What is the best/most convincing objection to the Ontological Argument?

Question

In A History of Western Philosophy, Bertrand Russell says (p. 568)

Kant countered this argument by maintaining that “existence” is not a predicate. Another kind of refutation results from my theory of descriptions. The argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies.

There are a good deal of objections to the ontological argument. My preferred being Kant's 'existence is not a predicate', rather it is only a word detailing a concept's occurrence in reality. Also his further formulation that a predicate is only really valid(?), when the concept it is applied to actually exists.

So firstly, is there a response/development of the ontological argument which evades this and if not, surely this is the best objection? If it isn't, what makes a different objection better? Finally, if Kant's objection is as strong as I believe, why did Russell (someone who had spent a good deal of time arguing against the existence of God in numerous books) say this, instead of agreeing with Kant? (Feel free just to link the SEP page/post/wikipedia article if you can't be bothered fully outlining it)

Answer 1

So, the argument you're referring to, paraphrasing the sep article, is:

1. Consider a being than which no greater can be conceived.
2. If such a being fails to exist in reality, then a greater being - namely, a being than which no greater can be conceived, and which exists in reality - can be conceived.
3. But the being of step 2 is a contradiction, because nothing can be greater than the being of step 1.
4. Therefore, the being of step 1 must exist in reality.

We are implicitly speaking here of a set of beings-that-can-be-conceived, which we can call S. The fallacy here is an equivocation between two different conditions of a being.

Condition A. We can conceive that the being exists-in-reality

Condition B. The being actually exists-in-reality

Members of S might have any combination of Condition A and Condition B. They might actually exist in reality, and we can conceive of them existing in reality (such as the moon). They might actually exist in reality, but we can't conceive of them existing (who says the human mind is capable of grasping everything in the universe?). They might not exist in reality, but we can conceive of them doing so (such as leprechauns). They might not exist in reality, and we can't conceive of them doing so.

The equivocation is over whether the being in step 2 of the argument has Condition B (exists in reality) or Condition A (we can merely conceive of it existing in reality). Let's restate the argument in clearer terms, without equivocating:

1. Consider a being than which no greater can be conceived.
2. If such a being lacks Condition B, then a greater being - namely, a being than which no greater can be conceived, and which has condition A - is in S.
3. But the being of step 2 is a contradiction, because nothing can be greater than the being of step 1.
4. Therefore, the being of step 1 must have Condition B.

The clarified argument falls flat, because the being of step 2 is not necessarily greater than the being of step 1. Even assuming the being of step 1 lacks Condition B, it may still have Condition A, just like the being of step 2.

Now, we might try to fix the argument by resolving the equivocation in a different way, so that the being of step 2 has Condition B instead of condition A:

1. Consider a being than which no greater can be conceived.
2. If such a being lacks Condition B, then a greater being - namely, a being than which no greater can be conceived, and which has condition B - is in S.
3. But the being of step 2 is a contradiction, because nothing can be greater than the being of step 1.
4. Therefore, the being of step 1 must have Condition B.

But still it falls flat, because now we can't guarantee that the being of step 2 is in S at all; it would have to actually exist-in-reality, and we have no way to establish that.

So either way we resolve the equivocation, the argument doesn't work.

Answer 2

Kant's argument is probably the best, except not in the way he directly stated it. He did state the following via a set of statements throughout his discourse on the topic (in the first Critique), however:

To define something as necessarily existing means defining it as given in all possible intuition. But one cannot define an object into intuition. I can say the phrase "a visible five-headed unicorn" such that, "A visible five-headed unicorn is invisible," is self-contradictory. This does not mean that there are any five-headed unicorns. Vision is a class of intuition, so the point generalizes: unless we actually have an intuition of a divine nature, saying, "The always-intuited divine nature is not intuited," does not go through. We do not and cannot see or indeed have any spatiotemporally limited intuition that is adequate to the concept of the divine nature. There is no burning bush or heavenly trumpet or whatever else along those lines, that sufficiently resembles what the divine nature is supposed to be so as to certify that our intuition of such things is an intuition of God. So not even God can cause us to have an intuition of God (It might instill an incorrigible belief in Its existence, in us, but that is another matter).

Clarification: since Kant is not a pure rationalist, he does not think that substantial existence claims can be proven without intuition. Note that what he means by intuition is particular representation: our minds lead us inescapably towards a general maximum which is our concept of God, but as a generalization this is not an intuition. The point might seem obvious, then: unless we have a direct perception of God, nothing in Heaven or on Earth can show to us that God as a particular being exists.