Pyrocl.
You may call this an Advice, but I doubt others will style it a Paradox, and possibly, think it one of the greatest that ever was broach’d.
Arnob.
Yet perhaps you will find by and by, that it may be in great part made good by what has been already discoursed, and by you admitted. I think it will not be doubted, but that there are, or may be conceived streight Lines, whereof one is a hundred or a thousand times longer than another: ‘Tis also generally granted, that a longer Line consists of, or may afford more parts than a shorter; for a Line equal to the shorter, being taken out of the longer, and consequently just as divisible as it, there will remain of the longer Line another Line, perhaps many times exceeding the shorter Line: And lastly, ‘tis generally acknowledged, that no Number can be greater than infinite; since if the lesser number were capable of accession (as it must be, if it fall short of another number) it would need that accession (or a greater) to make it infinite, which yet ‘tis supposed to be already.
Pyrocl.
I see not yet to what all this may tend.
Arnob.
You will quickly perceive it, when I shall have desired you to reconcile these Propositions with the demonstrations of Geometers of the endless Divisibility of all streight Lines; whence they deduce, that tho they be very unequal among themselves, yet the shortest of them contains, or may afford infinite parts.
Pyrocl.
But is there any thing more clear to humane understanding, or more supposed in almost all our Ratiocinations, than that two Truths cannot be contradictory to each other.
Arnob.
Tho I am far from affirming, that one Truth can really contradict another truth; yet I think that which is but a gradual or limited truth, may in some few cases not be reconcileable by Us, to an absolute and universal Truth. For, I think we may (with Sophronius) distinguish those Propositions we call true, into Axioms Metaphysical, or Universal, that hold in all Cases without reservation; and Axioms collected or emergent; by which I mean such as result from comparing together many particulars that agree in something that is common to them all. And some of these, tho they be so general, that in the usual Subjects of our Ratiocinations they admit of no exceptions; yet may not be absolutely and unlimitedly true; of which I know not whether I formerly gave you an instance, even in that Axiom which (almost) all meerly Natural Philosophers have supposed and built on, that, ex nihilo nihil fit, which, tho at least one of the highest of gradual or collected Truths, may yet be not universally true, since, for ought we know, God that is acknowledged to be a Being that is infinitely perfect, may have, and may have exercised, the power of Creating. And in such Cases as this, not to be able to reconcile a truth concerning a privileged thing with a Proposition that generally passes for true (and in other Cases is so indeed) will not presently oblige us to reject either Proposition as false, but sometimes, without destroying either, only to give one of them a due limitation, and restrain it to those sorts of things, on which ‘twas at first grounded, and to which ‘twas, because of mans ignorance, or inconsiderateness, that ‘twas not at first confin’d. And if the Miracles vouch’d either for the Christian, or for any other Religion, be any of them granted to be true; (as almost all mankind agrees in believing in general, that there have been true Miracles;) it cannot well be deny’d but that Physical Propositions are but limited, and such as I called Collected Truths, being gathered from the settled Phaenomena of Nature, and are lyable to this limitation or exception, that They are true, where the irresistible power of God, or some other supernatural Agent is not interpos’d to alter the course of Nature.
Pyrocl.
But do you think, there are no inconsistent Propositions that you would call Truths, wherein you cannot shew that one of them is but a gradual or emergent Truth?
Arnob.
‘Tis one thing to inquire whether men have yet discerned, or I am able to make out, that one of the Propositions you speak of is but a limited truth; and another, to inquire, whether speaking absolutely and universally, it may to any Intellect appear to be no more than such. For first I consider, that the Reason why we judge things to be repugnant, Being, that the Notions or Ideas we have of them seem to us inconsistent, if either of these notions be wrong framed, or be judged of by an unfit Rule, we may think those Propositions, to be contradictory that really are not so; as, if you heedfully mark it, you shall find, that those that are wont to employ their imaginations about things that are the proper Objects of the Intellect, are apt to pronounce things to be unconceivable, only because they find them unimaginable; as if the Fancy and the Intellect were Faculties of the same extent: Upon which account some have so grosly err’d, as to deny all immaterial Substances, and chose rather so far to degrade the Deity it self, as to impute to it a Corporeal Nature, than to allow any thing to have a Being that is not comprehensible by their Imagination, which themselves acknowledge to be but a Corporeal Faculty. But besides this mistake of things repugnant, which arises from the mis application or mis-management of our discerning Faculties, I consider in the next place, that there may be another that proceeds from the Imperfection and Limitedness of our Understanding, which being unable to judge of privileged things at the same rate that it does of other Objects, may sometimes be unable to discover that reconcileableness that a more illuminated and penetrating Faculty may discern. This may be illustrated by what usually happens at Sea, (for there mens Prospect is the most free) when looking towards the Main, the Sky and the Waters seem to meet at the edge of the (sensible) Horizon, tho indeed they are as far distant as Heaven is from Earth; and on the other side if you skillfully mix together the dry and fine powder ef Orpiment, and that of Indico, you will produce a green colour, as is known to Painters, and the eye takes notice but of an uniform mixture, in which it sees neither blew nor yellow: But if, (as experience shews) you look on this mixture with a very good Microscope, the emergent colour will disappear; and you will plainly see instead of it, blew and yellow grains of the powders distinct from one another. Which Instances may serve to shew the imbecillity of our visive Faculty; and the later of them may teach us, that a thing may appear one and differing, as ‘tis looked upon by a more or less discerning sight. But an instance more home to our present purpose may be afforded by yellow Diamonds, which because of their Colour, not only other Men, but the generality of Goldsmiths (in whose error I have sometimes shared) take to be counterfeit Gems, or at best but right Topazes, whereas very skillful Lapidaries, will by sure signs discover and acknowledge them to be true Diamonds, notwithstanding their seeming difference from unquestion’d ones, and account them to be of the same nature with that noblest kind of Jewels. Whence we may learn that a more skillful Judge may discern an agreement in things that almost all other men think they see manifestly to be of distant natures.