Philoponus

In this part of the Posterior Analytics Aristotle elaborates his assessment of how universal truths of science can be scientifically explained as inevitable in demonstrative proofs. But he introduces complications: some sciences discuss phenomena that can only be explained by higher sciences and again sometimes we reason out a cause from an effect, rather than an effect from a cause. Philoponus takes these issues further. Reasoning from particular to universal is the direction taken by induction, and in mathematics reasoning from a theorem to the higher principles from which it follows is considered particularly valuable. It corresponds to the direction of analysis, as opposed to synthesis.