Monthly Archives: October 2019

An Argument from Wayne and Garth

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P1.  If a maximally great being is impossible, then it is possible that I am worthy of worship.

P2. It is not possible that I am worthy of worship.

C1. A maximally great being is not impossible [from P1 and P2 Modus Tollens].

C2. A maximally great being is possible [from C1 by Obversion].

P3. If a maximally great being is possible, there is a maximally great being.

C3. There is a maximally great being [C2 and P3 Modus Ponens].

QED

Defense of Premises:

P1.  If there are no possible worlds where there is a being that has a maximal set of compossible great-making properties, then there is at least some possible world where I, or my counter-part, is the greatest being that happens to exist, and so I would be of greatest worth, i.e. worthy of worship.

P2. I know, through direct intuitional self-knowledge, that it is metaphysically impossible that I am a being worthy of worship.

P3. A maximally great being is a being that, if it exists in any possible world, exists in all possible worlds, including in the actual world.

An Ontological Argument from Pure Actuality

Informal Argument

D1. God is the being of pure actuality.
P1. For all x, if x exists in the intellect but not in reality, then there is a y such that x is causally dependent on y.
P2. For all x, if x is purely actual, then there is not a y such that x is causally dependent on y.
P3. God is in the intellect.
C. God is in reality

Defense of Definitions and Premises

It should be noted, at the outset that this argument is in Free Logic. As such, the existential quantifier carries no existential import in the argument. This prevents any inference of the existence of God from the definition alone.

D1: A being of pure actuality is simply a being that lacks any potentiality. Such a being has, as Aquinas argues, the divine attributes of omnipotence, omniscience, immutability, eternity, immateriality, and uniqueness. It is this last feature, uniqueness, that justifies the use of a definite description, since there can be only one such being. Instead, existential claims are made by the predicate “R” in the formal argument below, which means that something exists in sense of being real, as opposed to existing in a fictitious or imaginary way.

P1: This premise is motivated by the fact that if something exists in the intellect alone, then its existence is causally dependent on some mind.

P2: A being of pure actuality exists a se, and uncaused, as Thomas proves in his five ways.

P3: Every Thomist who contemplates the implications of a being of pure actuality has the Thomistic conception of God in mind.

The Formal Proof

Let,

Ix ≝ x is in intellectu
Rx ≝ x is in re
Dxy ≝ x is is causally dependent on y
Ax ≝ x is purely actual
g ≝ (ɿx)Ax

1. (∀x)[(Ix ∧ ~Rx) → (∃y)Dxy] (premise)
2. (∀x)(Ax → ~(∃y)Dxy) (premise)
3. Ig (premise)
4. (Ig ∧ ~Rg) (IP)
5. (Ig ∧ ~Rg) → (∃y)Dgy (1 UI)
6. (∃y)Dgy (4,5 MP)
7. Dgμ (6 EI)
8. (∃x){[Ax ∧ (∀y)[Ay → (y = x)]] ∧ Dxμ} (7 theory of descriptions)
9. [Aν ∧ (∀y)[Ay → (y = ν)]] ∧ Dνμ (8 EI)
10. Aν ∧ (∀y)[Ay → (y = ν)] (9 Simp)
11. Aν (10 Simp)
12. Aν → ~(∃y)Dνy (2 UI)
13. ~(∃y)Dνy (11,12 MP)
14. (∀y)~Dνy (13 QN)
15. ~Dνμ (14 UI)
16. Dνμ (9 Simp)
17. Dνμ ∧ ~Dνμ (15,16 Conj)
18. ~(Ig ∧ ~Rg) (4-17 IP)
19. ~Ig ∨ ~~Rg (18 DeM)
20. ~~Rg (3,19 DS)
21. Rg (20 DN)

QED