Cartesian-style ontological arguments

Cartesian-style ontological arguments run like this:

1. God has all perfections.

2. Existence is a perfection.

3. So, God exists.

These arguments are singularly unconvincing. Here is a simple reason they are unconvincing. Suppose we are undecided on whether there are any leprechauns and, if so, whether they have a king, and someone tells us:

4. The leprechaun king is very magical.

This sure sounds plausible in a certain frame of mind, and we may accept it. When we accept (4), while remaining undecided on whether there are leprechauns and, if so, whether they have a king, what we are accepting seems to be the conditional:

5. If the leprechaun king exists, he is very magical.

By analogy, when the agnostic accepts (1), it seems they are accepting the conditional:

6. If God exists, God has all perfections.

Given premise (2), we can conclude:

7. If God exists, God exists.

But every atheist accepts (7).

It seems to make little difference if in (2) we replace “existence” with “necessary existence”. For then we just get:

8. If God exists, God necessarily exists.

That’s not quite as trivial as (7), but doesn’t seem to get us any closer to the existence of God.

The above seems to perfectly capture why it is that Cartesian-style ontological arguments are unconvincing.

Even if the above is adequate as a criticism of Cartesian-style ontological arguments, I think there is still an interesting question of what sort of a conditional we have in (5)–(8)?

It’s not a material conditional, for then (5) would be trivially true given that there are no leprechauns, while (5) is non-trivially true.

Should it be a subjunctive conditional, like “If the leprechaun king existed, he would be very magical”? I don’t think so. For suppose that in the closest possible leprechaun world to ours, for some completely accidental reason, the leprechaun king is very magical, but in typical possible worlds with leprechauns, leprechaun kings are are actually rather a dud with regard to magicality. Then it’s true that if the leprechaun king existed, he would be very magical, but that shouldn’t lead us to say that the leprechaun king is very magical.

Perhaps it should be a strict conditional: “Necessarily, if the leprechaun king exists, he is very magical.” That actually sounds fairly plausible, and in light of this we would actually want to deny (4). For it is not necessary that the leprechaun king be very magical. But if we take it to be a strict conditional, we still have a triviality problem. Imagine an atheist who thinks that God is impossible. Then the strict conditional

9. Necessarily, if God exists, God has all perfections

is true, but so is:

10. Necessarily, if God exists, God has exactly 65% of the perfections.

But while it seems that our atheist would be likely to want to say that God has all perfections (indeed, that might be a part of why the atheist thinks God necessarily does not exist, for instance because they think that the perfections are contradictory), it doesn’t sound right to say that God has exactly 65% of the perfections, even if you think that necessarily there is no God.

I think the best bet is to make the conditional be a strict relevant conditional:

11. Necessarily and relevantly, if God exists, God has all perfections.

It is interesting to ask whether (11) helps Cartesian-style ontological arguments. Given (11), if all goes well (it’ll depend on the modal relevance logic) we should get:

12. Necessarily and relevantly, if God exists, God exists.

That sounds right but is of no help. We also get:

13. Necessarily and relevantly, if God exists, God necessarily exists.

Again, that sounds right, and is less trivial, but still doesn’t seem to get us to the existence of God, barring some clever argument.