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Source material:

Proslogium - https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp

Why the God-man? (Cur Deus Homo) - https://sourcebooks.fordham.edu/basis/anselm-curdeus.asp

Anselm's ontological argument for the existence of God:

By definition, God is the greatest possible being that can be imagined.

God exists as an idea in the mind.

A being that exists as an idea in the mind AND in reality is greater than a being that exists only as an idea in the mind.

Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God.

But we cannot imagine something that is greater than God (for it is a contradiction to imagine a being greater than the greatest possible being that can be imagined.)

Therefore, God exists.