Matter and Form
“EVERY individual thing in the world except minds is a union of form with at least “local matter” [matter for locomotion, matter for alteration, for change of size, for coming into being and passing away]. But a still more attenuated kind of matter may be distinguished by thought though it never exists without “sensible matter,” i.e. without, at least, local matter. This is “intelligible matter” —in other words, spatial extension. The recognition of this comes late in Aristotle’s thought and is confined, so far as explicit mention goes, to the “Metaphysics.” From any sensible thing you may think away its whole sensible matter. In the case of terrestrial things you can abstract from their possession of the fundamental qualities—heat or cold, dryness or fluidity—and of all the consequential qualities; in the case of celestial things you may abstract from their capacity for rotation; both alike will still have shape and size. You will have passed by abstraction from actual bodies to the objects of mathematics.
“You can think first of these bodies simply as three-dimensional objects and nothing more. You can then consider the plane sections of these solids apart from the third dimension from which they are in fact inseparable. Similarly you can consider apart the linear sections of these planes, though these have again have no separate existence. Though you have now abstracted from all that would in ordinary language be called matter, you have not yet come to pure form. For a particular straight line or plane or solid (which some Platonists naïvely indentified with the numbers, 2, 3, 4 respectively, and which modern mathematics with greater accuracy represents by equations) by being embodied in extension. Abstract from extension or “intelligible matter,” and nothing but pure form is left.”
~From Aristotle: A Complete Exposition of His Works & Thought, by W.D. Ross.
