But I remember that the Captain warned me against attributing to mind extension or divisibility or any property of matter.
Divisibility is of matter; if the infinite mind has parts, then infinity is divisible--which is a contradiction.
Divisibility means merely the possibility of separating the whole into parts, and not that the whole is compounded out of parts and thus came into being.
For it is just to the quantity, and not to the quality of matter that its mechanical (not chemical) divisibility is related.
On the other hand, the infinite divisibility of matter, which the antithesis asserts, follows a priori and incontrovertibly from that of space, which it fills.
Aristotle infers quite rightly from the infinite divisibility of Time, that everything which fills it, therefore every change, i.
If it doth not, you might as well argue from the infinite divisibility of extension against the Divine prescience, as from such a difficulty against Immaterialism.
What we have here observed seems to be the chief cause, why to suppose the infinite divisibility of finite extension has been thought necessary in geometry.
They who knew not glasses had not so fair a pretence for thedivisibility ad infinitum.
Moreover it may perhaps be necessary to suppose the divisibility ad infinitum, in order to demonstrate that the radius is equal to the side of the hexagon.
To prove against Keill yt the infinite divisibility of matter makes the half have an equal number of equal parts with the whole.
Infinite divisibility of extension does suppose the external existence of extension; but the later is false, ergo ye former also.
Demonstrations of the infinite divisibility of extension suppose length without breadth, or invisible length, wch is absurd.
This follows from the divisibility of extension ad infinitum.
Philosophers have adopted different opinions as to thedivisibility of matter.
If you say no, you seem to place limits to his omnipotence; if you say yes, we shall have arrived at simple points, as otherwise the divisibility would not be exhausted.
The divisibility of matter is a question that torments philosophers.
The arguments for or against unextended points, for or against the infinite divisibility of matter seem equally conclusive.
Although our experience of division is limited, divisibility itself is unlimited.
This distinction seems to have originated in the attempt to avoid the necessity of admitting infinite divisibility in natural bodies.
This last consequence can be avoided only by recourse to the infinite divisibility of matter, and even this is a means of escaping the difficulty rather than a true solution.
I intimated elsewhere[52] that infinite divisibility seems to suppose the very thing which it denies.
Evidently there is either something wrong with this doctrine of the infinite divisibility of space, or there is something wrong with our understanding of it, if such absurdities as these refuse to be cleared away.
As to the infinite divisibility of space, have we not, in addition to the seeming reasonableness of the doctrine, the testimony of all the mathematicians?
The divisibility of space and the divisibility of matter are quite different.
An inch as a spatial determination is infinitely divisible, but the divisibility of the actual stuff which any inch may measure is a matter of empirical investigation, and ought to admit of a definite answer.
The infinite divisibility of space implies that of time, as is evident from the nature of motion.
This would be perfectly decisive, were there no medium betwixt the infinitedivisibility of matter, and the non-entity of mathematical points.
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.
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.
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.
Consider for example the infinite divisibility of matter.
It has, no doubt, by reason of its material principle, an absolutely necessary exigence for divisibility into distinct integral parts, for integral composition in other words.
Each body possesses its limit of divisibility; in amorphous bodies the high divisibility is but natural, but in crystalline bodies this division must be produced by grinding or washing.
Ordinary earth and several of the lake-colors take without wetting of edges with alum water, but these colors leave much to be desired in their divisibility and fineness and always appear rugged.
Not in weight but in divisibility rests the excellence, for instance I mention pure oxide of iron, cadmium, sulphate of mercury and mercury iodide.
By way of note we would here add, that the theory of the infinite divisibility of matter, which all the laws of chemistry seem to deny, has no good grounds for our acceptance.
Beginning with the ball, a perfect type of wholeness and unity, we are led through diversity, as shown in the three solids of the second gift, toward divisibility in the Building Gifts, and approximation to surface in the sixth gift.
We pass from the undivided to the divided unit, emphasizing the fact that unity still exists, though divisibility enters as a new factor.
All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinitedivisibility of lines or angles), must fall to the ground.
For, although divisibility presupposes composition, it does not necessarily require a composition of substances, but only of the degrees (of the several faculties) of one and the same substance.
The divisibility of a body rests upon the divisibility of space, which is the condition of the possibility of the body as an extended whole.
It certainly seems that, as a body must be cogitated as substance in space, the law of divisibility would not be applicable to it as substance.
The apparent divisibility of the relations which constitute spatial order, then, may be explained in two ways, though these are at bottom equivalent.
In this sense, the divisibilityof spatial relations is an unavoidable illusion.
When space is regarded, so far as it is valid, as only spatial order, unbounded extension and infinite divisibility both disappear.
These two ways of viewing the apparent divisibility are equivalent: for empty space, in so far as it is not illusion, is a name for the aggregate of possible space-relations.
But the second way of regarding divisibility is the better way, since it introduces a reference to the matter which differentiates empty space, without which, spatial figures, and therefore Geometry, could not exist.
But if we take infinite divisibility rigidly, the units can theoretically be taken so small as to obtain any required degree of approximation.
There is, however, a clear limit to compressibility, as there is to divisibility of matter.
What we have here observed seems to be the chief cause why, to suppose the infinite divisibility of finite extension has been thought necessary in geometry.
The intellectual difficulties implied in the divisibility of time and space and matter were developed by Zeno with a force and subtlety that justified Aristotle in calling him the founder of dialectic.
But it cannot be maintained that divisibility of sovereignty was universally recognised in the eighteenth century.
In spite of this condition of things, the old controversy regarding divisibility of sovereignty has by no means died out.
By this distinction the divisibility of sovereignty was recognised.
But many jurists deny the divisibility of sovereignty and maintain that a State is either sovereign or not.
Zeno here arrives at the infinite divisibilityof space; because space and time are absolutely continuous, there is no point at which the division can stop.
Zeno now brings forward four different arguments against motion; the proofs rest on the infinite divisibility of space and time.
Divisibility is, as potentiality, the universal; there is continuity as well as negativity or the point posited in it—but posited as moment, and not as existent in and for itself.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "divisibility" in a variety of sentences. We hope that you will now be able to make sentences using this word.
