Anselm’s God to Plantinga’s God

Prefatory Remarks:

There is a slight difference in the way Anselm and Plantinga define God.  Anselm’s definition is that God is that than which none greater can be conceived.  Plantinga’s God is a maximally great being, i.e. a necessarily existing being that has omnipotence, omniscience, and morally perfection.  Anselm’s definition is negative, while Plantinga’s is positive.  Anselm’s definition fits with the apophatic tradition of a negative theology, i.e. God is not among those things of which a greater can be conceived.  It is because Anselm’s definition is negative that I contend that Thomas Aquinas is incorrect in his central critique of the ontological argument.  Anselm isn’t offering a positive account of God’s essential nature.  I agree with Aquinas that a positive account of God’s essential nature cannot be completely and univocally known to us, but I should also say that although Plantinga’s definition is positive, it is not claimed to be complete and it need not be interpreted as perfections of “power”, “knowledge”, and “goodness” as those terms are understood univocally.

There is still a strong relationship between the Anselmian definition of God and the Plantingan definition.  Namely, one can derive from the Anselmian definition various divine attributes like necessary existence, omnipotence, omniscience, and moral perfection, among other perfections.  So one can argue that if there is an Anselmian God, then there is a maximally great being, in the Plantingan sense.  Indeed, that impication necessarily holds, given that it analytically follows from the Anselmian definition.  As an aside, I would argue that the two definitions are not equivalent in that one cannot derive the Anselmian definition from the Plantingan definition.  So, the existence of a maximally great being would not necessarily imply the existence of Anselm’s God.

Another interesting aspect of Anselm’s definition is that, since it is negative, I think the case for its metaphysical possibility can be firmly established.  Now, I am not suggesting that Anselm makes a modal inference that the metaphysical possibility of God, as he defines it, entails his actual existence.  Still, it is often disputed that conceivability does not entail metaphysical possibility. However, in this particular case, the conceivability of the Anselmian God makes the following falsehood self-evident, viz. that it is somehow metaphysically necessary that for any object, there will always be something else one could conceive of which would be greater.

Given that Plantinga’s maximally great being is a necessarily existing omnipotent, omnicient, and morally perfect being, I think there may be a powerful way to combine the fact that we can understand the Anselmian God, and show the Anselmian God possible, and use that to demonstrate the existence of a being that is omnipotent, omniscient, and morally perfect.  In what follows, I exploit Anselm to vindicate Plantinga.

Informal Expression of the Argument:

P1) If I can understand the Anselmian definition of God, then it is not necessarily the case that, for any given thing, there will be something conceivably greater.
P2) If it is possible that there is something than which none greater can be conceived, then it is possible that there is an Anselmian God.
P3) The existence of the Anselmian God necessarily implies the existence of a maximally great being.
P4) I can understand the Anselmian definition of God.
P5) If it’s possible that something is maximally great, then it’s possible that there is a necessarily existing, omnipotent, omniscient, and morally perfect being.
C) There is an omnipotent, omniscient, and morally perfect being.

A Formal Expression of the Argument:

P1) If it is possible that the Anselmian God is in the understanding, then it is not necessary that, for all x, it is conceivable that there is y and y is greater than x.
P2) If it is possible that there is something, x, such that it is not conceivable that there is some y and y is greater than x, then it is possible that there is something, z, and z is the Anselmian God.
P3) Necessarily, if there is something that is the Anselmian God, then there is something that is maximally great.
P4) It is possible that the Anselmian God is in the understanding
P5) If it is possible that there is something that is maximally great, then it is possibly necessary that there is something that is omnipotent, omniscient, and morally perfect.
C) There is something that is omnipotent, omniscient, and morally perfect.

Formal Deductive Proof of the Argument:

Let,

Mx ≝ x is maximally great
Ox ≝ x is omnipotent, omniscient, and morally perfect
Ux ≝ x is in the understanding
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)(~©(∃y)Gyx)
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. ♢Ug → ~☐(∀x)©(∃y)(Gyx) (premise)
2. ♢(∃x)~©(∃y)(Gyx) → ♢(∃z)(z = g) (premise)
3. ☐[(∃z)(z = g) → (∃x)Mx] (premise)
4. ♢Ug (premise)
5. ♢(∃x)Mx → ♢☐(∃y)Oy (premise)
6. ☐[(∃z)(z = g) → (∃x)Mx] → [♢(∃z)(z = g) → ♢(∃x)Mx] (Theorem of K)
7. ~☐(∀x)©(∃y)(Gyx) (1,4 MP)
8. ~~♢~(∀x)©(∃y)(Gyx)(7 ME)
9. ♢~(∀x)©(∃y)(Gyx)(8 DN)
10. ♢(∃x)~©(∃y)(Gyx)(9 QN)
11. ♢(∃z)(z = g) (2,10 MP)
12. ♢(∃z)(z = g) → ♢(∃x)Mx (3,6 MP)
13. ♢(∃x)Mx (11,12 MP)
14. ♢☐(∃y)Oy (5,13 MP)
15. ♢☐(∃y)Oy → ☐(∃y)Oy (Theorem of S5)
16. ☐(∃y)Oy (14,15 MP)
17. ☐(∃y)Oy → (∃y)Oy (Axiom M)
18. (∃y)Oy (16,17 MP)

QED

Posted on May 24, 2019, in Arguments for God and tagged , , . Bookmark the permalink. 2 Comments.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s