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Heidegger makes the distinction between the ontic (concerning beings themselves) and the ontological (the being of beings, being as such).

Would it be wise to say that the ontic covers the contingent possibilities concerning beings and the ontological concerns the universal and necessary structures that makes those beings possible? (a posteriori/priori)

One place where I can see this definition failing is that suddenly the ontic sciences, physics for example, are now “degraded” to studying just the contingent possibilities of beings, which hardly seems like the right categorization. In this definition, however, the sentence “the ontic fact that Dasein is ontological” makes much more sense, along with “the ontological fact that Dasein is pre-ontological.

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  • Not really, necessary/contingent are analytic terms that Heidegger is not concerned with, and a priori/ a posteriori are even further. Your could say crudely that ontic is about essence/descriptive and ontological is about existence/visceral, see Heideggerian terminology and Ontic vs. Ontological here.
    – Conifold
    Commented Oct 17, 2021 at 20:12

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Heidegger in his Kantbuch says that a synthetic cognition is one that is "revealed" by being itself. In turn, what is known in a priori cognitions is independent of what is experienced in certain contingent conditions, indeed, as opposed to a posteriori, ontic knowledge of particular beings.

Heidegger then interprets Kant's "Copernican Revolution" as saying that every ontic, a posteriori, cognition is grounded in ontological cognitions - synthetic, "revealed" by being, and a priori, related to Being as such, cognitions. This, Heidegger emphasizes, doesn't deconstruct the old definition of truth as adequacy of cognition to its object, but rather reasserts it, giving it a new meaning through the project of fundamental ontology.

As Heidegger sees it, Kant's 'critique of pure reason' is properly understood as an attempt at grounding ontological cognition, i.e. fundamental ontology, in 'anthropology'. Heidegger emphasizes especially the question What is man? found in Kant's Critique as the proper question of the ontological investigation. Since Dasein is us, as you say, this makes good sense of various Heidegger's claims about the relation of the ontological to Dasein.

Important note: This is quite a bold interpretation, but Heidegger was nevertheless a careful reader of Kant. He attempted to explore a dimension of Kant's writings which was ignored by his neo-Kantian predecessors, who understood Kant as doing primarily philosophy of science. And some of his claims, if we abstract from his obscure terminology, aren't really that controversial - Kant, indeed, as Heidegger says, is concerned with finitude of man, among other topics.

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