Dr. Alfonso Gomez-Lobo today pointed out to me the problem Aquinas has with Platonism . The argument runs:
1. If Plato's divided line is true, then all principles proceed from one principle- the form of the good.
2. If two or more principles proceed from one principle, the multiple principles are ultimately commensurable.
3. The law of non-contradiction is a logical principle.
4. The law of inertia is a logical principle.
5. The law of non-contradiction is incommensurable with the law of inertia.
6. There exist two principles which are not commensurable (3, 4, 5).
7. It is not the case that for all principles, they proceed from one principle (2, 6).
8. Plato's divided line is false (1, 7).