The Ontological Argument
P1: God is the greatest conceivable being (the being “than which nothing greater can be conceived”).
P2: If such a being didn’t exist in reality, you could imagine a being just like it except your imaginary being does exist in reality. In other words, if the greatest conceivable being didn’t exist in reality, you could conceive of a being greater than the greatest conceivable being.
P3: But that’s a contradiction (an absurdity): It’s not logically possible to conceive of a being greater than the greatest conceivable being.
C: Therefore, God, the greatest conceivable being, must exist in reality.
Descartes’ Version (in Meditation V)
P1: God is the greatest conceivable being.
P2: The greatest conceivable being must possess all perfections to the highest degree.
P3: Existence is a perfection. (An existing X is always better – more perfect – than an imaginary or non-existent one.)
C: Therefore, God, the greatest conceivable being, must exist.
You might think both these arguments are circular — that they assume in advance exactly the point they are trying to prove. Why? P1 in both cases already appears to state that “God is the greatest conceivable being”. But he couldn’t be greatest conceivable being if he didn’t exist already. Yet Anselm and Descartes were both good logicians; they wouldn’t advocate an obviously circular argument.
Rather, P1 in both arguments is not an implicit claim that God already exists; rather, it is intended as a claim about the meaning or definition of the word “God”. P1 should be re-written as follows, adhering to conventions regarding use and mention:
P1: “The word ‘God’ means ‘the greatest conceivable being’.”
The subject of P1 is now a word, not a being. So circularity isn’t the real problem. The critiques that follow are more to the point.
“Perfections,” whatever else they may be, are at least predicates. So by modus tollens, if existence if not a predicate, it can’t be a perfection. The argument goes:
P1: If existence is a perfection, it’s a predicate like other predicates.
P2: Existence is not a predicate like other predicates.
C: Therefore, existence is not a perfection.
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