The immediate knowledge which we seem to have of them proves, when examined,to be total ignorance. While our belief in their objective reality is insurmountable,we are unable to give any rational account of it. And to posit the alternativebelief (possible to state but impossible to realize) is merely to multiplyirrationalities. §16. Were it not for the necessities of the argument, it would beinexcusable to occupy the reader's attention with the threadbare, and yetunended, controversy respecting the divisibility of matter. Matter is eitherinfinitely divisible or it is not: no third possibility can be named. Whichof the alternatives shall we accept? If we say that Matter is infinitelydivisible, we commit ourselves to a supposition not realizable in thought.
We can bisect and re-bisect a body, and continually repeating the act untilwe reduce its parts to a size no longer physically divisible, may then mentallycontinue the process. To do this, however, is not really to conceive theinfinite divisibility of matter, but to form a symbolic conception not admittingof expansion into a real one, and not admitting of other verification. Reallyto conceive the infinite divisibility of matter, is mentally to follow outthe divisions to infinity. and to do this would require infinite time. Onthe other hand, to assert that matter is not infinitely divisible, is toassert that it is reducible to parts which no power can divide; and thisverbal supposition can no more be represented in thought than the other.
For each of such ultimate parts, did they exist, must have an under and anupper surface, a right and a left side, like any larger fragment. Now itis impossible to imagine its sides so near that no plane of section can beconceived between them; and however great be the assumed force of cohesion,it is impossible to shut out the idea of a greater force capable of overcomingit. So that to human intelligence the one hypothesis is no more acceptablethan the other; and yet the conclusion that one or other must agree withthe fact, seems to human intelligence unavoidable.
Again, let us ask whether substance has anything like that extended soliditywhich it presents to our consciousness. The portion of space occupied bya piece of metal, seems to eyes and fingers perfectly filled: we perceivea homogeneous, resisting mass, without any breach of continuity. Shall wethen say that Matter is actually as solid as it appears? Shall we say thatwhether it consists of an infinitely divisible element or of units whichcannot be further divided, its parts are everywhere in actual contact? Toassert as much entangles us in insuperable difficulties. Were Matter thusabsolutely solid it would be -- what it is not -- absolutely incompressible;since compressibility, implying the nearer approach of constituent parts,is not thinkable unless there is unoccupied space among the parts.
The supposition that Matter is absolutely solid being untenable, therepresents itself the Newtonian supposition, that it consists of solid atomsnot in contact but acting on one another by attractive and repulsive forces,varying with the distances. To assume this, however, merely shifts the difficulty.
For granting that Matter as we perceive it, is made up of dense extendedunits attracting and repelling, the question still arises -- What is theconstitution of these units? We must regard each of them as a small pieceof matter. Looked at through a mental microscope, each becomes a mass suchas we have just been contemplating. Just the same inquiries may be made respectingthe parts of which each atom consists; while just the same difficulties standin the way of every answer. Even were the hypothetical atom assumed to consistof still minuter ones, the difficulty would reappear at the next step; andso on perpetually.
Boscovich's conception yet remains to us. Seeing that Matter could not,as Leibnitz suggested, be composed of unextended monads (since the juxtapositionof an infinity of points having no extension could not produce that extensionwhich matter possesses), and perceiving objections to the view entertainedby Newton, Boscovich proposed an intermediate theory. This theory is thatthe constituents of Matter are centres of force -- points without dimensions-- which attract and repel one another in such wise as to be kept at specificdistances apart. And he argues, mathematically, that the forces possessedby such centres might so vary with the distances that, under given conditions,the centres would remain in stable equilibrium with definite interspaces;and yet, under other conditions, would maintain larger or smaller interspaces.
This speculation, however, escapes all the inconceivabilities above indicatedby merging them in the one inconceivability with which it sets cut. A centreof force absolutely without extension is unthinkable. The idea of resistancecannot be separated in thought from the idea of something which offers resistance,and this something must be thought of as occuppying space. To suppose thatcentral forces can reside in points having positions only, with nothing tomark their positions -- points in no respect distinguishable from surroundingpoints which are not centres of force -- is beyond human power.
