The judgment, " not-being is thinkable," cited by Aristotle; the judgment, " A square circle is impossible," cited by Herbart; the judgment, " A centaur is a fiction of the poets," cited by Mill.
Of such primitive principles, the absolutely necessary conditions of possible cognition, only three are thinkable - one perfectly unconditioned both in form and matter; a second, unconditioned in form but not in matter; a third, unconditioned in matter but not in form.
- As Aristotle remarked both in the De Interpretatione and in the Sophistici Elenchi, " not-being is thinkable " does not mean " not-being exists."
The English thinkers influenced by Hegel are inclined to assert mechanism unconditionally, as the very expression of reason - the only thinkable form of order.
But of these universal propositions the first imperfectly expresses a categorical belief in existing things, the second in thinkable things, and the third in nameable things, while the fourth is a slipshod categorical expression of the hypothetical belief, " If any candidates arrive late they are fined."
But really a judgment is a belief that something, existing, or thinkable, or nameable or what not, is (or is not) determined; and inference is a process from and to such beliefs in being.
The cardinal assumption of Plato's metaphysic is, that the real is definitely thinkable and knowable in proportion as it is real; so that the further the mind advances in abstraction from sensible particulars and apprehension of real being, the more definite and clear its thought becomes.
But some conceptions are such that the more distinct they are made the more contradictory their elements become; so to change and supplement these as to make them at length thinkable is the problem of the second part of philosophy, or metaphysics.
A mark of the same concept) as N, while logic denies it; and so - it being impossible for one and the same M to sustain these contradictory positions - there is but one way open to us; we must posit several Ms. But even now we cannot say one of these Ms is the same as N, another is not; for every M must be both thinkable and valid.