- #1
nomadreid
Gold Member
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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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