Hartshorne's Modal Argument

Hartshorne's argument is a development of Anselm's ontological argument. From here:

The argument’s logical symbols are the tilde (~) for negation, the arrow (→) for strict implication, M for “is logically possible” (thus, “~M~” means “is logically necessary”), and p* stands for “God exists,” where God is defined as “a being unsurpassable by any other conceivable being.” (In Hartshorne’s dipolar theism, the divine can, in some senses, surpass itself but it is unsurpassable by any other being). The argument is presented as follows:

Mp*
Mp* → ~M~p*
Therefore, ~M~p*

If that is not clear, an easier to understand version can be found from Joe Hinman here and here:

(1) If God exists, he must exist necessarily, if God does not exist his existence is impossible.
(2) Therefore, God is either necessary or impossible.
(3) God can be conceived without contradiction
(4) therefore, God is not impossible
(5) Since God is not impossible he must be necessary.
(6) Since god is necessary he must exist.

The word "necessary" in this context means the entity is uncaused - not contiguent - and furthermore that it is impossible for it to not exist. I am putting it in purple to indicate this special meaning; if not in purple, I am using it in his conventional sense.

Number (1) above assumes a definition of God as a being that is - among other things - necessary. That is fine, and is made clear in the later text on the web page. I have no issue with that, but it is important to have that in mind later.

Here is another version, from Theism, by C. Dore:

(a) Since the concept of God is the concept of a being than which no greater being is logically possible, the concept of God is such that it is true in each possible world that if God exists in that world, then it is logically impossible for him to fail to exist there, i.e., his existence in that world is logically necessary.
(b) There is a possible world, W, in which God exists.
Hence
(c) in W, God's existence is logically necessary. (From (a) and (b) by modus ponens.)
But
(d) what is logically necessary in one possible world is logically
necessary in all possible worlds.
So
(e) God's existence is logically necessary in the actual world, i.e., God, a maximally great being, exists.

I want to focus on (3) in Hinman's version, or (b) in Dore's -  that is where the problem lies.

Is it true that if a thing can be "conceived without contradiction" then it must necessarily be possible? I can conceive a rock that floats. Does that make it possible? No. But we need to go a little deeper. Can I conceive a rock that floats without contradiction? Perhaps not, it depends what we mean exactly. Given the laws of nature, a floating rock does have a contradiction, it is subject to gravity and is considerably more dense than air; rocks fall.

So this hinges on exactly what is meant by "conceived without contradiction".

To a casual glance, of course we can imagine God. But that is not what (3) is claiming. What it really says is; the concept of a necessary God is consistent with the laws of nature.

It is worth noting that this is NOT saying; the concept of a necessary God is consistent with our understanding of the laws of nature. That would imply that the existence of God could depend on human knowledge, and we can imagine a hypothetical situation whereby as cosmologists learn more about the laws of he universe they reach a point where it is apparent the concept of God is not consistent with how we understand the universe, and at that moment God no longer exists and indeed never did. To illustrate this another way, the floating rock is impossible even before the discovery of gravity.

So is (3) true or false? Is the concept of a necessary God consistent with the laws of nature?

These supposed proofs blithely assumes it is, but offer no reason to suppose that that is so. It might be. But it might not. And to be frank, I do not think our understanding of the laws of nature are good enough to say either way.


A different way to think about this is with possible worlds. First a couple of examples to illustrate.

Is it possible to conceive of a world where rocks float? Yes, of course it is. I can think of two video games that feature floating rocks, so of course we can conceive it. But is this just about what we can imagine? I think not.

Is it possible to conceive of a world where rocks float without contradiction? Rocks float in those games because the laws of nature are very different to the real world. In any world we can hypothesise, rocks will fall towards the centre of gravity.


Is it possible to conceive of a world where the Nazis won WW2? Yes, of course it is. I can think of several TV shows and video games that explore that possibility.

Is it possible to conceive of a world where the Nazis won WW2 without contradiction? Again, yes. If the events had gone different (for example, Britain not entering the war in 1939, or the US not entering the war in 1941), then it is all too easy to imagine the Nazis winning. Nothing in the laws of nature forces the Nazi defeat, so this scenario can be conceived without contradiction.


Is it possible to conceive of a world where God exists? Yes, of course it is. Plenty of people believe it is so.

Is it possible to conceive of a world where a necessary God exists without contradiction? This is the big question that needs to be addressed - and these supposed proofs fail to do that.