Alexander of Aphrodisias included Aristotle’s first principles of rational thinking, in particular the principle of non-contradiction, in the domain of metaphysics, as would Syrianus. In this chapter I discuss this principle as it was understood by Syrianus, in particular with regard to its roots in divine Intellect, where the unity of intellection and its objects grounds the principles of reasoning in human intellection and the truth of its objects.

Chapter 4 discusses the protreptic structure of Iamblichus’ De communi mathematica scientia and of Proclus’ revision of this text in the First Prologue to his commentary on Euclid’s Elements. I note rhetorical patterns and styles of argumentation used by Iamblichus, which mean, for example, that the same arguments can be made both in support of the study of philosophy (in the Protrepticus) and in support of the study of mathematics (in the De communi mathematica scientia). I note Proclus’ use of Syrianus’ commentary on Aristotle’s Metaphysics in his revision of Iamblichus’ book and suggest that Iamblichus may have been influenced by the prolegomena of Ptolemy’s Syntaxis.

Chapter 25 introduces Alexander of Aphrodisias’ systematic reading of Aristotle’s Metaphysics. I show how Syrianus took over Alexander’s reading of Aristotle, combining it with Plato’s references to a supreme knowledge, ‘dialectic’, and explaining the possibility of scientific knowledge of the objects of metaphysics – transcendent divine first principles – in terms of concepts innate in the soul which both image these first principles and are available to discursive reasoning as sources of knowledge of these principles. The primary text for metaphysics, according to the Platonists, was Plato’s Parmenides. I show how Proclus’ interpretation of the Parmenides, inspired by Syrianus, underlies the composition of Proclus’ metaphysical masterpiece, the Elements of Theology. Finally, Damascius is shown to have brought out to the fullest extent the limits of human reasonings about transcendent divine principles, reasonings which incessantly lead to contradictions and impasses, the aporetical ‘birth-pangs’ of the reasoning soul where it meets what transcend it.