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Updated: May 6, 2025
Suppose the given number to be 7521: Add these together, and 15 will be produced; now 15 requires 3 to render it divisible by 9; and that number 3, being added to 7521, causes the same divisibility; 7521 plus 3 gives 7524, and divided by 9, gives 836.
The late revelations of chemistry, Roentgen rays, x-rays, radio-activity of metals, etc., throw an interesting light upon the seemingly infinite divisibility of matter. A small particle of a given substance may for many years throw off a continuous shower of corpuscles without perceptibly diminishing its volume. For an illustration we may take the odoriferous musk.
For example, in the judgement "All bodies are divisible," our conception of divisible applies to various other conceptions; among these, however, it is here particularly applied to the conception of body, and this conception of body relates to certain phenomena which occur to us. These objects, therefore, are mediately represented by the conception of divisibility.
Thus even upon the system of indivisible points, we can only form a distant notion of some unknown standard to these objects. Upon that of infinite divisibility we cannot go even this length; but are reduced meerly to the general appearance, as the rule by which we determine lines to be either curve or right ones.
He has already said that there is no argument against Berkeley's denial of matter any more than against the 'infinite divisibility of matter. But he adds, it is 'physically impossible' for us to admit the conclusion, at least without 'an instant dissent from a momentary logical admission. This, indeed, is but a version of Hume's familiar statement that Berkeley's arguments admit of no reply and produce no conviction.
Burke's pleasantry on the expression of very little, being greatly diminished; but my exchequer at this time was as well calculated to prove the infinite divisibility of matter, as that of the Welch principality. The guards of the republican Bastilles were paid by the prisoners they contained; and, in many places, the tax for this purpose was levied with indecent rigour.
The intimate connexion betwixt these parts of our system is the reason why we shall examine together the objections, which have been urged against both of them, beginning with those against the finite divisibility of extension.
If forms appear divisible in matter, it is only in considering them by abstraction, after the method, of geometricians; but this divisibility of form exists not in Nature, in which there is neither a point, an atom, nor form perfectly regular; it must therefore be concluded, that the forms of matter are not less indivisible than thought.
Infinite divisibility is applicable only to a quantum continuum, and is based entirely on the infinite divisibility of space, But in a quantum discretum the multitude of parts or units is always determined, and hence always equal to some number.
We may believe in the continuity and infinite divisibility of matter, but as long as this divisibility is only potentially infinite, actually always finite, our ability to traverse the space offers no difficulty.
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