Category Archives: Ontological Arguments

Intriguing but probably don’t work.

Ontological Argument Redux

This argument for the existence of God tries to deduce from the meaning of the term "God" the fact that this term also has a referent. Normally, semiotics teaches that the signified is a different beast than the referent. But is that true for the signifier "God"?

It seems that when God signifies "a being than which no greater can be thought" (TW), this conception includes within itself the fact of God's existence in reality.

So, what we do when trying to think of the greatest possible being is we start enumerating its attributes: the being than which no greater can be thought must be omnipotent, omniscient, 3, 4, 5, actually existing, 7, 8...

Now I have argued that its existence remains a conception, such that "from the idea of a perfect being only an idea of its actual existence follows, not its actual existence." Am I right?

Let me further suggest that there are two distinct criteria for something's existing at work here:

(a) (X)[X is a TW] -- normal existential statement; and
(b) (X)[X is TW X exists] -- from definition of the being than which no greater can be thought.

In (b), the universal quantifier ranges over both real and ideal things. If X is an idea, then, being in the mind, it cannot acquire actual existence. God can exist actually, and an idea of God can exist mentally, but an idea of God cannot exist in both ways.

If X is a real thing, then those who do not admit God's existence will insist that (a) is false. Then "X is TW" is false for all X, and the truth value of "X exists" in (b) is undefined.

In two sentences in (ST, I, 2, 1, reply 2), St. Thomas make both points. (1) "Yet, granted that everyone understands that by this word 'God' is signified something than which nothing greater can be thought, nevertheless, it does not therefore follow that he understands that what the word signifies exists actually, but only that it exists mentally."

(2) "Nor can it be argued that it actually exists, unless it be admitted that there actually exists something than which nothing greater can be thought; and this precisely is not admitted by those who hold that God does not exist." We can't argue for the consequent of (b) unless we admit (a), and (a) is not self-evident. (X)(X is a TW) is true, but we don't know at this stage of our proof whether X exists in the actual world.

(a) and (b) may be clarified as follows:

(a') (X)(X's essence is described by the phrase "TW");
(b') (X)(X's essence is described by the phrase "TW" X exists).

Consider a second version of the ontological argument. Let X be a being that is pure actuality. Let also it be possible for X to exist (lest it can be argued that in not existing X has no potency to come to exist, because its existence is impossible). Then if X did not exist or existed but could corrupt and perish, then existence would stand to X's essence as act to potency, and X would no longer be pure act, contrary to the definition. In other words, the meaning of the term "pure actuality" entails existence of pure actuality.

There are two interpretations of this argument. (1) If the concept of pure actuality is not incoherent, and it's not, then X exists. (2) If anything is pure act, then it has existence by its very nature, i.e., X is imperishable. The reasoning is similar.

Ontological Argument, Cont.

I think the correct proposition is

(X)[X's essence is described as "the thing than which no greater can be thought" X exists in reality].

Now we ask: to what does X refer? If it refers to an idea of TW, then an idea cannot exist in reality. If it refers to a real thing, then the proposition is a tautology and proves nothing.

Perhaps N (renamed from X) refers to the essence or form of the being than which no greater can be thought. N is a description, piece of information. Let me then rephrase it as a property P = "such that no greater can be thought of it," where "it" is whatever object has this property. Object B has property P whenever (C: C is an idea)[C ≤ B's essence].

Now there is the world of ideas and real world. In the former, there are thoughts. Let one such thought be X. When thinking, we can conceive of beings. One such is B. These beings can have properties, including P. So, the full "path" is World_of_Ideas.X.B.P. There also can be a Real_World.B.P.

The first B is an idea, conception. The second B is real God. They are not the same, just as file C:\World_of_Ideas\X\B.txt would be distinct from file C:\Real_World\B.txt.

Suppose there is no second B with P. There is no object in the real world than which no greater can be conceived. We can't say: ah, we have found a World_of_Ideas.Y.C, where Y is another thought, that is greater than the World_of_Ideas.X.B. This C has P and moreover, there is Real_World.C.P. The two Cs are distinct despite having the same property.

What if we say that P is a peculiar property which says that in the entire "filesystem," there can be only one C? Again this makes no sense, because an idea of God cannot be identical to God.

Again, let N refer to an essence. Define "greatest essence" counterfactually to be that description P which, if a real object had it, it would be the greatest possible thing (or TW).

Let World_of_Ideas.X.B answer to P. Then B is a conception of that thing that, if it existed in reality, then it would greatest. This at least has no hidden equivocations, but I don't know how to generate from it an argument for the existence of God.

An Attempt at Ontological Argument

Here's St. Anselm's original argument:

Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding.

And certainly that than which a greater cannot be conceived cannot be in the understanding alone.

For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived.

But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality.

Let X be a proper name, much like Chernikov is my own proper name, of a thing described by essence Ex = "than which nothing greater can be thought." Let's spell it out. Ex = "X is infinite & X is happy & X can create the world & X ought to be worshipped & ..." Ex is a conjunction of propositions describing X and is itself a proposition.

Ex is the meaning of X. Now if we propose that X exists in reality or has a reference, then we assert something new. X becomes greater by virtue of now designating two things, one in the understanding and the other in reality. But Ex is unaltered and is no greater than before. Kant then noticed rightly that "existence is not a predicate."

If, on the other hand, we say that Ex includes into itself the postulation of X's real existence, Ex' = Ex & "X exists in reality," then it's true that Ex' is now greater than Ex. But to no avail. For the idea of X or the form in the understanding is not infinite or happy or anything else; it's a mere abstraction. Therefore, it is to be understood as Ex' = "if X existed in reality, then it would be infinite, ..., and would exist." But that, "if X existed, then it would exist," obviously tells us nothing new. This time, Ex increases in greatness, but X does not, since it, even if described by Ex', need not exist really.

It follows that we can't just up and define things into real existence. But is that what the ontological argument is trying to do? Perhaps all it needs to do in order to succeed is stop at constructing Ex'. Then again, perhaps Ex' only seems to exceed Ex but not really.

No Ontological Argument Against God’s Existence

Pollock want to show that the being described by the proposition (Eg ⊃ □Eg) cannot exist (E in all of the following means "exists," and P means "perfect"). The ontological argument is used as fodder for Pollock's project throughout. He considers two versions of it, the second one being seemingly somewhat more Kant-proof:

(1) g =Df (the x such that Px);
(2) therefore, Pg;
(3') □(x)(Px ⊃ □Ex);
(4') therefore, □(Pg ⊃ □Eg);
(5') therefore, □Eg.

Our author says that the move from (1) to (2) is illegitimate. For what if we let 'Ax' in the definition of g as =Df (the x such that Ax) be 'Bx & ~Bx'? Then 'Bg & ~ Bg' will be true, which is absurd. The most we can get from (1) is

(2') □(Eg ⊃ Pg), from which we can derive with the help of (4')
(5'') □(Eg ⊃ □Eg) or "it is a necessary truth that if God exists, then He exists necessarily."

Now assuming that God exists necessarily if and only if the meaning of "God" requires that He exists,

(8) □Eg ≡ [(g =Df the x such that Px) → Eg].

But Eg does not follow, because the argument (1) - (5') is compromised at (2); hence

(9) ~□Eg and, by contraposition from (5''),
(10) ~Eg.

Therefore God does not exist; moreover, "it is necessarily true that God does not exist" (because if God existed in some non-actual possible world, then He would again exist necessarily, which we have proven He does not). (32-3)

Evaluation. There are two problems here. First, (2') does follow from (1), but it is far too weak. God would be perfect (in the understanding, which is all we need) even if He did not exist or rather existed only as a concept. Thus, we have

(2'') (Eg ⊃ Pg) & (~Eg ⊃ Pg) which is equivalent to Pg.

Further, (2) does not follow from (1) logically, but it does follow from it given the interpretation of (1) as "g is a being than which nothing greater can be conceived." The stronger inference is valid due to the nature of the predicate P, because P understood as "perfection" is surely not a self-contradiction, unlike 'Bx & ~Bx'.

If (2) follows from (1) after all, then either the OA works, or it doesn't. If it doesn't, then it's because (3') is false.

If OA works, then (9) is false. If it doesn't work, then (5'') does not obtain. In either case, (10) stands undefended.

Second, (8) should rather be

(8') [(g =Df the x such that Px) → Eg] → □Eg

in order to accommodate other possible definitions of necessary existence. So, even if the antecedent is false, we can conclude nothing about the consequent.

Pollock should have realized that proving that God does not exist "by logical means" is perilous business.

A Modal Ontological Argument

The argument looks like this:

  1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
  2. A being has maximal greatness if it has maximal excellence in every possible world.
  3. It is possible that there is a being that has maximal greatness. (Premise)
  4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
  5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
  6. Therefore, an omniscient, omnipotent and perfectly good being exists.

(NB: if X is possibly necessary, then it is necessary in some possible world. Or, in some possible world W' it is true that it exists in all possible worlds.

So, X "expands" into all the possible worlds from W', as opposed to from the actual world. But it makes no difference. Hence X exists in all possible worlds or is necessary. You need the right system of modal logic to make this conclusion. S5 works.)

However, why must we assume that (3) is correct? If maximal greatness is impossible, then it is impossible that any being has maximal excellence in every possible world: ~◊□(God exists) = □~□(God exists) = □◊(God does not exist) = there is a possible world in which God does not exist = (since God's existence is possible) God is contingent.

Thus, the modal ontological argument starts by attempting to prove that God is necessary and from that concludes that God exists in the actual world. Doesn't this seem like an overkill? Denying the crucial premise (3) does not lead to any absurdity but to a seemingly modest conclusion that God is a contingent being. And why can't God be contingent? If He is contingent, then it is unclear whether or not He exists in the actual world, because the actual world may happen to be a possible world in which God exists, or it may happen to be a possible world in which God does not exist. So Plantinga's argument does not work. What's more, I don't see how the modal ontological argument is at all equivalent to the Anselm's original version of the argument.

We might be tempted to say that (3) is contingent. But simple modal transformations show that that's not possible: either (3) is necessarily true, or it is necessarily false. At best we can say that it's conceivable that God is necessary, and it's conceivable that God is contingent. But we can't say: God is possibly necessary and is possibly contingent.