**Premise 1):** A necessary and maximally great being “B” possibly exist.

Every atheist I’m aware of will reject this premise. Many of them, who think theism is coherent, will still reject this premise. The reason why is directly due to the confused modal nature of the premise itself.

When you stipulate that a being is a necessary one, you are by consequence also stipulating that that being possibly exists. Let us translate this into talk about propositions (*pace* modality *de dicto* instead of modality *de re*). [1] One particular system of modal logic is called the Brouwer system. That system has a characteristic axiom. The axiom is: [L = the necessity operator; M = the possibility operator; p = a maximally great being exists]

(1) If p, then necessarily, possibly, p. [2]

(1’) If p, then *LM*p.

It’s clear from (1) and (1’) that when one says that p is true in a, then it is necessarily the case that p is possibly true. In other words, as soon as a proposition is true in the actual world, due to the nature of modal accessibility, that same proposition is possibly true in all other possible worlds. Your first premise is like (1) but you’ve chosen to stick the necessity operator in the antecedent, and put erase the necessity operator in the consequent.

Your first premise when understood in terms of modality *de dicto*, is saying:

(Premise 1) If necessarily p, then possibly p. [3]

Well, this premise is an obvious truism. If p is true in all possible worlds, then of course p is possible, since it’s true in all possible worlds. If it were impossible it couldn’t even be true in one possible world. Interestingly, because you have the necessity operator governing p in the antecedant, your argument (and premise 1) **begs the question**. As soon as someone admits that p is necessary, by virtue of that admission **you have** the existence of that maximally great being you’re trying to prove. So in order for me to accept the soundness of your argument I have to accept premise one, **but premise one has as its antecedent the claim that this maximally great being exists necessarily**, thus **one of your premises contains the conclusion you’re arguing for**. This is a fallacy in logic known as *petitio principii*. [4] Your argument is therefore invalid.

**Premise 2):** Therefore “B” exists in some possible worlds.

According to your first premise, B would actually exist in all possible worlds, not just “some” possible worlds. Why? Because you stipulate **in the antecedent** of premise one that this being is a necessary being.

**Premise 3): **If “B” exists in some possible worlds, then “B” must exist in all possible worlds.

This already follows from premise one.

**Premise 3a): **If “B” exist only some possible worlds, and not all possible worlds then “B’s” existence is contingent.

Yes.

**Premise 3b):** “B” however can not be necessary and contingent (law of non-contradiction)

The proposition p is necessarily true, and the proposition p is contingent do not contradict each other. The law of non-contradiction (LNC) is ~(p &~p). The proposition p is necessarily true may entail p is not contingent, but it itself does not contradict the statement p is contingent, it only entails the truth of a proposition which contradicts the statement about p’s contingent truth.

**Premise 4):** Since “B” exists in all possible worlds then “B” would exist in the actual world (since the actual world is a sub-set of the set of possible worlds)

** **

There is nothing wrong with this statement. I am curious about your use of the word “since.”

**Premise 5)**: Therefore “B” exists in the actual world.

** **

Again this follows from premise one alone.

**Premise 6)** Therefore “B” (which is a necessary and maximally great Being) exist.

Edit your argument, and make grammatical changes as well please. I’d love to see how you change it in light of the aforementioned criticisms.

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[1] Modality *de dicto* is modal talk about propositions, where as modality *de re* is modal talk about the exemplification of properties and their complements. Modality *de re* is also concerned with the mode of existence certain beings enjoy, i.e., whether the beings in view are contingent, or necessary. See Alvin Plantinga, *The Nature of Necessity *(Oxford: Clarendon Press, reprint 1982), 9-13; Alvin Plantinga, “De Re et De Dicto,” in Matthew Davidson (ed.), *Essays in the Metaphysics of Modality *(New York, NY: Oxford University Press, 2003), 25-45.

Recall that a being exists by necessity, or is a necessary being iff (this means “if and only if” by abbreviation) that being exists in all possible worlds. Recall that a being exists contingently, if it exists in the a (this represents the actual world), and does not exist in all other possible worlds. See Alvin Plantinga, *The Nature of Necessity *(Oxford: Clarendon Press, reprint 1982), 55-62.

[2] Michael J. Loux, “Introduction,” in Michael J. Loux (ed.), *The Possible and the Actual: Readings in the Metaphysics of Modality *(Ithaca, NY: Cornell University Press, 1979), 23.

[3] If Lp, then Mp.

[4] Irving M. Copi and Carl Cohen, *Introduction to Logic *(Upper Saddle River, NJ: Pearson Prentice Hall, twelfth edition 2005), 151.