Reason, acting within its own Jurisdiction or Compass; and the other is sufficiently proved by being mathematically demonstrated, or duly attested by Divine Revelation, we ought not to reject either of these propositions, as no truth, meerly because we do not yet know how to reconcile them: but we should rather think, that the collected Proposition, is but a gradual, or limited truth; or else we should consider, that we knowing but so imperfectly as we do the particular natures of privileg’d Subjects, for ought we know a superior Intellect may be able to discern a friendly agreement between what is deliver’d about that Subject, and the affirmation that seems repugnant to it, tho we are not quick-sighted enough to perceive this Agreement. And this, how strange soever you may think it, Pyrocles, may not only be countenanc’d by such things as Eug. lately said, but both you your self, and almost all mankind do de facto seem to practise it, in the case of the Divine Prescience of mans free Actions.
Eugenius.
What you contend for, Gentlemen, may perhaps be thought the more receivable, if one should argue thus: First either the Propositions said to be repugnant, are both really true, or they are not; If it be answered, that they are not, the difficulty is at an end: for there is none at all to conceive a true Proposition, should contradict a false one. But, secondly, if both the Propositions be supposed to be true, it must be affirm’d, either that they are reconcileable, or that they are not; if it be said, they are not, then Pyrocles his objection is out of doors; for it cannot then be reasonable to say, that the two Propositions, tho inconsistent with one another, must necessarily be one or other of them inconsistent with the truth. But this I presume he will by no means assert, and consequently, must say, that the Propositions are reconcileable. Upon which answer I shall demand, how that can be, unless a superior Intellect, such as unquestionably the Divine is, can discover an agreement between Propositions wherein we cannot discern it. For our not being able to discern it, is you know professedly supposed in the case we discourse of.
Pyrocles.
But, Arnobius, will not this Doctrine make us very liable to have falsities imposed on us at the pleasure of bold and dictating men?
Arnob.
Not, if it be limited to the subjects wherein alone I would have it admitted; for if neither of the things treated of be a privileg’d one, but both in the jurisdiction of ordinary reason, I do not only consent, but (in my first Advice) require, that the Propositions fram’d about them be estimated according to the common Dictates of Reason. And even in cases where one of the Propositions is about a privileg’d thing, I do not at all think fit, that it should be received in spite of its being repugnant to the gradual truth delivered in the other, unless it can by some other Argument sufficient in its kind be proved to be true; and in that case, that, what I plead for, ought to be admitted, is implyed by the suffrage of almost all mankind, in that case, which was just now pertinently mentioned by Timotheus: for tho men know not how to reconcile the Liberty of mans will, with the infallible knowledge that God has of those Actions that flow from it, yet they have unanimously judged it reasonable to believe both Free-will and Prescience; the former, because they felt it in themselves; and the later, partly because the foreknowledge of things being manifestly a perfection, ought not to be denyed to God, whom they looked upon as a Being supremely perfect; and partly because some actions and events that they all judg’d to flow from mens free-will, were, as the generality of men believ’d, foretold by Prophetick Oracles. But except in such cases as I have been naming, I am altogether of Pyrocles’s mind, that since we have scarce any way of discovering a Falsity, but by its being repugnant to somewhat that is true; to deny, that in cases within the juridiction of ordinary Reason, the repugnancy of a Proposition to any manifest truth, ought to sway our Judgments, were to deprive us of the usefullest Criterion to discriminate between Falshood and Truth.
Timoth.
For my part, who believe with many Philosophers, as well Heathen as Christian, that humane Souls owe their origine to God, and with almost all Philosophers, (for I know what the Stoicks held) that as he is the supreme Being, so he is a most free Agent, I see not why, as he has given to Corporeal Beings divers Qualities, very differing in their degrees of Nobleness; so he might not give to the Intelligent Productions of his Power and Will, various degrees of Intellectual Capacities as well as a limitedness of Nature. And as it will not follow, that because we can see with our eyes very small Objects, and imagine such as are yet much smaller, either the eye, or the imagination can ever reach to so small an Object as an Atome; so it will not follow that because we are able to frame Conceptions of immaterial Beings, we must therefore be able to understand the nature of God, and the Harmony of all his Monadical Attributes. A little Boy may have a clear notion of three, four, five, or other smaller numbers, and yet may be unable to frame good conceptions of Triangular and other Polygon Numbers (as some call them) and much more of the abstruse affections of surd Numbers, and the Roots of the higher Algebraical Powers. To discern particular Truths is one thing, and to be able to discover the Intercourse and Harmony between all Truths, is another thing, and a far more difficult one; as a Traveller may upon the English Shoar know that he sees the Ocean, and upon the Coast of Affrick be made to do the like, and at the East Indies also he may know that he sees the Ocean; and yet not know how those so distant Seas communicate with each other, tho that may be manifest enough to a Cosmographer.
Arnob.
What you say brings into my mind, that I have sometimes thought God and men enjoy Truth, as differingly as they do Time. For we men, as we enjoy time but by parcels, and always leave far the greatest part of it unreach’d to by us; so we know but some particular Truths, and are always ignorant of far more than we attain to. Whereas God, as his eternity reaches to all the portions of time (or measured Durations) so his Omniscience gives him at one view a prospect of the whole extent of Truth: (As if a man could see the whole River of Nilus with all its turnings and windings from its hidden Springs to its entrance into the Sea.) Upon which account he sees all particular Truths, not only distinct, but in their Systeme, and so sees a Connexion between those that to us seem’d the most distant ones.
Arnob.
There remains now, Gentlemen, but one part more of your penance to be undergone; for ‘tis high time, I should hasten to the relief of a Patience I have so long distress’d, and therefore I shall give it but one exercise more, and conclude your Trouble with some reflections on this last Advice.
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Footnotes
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See his Treatise de Sectionibus Conicis. ↩