Note on the distinction between quantity and substance

It belongs to substance properly to allow for the existence of change. If quantity were substance, then just as an individual man remains if he becomes larger, so too an individual number would remain if the number gets larger. Likewise, one and the same line would be at one time commensurate and at another time incommensurate with other lines. We could make a side of a square and its diagonal commensurate simply by changing the length of one, which would, ex hypothesi, leave us with the same line we had before, only larger (and now commensurate). We could make one and the same number even and odd, one and the same line rational and irrational. We could claim that five is “four” with perfect rigor and sincerity.

Notice that because quantity is not a substance, the eternal and timeless truths of the mathematician- which serve as examples of truth par excellence– do not follow from the ontological perfection of mathematical things (a perfection which is proper to substance). Rather, the supreme intelligibility of mathematical things follows necessarily from the ontological inferiority of quantity. The truths we establish about quantity cannot change only because quantity as such completely lacks a subject which would allow for it to change. We give no honor to the physical universe if, after we notice its beautiful proportions and mathematically expressible laws, we use this as evidence that the things in the universe are fundamentally mathematical. Such a claim is much more degrading than the claim that the universe is natural and changeable, for it is precisely as changeable that natural things manifest that they exist in themselves. It is as changeable that natural things are substantial, and as substantial they have a kind of transcendence over the merely sensible order. The kind of substantiality that we impute to the universe when we understand it according to the imagination is an ontological demotion of the universe itself.

%d bloggers like this: