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Reading Kit Fine's old paper on the varieties of necessity. He claims, with provisos, that there are three kinds of necessity irreducible to any of the other two. Metaphysical necessity, natural necessity and normative necessity. It is interesting that each notion of necessity yields a way to conceive of metaphysics. I'd also add what Fine calls logical necessity in the narrow sense - as opposed to logical necessity in the broad sense that would coincide with metaphysical necessity - necessity associated with identities. In fact, metaphysical necessity is connected to a project like Aristotle's ontology of substances: metaphysics as

an a priori necessary endeavor concerning things in themselves and about matters of fact.

A logical necessity in the narrow sense would be associated to the idea of metaphysics as logic:

an a priori necessary endeavor concerning things in themselves and about matters of reason

(a priori knowledge understood either as conventional or as guided by intellectuelle Anschauung). Fine takes natural necessity to be what is typically taken to be necessary and a posteriori. If cats are animals, this is naturally necessary. Fine argues that still there could be, say, Putnam-cats in another possible world that wouldn't be cats but something else that would necessarily be robots. Cats are (naturally) necessarily animals in this world but they are not (metaphysically) necessarily animals because this (natural) necessity doesn't preclude the existence of Putnam-cats in a possible world. If this is so, natural necessity is not metaphysical necessity. Then we can conceive of metaphysics based on natural necessity and take it to be

an a posteriori necessary endeavor concerning things in themselves and about matters of fact.

To complete, we have the Kantian notion of metaphysics based on normative necessity according to which it is

an a priori necessary endeavor concerning things for us and about matters of fact.

Thinking of M4 in Aristotle's Metaphysics, we can take Kant's conception of metaphysics as dealing with the absence of substantiality that makes all sensible things be in a perpetual flow. If there is no knowledge of the accidental because it carries no necessity (no substantiality) - and that means it carries no metaphysical necessity and arguably no natural necessity - then the only necessity left in normative. If there is no knowledge of the non-necessary we make it necessary by norms - at the price of making the judgments limited to what there is for us. We somehow impinge necessity on things (on phenomena) to make them intelligible to us - and known, to us.


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