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Updated: May 6, 2025
The infinite divisibility of space and of matter forms the chief difficulty in the problem of the continuous. Metaphysics demands the fixed or discrete line, although common thought is incapable of conceiving it. Space is a mere form of combination in representation or for the observer, and yet it is objective, i.e., it is valid for all intelligences, and not merely for human intelligence.
An example will serve more fully to explain what we have asserted, throw its correctness into light, and facilitate the application. The properties common to all matter, are extent, divisibility, impenetrability, figure, mobility, or the property of being moved in mass.
The all but infinite divisibility of matter is proved by every odor that the breeze brings us from field and wood, and by the delicate flavors that the tongue detects in the food we eat and drink.
This, together with its necessity for the statement of causal laws, seems to be the source of the entirely erroneous feeling that matter is more "real" than sense-data. Consider for example the infinite divisibility of matter. In looking at a given thing and approaching it, one sense-datum will become several, and each of these will again divide.
At the same time we may learn the reason, why geometry falls of evidence in this single point, while all its other reasonings command our fullest assent and approbation. And indeed it seems more requisite to give the reason of this exception, than to shew, that we really must make such an exception, and regard all the mathematical arguments for infinite divisibility as utterly sophistical.
As for units, some perhaps will say that I do not know them by the bodies, but only by the spirits; and, therefore, that my mind being one, and truly known to me, it is by it, and not by the bodies, I have the idea of unity. But to this I answer. It will, at least, follow from thence that I know substances that have no manner of extension or divisibility, and which are present.
But I go farther, and maintain, that none of these demonstrations can have sufficient weight to establish such a principle, as this of infinite divisibility; and that because with regard to such minute objects, they are not properly demonstrations, being built on ideas, which are not exact, and maxims, which are not precisely true.
But one may take the terms in an extended sense. He observes aptly that after all the changes of matter and after all the qualities of which it may be divested, there remain extension, mobility, divisibility and resistance.
In his "Theoria philosophiæ naturalis," he tried to prove that bodies are composed not of a continuous material substance but rather of innumerable point-like structures or particles which are without any extension or divisibility. Boscovich's philosophical system can be called a dynamistic atomismus.
Divisibility may not be predicable at all, in any intelligible sense, of Things in themselves, nor therefore of Matter in itself; and the assumed necessity of being either infinitely or finitely divisible, may be an inapplicable alternative. On this question I am happy to have the full concurrence of Mr. Herbert Spencer, from whose paper in the Fortnightly Review I extract the following passage.
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