The Ontological Argument and Necessary Being

Basic Idea

Why is there something rather than nothing?

God exists necessarily (necessary being).

God sustains the existence of everything else (contingent being).

Parmenides' Monism (c. 4th c. BC)

Nothing is not
So Being is.

Being is one.
For suppose being is two or more.
Then each part of being is not the other part.
So insofar as it is not the other, each part of being is not.
But being necessarily is
Contradiction

Being has no property P.
For suppose being is P.
Then being is not not-P
Insofar as being is not not-P, being is not.
But being necessarily is
Contradiction.

Plotinus (204-270 C.E.)

Mystical, systematic Platonist influential on early Christianity.

The One = the Good is above Being and non-Being.

emanates Nous = the light by which the One sees itself.

emanates Soul

emanates Nature

Is it Good or Bad to make God a Necessary Being?

Findlay: It's bad.

Necessary existence is required to make god worship-worthy.

But God must also make a "real difference" in life.

Necessary truth is vacuous truth reflecting linguistic conventions (e.g., "either it will rain or it won't").

But conventional, vacuous truths don't make a "real difference" in life.

Adams: It's good.

Not all necessary truths are vacuous.

It is possible that we could learn them through divine illumination (Plato, Augustine).

St. Anselm's Ontological Argument, strong version.

Assumption: There is a greatest thing in the understanding. Call it g.
Reductio hypothesis: Suppose it is possible that g does not really exist.
Assumption: There is something in the understanding just like g except that it has the property of necessarily really existing. Call it G.
Assumption: G is greater than g.
So g is not a greatest thing in the understanding.
Contradiction.
So it is not possible that g does not really exist.
So it is necessary that g really exists.
So some greatest thing in the undersanding really exists.

Corollary

What comes into being or goes out of being or has parts is not necessarily real.
So the greatest thing in the understanding is eternally real and has no parts.

Anselm's argument is aimed at the atheist who believes that God does not exist. Since the atheist does not take her belief to be nonsense, she accepts the first assumption.

Gaunilo's Objection

The argument proves too much. This version is a bit tighter than Gaunilo's lost island version, which is subject to avoidable objections.

The greatest conceivable house paint exists as a concept in the understanding.
Suppose we can conceive of the greatest conceivable house paint as not existing on my house.
It is also possible to conceive of the greatest conceivable house paint as existing on my house, which is greater.
So we can conceive of house paint greater than the greatest conceivable house paint.
Contradiction.
So it is inconceivable that the greatest conceivable house paint does not exist on my house.

Corollary

The greatest conceivable housepaint lasts forever, so I'll never have to paint my house!

Anselm's response:

A proof is a proof. Deny a premise, find a counterexample, or accept the conclusion!
The greatest conceivable house paint is inconceivable. If it were conceivable, it would be on Gaunilo's house. But why is this inconceivable when the greatest conceivable thing is conceivable. If anything, the unqualified version seems more risky.

Ontological argument reformulated in terms of concepts and instances

Assumption: There is a greatest concept G(x) (i.e., G(x) exists in the understanding).
Assumption: For some possible a, G(a) (i.e., G(x) is not contradictory).
Reductio hypothesis: Suppose G(x) does not entail A(x).
Assumption: If G(x) is a concept then so is (G(x) and A(x)).
Assumption: If G(x) does not entail A(x) then the concept (G(x) and A(x)) is a greater concept than G(x).
So G(x) is not the greatest concept (from 3, 4, 5).
Contradiction (from 1, 6).
So G(x) entails A(x) (from 3, 7).
So for some possible a, G(a) and A(a) (from 2, 8).

Substitution instances for A(x):

Actual(x), Necessarily actual(x), Eternal(x), Indivisible(x), Perfect(x), etc.

"Existence is not a Predicate" (Kant)

A necessary proposition is one in which the concept of the subject is included in the concept of the predicate:

Bachelor = unmarried male
Bachelors are unmarried = unmarried males are unmarried.

Necessary propositions do not necessitate the existence of their subjects. Bachelors do not necessarily exist.

Contradiction arises if we deny the predicate of a necessary proposition

Bachelors are not unmarried = unmarried males are not unmarried.

No contradiction arises from denying the subject as well:

There are no bachelors.

The ontological argument supposedly provides an example of a subject whose denial yields a contradiction.

But existence is the positing of a thing without all its predicates, not a predicate added to its concept.

Also, possibility does not follow from conceivability (non-contradiction).

Russell's theory of reference

If you have a staff, I'll give you mine.

If you have no staff, I'll take yours! (Zen koan)

Treating existence as a predicate allows you to say:

There are things that don't exist.
(There is an x such that x does not exist.)

You might think that there have to be such things.

God doesn't exist.

Who doesn't exist?

The possible God who exists only in the understanding but not really.

Russell wanted a way to get out of this argument, so that existence would not have to be viewed as a predicate. Then the argument can be rejected for talking about possible objects and using real existence as a predicate.

Consider

The zebra in your car is happy. This gets rewritten as:

There exists a unique x such that x is a zebra and x is in your car and x is happy. (false, entails existence of zebra) This entails that a zebra exists. Now consider:

The zebra in your car does not exist . On the same translation (existence is a predicate), we get

There exists a unique x such that x is a zebra and x is in your car and x does not exist. (false, contradictory) Anselm holds a view like this, but skirts the contradiction by distinguishing existence from real existence.

really

This implicit existence claim in nonexistence claims is the logical root of Platonism. Russell calls the problem "Plato's Beard" because it is so tough to cut.

Instead, Russell translates as follows:

There does not exist an x such that x is a zebra and x is in your car. (true, entails nothing about existence of unreal zebras.) This is farther from the surface grammar of the sentence but it frees us from talking about nonexistent things. But it doesn't prove that we can't talk about them either. Nor does it prove that we never want to.

Fictional Discourse

Fictional characters exist, but don't really exist.

Neither Holmes nor his greatest opponent really exist. (True)

Realism and Nominalism

Realism: Real existence is a property of existing things.

Nominalism: Don't be tricked by grammatical form into believing that things exist.