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Aristotle claims that we grasp the universal first principles of science by abstraction. Among the first principles he includes universal concepts, axioms, and postulates. The intellect (noûs ) in us intuits them directly. It can err not in intuiting them but in describing and identifying them. The intellect gains access to these universal principles by making inductions on sense perceptions, where they are contained confusedly in a disorganized, routed state. Induction is a type of abstraction where something more primary (and often more general) is abstracted from something less so. Via a series of inductions a hierarchy of universals is constructed. The hierarchy ends with the ultimate abstraction, mathematical objects . These have a relational structure but are treated as if they are subjects in their own right. Propositional first principles can be obtained by reading them off of the hierarchy, just as information can be read off of a map.As the intellect is what knows, it should be construed relationally. In line with Aristotle's theory of relations, "noûs " signifies both a relation and something being related in that relation , an individual substance like Socrates qua knower, which Aristotle seems to call the noûs in us. The relation , being active, exists always; the relatum perishes along with the substance.

DOI: 10.1007/978-3-319-04759-1_7

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