If no contradictions can obtain, conditionals with contradictory antecedents have empty domains of evaluation, and vacuous truth is the correct semantic verdict regardless of variable sharing.

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Antecedent(referring to causal conditions that would exist before Plato's decision): Something that comes before something else in time; in this case, an earlier event or cause.
Domain of evaluation(as used in semantics and logic): The set of situations, possibilities, or contexts that a logical statement is being checked against to see if it's true or false.
conditional(no-truth-value account of conditionals): A statement of the form 'if A, B' that involves the supposition that A and tells us nothing about what happens if A is false
contradictions(as something Descartes thought God could have made true): Two statements that cannot both be true at the same time, like 'it is raining' and 'it is not raining' happening together.
semantic(describing the level of word meaning): Relating to the meaning of words and sentences.
vacuous truth(Grounds the classical validity of (p → q) ∨ p): A conditional with a false antecedent is considered true regardless of the consequent in classical logic
variable sharing(a requirement some modern logicians argue for): In logic, this means that the symbols or ideas used in your starting assumptions must also appear in your conclusion—you can't pull new ideas out of nowhere.

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