- #1

nomadreid

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## Main Question or Discussion Point

In the paper

John Corcoran & Hassan Masoud (2014): Existential Import Today: New

Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions, History and Philosophy of

Logic, http://dx.doi.org/10.1080/01445340.2014.952947,

already in the introduction it says, as self-evident, that "The universalized conditional

∀x(x = 0 → x = (x + x)) implies the corresponding existentialized conjunction

∃x(x = 0&x = (x + x)). And ∃x(x = 0) is tautological (in the broad sense, i.e. logically true)."

There are two assertions here, and I have difficulty with each one. In the first assertion I do not see why a model in which there is no 0 (e.g., ZFC* obtained by negating all the axioms of ZFC), so that the conclusion of the implication is false and the premise would be (vacuously) true, would not be a counter-example.

In the second assertion, I don't see why the statement is tautological (since it is not satisfied by all models, such as ZFC*).

John Corcoran & Hassan Masoud (2014): Existential Import Today: New

Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions, History and Philosophy of

Logic, http://dx.doi.org/10.1080/01445340.2014.952947,

already in the introduction it says, as self-evident, that "The universalized conditional

∀x(x = 0 → x = (x + x)) implies the corresponding existentialized conjunction

∃x(x = 0&x = (x + x)). And ∃x(x = 0) is tautological (in the broad sense, i.e. logically true)."

There are two assertions here, and I have difficulty with each one. In the first assertion I do not see why a model in which there is no 0 (e.g., ZFC* obtained by negating all the axioms of ZFC), so that the conclusion of the implication is false and the premise would be (vacuously) true, would not be a counter-example.

In the second assertion, I don't see why the statement is tautological (since it is not satisfied by all models, such as ZFC*).

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