I will warn everyone that my arguments are very technical, and if you are unfamiliar with the concepts of modal logic, I encourage you to stop and read this primer on modal logic: https://plato.stanford.edu/entries/logic-modal/. 

S5 Modal Logic

Modal logic is a type of logic used to represent and study statements about what is necessary and what is possible. We use modal logic to understand concepts such as knowledge, obligations, and causations [1].

In modal logic, we can divide beings into three categories:

1. A necessary being - A being that exists in all possible worlds, including the actual one. 
2. A contingent being - A being that could exist in a possible world but could fail to exist in others. 
3. An impossible being - A being that exists in no possible worlds, often due to being logically incoherent. 

In addition, we can divide worlds into three types:

1. The actual world - The world we live in
2. A possible world - A world that could have existed 
3. An impossible world - A world that could never exist 

In S5 modal logic, all possible worlds are accessible from each other, which means that what is possible, true, or necessary is consistent across the modal landscape. 

The MOA

Let a maximally great being ( MGB hereafter) = A maximally great being who possesses all great-making properties, including, but not necessarily limited to:

1. Moral perfection 
2. Maximal knowledge
3. Maximal power 
4. Present everywhere 
5. Necessary existence 

Here is Alvin Plantinga's modal ontological argument [2]: 

1. It is possible that an MGB exists.  

2. If an MGB may exist, then a maximally great being exists in some possible worlds.

3. If an MGB in some possible world, then it exists in every possible world.

4. If an MGB exists in every possible world, then it exists in the actual world.

5. If an MGB exists in the actual world, then a maximally great being exists.

6. Therefore, an MGB exists.

1. It is possible that a maximally great being exists

When we state that it is possible for a maximally great being to exist, we are saying that there is a possible world in which there is an MGB. This MGB would possess all great-making properties to the maximum degree. This first premise is modest and only suggests that such a being is possible.

This premise is reasonable because there is nothing logically incoherent about such a being. 

2. If an MGB may exist, then a maximally great being exists in some possible worlds. 

Premise 2 is a logical continuation of modal logic. If something is possible, then it is possible in some possible state of affairs and some possible world. In addition, if something is possible in one world, then due to the accessible relationship between worlds in S5 logic, it holds that it is possible in every single possible world. 

3. If an MGB in some possible world, then it exists in every possible world.

Because an MGB is defined as having all great-making properties, including necessary existence, then by definition it must exist in every single possible world. 

4. If an MGB exists in every possible world, then it exists in the actual world.

By definition, our world is a possible world. 

5. If an MGB exists in the actual world, then a maximally great being exists.

6. Therefore, an MGB exists.

These follow logically from premise 4. If such a being exists in the actual world, then such a being exists. 

Conclusion

The first premise of the MOA is modest - it is merely possible that such a being exists. Within the S5 framework, we have shown that if it is even possible for an MGB to exist, then such a being must exist in every possible world, including the actual.

I look forward to your rebuttals.

Sources

1. https://en.wikipedia.org/wiki/Modal_logic

2. https://plato.stanford.edu/entries/ontological-arguments/#Moda