Modal Versions of the Ontological Argument

1
Modal Versionsofthe Ontological Argument
Based on Alvin Plantingas discussion in God,
Freedom, and Evil (1974).
2
(1) It is possible that there is a greatest
possible being, B.
Possibility here is logical possibility,
roughly the absence of any internal contradiction.
Greatest possible being entails a being with
the properties of omniscience, omnipotence, and
moral perfection.
W1
W2
W3
W4
ltBgt W1
actual
So (2) There is a possible being, B, that in some
world (W1) has a maximum degree of greatness, a
degree of greatness nowhere exceeded.
3
(3) A being, B, has the maximum degree of
greatness in a given possible world, W1, only if
B exists in every possible world (W2, W3, W4).
ltBgt W2
ltBgt W3
ltBgt W1
ltBgt W4
If W1 had been actual, instead of W4, then Bs
non-existence would have been impossible.
ltBgt W2
ltBgt W1
ltBgt W3
ltBgt W4
4
(4) What is logically impossible in one possible
world is logically impossible in all possible
worlds.
So (5) Bs non-existence is logically impossible.
(from (2), (3), (4))
ltBgt W1
ltBgt W2
ltBgt W3
ltBgt W4
ltBgt W4
Therefore, (6) There exists a being, B, with
maximum greatness. (from (5))
Given that B has the properties omnipotence,
omniscience, and moral perfection (divine
attributes), we must conclude that God exists.
5
Problem in the Argument?
6
If (i) it is possible that there is a greatest
possible being and (ii) the idea contains the
idea of necessary existence, then in fact there
is some being that exists in every possible world
and in some worlds has a degree of greatness
nowhere exceeded.
The problem is subtle though apparent on closer
examination.
The original premises only support the conclusion
that there is a being, B, who exists in all
possible worlds and in some of those worlds has
maximum greatness.
B in W1 max-great
B in W2
B in W3 max-great
B in W4
7
Mistaken Assumption Greatness of B in some world
W is the only thing that counts towards the
greatness of B in W. However, the argument
forces us to consider greatness of B across
possible worlds.
In other words, we must distinguish between the
properties that S has in world W and the
properties that S has in other worlds.
This will require a distinction between two ways
of rating a being, in terms of its excellence and
in terms of its greatness.
EXCELLENCE is concerned with the properties a
being has in a particular world.
GREATNESS is concerned with the properties a
being has across all possible worlds.
8
Let excellence in W be a function of the
properties B has in W.
B in W1 a, q, z
B in W2 a,b,c
B in W3 a,e,f
B in W4 r,s,t
Suppose that a,q,z involve maximal excellence.
B will have maximal excellence in W1, but not in
W2, W3, and W4. B might be great in W2, W3, and
W4, but B would be surpassed by greatness in W1.
We can see here that even if Bs non-existence is
impossible (and so B must exist), B might not
exist with maximal excellence. If maximal
excellence involves omnipotence, omniscience, and
moral perfection, then B might exist but without
this set of properties.
Hence, if God is a maximally excellent being, we
cannot conclude that God exists.
9
Let greatness in W be a function of the
properties B has across all possible worlds. Let
maximal greatness entail maximal excellence in
all worlds.
(7) It is possible that there is a being, B, that
has maximal greatness.
So (8) There is a possible being that in some
world, W, has maximal greatness
B in W1 g-max
W2
W3
W4
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(9) A being B has a maximum degree of greatness
in a given world W only if it has maximal
excellence in all possible worlds.
B in W2 e-max
B in W3 e-max
B in W1 g-max
B in W4 e-max
(10) A being has maximal excellence in a given
world W only if it has omniscience, omnipotence,
and moral perfection in W.
If W1 had been actual (instead of W4), then B
would have had omnipotence, omniscience, and
moral perfection in every possible word. If W1
had been actual, then it would be impossible for
there not to exist some omnipotent, omniscience,
and morally perfect being.
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(11) What is logically impossible in one possible
world is logically impossible in all possible
worlds.
B W4
B W1
B W2
B W3
Therefore, (12) Bs non-existence as a maximally
great being is logically impossible. (from (7),
(9), (10), and (11)). (13) A maximally great
being B exists, together with the properties of
omnipotence, omniscience, and moral perfection.
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Final Overview of the Argument
(14) There is a possible world in which maximal
greatness is instantiated.
W2
W3
W4
B in W1 g-max
(15) Necessarily, a being is maximally great in
one world W1 only if B has maximal excellence in
every world.
B in W2 e-max
B in W3 e-max
B in W1 g-max
B in W4 e-max
13
It follows from (14) that there is a possible
world W1 such that had it been actual, then there
would have existed an omnipotent, omniscient, and
morally perfect being. But this being would have
had these qualities in every possible world, not
just W1. So had W1 been actual it would have been
impossible for there to be no such being.
B in W3 Omnipotence Omniscience Moral Perfection
B in W2 Omnipotence Omniscience Moral Perfection
B in W4 Omnipotence Omniscience Moral Perfection
B in W1 g-max
(16) What is logically impossible in one possible
world is logically impossible in all possible
worlds.
So (17) The non-existence of a maximally great
being, B, is logically impossible.
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(18) Necessarily a being has maximal excellence
in every world only if he has omnipotence,
omniscience, and moral perfection in every world.
B in W1 Omnipotence Omniscience Moral Perfection
B in W4 Omnipotence Omniscience Moral Perfection
B in W3 Omnipotence Omniscience Moral Perfection
B in W2 Omnipotence Omniscience Moral Perfection
So (19) There exists no omnipotent, omniscient,
and morally perfect being is a logically
impossible statement. Therefore, (20) God exists.
God exists W4
Actual