Sentence examples for equivalent proposition from inspiring English sources

Conversion yields an equivalent proposition (and is hence a valid inference) in general only with so-called E and I propositions (universal negatives and particular affirmatives).

It seems that the equivalent proposition is a known fact.

It indeed generalizes the Axiom of propositional extensionality mentionned by Church 1940, which states that two logically equivalent propositions are equal.

Some understand this as the warrant failing as a warrant for equivalent propositions.

Russell, however, sticks to an intensional point of view, stressing that equivalent propositions often can be quite different.

Interestingly this is connected there to the question of the identity of equivalent propositions and of the logical product of a class of propositions.

Of course, if one were to adopt the extensional point of view, and hence identify equivalent propositions, the contradiction above could not be derived.

Jaynes' invariance condition bids us to assign equal probabilities to equivalent propositions, reformulations of one another that are arrived at by such admissible transformations of our problem.

But as a first approximation to the concept, we will assume that it is not hyperintensional and that logically equivalent propositions have the same degree of truthlikess.

First, as was mentioned above, structured proposition accounts, unlike possible world accounts of propositions, allow for distinct necessarily equivalent propositions, and thus individuate propositions more finely than possible worlds accounts.

Since the structured proposition expressed by a sentence has a structure similar to that of the sentence and has as constituents semantic values of expressions occurring in the sentence, the theory of structured propositions allows for distinct necessarily equivalent propositions.