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EXAMINATION OF ANTINOMIES. 529 
often as we please; that there never needs be an end to the subdivisions of the distance, 
nor, consequently, to those of the time in which it is performed. But an unlimited 
number of subdivisions may be made of that which is itself limited. The argument 
proves no other infinity of duration than may be embraced within five minutes. As long 
as the five minutes are not expired, what remains of them may be divided by ten, and 
again by ten, as often as we like, which is perfectly compatible with their being only five 
minutes altogether. It proves, in short, that to pass through this finite space requires a 
time which is infinitely divisible, but not an infinite time.”* 
256. Kant’s definition, that “the Infinity of a series consists in this very thing, that it 
can never be completed by successive synthesis,” should be qualified by adding,—wnless 
the succession is infinite. Every finite quantity, being infinitely divisible, is the completion 
or sum of an infinite number of infinite series; every now is the termination of one in- 
finity, and the commencement of another infinity of successive moments. It is quite true, 
as Kant remarks in his Observation upon the Thesis, “that an eternity of real states fol- 
lowing upon one another, can never have elapsed up to a given (the present) point of 
time,” provided we mean by eternity, duration that has neither beginning nor end, but 
our Thesis and Antithesis refer merely to the beginning, and it is quite certain that a 
terminated ‘succession of real states,” infinite in regard to its commencement, must have 
elapsed at every given point of time. 
257. A third ambiguity arises from the equivocal meaning of space and time. In a por- 
tion of the reasoning, they are regarded as mere forms of thought; in another portion, as 
real entities. If space is included in the phenomena of the world, being itself infinite, the 
world must also be infinite. But if space is a mere form of thought, and in no sense phe- 
nomenal, we may easily imagine “not only a relationship of things in space, but also of 
things to space,” and the world may, therefore, be conceived as “inclosed as to space, in 
limits.” 
258. This brief discussion is, perhaps, sufficient to show that the Antinomies do not 
necessarily result from the legitimate use of Reason, but that they are pure fallacies, and 
that, like other fallacies, they will be self-detected, provided all the terms are clearly and 
unequivocally defined. 
259. The following are the remaining Kantian Antinomies :f 
* Mill, Logic, p. 508. Mill disclaims the invention of this solution, but does not mention the author. I 
thought it was from Hamilton, but I have not been able to turn to it. 
{ Kant, pp. 308, 314, 319. 
