We reveal their essential dependence on the value of p, which resembles the difference in the classical theorems of Bourgain and Bachelis Ebenstein on Λ(p -sets.
His specific contributions were many and deep; but they include, for example, his principle of radical difference, his principle of thought's essential dependence on and bounding by language, and his principle of holistic interpretation.
Schlegel and von Humboldt were in particular both fundamentally motivated by the Herder-inspired insight that because of thought's essential dependence on and bounding by language and the radically different ways of thinking supported by different languages, the empirical study of languages can afford a sort of window onto the radically different ways of thinking in question.
When analyzing gg/ gt/ tg conformations of ω dihedral angle, there is an essential dependence on the model used for the calculations.
One obvious reason for this is that if one adopts the usual "modalist" analysis of essence, essential dependence will collapse into a form of modal-existential dependence (one classic defence of the "modalist" analysis is Marcus 1967).
Seen in this light, identity-dependence as defined by (ID) is simply a species of essential dependence, that is, a way in which the essence of a certain thing is determined by a relation in which it stands to another thing.
The latter varieties of ontological dependence may accordingly be called species of essential dependence.
The notion of essential dependence, which involves requirements for identity or essence, may better express what God's supposed ontological independence is about.
It should also be noted that even though the notions of essential dependence defined above are no doubt more fine-grained than the modal-existential notions, there may be reasons to think that even they are not sufficiently fine-grained for all purposes (as argued in Koslicki 2012).
However, even though x is necessarily identical with the sole member of {x}, it is plausibly not part of the essence of x that x is the sole member of {x} (cf. Fine 1994a: 4–5; see also Fine 1994b for a related discussion of the notion of essence and essential dependence).
