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Anselm's Ontological Argument
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1. G-d exists in the understanding.
2. G-d might have existed in reality (G-d is a possible being).
3. If something exists only in the understanding and might have existed in reality, then it might have been greater than it is.
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From these three basic premises. Anselm believes, it follows that G-d exists
in reality; i.e. if we accept (1) - (3), we are committed by the rules of logic that
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4. If G-d is understood as "the being than which none greater is possible," G-d must necessarily exist not only in the understanding, but in reality as well."
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Instead of showing, however, that the existence of G-d follows directly from steps (1) through (3), Anselm invites us to suppose that G-d does not exist and then he proceeds to show by a reductio ad absurdum argument that if we suppose as much, such a supposition combined with (1) through (3) will lead to an absurd and/or contradictory result. Since the supposition that G-d does not exist leads to an absurdity, it must be replaced by the conclusion that G-d does exist.
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4'. Suppose G-d exists only in the understanding.
5. G-d might have been greater than He is.
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Step (5) follows from steps (2), (4') and (3)
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6. G-d is a being than which a greater is possbile.
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If we accept steps (1) through (4'), we must accept (6), but (6) is unacceptable. (6) is the absurdity Anselm was after. By substituting "G-d" in (6) with "the being than which none greater is possible, we get
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7. The being than which none greater is possible is a being than which a greater is possible.
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If we accept that steps (1) through (3) are true, then we must reject (4') as false:
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8. It is false that G-d exists only in the understanding.
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And since step (1) tells us that G-d exists in the understanding, and (8) tells us that G-d does not exist only there, we can conclude that
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9. G-d exists in reality as well as in the understanding.
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