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I have seen the term "trivial property" used several times, and some authors seem to be attributing it to Plantinga, but I cannot find his definition. I have seen others define it as a property necessary to x, regardless of what you take x to be.

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Plantinga uses the concept of non-trivial properties in his transworld depravity defense of God's benevolence, see How does free will defense of God's benevolence work? Ciprotti in Theological Compatibilism and Essential Properties discusses Plantinga's trivial and non-trivial properties with PDO (power to do otherwise, a.k.a. free will) as central example:

"According to him [Plantinga], a property P is trivial iff it constitutes a necessary condition for some thing to exist, e.g. being self-identical, being P or not-P, and the like. To the contrary, PDO does not seem so: for x to exist it is not required that x be free."

The reference for the definition is to Plantinga's Nature of Necessity (1974), Clarendon Press, NY, pp. 60-61. The notion of trivial is similar to what is called "essential property" by Kripke, but the sense of modality is strengthened from metaphysical to something close to logical. If an "essential property" is taken away from x it would not be x anymore, but what is "left" can logically exist, while removing a trivial property makes even that impossible. Plantinga intends it to be somewhat stricter than just logical, e.g. "being a creature" might still be trivial in his context.

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