equivalent propositions

equivalent propositions

[i‚kwiv·ə·lənt ‚präp·ə′zish·ənz]
(mathematics)
Two propositions, either of which is true if and only if the other is true.
References in periodicals archive ?
With this we derive one of the most important, but also most problematic, doctrines of the Tractatus, namely, that necessarily equivalent propositions are identical.
"a is a thing x such that x is both large and seaworthy"), typically express different albeit logically equivalent propositions. Saul Kripke objects on three independent grounds: (i) the alleged distinction can be employed to challenge the legitimacy of the standard proof of the necessity of identity, as well as the author's own proof of the universal determinacy of identity; (ii) the alleged distinction leads to an implausible proliferation of k-convertible contents; and (iii) neither Bertrand Russell nor Alonzo Church drew such a distinction in content, and they were correct mathematically not to do so.
Another concern with the possible-worlds reduction is that it implies that all necessarily equivalent propositions are identical--a plainly unacceptable consequence.
But if they expressed distinct but necessarily equivalent propositions, then it would seem utterly mysterious how adopting a propositional attitude to a given content just is to adopt that attitude to the content expressed by the corresponding truth ascription.
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