In claiming that the right of nature is coextensive with the power of nature and that the coextensivity of right and power applies mutatis mutandis to the individuals in nature, Spinoza is simply rejecting non-naturalism, rather than making a positive normative claim.
The two notions are not coextensive.
These definitions are not perfectly coextensive.
Of course the concepts may be coextensive.
To that freedom corresponds a coextensive responsibility.
To be sure, few people are guilty of such blatant lapses, but we can certainly make mistakes when necessarily coextensive properties are described in more complicated ways (such errors are routine in mathematics and logic).
Two ideas A and B are compatible if they have (represent) at least one object in common, i.e., if at least one object falls under both A and B. In the case in which not only some but all objects represented by A are also represented by B, A is included in B. If this relation is reciprocal, i.e., if A is included in B and B included in A, the ideas A and B are equivalent (coextensive).
Let '\(X\)' abbreviate the definite description 'the quale distinctive of Humbert's experiences of red things' (by hypothesis, this definite description is coextensive with 'the quale distinctive of Nonvert's experiences of red things in the counterfactual inversion scenario').
Although these two theses are advanced separately, they are mutually coextensive.
Inspired by the theory of descriptions, Russell proposed that to say something $G$ of the class of $F$s, $G$$$\{x: Fx \}$, is to say that there is some (predicative) property $H$ coextensive with (true of the same things as) $F$ such that $H$ is $G$.
Whereas Field takes this as an argument to the effect that mathematical necessity is not coextensive with logical necessity, one could turn the tables around: mathematical necessity is unrestricted, so false mathematical theories are just impossible theories.
