Free Logic and a Modal Ontological Logic Argument.

I have begun studying "non-predicate" logics (non-Aristotelian/Fregian) such as "Free Logic" and the modal logics. (There is a predicate logic tutorial here.) Because they go so far outside the standards of universals-grounded, deduced, necessary and sufficient, premise/conclusion-type of logic, they are difficult to follow, at least at first. And I currently have no idea of their value for determination of personal worldviews. Deontic logic, for example, seems related to the personal assumption of moral authority, which in turn presupposes Atheism as an unsupported axiom.

Modal Ontological Logic deals with the probabilities of what is "possible" and "necessary". Plantinga offers this Modal Logic argument for the existence of God. I usually don't present arguments (theodicies) like this, since they devolve into disputations of the meanings of words, rather than the premised existence of events and things.

Perhaps Atheists would care to use their logical capacities to refute this argument.

From Philosophy of Religion:

Plantinga favours a possible world analyis of statements about possibility and necessity. Possible worlds are ways that the world might have been. Any logically consistent description of a world is a possible world. On Plantinga’s view, to say that something is possible is to say that there is a possible world in which it is actual, and to say that something is necessary is to say that in every possible world it is actual.

The modal ontological argument, like Anselm‘s, begins with a statement about God. God, if he exists, is a necessary being. That is, if God exists at all then he exists in every possible world.

The next element in the modal ontological argument concerns the possibility that God exists. It is possible that God exists, according to the modal ontological argument. These two claims are sufficient, according to the modal ontological argument, to establish the existence of God.

For if it is possible that God exists, then there is some possible world in which God exists. If God exists in some possible world, though, then, because he is a necessary being, he exists in all possible worlds. God, then, exists in all possible worlds. If God exists in all possible worlds, though, then he certainly exists in this one. God, therefore, exists.

A more formal analysis of this argument goes like this:

(1) If God exists then he has necessary existence.

(2) Either God has necessary existence, or he doesn‘t.

(3) If God doesn‘t have necessary existence, then he necessarily doesn‘t.

Therefore:

(4) Either God has necessary existence, or he necessarily doesn‘t.

(5) If God necessarily doesn‘t have necessary existence, then God necessarily doesn‘t exist.

Therefore:

(6) Either God has necessary existence, or he necessarily doesn‘t exist.

(7) It is not the case that God necessarily doesn‘t exist.

Therefore:

(8) God has necessary existence.

(9) If God has necessary existence, then God exists.

Therefore:

(10) God exists.

The first premise is based on the idea that God is perfect, and that something is better if it has necessary existence than if it has merely contingent existence.

The second premise of the argument is simply the law of the excluded middle.

The third premise, “Becker’s Postulate”, is a widely accepted principle of modal logic. All modal properties are generally accepted to be necessary.

Four follows straightforwardly from the second and third premises.

Five is entailed by premise one.

Six follows from four and five.

Seven is plausible at first glance, but is widely thought to be the greatest point of weakness in the argument.

Eight follows from six and seven.

Nine is self-evident.

Ten follows from eight and nine.

There is an alleged refutation from a person self-appellated "The Incredible Halq", here.

However, his argument is less with Plantinga's specific argument than with the concept of modal logic, itself.

If one insists on first order predicate logic (which follows universal axioms and empirical observations) for the rational basis for one’s worldview, perhaps the higher order and modal logics are not applicable. I suspect that they are objects of curiosity more than utility for worldviews, unless, like Nietzsche, the observable is rejected, which negates classical logic in favor of AntiRationalism.