Three Ontological Arguments

An ontological argument is an argument which contends that an understanding of the very concept of “God” is sufficient to establish the actual existence of God. Or, as Brian Davies puts it, “that the meaning of ‘God’ entails God’s existence” [1]. It differs from other families of arguments within natural theology (such as cosmological arguments, teleological arguments, etc.) in that it is a priori rather than a posteriori, meaning that it does not start from an observation or experience of some reality about the world, but rather starts from a premise derived purely from reason [2].

Historically, there have been several key versions of ontological arguments, but three of the most significant come from three of philosophy’s great minds: Saint Anselm, Descartes, and Alvin Plantinga. Here we’ll briefly examine all three.

Saint Anselm

Anselm’s Proslogion was written sometime around the year 1059. In it he makes the following argument:

  1. God is that than which nothing greater can be thought
  2. This concept of God is understood when it is heard
  3. Whatever is understood exists in the mind
  4. Therefore, that than which nothing greater can be thought exists in the mind
  5. To exist in reality is greater than to exist solely in the mind
  6. If that than which nothing greater can be thought exists in the mind, it is possible to think of it as also existing in reality
  7. If that than which nothing greater can be thought can be thought to exist in reality, but only actually exists in the mind, then something greater than it can be thought of
  8. Nothing greater than that than which nothing greater can be thought can be thought of
  9. Therefore, that than which nothing greater can be thought exists both in the mind and in reality

In this first stage, he establishes that “that than which nothing greater can be thought” actually exists. But what is that than which nothing greater can be thought? Here he extends the argument:

  1. Something can be thought to exist that cannot be thought not to exist
  2. What cannot be thought not to exist is greater than that which can be thought not to exist
  3. If that than which nothing greater can be thought can be thought not to exist, then something greater than it can be thought of
  4. Nothing greater than that than which nothing greater can be thought can be thought of
  5. Therefore, that than which nothing greater can be thought cannot be thought not to exist

In other words, that than which nothing greater can be thought must exist necessarily through itself. Anselm goes on to argue that, since that than which nothing greater can be thought must be whatever it is better to be than not be, that than which nothing greater can be thought must be omnipotent, the creator of all things, the supreme good, just, truthful, happy, eternal, etc. This is what God is.

So what should we make of the argument? I take it that, after God is defined as that than which nothing greater can be thought, there are essentially two crucial steps the argument must make. First it must show that the something than which nothing greater can be thought exists in the mind. Then it must show that if that something exists in the mind, it exists also in reality.

How does St. Anselm argue for the first step? Suppose you are presented with the proposition “God is that than which nothing greater can be thought.” If you agree, then you must understand the concept of “that than which nothing greater can be thought,” for how could you agree with something you do not comprehend? Similarly, if you disagree you must also understand the concept, for how could you disagree with a concept unless you first understood it? In short, St. Anselm suggests that we all at least grasp the idea of that than which nothing greater can be thought. And if we grasp the idea of it, then it exists in our minds.

And if it exists in the mind, it must also exist in reality. For what exists in reality and the mind is greater than what exists merely in the mind. Since we can conceive of this greatest possible being existing in reality, if it does not actually exist in reality, then there is something which can be thought of greater than that than which nothing greater can be thought, which is absurd. Hence, something than which nothing greater can be thought really exists, and this is what God is.

While St. Anselm’s argument is certainly interesting, unique, and philosophically significant, is it ultimately successful? A few centuries after Anselm, Saint Thomas Aquinas gave a response. In his Summa Theologiae, he considers the question of whether the existence of God is “self-evident”. In doing so he distinguishes between two senses of being self-evident. Something can either be self-evident in itself but not to us, or self-evident in itself and to us.

A proposition is self-evident in itself if “the predicate is included in the essence of the subject.” For instance, “bachelors are unmarried” is a self-evident proposition because “unmarried” is a part of the essential definition of the concept of “bachelor.” But it is possible to imagine that someone has never heard the word bachelor before, and hence has no idea what it means. If they were presented with the same proposition — “bachelors are unmarried” — it would not be self-evident to them. It would only become self-evident once they learn what a bachelor is.

Saint Thomas agrees that the proposition “God exists” is self-evident in itself. But, he suggests, in order for the ontological argument to succeed, it must also be self-evident to us. It is self-evident in itself because in God essence and existence are identical, i.e. Gods’s existence is intrinsic to his essence, it is his essence to exist. God is existence. But we can only know this after we have reasoned to the existence of God from his effects, a posteriori. In other words, the whole project of the ontological argument seems problematic from the start. In order to even begin, the argument must be able to point to essential properties of God; but we can only know these properties on the basis of a posteriori arguments, such as a first cause argument.

But Aquinas thinks the argument suffers even more difficulties. Let us suppose, he says, that somehow we do actually know that God is that than which nothing greater can be thought. Does it follow, as Saint Anselm suggests, that God must actually exist?

Saint Thomas thinks not. In essence, his reply is that Anselm’s argument is an unfulfilled conditional. A conditional argument is one with the following structure:

  1. If p, then q
  2. p
  3. Therefore q

Anselm’s ontological argument has the implicit structure of a conditional, but one which is never fulfilled. When the argument’s conditional nature is made explicit, it looks like this:

  1. If God exists, then God is that than which nothing greater can be thought
    • This concept of God is understood when it is heard
    • Whatever is understood exists in the mind
    • Therefore, that than which nothing greater can be thought exists in the mind
    • To exist in reality is greater than to exist solely in the mind
    • If that than which nothing greater can be thought exists in the mind, it is possible to think of it as also existing in reality
    • If that than which nothing greater can be thought can be thought to exist in reality, but only actually exists in the mind, then something greater than it can be thought of
    • Nothing greater than that than which nothing greater can be thought can be thought of
  2. Therefore, that than which nothing greater can be thought exists both in the mind and in reality

The argument presents the conditional in premise 1 (if p then q) and presents the conclusion in premise 2 (therefore q), but never presents a premise to fulfill the initial conditionalIn short, the established conclusion is not really “that than which nothing greater can be thought exists both in the mind and in reality,” but only “If God exists, then that than which nothing greater can be thought exists both in the mind and in reality.” But that just amounts to saying “if God exists, then God exists,” which still doesn’t tell us whether or not God actually exists.

Descartes

A few centuries later, the French philosopher and mathematician Rene Descartes presented another version of an ontological argument in his Meditations on First Philosophy. It goes as follows:

  1. We have ideas of things which we perceive contain fixed, determinate, immutable natures with essential properties necessary to their definition
  2. When we perceive that an idea possesses a fixed and determinate property, that property is clearly and distinctly perceived to belong to that idea
  3. Whatever is clearly and distinctly perceived to belong to an idea really does belong to it
  4.  Necessary existence is clearly and distinctly perceived to belong to the idea of God
  5. Therefore, necessary existence really belongs to God
  6. Whatever has necessary existence, necessarily exists
  7. Therefore, God exists

This argument is different from Saint Anselm’s in both structure and content, but does share some significant similarities. The version given above is highly condensed, so to see what Descartes is actually getting at we’ll have to extrapolate a bit.

Early on in the Fifth Meditation, Descartes notes that “I find within me countless ideas of things which even though they may not exist anywhere outside me still cannot be called nothing; for although in a sense they can be thought of at will, they are not my invention but have their own true and immutable natures” [3]. He uses as his primary example of this premise our ideas of triangles. Whether or not any triangles actually exist outside of the mind, the very concept of triangle has certain fixed and determinate properties, such as “possessing three angles.” This is, he notes, an immutable and eternal truth; for even if every human dies, and the whole physical universe perishes, it will still be a true proposition that “triangles have three angles.” This is a property which belongs necessarily to the concept of triangle.

From this he concludes that “the mere fact that I can produce from my thought the idea of something entails that everything which I clearly and distinctly perceive to belong to that thing really does belong to it” [4]. In other words, if we have an idea of some concept, and we see that the concept possesses certain properties necessarily, then, in Descartes’ language, we “clearly and distinctly perceive” that the property belongs to the concept. And a property that is clearly and distinctly perceived to belong to a concept, really does belong to it. For how could we perceive that the property of being unmarried belongs essentially to the concept of “bachelor” without knowing that any bachelor is therefore really unmarried?

Next, Descartes points out that we have an idea within us of God, or a “supremely perfect being.” And it seems that the property of necessary existence belongs essentially to the concept of a supremely perfect being, for surely a being which has necessary existence is more perfect than a being which does not.  A being which lacks necessary existence lacks perfection; and a supremely perfect being cannot lack perfection. Descartes writes:

“It is quite evident that existence can no more be separated from the essence of God than the fact that its three angles equal two right angles can be separated from the essence of a triangle, or than the idea of a mountain can be separated from the idea of a valley. Hence it is just as much of a contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection), as it is to think of a mountain without a valley” [5].

But whatever possesses the property of existence, exists. And whatever possesses the property of necessary existence, necessarily exists. Therefore, God necessarily exists.

Our response to Descartes’ argument is essentially the same as that to Anselm’s. Both arguments are unfulfilled conditionals. Both fail to make a distinction between: 1) The idea of God; 2) God actually existing; and 3) The idea of God actually existing.

The implicit form of Descartes’ argument is:

  1. If God exists, God possesses the property of necessary existence
  2. If God possesses the property of necessary existence, God exists
  3. Therefore God exists

But the conclusion does not follow. The actual conclusion should be “If God exists, God exists,” which, once again, does not tell us whether or not God really exists.

Most of the work in Descartes’ argument is in establishing that the concept of God possesses the property of necessary existence. But it does not follow from this that God actually exists. The idea of God is different from the idea of the idea of God (or perhaps a better way to put it: the idea of the concept of God), just as the idea of God is different from God himself. If we can distinguish between actual God and the idea of God, then we can likewise distinguish between the idea of actual God, and the idea of the idea of God.

This is all quite abstract, so let’s consider an example to bring it down to earth a bit. Suppose you think in your head “a triangle has three angles.” This is the idea of a triangle. But this idea makes no reference to any actual triangles. Now suppose you close your eyes and imagine that there’s a triangle floating right in front of your face. In this case, you do not just have an idea of a triangle, you have an idea of a triangle that is actually existing. Is it really existing? No. But you have the idea of it really existing. The fact that we can distinguish these two instances shows that there is a distinction between the idea of the idea of a triangle, and the idea of an actual triangle.

The two ontological arguments we have considered thus far take us from the idea of God, to the idea of God actual existing. They establish that if God exists, God will necessarily exist. But they do not establish that God really exists. The fact that the concept of God contains the property of necessary existence does not show that God exists; but only that if the concept of God corresponds to anything that actually exists, the actually existing thing will possess the essential properties of the concept.

Plantinga

Fast forward another few hundred years to the twentieth century, and we come to philosopher Alvin Plantinga. Plantinga presents what is known as a modal ontological argument, which goes like this:

  1. The property maximal greatness entails having maximal excellence in every possible world
  2. Maximal excellence entails omnipotence, omniscience, and moral perfection
  3. Maximal greatness is possibly exemplified
  4. If maximal greatness is possibly exemplified, there is a possible world W in which a being possesses maximal greatness
  5. Therefore, there is a possible world W in which a being possesses maximal greatness.
  6. If there is a being which possesses maximal greatness, then there is a being which possesses the property of having maximal excellence in every possible world
  7. Therefore, in possible world W, there is a being which possesses the property of having maximal excellence in every possible world
  8. A being can only possess a property if it exists
  9. Hence, in possible world W, there is a being which possesses the property of existing and having maximal excellence in every possible world
  10. Whatever is exemplified in every possible world, is impossible not to be exemplified
  11. Therefore, in possible world W, there is a being which is impossible not to exist and have maximal excellence
  12. What is impossible does not vary from world to world
  13. Therefore, in the actual world, there is a being which is impossible not to exist and have maximal excellence
  14. Therefore, there exists a being which possesses maximal excellence
  15. Therefore, there exists a being which is omnipotent, omniscient, and morally perfect

This argument is quite complex, so we’ll take some space to break it down. For Plantinga both maximal excellence and maximal greatness are in reference to certain properties known as “great-making properties.” A great making property is basically a property which would be better to possess than not to possess, such as goodness, knowledge, power, etc. Maximal excellence entails having all such properties, to the highest degree, within a specific, individual possible world. Maximal greatness, on the other hand, is the property of having maximal excellence in every possible world. Maximal excellence is relative to a single possible world; maximal greatness to all possible worlds.

Premise three above might be reworded to say “it is logically possible that there could exist some being which has the property of maximal greatness.” This seems true enough; there is nothing logically incoherent about the notion of maximal greatness.

Premise four invokes the philosophical notion of “possible worlds.” A possible world is “a complete way things could be” [6], or an overall possible state of affairs. The actual world is the world we really exist in. In the actual world, the Union won the Civil War. But it is logically possible that the Union could have lost the Civil War. Hence we say that there is a possible world in which the Union lost the Civil War. So, by definition, premise four follows from premise three, and premise five from premise four. There is a possible world in which a being possesses maximal greatness. And hence there is a possible world in which a being possesses the property of having maximal excellence in every possible world.

Plantinga argues that for a being to possess a property in some world, it must exist in that world. So if there is a possible world in which a being possesses the property of having maximal excellence in every possible world, then there is a possible world in which a being exists and possesses the property of existing and having maximal excellence in every possible world.

Premise ten likewise is true by definition. In order for something to not be exemplified in a possible world, it must be impossible. So if something is true in every possible world, it is impossible for it to not be true. Plantinga likewise argues that impossibility and necessity do not vary between possible worlds. This is because, Plantinga suggests, if something is possible in some world, it is possible in every possible world.

This might seem suspicious at first glance. It is possible in the actual world for Donald Trump Jr. to grow up and be president. But suppose there is some possible world in which Donald Trump never has any children. In that possible world would we not have to say that it is impossible for Donald Trump Jr. to grow up and be president? Yes, Plantinga would respond: in that world it is in fact impossible for Donald Trump Jr. to be president, but it is still logically possible, and hence it is still true in that possible world that “there is some possible world in which Donald Trump Jr. grows up to be president.” In other words, this amounts to saying that if something is logically possible in one possible world, it is logically possible in every possible world. And the same with impossibility.

Now the statement “that which has maximal excellence in every possible world fails to have maximal excellence in some possible world” is logically impossible; and hence it is impossible in every possible world. From this follows premise thirteen: in the actual world, there is a being which is impossible to not exist and have maximal excellence. But if in the actual world there is a being which is impossible to not exist and have maximal excellence, then in the actual world there is a being which really exists and really has maximal excellence. Hence there exists a being with maximal excellence.

The previous two arguments we’ve examined could both be addressed with generally the same response. Is that the case here, as well? I think so. Once again, I think that the argument is an unsatisfied conditional.

A possible world is essentially a kind of hypothetical state of affairs, and a hypothetical is just a conditional. To say “Object X exists in possible world W” is effectively the same as to say “If W is actual, then X is actual.” As such, to say “In possible world W there exists a being X which possess the property of having maximal greatness in every possible world,” can be translated: “If W is actual, then X is actual; and if X is actual, then X is actual in any actual state of affairs.” The argument consists of a long string of conditions which are never satisfied. The conclusion is taken to follow from the fact that if X is actual in every possible world, then X is actual in the actual world. But X is only actual in every possible world if W is actual. And the argument never establishes that W is actual.

The problem is that it seems we must posit that every possible world contains an entire set of all possible worlds, and hence that there are possible worlds within possible worlds. To say that there is a possible world W where there exists a being that has maximal excellence in every possible world, is to say that within possible world W, every possible world has a being that possesses maximal excellence.

But, Plantinga might respond, must we not say that every possible world contains the same set of all possible worlds, since whatever is logically possible is the same across all possible worlds? To see why I don’t think this is the case, consider the following:

Suppose there are five overall possible worlds: A, B, C, D, and E. Let’s say that A is the actual world. Within A, there is still the same set of possible worlds, with A being actual (Aa), and the others being possible but not actual (Bp, Cp, Dp, Ep). Now, within Bp, B is the actual world (BpBa), and the others are merely possible (BpAp, BpCp, BpDp, BpEp), and similarly with the others.

So let’s say that Bp is the possible world in which there exists some being X that possesses the property of maximal excellence M in every possible world. What that means is that X exists within BpBa, and within BpAp, BpCp, BpDp, and BpEp. But none of these are the actual world. None are Aa. The premise establishes that X exists in every possible world with respect to B, not with respect to the actual world. In short, it seems to me possible to say that every possible world has the same set of possible worlds, but that within each possible world specific entities/propositions can have different relations to actuality. “Santa Clause exists” is a logical possibility in every world, even in the actual world. But “Santa Clause exists” is not actual in every possible world.

In conclusion, I think the essence of Saint Thomas’ response to Saint Anselm’s ontological argument can be successfully applied to each of the other two versions.

 

 

Sources

[1]. Brian Davies. An Introduction to the Philosophy of Religion. Third edition. New York: Oxford University Press, 2004. Page 98.

[2]. See: Oppy, Graham, “Ontological Arguments”, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2017/entries/ontological-arguments/&gt;.

[3]. Descartes. Meditations on First Philosophy: With Selections from the Objections and Replies. Revised edition. Edited by John Cottingham. Cambridge: Cambridge University Press, 1996. Page 44.

[4]. Ibid, page 45.

[5]. Ibid, page 46.

[6]. Davies, Introduction, page 101.

Plantinga’s argument taken from: Plantinga, Alvin. “God and Necessity.” The Nature of Necessity. : Oxford University Press, 1978-02-01. Oxford Scholarship Online. 2003-11-01. Date Accessed 24 May. 2018 <http://www.oxfordscholarship.com/view/10.1093/0198244142.001.0001/acprof-9780198244141-chapter-10&gt;.

Anselm’s argument taken from: Anselm of Canterbury. “Proslogion” in The Major Works. Edited by Brian Davies and G. R. Evans. New York: Oxford University Press, 1998.

Aquinas’ response taken from: Thomas Aquinas. Summa Theologiae. Translated by Fr. Laurence Shapcote, O.P. The Aquinas Institute for the Study of Sacred Doctrine, 2012. I, Q. 2, Art. 1.

 

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