I sort of agree with the other commenter: this argument conflates metaphysical and epistemic modality. Suppose that a world is a set of propositions. We interpret someone saying "Dialetheism might be correct" (where "might" is an epistemic modal) as: at least one of the worlds that represent that person's epistemic state has a contradiction. There is nothing about this that prevents us from saying that a possible world is a maximal consistent set of propositions. It's just that the set of possible worlds won't contain the set of worlds that are epistemically possible for that person.
If there's a world that has a contradiction, then worlds aren't maximal consistent sets of propositions; if there's a contradiction, it's not consistent!
Correct me if I'm missing something, but I thought that the speaker in premise 1 would be using "might" in an epistemic sense, not in a modal sense. I assume that if dialetheism is false (as it seems to be!), then it's necessarily false. But for the argument to work, we've got to know that "there's a possible world in which dialetheism is true."
'Might' is a modal term. There's no way to use the word 'might' in a non-modal sense. When you use 'might' in an epistemic sense, it's an "epistemic modal."
The standard semantics for all modal terms (including 'might'), as they are used in any context, involves quantification over "possible worlds."
I don't know what you mean by an "epistemic modal." That sounds like a conflation of two things. If the votes in an election have been cast, but not tallied, and I say "Smith might be the winner"-- "not could have been" -- that just means "as far as I know, Smith is the winner." Likewise, the student is saying "as far as I know, dialetheism is true" not "there exists a possible world in which it's true."
"Modal" is a linguistic category, not a metaphysical category. When you use a modal term like 'might' to refer to something epistemic, that's known as an "epistemic modal." There is a huge literature on epistemic modals.
"Smith might be the winner" means "there exists a possible world where Smith is the winner" according to standard linguistic models of modals. See Angelika Kratzer's "The Notional Category of Modality."
"Smith might be the winner" means "there exists a possible world where Smith is the winner" according to standard linguistic models of modals.
So philosophers have imported this possible world talk to epistemic uses of "might" too? Very strange. But the standard objection to the modal ontological argument is that it conflates metaphysics and epistemology. The fact that *as far as I know God exists* doesn't allow you to run Plantinga's argument. I see the same mistake here.
It's more accurate to say that possible world talk was resurrected from its Leibnizian grave in order to explain what's going on with modal terms like 'might,' as used in any context. But remember, CARNAP was the guy who did this; he wasn't talking about "possible worlds" in any metaphysically weighty sense. "Possible worlds" are just a kind of dummy variable for the domain of quantification in quantified modal logic.
There are SO MANY problems with Plantinga's modal ontological argument I hardly know where to start. One of the problems is that he treats possible worlds as something more than a dummy variable for the domain of quantification in QML.
I sort of agree with the other commenter: this argument conflates metaphysical and epistemic modality. Suppose that a world is a set of propositions. We interpret someone saying "Dialetheism might be correct" (where "might" is an epistemic modal) as: at least one of the worlds that represent that person's epistemic state has a contradiction. There is nothing about this that prevents us from saying that a possible world is a maximal consistent set of propositions. It's just that the set of possible worlds won't contain the set of worlds that are epistemically possible for that person.
If there's a world that has a contradiction, then worlds aren't maximal consistent sets of propositions; if there's a contradiction, it's not consistent!
I only said that a world is a set of propositions.
Ah! Well then, we're in agreement. Worlds are sets of propositions. They are not maximal consistent sets of propositions. (That is my whole point.)
Ah I see. To be clear I am saying that this is compatible with the view that *possible* worlds are maximally consistent sets of propositions.
Correct me if I'm missing something, but I thought that the speaker in premise 1 would be using "might" in an epistemic sense, not in a modal sense. I assume that if dialetheism is false (as it seems to be!), then it's necessarily false. But for the argument to work, we've got to know that "there's a possible world in which dialetheism is true."
'Might' is a modal term. There's no way to use the word 'might' in a non-modal sense. When you use 'might' in an epistemic sense, it's an "epistemic modal."
The standard semantics for all modal terms (including 'might'), as they are used in any context, involves quantification over "possible worlds."
I don't know what you mean by an "epistemic modal." That sounds like a conflation of two things. If the votes in an election have been cast, but not tallied, and I say "Smith might be the winner"-- "not could have been" -- that just means "as far as I know, Smith is the winner." Likewise, the student is saying "as far as I know, dialetheism is true" not "there exists a possible world in which it's true."
"Modal" is a linguistic category, not a metaphysical category. When you use a modal term like 'might' to refer to something epistemic, that's known as an "epistemic modal." There is a huge literature on epistemic modals.
"Smith might be the winner" means "there exists a possible world where Smith is the winner" according to standard linguistic models of modals. See Angelika Kratzer's "The Notional Category of Modality."
"Smith might be the winner" means "there exists a possible world where Smith is the winner" according to standard linguistic models of modals.
So philosophers have imported this possible world talk to epistemic uses of "might" too? Very strange. But the standard objection to the modal ontological argument is that it conflates metaphysics and epistemology. The fact that *as far as I know God exists* doesn't allow you to run Plantinga's argument. I see the same mistake here.
It's more accurate to say that possible world talk was resurrected from its Leibnizian grave in order to explain what's going on with modal terms like 'might,' as used in any context. But remember, CARNAP was the guy who did this; he wasn't talking about "possible worlds" in any metaphysically weighty sense. "Possible worlds" are just a kind of dummy variable for the domain of quantification in quantified modal logic.
There are SO MANY problems with Plantinga's modal ontological argument I hardly know where to start. One of the problems is that he treats possible worlds as something more than a dummy variable for the domain of quantification in QML.