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Wednesday, May 08, 2013

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Does "necessarily true" imply "necessarily existent?" I think not.

Take the de re assertion "Socrates exist." (I'll get to de dicto assertions later) That assertion could have been false. If it had been false (taking 'exist' tenselessly) then there would not have been any x for the subject to refer to. It's not just that the word 'Socrates' would not have referred to him, but there couldn't be any proposition that said of him that he exists, since there would be no him, no res for the de re assertion to be about. Yet, surely it is in some sense true that "Socrates exists" would have been false if he had never been born.

No problem: The assertion exists in the actual world, and it misdescribes world W, so we can say that's what it is for the assertion to be false at W: The state of affairs that the proposition indicates is not such in the world about which we are asking. Perhaps we should distinguish "p is true in W" (meaning that, in W, p points to a state of affairs that obtains) from "p is true of W (meaning that the state of affairs pointed to by p [which pointing occurs in the actual world] obtains in W).

Once we make this distinction, we can apply it to de dicto assertions as well. And then the inference from necessarily true to necessarily existent will not work if "necessarily true" means true of every possible world. It will work if "necessarily true" means true in every possible world. But no one will grant that the assertion is true in every possible world without independent reason for believing that the proposition exists in those worlds.

Thank you for the intelligent comment. The move from 'p is necessarily true' to 'p is necessarily existent' does need examination.

I am concerned above with Fregean as opposed to Russellian propositions. If 'The Charles River is polluted' expresses a Fregean proposition, then the Charles itself is not a constituent of the proposition. If 'Socrates exists' expresses a Russellian proposition, then the proposition has Socrates himself, warts and all, as a constituent. I would agree with you that a possible world at which that Russellian proposition is false needn't be, indeed can't be, a world in which that proposition exists.

When I say that a Fregean proposition is necessarily true, I mean that it is true in every broadly-logically possible world. To which you object:

>>But no one will grant that the assertion is true in every possible world without independent reason for believing that the proposition exists in those worlds.<<

This is where I don't follow you. The proposition *7 is prime* is necessarily true. That is to say: Given the way things are and all the total (maximal) ways things might have been, the proposition is true. It is true in every possible world. But truth is a property (assumption that could be questioned) and if an item has a property, then that item exists (a second assumption that could be questioned), so, given that *7 is prime* is true in every world, *7 is prime* exists in every world.

A world, after all, is just a maximal (consistent) proposition. To say that *7 is prime* is necessarily true is just to say that every maximal proposition entails *7 is prime.* But a proposition p cannot entail a proposition q unless both exist. Therefore, *7 is prime* exists in every world. That's equivalent to saying that every maximal proposition has the proposition in question as a conjunct.

This paper arguing that the laws of logic being divine thought might interest you. It covers similar ground to what your post covers.

http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf

I've studied it. In fact, the above entry is preliminary to a discussion of it.

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