Physiologia Epicuro-Gassendo-Charltoniana, or, A fabrick of science natural, upon the hypothesis of atoms founded by Epicurus repaired [by] Petrus Gassendus ; augmented [by] Walter Charleton ...

The Demonstration.

If in a Finite Body, the number of Parts, into which it may be divided,* 1.1 be not Finite also; then must the Parts comprehended therein be really Infinite: and, upon Consequence, the whole Composition resulting from their Commix∣ture, be really Infinite; which is repugnant to the supposition.

So perfectly Apodictical, and so inoppugnably victorious,* 1.2 is this single Argument, that there needs no other to the justification of our instant Cause: nor can the most obstinate and refractory Champion of the Pe∣ripateticks, refuse to surrender his assent thereto, without being reduced to a most dishonourable exigent. For, He must allow either that the whole of any Body is something besides, or distinct from the Aggeries, or Mass of Parts, of which it is composed: or, that all the Parts, to∣gether taken, are somewhat greater then the whole amassed by their convention and coalescence. If so; there must be as many parts in a grain of Mustard seed, as in the whole Terrestrial Globe: since in either is supposed an equal Inexhauribility; which is contrary to the First Notion of ••uclid, Totum est majus sua parte. And if any mans skull be so soft, as to admit a durable impression of an opi∣nion so openly self-contradictory, as this, that the Whole is less then its Parts; we judge him a fit Scholer for Chrysippus, who blusht not publiquely to affirm, that one drop of Wine was capable of commistion with every particle of the Ocean, nay, diffusive enough to extend to an union with every particle of the Universe, were it 1000••0 times greater, then now it is. Nor, need we despair to make him swear, that Arcesilas did not jeer the Disciples of Zeno, when he exemplified the inexhaurible division of Magnitude, in a mans Thigh, amputated, pu∣trified, and cast into the Sea; ironically affirming the parts thereof so infinitely subdivisible, that it might be incorporated per mi∣nimas, to every particle of Water therein; and consequently, that not only Antigonus Navy might sail at large through the thigh, but

also that Xerxes thousand two hundred ships might freely maintain a Na∣val fight with 300 Gallies of the Greeks, in the compass of its dispersed parts. We deny not, but Zeno's Argument against Motion, grounded on the supposition of interminable Partibility in Magnitude, is too hard and full of Knots, to be undone by the teeth of common reason: yet who hath been so superlatively stupid, as to prefer the mere plausibility thereof to the contrary Demonstration of his sense, and thereupon infer a belief, that there is no Motion in the World? What Credulity is there so easie, as to entertain a conceit, that one granule of sand (a thing of very small circumscription) doth contain so great a number of parts, as that it may be divided into a thousand millions of Myriads; and each of those parts be subdivided into a thousand millions of Myriads; and each of those be redivided into as many; and each of those into as many: so as that it is impossible, by multiplications of Divisions, ever to arrive at parts so ex∣tremely small, as that none can be smaller; though the subdivisions be repeated every moment, not only in an hour, a day, a month, or a year, but a thousand millions of Myriads of years? Or, What Hypochondri∣ack hath been so wild in Phansie, as to conceive that the vast mass of the World may not be divided into more parts then the Foot of a Handworm, a thing so minute as if made only to experiment the perfection of an Engy∣scope? And yet this must not be granted, if we hearken to the spels of Zeno and the Stoicks; who contend for the Divisibility of every the smallest quantity into infinite parts: since, into how many parts soever the World be divided, as many are assumable in the Foot of a Hand∣worm, the parts of this being no less inexhaustible, nor more terminable by any continued division, then the parts of that, according to the suppo∣sition of Infinitude. And, hereon may we safely conclude, that albeit the Arguments alledged in defence of Infinite Divisibility of every Phy∣sical Continuum, were (as not a few, nor obscure Clerks have reputed them) absolutely indissoluble: yet notwithstanding, since we have the plain Certificate of not only our Reason, but undeluded sense also to evi∣dence the Contrary, ought we to more then suspect them of secret Falla∣cy and Collusion; it being a rule, worthy the reputation of a First No∣tion, that in the examination of those Physical Theorems, whose Verity, or Falsity is determinable by the sincere judicature of the sense, we ought to appeal to no other Criterion, but to acquiesce in the Cer∣tification thereof; especially where is no Refragation, or Dissent of Reason.

Notwithstanding the manifest necessity of this apodictical Truth, yet have there been many Sophisms framed, upon design to evade it: among which we find only Two, whose plausibility and popular approbation seem to praescribe them to our praesent notice.

* 1.3The First is that famous one of Aristotle (de insecabil. lineis) Non crea∣ri propterea infinitum actu ex hujusmodi partibus infinitis, quoniam tales par∣tes non actu, sed potestate duntaxat infinitae sunt; adeo proinde ut creent so∣lùm infinitum potestate, quod idem sit actu finitum: that the division of a finite body into infinite parts doth not make it actually infinite, because the parts are not actually, but only potentially infinite; so as they ren∣der it infinitely divisible only potentially, while it still remains actually Finite.

The Collusion of this Distinction is not deeply concealed. For,* 1.4 every Continuum hath either no parts in actu, or infinite parts in actu. Since, if by parts in actu, we understand those that are actually divided: then hath not any Continuum so much as two or three parts; the supposed Conti∣nuity excluding all Division. And if we intend, that a Continuum hath therefore two parts actually, because it is capable of division into two parts actually: then is it necessary, that we allow a Continuum to have parts actually infinite, because we presume it capable of division into infinite parts actually; which is contradictory to Aristotle. Nor can any of his Defendants excuse the consequence by saying; that the Division is never finishable, or terminable, and that his sense is only this, that no Conti∣nuum can ever be divided into so many parts, as that it may not be again divided into more, and those by redivision into more, and so forward without end. Since, as in a Continuum two parts are not denyed to exist, though it be never divided into those two parts: so likewise are not infi∣nite parts denied to exist therein, though it be never really divisible into infinite parts. Otherwise, we demand, since by those requisite divisions and subdivisions usque ad infinitum, still more and more actuall parts are discovered; can you conceive those parts, which may be discovered to be of any Determinate Number, or not? If you take the Affirm. then will not there be parts enough to maintain the division to infinity: if the Ne∣gat. then must the parts be actually infinite. For, how can a Continuum be superior to final exhaustion, unless in this respect, that it contains infinite parts, i. e. such whose Infinity makes it Inexhaustible. Because, as those parts, which are deduced from a Continuum, must be praeexistent therein before deduction (else whence are they deduceable?) so also must those, which yet remain deduceable, be actually existent therein, otherwise they are not deducible from it. For, Parts are then Infinite, when more and more inexhaustibly, or without end, are conceded Deducible.

The other, with unpardonable confidence insisted on by the Stoicks,* 1.5 is this; Continuum non evadere infinitum; quoniam illud propriè resultat non ex Proportionalibus, sed ex Aliquotis partibus, quas constat esse Definitas, cùm inter extrema Corporis versentur: that [by admitting an infinity of parts in a Finite Continuum] a Continuum doth not become infinite; because that results properly not from Proportional, but Aliquotal parts, which are therefore confess'd to be Definite, because they relate only to the Extremes of a Body.

First, this subterfuge is a mere Lusus Verborum,* 1.6 sounding nought at all in the ears of Reason. For since every thing doth consist of those parts, into which it may be at last resolved; because every Continuum is at last resolved into, therefore must it con••ist of Proportional Parts. Again, since every one of Aliquotal parts is Continuate, each of them may be divided into as many Aliquotal parts, as the whole Continuum was first divided into, and so upwards infinitely: so as at length the Division must revert in∣to Proportional Parts, and the Difficulty remain the same.

Notes

• * 1.1

  Art. 4. The veri••y of the Thesis, de∣monstrated.
• * 1.2

  Art. 5. Two detesta∣ble Absurdities, inseparable from the posi∣tion of Infinite parts in a Con∣tinuum.
• * 1.3

  Art. 6. Aristotles sub∣••erfuge of In∣finitude Poten∣tial▪
• * 1.4

  Art. 7. Found openly Collusive.
• * 1.5

  Art. 8. A second sub∣terfuge of the Stoick;
• * 1.6

  Art. 9. Manifestly dis∣sentaneo••s to Reaso••.