Physiologia Epicuro-Gassendo-Charltoniana: or a fabrick of science natural, upon the hypothesis of atoms / Founded by Epicvrvs, repaired [by] Petrvs Gassendvs, augmented [by] Walter Charleton ... The first part.

  • Charleton, Walter, 1620-1707.
Date:
1654
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Licence: Public Domain Mark

Credit: Physiologia Epicuro-Gassendo-Charltoniana: or a fabrick of science natural, upon the hypothesis of atoms / Founded by Epicvrvs, repaired [by] Petrvs Gassendvs, augmented [by] Walter Charleton ... The first part. Source: Wellcome Collection.

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    Chap.H. injiaitely Di<z/ifible. The Collufion of this Diftin<ffion is not deeply concealed. For, every Art. 7. Continuutn hath cither partsot injinitc in Since> if found openly by parts/A? we underftand thofe that are a^uallj divided: then hath not any Continuum fo much as two or three parts 5 the fuppofed Conti- vuity excluding all Divifion. And if we intend, that a Continuum hath therefore two parts actually, becaufe it is capable of divifion into two parts adually: then is it necelTary, that we allow a Continuum to have parts adlually infinite, becaufe we prefumc it capable of divifion into infinite parts a(5lually i which 10 Arijlotle. Nor can any of his Defendants confequcnce by faying 5 that the Divifion is never finifhable, or terminable, and that his fenfe is only this, that no ContL nuum can ever be divided into fo many parts, as that it may not be again divided into more, andthofe by redivifion into more, andfo forvvard without end. Since, as in a Continuum two parts are not denyed to exift though it be never divided into thofe two parts: fb likewife are not infi¬ nite parts denied to exift therein, though it be never really divifible into infinite parts. Otherwife, we demand, fince by thofe requifite divifions and fubdivifions ufyue ad infnitum^ ftill more and more adluall par,ts are difeovered 5 can you conceive thofe parts, which may be difeovered to be of any Determinate Nismber^ ox not? If you take the Affirm, then will not there be parts enough to maintain the divifion to infinity: if the Ne- gat, then muft the parts be adually infinite. For, how can a Continuum be fuperior to final exhauftion, unlefs in this refpe^l, that it contains infinite parts, i.e. fuch whofe Infinity makes it Inexhauftibic. Becaufe, as thofe parts, which are deduced from a Continuum, muft be prreexiftent therein before dedu<ftion (clfe whence arc they deduccable fo alfo muft thofe, which yet remain deduccable, be a(5lually cxiftenc therein, otherwife they arc not deducible from it. For, Parts are then Infinite, when more and more incxhauftibly, or without end, arc conceded Deducible. The other, with unpardonable confidence infifted on by the Stoicks, is this i Continuum non evadere inf nitum- quoniam illudproprie refultatmn t^rfu^e^of the ex Proportionalibus^fedex Aliquotis partibus^ quaseonfateffeDefinitas^cum StoiX; ° inter extrema Corporis verfentur: that [by admitting an infinity of parts in a Finite Continuum] a Continuum doth not become infinite-, becaufe that rcfults properly not frombut Aliquotal^ms, which arc therefore confeff’d to be Definite^ becaufe they relate only to the Extremes of a Body. ^ Firft, this fubterfuge is a mere Lufus Verhorum^ founding nought at all 9* in the ears of Reafon. For fince every thing doth confift of thofe parts into which It may be at laft refolvcd becaufe every Continuum is at laft Reafon. rcfolved into, therefore muft it confift of Proportional Parts, Again, fince every one of Aliquotal parts is Continuate, each of them may be divided into as many Aliquotal parts, as the whole Continuum was firft divided into, andfo upwards infinitely: fo as at length the Divifion muft revert in¬ to Proportional Parts, and the Difficulty remain the fame. Sect.