That this Advice may be the more easily admitted, I shall separately suggest three things, which I desire may be afterwards considered all together.
First, that clear positive proofs, proportionate to the nature of things, are genuine and proper motives to induce the understanding to assent to a proposition as true; so that ‘tis not always necessary to the evidence and firmness of an Assent, that the Intellect takes notice of the Consequences that may be drawn from it, or the difficulties wherewith it may be incumbered. This is plain in those Assents which of all others, at least that are meerly natural, are by knowing men thougt to be the most undoubted and the best grounded; I mean the Assents that are given to the Truth of Geometrical Demonstrations: And yet, Euclid, for instance, in all his Elements of Geometry, in some of which surprising Paradoxes are delivered, (as in the sixteenth proposition of the third Book, and the 117th of the tenth Book, to name no more) contents himself to demonstrate his Assertions in a Mathematical Way, and does not, that I remember, answer or take notice of any one Objection: and the Geometricians of our days think they may safely receive his Propositions upon the Demonstrations annexed to them, without knowing or troubling themselves about the subtleties employed by the Sceptick Sextus Empiricus, or others of that Sect in their writings against the Mathematicians, and all Assertors of assured knowledge.
The second thing I would offer to your consideration, is, that the former part of our Discourse has manifested, that there are some things which our humane and imperfect understandings either cannot, or at least do not, perfectly comprehend: and that nevertheless men have not refrain’d from presuming to dogmatize and frame Notions and Rules about such things, as if they understood them very well. Whence it must needs come to pass, that if they were mistaken (as in things so abstruse, ‘tis very like they often were) those that judge by the Rules they laid down, must conceive the Propositions opposite to their mistakes, to be liable to very great, if not insuperable Difficulties and Objections.
And this second Consideration, in conjunction with the first, will make way for the third, as a natural production of them, which is, That, as we need not wonder that privileged things, which are wont to be so sublime as to have been out of the view of those that fram’d the Rules whereby we judge of other things, should be thought liable to great Objections by them who judge of all things only by those Rules; so we should not require or expect more evidence of a Truth relating to such things, than that there are for it such sufficient positive Reasons, as notwithstanding Objections and Inconveniences, make it, upon the whole matter, worthy to be embraced.
Pyrocles.
But can that be worthy to be assented to, which is liable to Objections and Inconveniences, which the maintainers confess they know not how to avoid? Does not your Euclid himself in some of his Demonstrations imploy that way of reasoning which some of his Latine Interpreters call Deductio ad Absurdum?
Arnob.
Euclid indeed (as well as other Mathematicians) besides that more satisfactory way of direct probation, which perhaps he might have oftner imployed than he did, has sometimes where he thought it needful, made use of the […] you speak of. But in these cases he never goes out of the Discipline he treats of, and confining himself to Arguments drawn from quantity, he urges nothing as absurd, but what is undeniably repugnant to some Truth he had already demonstrated, or to those clear and undisputed Definitions, Axioms, or Postalata, which he supposes to have been already granted by those he would convince. But tho he thus argues to prove that his Readers cannot contradict him without contradicting themselves; yet we find not that he was at all solicitous to clear those Difficulties that so quick-sighted a man could not but know some of his Theorems to be attended with: but contents himself to demonstrate the incommensurableness of the Side and Diagonal of a Square, without troubling himself to take notice of the Difficulties that attend the endless Divisibility of a Line, which would follow from what he demonstrated. But, Pyrocles, to look back to the first part of your Objection, tho what you say will hold in ordinary Cases, yet such peculiar ones, as we are speaking of, deserve a particular Consideration. About some privileged things there are, and about some others there may be contradictory Opinions (taking that term in a strict sense) maintain’d. Now as both of these cannot be true, so one of them must be so: as, tho it be hotly disputed whether Quantity be endlesly divisible, yet certainly it either must, or must not be divisible without end: And as was formerly observed which side soever you take, the Inconveniencies will be exceeding great, and perhaps there will lye Objections scarce to be directly answered. And since one of the two opposite Opinions must be true, it will not always be necessary, that an opinion must be false, which is incumbred with great difficulties, or liable to puzzling Objections. And therefore if the positive proofs on one side be clear and cogent, tho there be perplexing Difficulties objected by the other; the truth ought not for their sake to be rejected; because such difficulties proceeding usually either from notions that men presume to frame about things above their reaches, or from Rules that were not made for such points as are in dispute, the Objections are not to be judged so well founded, as is that acknowledged Principle in Reasoning, that from Truth, nothing but truth can be legitimately inferr’d.
Eugen.
I confess I have always thought it reasonable in such Cases to compare, as well the positive proofs of one opinion with those of the other, as those Objections that are urg’d on either side; and there make my estimate upon the whole matter; tho with a peculiar regard to that opinion that has a great advantage in point of positive Arguments; Because, as Arnobius observ’d, those are the proper Inducements to the Assent of the Intellect: And then the Objections may well enough be suspected to proceed from the abstruse nature of privileg’d things, and the over-great narrowness of the Rules that men are wont to judge of all things by. For we may have a sufficiently clear proof that a thing is, whilst we have no satisfactory conception of its manner of existing or operating; our illative knowledge, if you will allow me so to speak, being clearer, and extending further than our intuitive or apprehensive knowledge.
Arnob.
But even about things that we cannot sufficiently understand, we may in some cases exercise our Reason, in answering objections that are thought not to be at all answerable, because they are not directly so. For we may sometimes shew, by framing in another case a like Argument, which, the Adversary must confess, does not conclude well, that neither does the Argument that contains his Objection conclude aright.
This I could exemplifie (tho that may seem no easie Task) but that I fear I should want time to propose Examples, whose being very paradoxical would make them need much proof; which you who I fear are quite tired already, would want patience to hear. Wherefore I shall rather recommend to you one Observation, which I take to be of no small moment and use, when we contemplate things of the nature of those we have been discoursing of: and it is this, that we must not expect to be able, as to privileg’d things, and the Propositions that may be fram’d about them, to resolve all Difficulties, and answer all Objections; since we can never directly answer those, which require for their solution a perfect comprehension of what is infinite: as a man cannot well answer the Objections that may be made against the Antipodes, the Doctrine of Eclipses, that of the different Phases of the Moon, and of the long days and nights of some months apiece, near the Poles, (not now to name that more abstruse part of Astronomy, the Theory of the Planets) unless he understand the nature of the Sphere, and some other Principles of Cosmography.
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