Mediation is any kind of dependency of things on other things. With such dependencies in mind, Euclid the geometer is famously reported to have said that there is no royal road to science, but the point also applies more broadly to all kinds of meanings. Paul Ricoeur called mediation the “long detour” essential to understanding.
Mediation makes things intelligible. We understand things in terms of other things. Mediation involves a complicity of different kinds of meant realities with one another, which gives metaphorical “thickness” to the temporal present we experience. It initially appears as a kind of quasi-recursive accumulation of “layers” of partial determination that is retrospectively elicitable, and is subject to a kind of further accumulation of layers. (See also Aristotelian Matter; Potentiality, Actuality; Efficient Cause, Again; Kantian Synthesis; Transcendental Field.)
Mediation is the substance of Hegel’s Geist and the soul of Hegelian dialectic. Hegelian mediation exhibits or just “is” a kind of form or structure discernible in the Aristotelian semantic “materiality” of concrete things, made explicit by articulating intermediate relations of material incompatibility (Hegel’s “determinate negation”) and material consequence. It is what Hegel calls the determinate rather than the indeterminate, “infinite”, or classical negation of immediacy. (See also remarks on mediation at end of Ricoeur on Justice.)
While mediation broadly corresponds to Aristotelian materiality, Hegel tilts the balance in the complex hylomorphic relation between form and matter, so that whereas for Aristotle, form — as the way of being of a thing, or its effectively operative orientation to ends — has a kind of conceptual priority over materiality, Hegel wants to emphasize that our very discernment of Aristotelian form depends on mediation. Hegel is also influenced by Kant’s talk about form and content, which pushes over to the side of content much of what Aristotle treated as form. (See Mutation of Meaning.)