"argument of incompatibility" is a correct and usable phrase in written English.
You can use it when discussing two incompatible ideas or courses of action. For example, "Since the proposed policy would prevent us from achieving our goals, we can use an argument of incompatibility to show why it shouldn't be implemented."
Arguments for incompatibility are usually of two kinds.
Unless there is something wrong with one of these two arguments, the argument for the incompatibility of free will and determinism or the argument for the incompatibility of free will and the falsity of determinism, free will is impossible.
Another type of incompatibility argument (McKinsey (1991), Brown (1995), Boghossian (1998)) aims to show that externalism leads to some implausible conclusions about what can be known a priori.
(See also Gallois and O'Leary-Hawthorne (1996).) Davies (1998) and Wright (2000) offer a different reply to this second type of incompatibility argument.
It would merely mean that one argument for the incompatibility of determinism and regulative control is untenable.
His philosophical analysis and the quest for formalisation of the arguments for "the incompatibility of foreknowledge (and fore-truth) and indeterminism" lead him to consider two formalizations of temporal logic of branching time, reflecting the "Ockhamist" (or "actualist") and "Peircean" views mentioned earlier.
First, there is van Inwagen's point, namely that arguments for the incompatibility of abilities and determinism are, inter alia, arguments against any theory of ability that is congenial to the compatibilist.
We paid the price of incompatibility for a long time.
The court therefore grants a certificate of incompatibility".
They can only issue a "declaration of incompatibility".
Only if this is not possible should they make a declaration of incompatibility.
