If necessary existence is incoherent as a real predicate, the contrast between contingent and necessary beings that the argument's force entirely depends upon collapses, undermining both the regress-independent and regress-dependent versions equally.

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Incoherent(describing whether moral responsibility can exist): Logically impossible or contradictory; something that cannot make sense or cannot exist at the same time as something else.
Necessary existence(Contrasted with contingent existence in discussion of God's mode of being): Existence that is not contingent; the being does not just happen to exist or not exist.
Regress-independent and regress-dependent versions(philosophy of religion and logic): Two different forms of the cosmological argument: the regress-independent version claims we need a first uncaused cause to stop the chain; the regress-dependent version says the universe itself needs an explanation or cause.
contingent being(Boethius's characterization of human beings to counter necessity-based arguments): A being whose existence is not necessary — it can fail to exist

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