Anselm's Ontological Argument for God's Existence Reconstructed

Anslem's Ontological Argument in Proslogion 2 is one of the most fascinating ontological arguments.  Moreover, I think it is one of the most fascinating arguments, period.  The very short of it is that if you have the idea of God, you're committed to a contradiction if you believe that God only exists in your mind and not in extra-mental reality.  The key to the argument--the most controversial assumption, I think, is that there are two modes of being--being-in-the-mind and being-in-reality.  For Anselm, a property may be had-in-reality or may be had-in-thought.  Pegasus--the winged horse--has-in-thought the property of being a horse.  If Pegasus existed outside of thought, Pegasus would have the property had-in-reality of being a horse.  Alas, Pegasus does not have the latter property.  I said that this modal assumption is controversial, nonetheless, it seems to me plausible.

Below is my reconstruction of Lynne Rudder Baker and Gareth Matthews' very interesting 2010 The Review of Metaphysics article, "Anselm's Argument Reconsidered," explicating and defending Anselm's argument:

Reconstruction of Anselm’s Argument in the Proslogion 2

First, here is a sub-argument to support Anselm’s Argument:

a. The theist and the atheist refer to the same object with the words “that than which nothing greater can be conceived.” ["that than which nothing greater can be conceived" being the definition of "God"]

Therefore,

b. That than which nothing greater can be conceived is an object that exists in both the theist’s and atheist’s understanding [by (a) and the meaning of “existing in the understanding”].

Let S be the object that exists in the theist’s and atheist’s understanding and that is such that nothing greater can be conceived.  So,

c. S is the object that exists in the theist’s and atheist’s understanding and that is such that nothing greater can be conceived [(b) and stipulation of “S”].

Therefore,

d. S exists in thought [[c] and stipulation “exists in the understanding”= “exists in thought”]

The Main Argument

1. S exists in thought and S does not exist in reality [supposition for reductio ad absurdum].

2. An otherwise exact same thing as S that existed both in thought and in reality is conceivable.

3. Greatness Principle (G): For anything x that existed only in thought, an otherwise same thing that existed both in thought and in reality would be greater (not just greater in thought) than x.

4. If S exists in thought and not in reality and an otherwise exact same thing as S that existed both in thought and in reality is conceivable, then an otherwise exact same thing as S that existed both in thought and in reality would be greater than S [by 1 and (G)].

5. An otherwise exact same thing as S that existed both in thought and in reality would be greater than S [1, 2, conjunction, 4, modus ponens].

6. If an otherwise exact same thing as S that existed both in thought and in reality and is conceivable would be greater than S, then there can be a conceivable object that is greater than S [namely, an otherwise exact same thing as S that also existed in reality].

Therefore,

7. There can be a conceivable object that is greater than S [5, 6 modus ponens].

8. There can be no conceivable object that is greater than S [line (c) above].

9. There can be a conceivable object that is greater than S, and there can be no conceivable object that is greater than S [7, 8 conjunction].  Contradiction!

Therefore,

10. It is not the case that: S exists in thought and S does not exist in reality [1-9, reductio ad absurdum]

Therefore,

11. S does exist in reality [10, DeMorgan’s rule (~(p&q)= ~p v ~q); line (d); disjunctive syllogism (pvq &~p then q].