PHYSICS inWnitely divisible, but that by proper distinctions and separations we may run up this idea to inferior ones, which will be perfectly simple and indivisible In rejecting the inWnite capacity of the mind, we suppose it may arrive at an end in the division of its ideas; nor are there any possible means of evading the evidence of this conclusion ’Tis therefore certain, that the imagination reaches a minimum, and may raise up to itself an idea, of which it cannot conceive any sub-division, and which cannot be diminished without a total annihilation (T, 27) What goes for ideas, goes also for impressions: ‘Put a spot of ink upon paper, Wx your eye upon that spot, and retire to such a distance, that at last you lose sight of it; ’tis plain, that the moment before it vanished the image or impression was perfectly indivisible’ (T, 27) Kant’s Antinomies Kant had a novel way of dealing with the problems of the continuum He took over the arguments of his predecessors (for and against inWnite extension of time, for and against the inWnite divisibility of matter), and instead of taking sides between them he proclaimed that the impossibility of resolving the debate showed that it was a mistake to talk of the universe as a whole or to treat space and time as having reality in themselves This is the tactic he adopted in the part of the transcendental dialectic called ‘the antinomies of pure reason’ The Wrst antinomy concerns the extension of time and space If we leave aside space for the moment, the thesis is ‘The world had a beginning in time’ and the antithesis is ‘The world had no beginning in time’ Both propositions had long been discussed by philosophers Aristotle thought the antithesis could be proved, Augustine thought the thesis could be proved, and Aquinas thought that neither could be proved Kant now proposes that both can be proved: not, of course, to show that there are two contradictory truths, but to show the impotence of reason to talk about ‘the world’ as a whole (A, 426–34) The argument for the thesis is this An inWnite series is one that can never be completed, and so it cannot be the case that an inWnite series of temporal states has already passed away This argument fails, because of an ambiguity in the word ‘completed’ It is true that any discrete series which has two termini cannot be inWnite; but such a series may be closed at one end and go 177