Anselm's ontological argument

Here is my favorite version of the “existence is not a property” objection to Anselm’s first ontological argument.

It makes no sense to talk of the greatness of a nonexistent being except hypothetically as the greatness it would have if it existed. When we compare the greatness of things, we compare what the things would be like if they existed. Thus, when we say that Thor is greater than Hermes, we mean something like this: if Thor existed, he would be greater than Hermes would be if Hermes existed. And to exist is to exist in reality.

But now take the crucial claim in Anselm’s argument that it is greater for x to exist in mind and in reality than just in mind. This claim is simply false when we understand it in the hypothetical way. For we need to compare the greatness of the x that exists in mind and reality to the greatness that the x that exists only in mind would have if it existed in reality. But that’s the same greatness!

Anselm’s second argument makes no such slip, for it is based on a comparison between contingent and necessary existence, and that comparison survives the criticism.

Anselm's ontological argument

Consider this very simple formulation of Anselm's first argument:

1. (Premise) A maximally great being exists in my mind.
2. (Premise) If x exists in my mind and not in reality, then x is not a maximally great being.
3. Therefore, a maximally great being exists in my mind and reality.

This argument feels fishy. But now consider this parallel:

4. (Premise) A maximally great being exists in my room.
5. (Premise) If x exists in my room and not in the rest of the universe, then x is not a maximally great being.
6. Therefore, a maximally great being exists in my room and in the rest of the universe.

This argument is clearly valid. Moreover, premise (5) is very plausible true. A maximally great being cannot exist merely in one room without existing elsewhere, just as a maximally great being cannot be the creator of merely one human being without being the creator of all others. And there are at least circumstances in which (4)-(6) does not beg the question, for instance when the person who is concluding to (6) is having a religious experience as of a maximally great being in this room.

So, (1)-(3) feels odd in a way in which (4)-(6) does not. Why? I suppose it is that to exist in my mind does not appear to be parallel to existing in my room. To exist in my room is to exist and be located in my room. But to exist in my mind does not seem to be the same as to exist and be located in my mind. Still, this does show that there is a way of taking (1)-(3) that makes it be a decent argument. For there is a sense of "exists in my mind" that does make it be parallel to "exists in my room". If my mind occupies a region of space, this is particularly easy: to be in my mind could be like being in my room or in the core of the earth. But if my mind does not occupy a region of space, there can still be a parallel. According to Aquinas, God counts as spatially omnipresent by virtue of knowledge and power. Well, he can be present in my mind by virtue of knowledge and power. Indeed, Christians talk of the Holy Spirit dwelling in them.

So now we have a reading of (1)-(3) that makes it a perfectly fine argument, as long as one has reason to accept (1), say due to an experience of the Holy Spirit's dwelling in one's mind.

I doubt that this is actually Anselm's argument. The main textual evidence against it is that Anselm takes God's existing in mind to be simply a matter of having the concept of God. I don't know how conclusive this is against the above reading. Anselm distinguishes between having a concept and being able to use the relevant words. It could turn out that in the case of God, to have the concept of God requires that God dwell in the mind. But all in all, as I said, I doubt this is Anselm's argument.

That said, the above reading does show that there are ways of reading (1)-(3) that make it be a fine argument. And I think it also highlights another point that not enough, perhaps, has been made of. The more existing in my mind is a genuine way of existing, like existing in my room, the better the argument sounds. But we know that at least the somewhat later medievals were drawn to views of mind on which to know an essence is to have that essence genuinely in one's mind, informing one's mind. On such views of mind, the argument may well be plausible, assuming one has reason to affirm (1) (for instance, because there is a presumption that if one has mastered C-talk, then one has the concept C).

Yet another ontological argument

I've never heard the following version of the ontological argument put quite in this way, though there may be things in Anselm and Descartes that suggest it:

1. (Premise) An impossible being is imperfect.
2. A perfect being is possible. (By (1))
3. (Premise) Necessarily, a contingently existing being is imperfect.
4. A perfect being exists necessarily. (By 2 and 3)
5. (Premise) What exists necessarily also actually exists.
6. A perfect being actually exists. (By 4 and 5)

I don't know if (2) validly follows from (1). Or maybe there is a problem with (1), in that we simply cannot attribute about impossibilia?

Why believe (1)? Well, one line of thought is that impossibility is an impotence. Another is that an impossible property entails all properties, and in particular such properties as being imperfect, and no imperfect being is perfect.

Ontological arguments

Continuing my project of reading my hitherto unread reading assigned for the medieval comp, I've been reading Anselm's replies to Gaunilo. As it happens, I never read all of it. When I assigned the text for class, I assigned only an abridged version which at one point says "Anselm continues as some length, but much of what he says seems repetitive". Well, maybe it seems that way to the translator, but the full text is really good stuff. I haven't digested it all, but I think there may be more to Anselm's ontological argument than has caught my eye before. It's at least as good as the S5 ontological argument.

That said, here's another ontological argument, inspired, if memory serves, by a humorous remark my wife made to me once.

1. (Premise) To be incapable of existing is a great impotence.
2. (Premise) Necessarily, anything that is all powerful lacks all impotence.
3. (Premise) A being that exists and is all powerful in one world must exist in all other worlds.
4. (Premise) God is essentially all powerful.
5. God lacks all impotence. (2 and 4)
6. Possibly God exists. (1 and 5)
7. There is a world at which God exists and is all powerful. (4 and 6)
8. God exists in all worlds. (3, 7 and S5)
9. God exists and is omnipotent. (4 and 8)

Step 3 gets a subsidiary argument. More than one comes to mind. But here is one:

10. (Premise for reductio) Suppose x exists and is all powerful at w but does not exist at w*.
11. (Premise) Necessarily, to be unable to be an efficient cause of any sort (remote or immediate, full or contributing, etc.) of a possible but non-necessary state of affairs is an impotence.
12. (Premise) Necessarily, nothing is able to be an efficient cause of any sort of its own failure to ever exist.
13. x's failure to ever exist is a possible but non-necessary state of affairs. (10)
14. It is true at w that x is unable to be an efficient cause of any sort of its failing to ever exist. (12)
15. It is true at w that x is not all powerful. (2, 11, 14) Which absurdly contradicts (10).
16. So if x exists and is all powerful at w, it must exist at every other world w*.

I don't know how seriously this argument is to be taken. By the way, it reminds me of something I heard attributed to Scotus.

St. Anselm on the magnitude of sin

St. Anselm believes that the least of our sins puts us in an infinite debt to God and is infinitely bad. Anselm's own argument for this thesis is uses some implicit premises. Here is my best reconstruction:

1. (Premise) To sin is to oppose the will of God.
2. (Premise) If it is not permissible to do A in order to preserve a good G, then A is at least as bad as the loss of G.
3. (Premise) It is not permissible to oppose the will of God "even to preserve the whole of creation", even "if there were more worlds as full of beings as this", and even if "they increased to an infinite extent".
4. (Premise) The badness of the loss of the whole of creation if the whole of creation consisted of planets as full of beings as Earth and increased to an infinite extent would be infinite.
5. (Premise) If something is at least as bad as an infinite bad, then it's infinitely bad.
6. To oppose the will of God is at least as bad as something infinitely bad. (2, 3 and 4)
7. To oppose the will of God is infinitely bad. (5 and 6)
8. Every sin is infinitely bad. (1 and 7)
9. (Premise) To do something infinitely bad puts us in infinite debt.
10. Every sin sin is infinitely bad and puts us in infinite debt. (8 and 9)

Probably the most obvious thing to worry about is the conjunction of (2) and (3). Premise (2) appears to be a consequentialist claim. Premise (3), on the other hand, is a premise that the Christian tradition does indeed endorse, but the Christian tradition is not a consequentialist tradition (witness St Augustine on lying and St Paul's insistence that we do not do evil that good might come of it). Thus the argument brings together premises that originate in two competing moral theories, and it is unsurprising that when you do that, you can derive surprising things from their conjunction.

But this is too quick. For there is a lot of plausibility to the consequentialist intuition that Anselm invokes in (2). When one thinks about Augustine and Kant on lying, it "feels right" to say that they value honesty over life. On the side of Kant at least, this is mistaken. Kant's objection to lying isn't that honesty is a greater good than life, because Kant's ethics is not centered on the good (at least not in a way that would make this statement work). So perhaps it is right to affirm the consequentialist intuition in (2) as well as the deontological intuition in (3). And if one does that, then one gets the view that certain actions are infinitely bad.

However, this approach is mistaken. For one does not do justice to both consequentialist and deontological intuitions by supposing that wrong actions are infinitely bad. For consider this situation: If you don't kill an innocent person, a hundred other people will each kill one innocent person. (How can you set this up? One way is statistical. You know that if a certain temptation T is given to people, one percent of people will commit a murder. So you're told that if you don't kill one person, temptation T will be offered to 10,000 people.) Clearly the hundred murders are worse than one murder, and yet it's wrong, according to the deontologist, to kill one innocent person. Moreover, this case is directly a counterexample to (2).

One might try to get out of this counterexample by denying that infinities can be compared. But if one does that, then one can no longer say things that mortal sin is worse than venial sin, and the like. Besides, one does want to be able to compare infinities. If I had a choice between preventing one stranger from committing one murder of a stranger and a hundred strangers from committing one murder apiece, obviously I should prevent the latter.

A different kind of objection to the argument would be that in (2), "at least as bad" should be read as "not less bad" (I am worried about cases of incommensurability). But if one makes the same replacement in (5), it is far from clear whether (5) remains true. For it may be that something is infinitely bad in an aesthetic way (say, an infinitely long bad novel) and something else is finitely bad in an incommensurable way (say, a toothache of finite length); the latter is not less bad than the former, but it does not follow that the latter is infinite.

Nonetheless, even though St Anselm's argument for the infinite badness of sin fails, I think there are alternate ways to make the thesis plausible. But that's a subject for another post (hopefully over the next couple of days).