(Despite the way he talks, Scotus does not mean here to deny that similarity is a reflexive relation; his view is that reflexivity is a property merely of what the medievals labeled "rational relations," and that the similarity that obtains between two distinct objects is not such a rational relation. The point is not worth dwelling on).
A reflexive relation is of course also quasi-reflexive.
The identity axiom and the rule of transitivity imply that ≥ is a transitive and reflexive relation.
It is easy to see that \(\leq_P\) is a reflexive relation.
Usually it is defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the principle of the indiscernibility of identicals, that if x is identical with y then everything true of x is true of y.
Neither denotative nor expressive, neither speaking of woman (as though woman were a determinate object of study) nor speaking as one (as though the aim were to express an inner essence), Irigaray's writing establishes a reflexive relation to language.
Trust annotations in types are subjected to a subtyping relation (spreceq s'), meaning that trust type (s) is a subtype of (s'), which is defined as the smallest reflexive relation (encoded as an inductive type) such that (the only non-reflexive element of relation (preceq ) is ) tr(preceq )dis.
More precisely, the referential structure in self-referential paradoxes such as the liar is a reflexive relation on a singleton set (a cycle), whereas the referential structure in Yablo's paradox is isomorphic to the usual less-than ordering on the natural numbers, which is a strict total order (contains no cycles).
A variety of incoherencies might be alleged here, including the incoherency of changing what is already fixed (causing the past), of being both able and unable to kill one's own ancestors, or of generating a causal loop and thus a reflexive relation of "self-causation", or of generating inconsistent probability assignments (Mellor 1995).
This can be justified, e.g., keeping fixed the usual interpretation of "0" and "N" but observing that "M" can be interpreted by means of the reflexive relation of being less than or equal to; under this interpretation, "∀x(Nx→¬Mxx)" is false, although "N0" is true.
