By Professor of Philosophy Dale Jacquette
This research of Hume's philosophy of arithmetic seriously examines his objections to the idea that of infinity in its historic context as a made from Enlightenment idea of data, and assesses the clients of his strict finitism within the gentle of latest arithmetic.
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Additional info for David Hume's Critique of Infinity (Brill's Studies in Intellectual History)
46 The deﬁnitions of body and place vary, therefore the things themselves must also be diﬀerent. In fact, the usual sense of ‘place’ is really a kind of body: human beings at a certain point on the earth are, materially speaking, bodies within bodies (478B): . . place is nothing else but the boundary and enclosures of things which are contained within a ﬁxed limit . . this world with its parts is not a place, but is contained within place, that is, within the ﬁxed limit of its deﬁnition .
Locus siquidem et tempus inter omnia, quae creata sunt, computantur. In his namque duobus totus mundus, qui nunc est, consistit, et sine quibus esse non potest. Ideoque a Graecis dicuntur, VN ANEY TO PAN id est, quibus sine universitas esse non valet. ’ 68 Ibidem, 56, 482B, ll. 1702–1712: ‘Si autem aliquo modo, sed non universaliter ea, quae sunt, habent esse, quemadmodum sub loco esse, per positionem et ﬁnem rationum, in quibus secundum naturam sunt, et sub tempore esse, omnino per principium, non ostendentur?
64 It would seem to follow then, ﬁrst, that when we know the deﬁnition of any given thing which we did not create, this is something which we have discovered rather than invented, and second, that when we do make up a deﬁnition, either it will be of something we make ourselves, or it will be what Eriugena calls a phantasm, an illusion. Eriugena divides up the categories according to whether they are at rest or in motion. 65 Motion, in fact, is the principle of time, and place and 59 Ibidem, 58, 483D, ll.
David Hume's Critique of Infinity (Brill's Studies in Intellectual History) by Professor of Philosophy Dale Jacquette