 Thought, Aristotle insists, always requires a phantasma (On the Soul III 7, 431a16–17, b2; III 8, 432a8–10; On Memory 1, 449b31). But the content of even the simplest concept goes beyond that contained in any such quasi-perceptual representations (On the Soul III 8, 432a12–14). At a minimum, in thought we are able to focus selectively on certain features, by ignoring many of the other features in such representations, just as we can use a diagram of a triangle for mathematical purposes without being concerned with its particular dimensions, and so effectively abstract them (On Memory 1, 449b31–450a17). But we are also capable of using one concept to form the opposite concept and of applying one concept to another to result in a compound propositional thought capable of truth or falsehood (On the Soul III 6; Metaphysics VI 4, IX 10; On Interpretation 1). The abstract content that results from such operations allows us to use symbols to speak and understand one another (On Interpretation 1, 16a3–9).