Higher Order

Before and after early modern mechanism and in contrast to it, Plato, Aristotle, Kant, and Hegel all broadly agreed on the normative importance of higher-order things.

In modern terms, Plato’s forms are higher-order things, as distinct from first-order things. Plato trusts higher-order things more than first-order ones, because he considers only higher-order things to be knowable in the sense of episteme, because only higher-order things contain an element of universality, and episteme applies only to universals, not particulars.

Aristotle agrees that higher-order things are ultimately more knowable, but believes it is possible to say more about first-order things, by relating them to each other and to higher-order things; that our initial rough, practical grasp of first-order things can help us to begin to grasp higher-order things by example; and that going up and down the ladder of abstraction successively can help us progressively enrich our understanding of both.

(Incidentally, I have always read the Platonic dialogues as emphasizing the normative importance of acquiring a practical grasp of forms more than specific existence claims about “the forms”. Aristotle’s criticisms make it clear that at least some in the Platonic Academy did understand Plato as making such existence claims, but particularly in what are regarded as later dialogues like Parmenides, Sophist, and Theaetetus, what is said about form seems relatively close to an Aristotelian view. It is even possible that these dialogues were influenced by the master’s even greater student.)

Early modern mechanism completely discarded Plato and Aristotle’s higher-order orientation. Descartes famously recommends that we start by analyzing everything into its simplest components. This temporarily played a role in many great scientific and technological advances, but was bad for philosophy and for people. Hegel calls this bottom-up approach Understanding, as distinct from Reason.

Early and mid-20th century logical foundationalism still adhered to this resolutely bottom-up view, but since the later 20th century, there has been an explosion in the use of higher-order formal concepts in mathematics, logic, and computer science. It turns out that even from an engineering point of view, higher-order representations are often more efficient, due to their much greater compactness.

Leibniz already tried to reconcile mechanistic science with a higher-order normative view. He also contributed to the early development of higher-order concepts in mathematics.

Kant and Hegel decisively revived an approach that is simultaneously higher-order and normative.

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