What is the difference between "nature" (φύσις) and "essence" (οὐσία)? And how should we understand "substance" and "energy" in the Orthodox Patristic tradition?
In the theology of the Fathers, from the fourth century onwards, these terms became synonymous (this is not the case, however, in philosophy, where "essence" is one thing and "nature" another). So, the nature or essence of God, according to the Holy Fathers refers to the inner being of God, what God is in Himself, which is not only unknowable but also unapproachable, that aspect of God which is never-to-be-known, and so beyond definition (see St. Basil the Great, Letters 233-235). The Fathers taught that neither angels nor human beings are capable of knowing the inner being of God, of knowing or approaching the essence of God, neither in this life nor in the next.
Please also note that the Western term “substance” (Lat. substantia), in the Orthodox theological tradition, is understood as having the same meaning as nature and essence.
In Aristotelian philosophy, however, “nature” refers to the the innate urge to grow; “essence” is "form" and "structure". More specifically, “nature” denotes the innate natural urge that causes a thing to realize its “formal-final cause”, that is, it causes an offspring to grow into the “form” of its parent. “Essence” is the form or shape or structure of a thing, which determines its function. The Aristotelian supreme being - the Unmoved Mover - is pure form, inasmuch as it is perfect (and so static) and so no motion is needed for growth - its potential is by definition fully realized (entelechy). As you can see from my attempts to define these terms, the philosophical definitions belong to a completely different context and “world-view”.
And for fuller clarity on “energy” or “energies” in Patristic theology, these terms denote the life of God, His grace, and so His immediate active presence in the world, creating, sustaining, providing for, and (in the case of His reasonable creatures) sanctifying them. The divine energy is the natural or essential energy, that is to say, it is the energy of the divine nature or the divine essence, and is not therefore a separate entity, something other than, and apart from, God: it is in fact the life of God Himself.
In Greek philosophy, and specifically in the context of Aristotle’s concepts of “potential” (dynamis) and “actuality” (energeia), “energy” or “actuality” (energeia) signifies the realization of a thing’s “potential” (dynamis); thus the Aristotelian Unmoved Mover is pure “actuality” (energeia).
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For further information, see Christopher Veniamin, ed., Saint Gregory Palamas: The Homilies (Dalton PA: 2022).