I was reading Leibniz recently and had this epiphany, and thought why not see if any others out there might share a similar intuition.
Concerning Leibniz's two principles of identity
The princple of indiscernibility of identicals
Restated as I Am What I Think (or maybe ;I am identical to the methods I use to think.)
The first principle to me suggest that identity is a product of causality, that is, the causes and effects that together can give rise to a sense of identity ( and its relevant properties)
The second principle might suggest, intuitively, that any 'identity' is a principle product of the self organizing collection of properties ofitself, or that identity itself can give rise to causality.
The restatements at first where a intuition on what I thought Leibniz was trying to capture in his Laws of identity. Namely, two objects relative to each other are unique because of the intrinsic properties as opposed to their extrinsic.
The first principle is to suggest two entities are different by their extrinsic properties, which is why it is considered logical by many.
The second principle suggests the inverse of that notion, which is that two properties can exist distinct from each other only because of their intrinsic properties. This also is to suggest causality, namely space/time are not intrinsic.
My restatements where trying to capture the logic semantically. In the case of “I think, therefore …" seems to capture the intrinsic properties of a being, whereas “I am what I think” seems to capture the extrinsic properties. But I do feel I might be mixing other principles of Leibniz haphazardly, and on top of that I'm not by any means academically inclined on these subjects. So, at this point I'm all ears, and very appreciative of the input/feedback.