Abstract
In this chapter, I discuss the third metaphysical implication of the Idealist reading, pertaining to the divisibility of space. Is space infinitely or merely finitely divisible? I rebut Hume’s argument for the latter possibility, showing that it is invalid on both readings – the Materialist and the Idealist. I then show that there is a better Idealist argument in support of the merely finite divisibility, drawing on other assumptions in Hume’s system, and (to the best of my knowledge) no Materialist counterpart. So whereas on the Idealist reading, the finite divisibility of space is defensible within the Treatise, on the Materialist interpretation, Hume must remain agnostic on this question (even if he can wield other assumptions he makes in the Treatise).
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Notes
- 1.
Berkeley also says (PHK, §124) that “to say a finite quantity or extension consists of parts infinite in number is manifest a contradiction”, a claim that is in need of justification. If infinite divisibility is contradictory, the contradiction is not “manifest” (as is “a line longer and shorter than line L”). Unable to adduce an argument in its defence, Berkeley demagogically likens it to “[a]ncient and rooted prejudices [that] do often pass into principles”.
- 2.
This claim seems eminently plausible: when I encounter Paris from the tower of Notre Dame cathedral, for instance, I see only some of its features. But it is problematic in the case of the vulgar. The supposition that impressions do not include all their object’s details is incompatible with Hume’s Idealist identification of an object with a single impression. There is no problem with respect to the Idealist philosophers’ Paris. The impression it engenders in the mind needn’t precisely copy the original.
- 3.
Johnson (1995, p. 96) repeats Kemp Smith’s error, conflating “unextended” with “having 0 extension”, when he says that Hume “cannot generate extension out of the multiplication of extensionless points”. In fact, modern measure theory makes respectable even the possibility Hume views as absurd: a (non-denumerable) collection of 0-length points forming a line with a positive length.
- 4.
I am grateful to Ariel Meirav for suggesting this argument to me.
- 5.
Even if perceptions and objects are spatially related, it does not straightforwardly follow that there can be no smaller perception than an indivisible one. Baxter’s Hume thinks the analogous temporal claim is false: a temporally indivisible object (perception) can precisely overlap a sequence of perceptions (Sect. 5.4). Analogous reasoning can be employed to show the consistency of the spatial analogue. If it obtains, Hume’s claim that nothing can be smaller than an indivisible perception is clearly false. But, in analogy to the temporal case, we can argue on Hume’s behalf that this possibility is more complex than the one in which precise overlapping can only occur when two spatial segments have the same number of indivisible constituents. And it will then be true that nothing is smaller than a minimal idea.
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Weintraub, R. (2024). Consequences of the Idealist Interpretation for the Divisibility of Space. In: Humean Bodies and their Consequences. Jerusalem Studies in Philosophy and History of Science. Springer, Cham. https://doi.org/10.1007/978-3-031-50799-1_7
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