The material and formal infinite

The first infinite we know is infinite only secundum quid. An infinite number line is still finite in its genus and even in its sub-genus as it doesn’t have quantity like shapes, motions, or times do. If I visualize an infinite white sheetrock wall it is still finite in its color, its material, its position. Thomas calls this the material infinite, and it’s based on the intellectual insight into the division of subject and form. What we visualize as infinite numbers are rather pre-numbers, or a subject considered its its difference to the form of a species of number, just as our infinite wall is just a pre-wall consisting in an intellectual judgment that the subject as such need not end here or there. Our imagined infinities are intellectual insights about the nature of matter, whether as the homogeneity of mathematical quantity or the sensible matter of e.g. sheetrock.

Form is understood in opposition to this above infinity. At first blush, however, it seems like form is a negating or restricting factor since, for example, the form imposed on our infinite sheetrock wall is just that it end when it is e.g. eight feet tall. This overlooks that we only bought the sheetrock in the first place to make our eight-foot wall, and so the material spanning to the proper height is not a negation of a possible infinite but a fulfillment of desire and therefore the good of something ordered to a good.

Aren’t there times when we get material infinity, though? Inertial motion seems like one, and it is a component in any motion. Inertial motion is however not a natural body being fulfilled by its order to the infinite but the absence of self-determination and the consequent inability to cease carrying out the activity of another, irrespective of that other being an agent accelerating it from its rest or decelerating its progress by impediment. The absence of self-activity and self-determination is equally stasis and perpetual motion al la the pail set in motion by the sorcerer’s apprentice.

The material infinite is thus an abstraction from the good, or an insight into how matter is imperfect with indefinite possible perfections and therefore can have indefinite privations. Mathematics by its nature abstracts from these goods and privations, except in the sense that the solution to a problem or equation always has the character of a form and the absence or failure of solution of a privation.

So we understand the object of desire or the good in opposition to the material infinite, and as a consequence we understand all other formal perfections in the same way: true, dignified, existent, definite, actual, powerful, one. Since even a form in matter is proportioned to all the ways in which matter is indefinite, however, form also has its own proper infinity in opposition to matter.

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