A Cartesian Ontological Argument

The following argument shall be in free logic:

D1. God is the x such that for all attributes Y, if Y is a perfection, Y belongs to x.
P1. Necessarily existing is a perfection
P2. For all x, if it is not the case that x exists, possibly it is not the case that x exists.
C. God exists.

Defense of the definition and premises:

D1: A defense of a stipulation should be addressed in three ways: (i) does the definition beg the question, and (ii) is the definition coherent, and (iii) is it fair to consider the definition a definite description, i.e. the description is uniqualizing.
With respect to (i), the argument is set within the context of free logic, where the “existential quantifier” does not carry existential import (i.e. the argument does not define God into existence in a question-begging manner). Moreover, this argument requires two premises that are quite independent from the definition of God. One cannot derive “God exists” from “God is the x such that for all attributes Y, if Y is a perfection, Y belongs to x” apart from the other premises. Therefore, the objection that the definition begs the question is incoherent.
With respect to (ii) it is important that we establish that the definition is coherent, since a contradiction buried in the definition could be the reason that we are able to derive our conclusion ex falso quodlibet. Leibniz’s proof for the self-consistency of the concept of a supremely perfect being is through an analysis of a perfection, which he says is simple, positive, and unlimited. If any two perfections are inconsistent, one of them would have to be negative, or contain a part that is negative. But a perfection cannot, by definition, be negative, or contain more simple conceptual parts. So any two perfections can cohere. Leibniz reasons that if this is so, then all perfections cohere, and so a being that has all perfections is coherent. Those who attempt parody, by the way, by posting perfect islands, pizzas, etc. must likewise demonstrate coherence, but with the added difficulty of positing some finite, or incomplete attributes, along with all perfections. If they skip such a proof an opt for an ad hoc list of perfections, including necessary existence, they will violate the first concern, and beg the question.

Lastly, (iii) you might say that there is no definite description of a perfect being, i.e. there could be multiple perfect beings. However, I would argue that there cannot be two omnipotent beings, since a simple reductio would rule out this possibility. That is, if there are two omnipotent beings, then any power the one has would be limited by whether or not the other being wills to bring about a contradictory state of affairs. Since they cannot both bring about contradictory states of affairs, they cannot both be omnipotent. So there cannot be two beings that have all perfections, given that omnipotence is a perfection. So “the” perfect being is necessarily unique, or definite.

P1: Necessary existence is a perfection because a perfection is any attribute that is of a simple kind that is positively complete. So, necessary existence is an attribute regarding the simple kind “modes of existence” that is positively complete. Existence is simple, since it is the most universal class, and so cannot be divided by genus and species, conceptually. Existence is positive, since to exist simply is “to posit in reality”/ Whatever exists necessarily exists in all possible situations, so it does not lack positive existence given any other state of affairs. Thus necessary existence is a perfection. One might object that “existence is not a perfection” or “existence is not a real predicate”. This is a slogan of Kant, but aside from appeal to Kant’s authority, there is little reason to think we cannot predicate existence of individuals. Moreover, while existence is not a predicate, it certainly is the case that necessary existence is a kind of perfection, and one that has always been traditionally ascribed to the God of Classical Theism.

P2: This is a statement of a completely uncontroversial modal axiom. The axiom says that if something is necessarily true (system M of modal logic), then it is true. Assume P2 is false: ~(~E!x ⊃ ♢~E!x), this is logically equivalent to saying ~E!x ∧ ☐E!x (x does not exist and necessarily x exists). Given system M, ☐E!x implies E!x, so P2 cannot be false. In order to object to P2, you would have to say that some necessary truths are not actually true, which is a blatantly absurd position to take.
The formal deduction is as follows:
Let,
E!x ≝ x exists
P(Y)≝ Y is a perfection
g ≝ (ɿx)(∀Y)(P(Y)⊃ Yx)
1. P(☐E!) (premise)
2. (∀x)[~E!x ⊃ ♢~E!x] (premise)
3. ~E!g (IP)
4. (∃x){[(∀Y)(P(Y) ⊃ Yx) ∧ (∀y)[(∀Y)(P(Y) ⊃ Yy) ⊃ (y = x)]] ∧ ~E!x} (3 theory of descriptions)
5. [(∀Y)(P(Y)⊃ Yμ) ∧ (∀y)[(∀Y)(P(Y)⊃ Yy) ⊃ (y = μ)]] ∧ ~E!μ (4 EI)
6. ~E!μ ⊃ ♢~E!μ (2 UI)
7. ~E!μ (5 Simp)
8. ♢~E!μ (6,7 MP)
9. ~☐E!μ (8 MN)
10. (∀Y)(P(Y) ⊃ Yμ) ∧ (∀y)[(∀Y)(P(Y) ⊃ Yy) ⊃ (y = μ)] (5 Simp)
11. (∀Y)(P(Y) ⊃ Yμ) (10 Simp)
12. P(☐E!) ⊃ ☐E!μ (11 UI)
13. ☐E!μ (1,12 MP)
14. ☐E!μ ∧ ~☐E!μ (9,13 Conj)
15. ~~E!g (3-14 IP)
16. E!g (15 DN)
QED

Posted on April 20, 2017, in Arguments for God and tagged , . Bookmark the permalink. 1 Comment.

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