TWO ARGUMENTS OF ST. ANSELM 1. In Proslogium II, St. Anselm argues as follows

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APPENDIX
TWO ARGUMENTS OF ST. ANSELM
1. In Proslogium II, St. Anselm argues as follows:
And assuredly that than which no greater being can be conceived, cannot exist in
the understanding alone. For suppose it exists in the understanding alone: then it
can be conceived to exist in reality; which is greater.
Therefore, if that than which nothing greater can be conceived exists in the
understanding alone, the very being than which nothing greater can be conceived,
is one, than which a greater can be conceived. But obviously this is impossible.
Hence, there is no doubt that there exists a being, than which nothing greater can
be conceived, and it exists both in the understanding and in reality. 1
I shall take "exists in the understanding alone" to mean "is logically
possible but not actual", and I shall take "a being than which no
greater can be conceived" to mean "a being than which no greater
being is logically possible", i.e., "a maximally great being". Moreover,
I shall take "[If X] exists in the understanding alone, [then] it can be
conceived to exist in reality, which is greater" to mean "If X is merely
logically possible, then it would be greater if it were actual"; and I
shall take it that the bearer of the predicate "would be greater if it were
actual" is, at least, a logically possible object.
Given these interpretations, Anselm's argument can be restated as
follows:
(1) If there were a logically possible object which is a maximally
great being and it were merely logically possible (rather
than both logically possible and actual), then it would be
greater if it were actual.
But
(2) "X is a logically possible object which is maximally great"
entails "X could not (and would not) be greater under any
conditions, including its actuality".
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So
(3) there is no logically possible object which is both maximally
great and merely logically possible.
But
(4) there is in fact a logically possible object which is maximally
great (namely, God).
Hence
(5) there is a logically possible object (i.e., God) who is not
merely logically possible but both logically possible and
actual as well.
2. Premisses (1) and (4) of this argument are, of course, contro
versial. Premiss (4) is false unless (a) there are logically possible
objects and (b) God is among their number. However, I have
defended the thesis that there are logically possible objects in 7.5, and
I have discussed the question whether God is logically possible in
Chapters 6 and 9; so I shall say no more about premiss (4) here.
But now what are we to make of premiss (1) - the claim that if there
were a merely logically possible object which is maximally great, then
it would be greater if it were actual? Isn't that claim suspiciously
similar to the claim that, e.g., a merely logically possible glass of beer
would, ceteris paribus, contain more beer if it were actual? Reflection
will show that the answer is "No". Qua glass of beer, the only
difference between a merely logically possible glass of beer and an
actual one is just that the former is merely logically possible and the
latter is actual. Actuality is not a beer-increasing property and being
merely logically possible is not a beer-diminishing property. However,
things are otherwise with respect to greatness. Actuality is a
greatness-increasing property relative to God, as the following will
show.
We can say with perfect propriety about some individuals (e.g., St.
Francis) that it is better than not that they are (or were) actual. And
it is even clearer that it is better than not that God, a maximally great
being, be actual. But maximal greatness entails having every property
TWO ARGUMENTS OF ST. ANSELM 143
which is such that it is better than not that an omnipotent, omniscient
and perfectly good being have it. Hence, even though, for most
predicates, it is false that the actuality of the object which bears them
increases the amount or degree in which they are possessed, actuality
is a greatness-increasing property relative to God (though not relative
to, say, Hitler). But now it is surely a necessary truth that if an
individual, X, lacks a given greatness-increasing property, G, then,
ceteris paribus, it would be greater if it possessed G. It follows that if
God is merely logically possible, then he would be greater if he were
actual.
It is of note that, even if we subscribe to a relativistic interpretation
of actuality - even if we hold that "X is actual" always expands into
"X is actual relative to a given possible world, W' and that, hence,
the possible world, which is actual from our point of view, has no
privileged status with respect to actuality, my argument will still hold.
For, whatever may be thought of other possible worlds, it is plainly
better than not that God exist in the world which is actual from our
point of view. And, again, it is a necessary truth that a maximally great
being would have every property which is such that it is better than
not that he possesses it.
But, finally, does God exist, not only in our world, but in every
possible world? Anselm's Proslogium II argument does not require
this to be the case; but if it is not the case, then God does not exist
with SS necessity. And it is not, perhaps, just intuitive that God
occupies every possible world. (Aren't there possible worlds in which,
e.g., the only non-divine things are mud and rain? And if so, is it really
better than not that God occupy those worlds?) But fortunately we
need not simply rely on our intuitions here, since Chapter 5 provides
us with a demonstration that if God exists in one possible world, then
he exists, with SS necessity and qua maximally great, in all possible
worlds, including our own. (If it is clear that God would not inhabit
worlds in which the only non-divine things were, e.g., mud and rain,
then, if God exists in some possible world, so much the worse for
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mud-and-rain 'worlds'. They are demonstrably not possible.)
3. In Responsio I, Anselm presents the following argument:
Furthermore, ifit can be conceived at all, it must exist. For no one who denies or
doubts the existence of a being than which a greater is inconceivable [i.e., God]
denies or doubts that if it did exist, its non-existence would be impossible. For
otherwise it would not be a being than which a greater cannot be conceived. But
as to whatever can be conceived but does not exist - if there were such a being,
its non-existence ... would be possible. Therefore if a being than which a greater
is inconceivable can even be conceived, it cannot be non-existent.2
Norman Malcolm has written as follows about this argument:
Let me summarize the proof. If God, a being greater than which cannot be
conceived, does not exist then He cannot come into existence. For if He did He
would either have been caused to come into existence or have happened to come
into existence, and in either case He would be a limited being, which by our
conception of Him He is not. Since He cannot come into existence, if He does not
exist His existence is impossible .... Thus God's existence is either impossible or
necessary. It can be the former only if the concept of such a being is se1f
contradictory or in some way logically absurd. Assuming that this is not so, it
follows that He necessarily exists.3
What Malcolm writes here is a considerable departure from what
Anselm actually says. Anselm does not claim, in the envisaged
argument, that if God does not exist, then his existence is impossible.
This is in fact demonstrable. (One way of demonstrating it is to point
out that (1) the denial of the conclusion of modal argument M
(Chapter 5), namely, that God exists, entails the denial of one of M's
premisses and (2) the premiss which affIrms God's logical possibility
is the best candidate for being rejected.) But Anselm does not
demonstrate it - at least not in connexion with the present proof.4
Another defect in Malcolm's interpretation is that Anselm evidently
intends to reach his conclusion via modus tollens, but there is no hint
of this in Malcolm's interpretation.5
4. Let me say more about the modus tollens character of Anselm's
proof. One not implausible interpretation of the proof is as follows:
TWO ARGUMENTS OF ST. ANSELM 145
(1) If God does not exist, then if God existed, his non-existence
would be possible.
But
(2) if God existed, then his non-existence would not be
possible.
So
(3) the antecedent of (1) is false, i.e., God exists. (From (1) and
(2) by modus tollens.)
On this interpretation, Anselm holds that "If God existed, his non
existence would be possible" is contradicted by "If God existed, his
non-existence would not be possible". But in fact it is doubtful that
these are contradictories. For, again, it is demonstrable that if God
does not exist, then it is logically impossible that he exists. So if God
does not exist, the antecedents of the allegedly contradictory condi
tionals are neessary falsehoods. But then, if we treat them as
counterfactual conditionals, they are, if David K. Lewis is right,6 both
vacuously true and, hence, not contradictories. And, of course, the
same is true of them if we take them to be material conditionals. But
Anselm cannot presuppose that it is false that God does not exist
without begging the question. So, on the present interpretation,
Anselm's argument is a spectacular failure.
But there is another, more charitable interpretation of Anselm, on
which it turns out to be true that if God does not exist, then it is
possible that his non-existence is both possible and not possible. And
the (necessarily true) denial of this consequent entails, by modus
tollens, the denial of the antecedent, i.e., it entails that God exists. On
this interpretation, we capture the modus tolle ns character of Anselm's
argument, while avoiding the mistake which is embodied in the first
interpretation. In presenting the new interpretation, I shall avoid
using counterfactual conditionals, since the argument really does not
need them. I have the following interpretation in mind:
(1) It is necessarily true that if God exists, then his non
existence is logically impossible.
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Hence
(2) if God does not exist, then it is necessarily true that if God
exists, then his non-existence is logically impossible. (Since
the consequent of the conditional is necessarily true, it is
entailed by every proposition, including the antecedent.)
So
(3) if God does not exist, then each possible world is such that
if God exists there, then his non-existence is logically
impossible there.
(4) There is a possible world in which God exists.
So
(5) if God does not exist, then there is a possible world in
which his non-existence is logically impossible. (From (3)
and (4) by modus ponens.)
But now assume that
(6) God does not exist.
Then
(7) there is a possible world in which God does not exist and,
hence, in which God's non-existence is logically possible.
But
(8) what is logically possible in one possible world is logically
possible in all possible worlds: every possible world is such
that God's non-existence is logically possible there.
Hence
(9) if God does not exist, then there is a possible world in
which God's non-existence is both logically impossible
and logically possible. (From (5) and (8).)
But
(10) the consequent of (9) is false.
So
(11) the antecedent of (9) is false, i.e., God exists. (From (9) and
(10) by modus tollens.)
5. So goes the charitable interpretation of Anselm's argument. The
TWO ARGUMENTS OF ST. ANSELM 147
only controversial premisses are (1), (4), and (8). (1) and (4) have
been defended in Chapters 5, 6, and 9; and the following is a proof
of (8): If a philosopher claims that some proposition, p, which is
possibly true in the actual world is necessarily false in another
possible world, then he owes us an example of such a proposition;
and it is very unlikely that such an example can be cited. So what is
possibly true in the actual world is possibly true in all other possible
worlds. And if someone claims that our world is special in that
respect, then he owes us an explanation of why that should be so; and
it is very doubtful that he can produce such an explanation.
Actually, as we saw in Chapter 5, premisses (1) and (4) alone entail
that God exists: Anselm's argument is unnecessarily complicated.
But the surprising thing is not Anselm's lack of elegance, but the
essential soundness of his 11th century modal intuitions.
NOTES
PREFACE
1 Plantinga, The Nature of Necessity (Oxford: The Clarendon Press, 1974).
2 See, for example, Plantinga, 'Is Belief in God Properly Basic?', Nous XV (March,
1981), and 'Is Belief in God Rational?' in Rationality and Religious Belief, ed. C.
Delaney (Notre Dame: University of Notre Dame Press, 1979).
CHAPTER 1
1 I have discussed this topic in detail in 'An Examination of the 'Soul-Making'
Theodicy', Amercan Philosophical Quarterly 7 (1970) and 'Do Theodicists Mean
What They Say?' Philosophy 49 (1974).
2 Another way of meeting the objection is just to affirm that all that God has
brought about with respect to nature is the 'singularity' which gave rise to the big
bang, and that it is doubtful that any scientific laws were in effect at that time and
afortiori doubtful that God's actions violated any scientific laws. However, I prefer
the approach which I present in the text, since (1) it is unwise for religionists to
commit themselves to scientific hypotheses which are far from certain and, indeed,
in a state of flux, and (2) my approach in the text explains how God could have
sometimes intervened in nature after the big bang; and this will be welcomed by
the many theists who believe, or would like to believe, that he has done so.
3 Someone may wish to say here that God's not making us clairvoyant is itself
logically necessary for E. But the person who makes this claim in effect abandons
the envisaged attempt to specify Es nature. I shall, for simplicity, henceforth ignore
this complication.
4 See W. V. Quine, The Ways of Paradox, (New York: Random House, 1966),
p.4.
CHAPTER 2
1 William L. Rowe, The Cosmological Argument (Princeton, N.J.: Princeton Univer
sity Press, 1975). All Chapter 2 references to Rowe's writing but one will be to this
book.
2 It should be pointed out that Clarke would not be satisfied with the thesis that,
since, e.g., sets are logically necessary beings, all of reality does not consist merely
148
NOTES 149
of contingent things. For Clarke wants to establish the conclusion, not just that
there is a logically necessary being, but a logically necessary being who is a cause
of contingent things.
3 See Rowe, pp. 222-269.
4 For simplicity, I am assuming, throughout my discussion of Clarke's argument,
that all contingent things are subject to causal explanation, i.e., I am ignoring, for
the time being, the exceptions which are found in quantum mechanics.
5 Rather than states of affairs. The reason for this qualifier can be found on pp.
97-114. See also pp. 149-151.
See note 5.
6
7 William L. Rowe, Philosophy of Religion, An Introduo::tion (Belmont, California:
Dickenson, 1978), p. 57.
8 There is a question which even more obviously does not have a true answer, given
that the only true answer would refer to a cause outside the envisaged set, viz.,
"Why are there any causes at all?"
9 Actually, however, Clarke's subsequent argument for the infinity of the logically
necessary cause (pp. 227-233), which is in essence an argument of St. Anselm
which I shall discuss in Chapter 6, should, for a reason I shall present there, be
taken as an argument that God is in fact essentially disembodied.
10 Perhaps it would be better to say that there is a prima facie case against the
existence ofthe envisaged series, but one which can, in the end, be overthrown by
science.
CHAPTER 3
Though, instead of considering the more specific claim that the eye is camera-like,
I
Plantinga considers the claim that the universe resembles "the productions of
human contrivance" (p. 97), inasmuch as "it exhibits curious adaptation of means
to ends" (p. 101). See Alvin Plantinga, God and Other Minds (Ithaca: Cornell
University Press, 1967), Chapters 4 and 10.
2 David Hume, Dialogues Concerning Natural Religion in The Empiricists (Garden
City, New York: Doubleday, 1974), pp. 466-469.
3 Ibid., pp. 459-461.
4 God and Other Minds, p. 104.
5 Ibid., pp. 104-106.
6 Ibid., p. 102.
Another pseudo-argument which this description fits (which is cited by Plantinga
on pp. 101-102) is:
(1) Every member of the class ofChevrolets plus the universe, of which we know
whether or not it is the product of intelligent design, is indeed the product
of intelligent design.
150 NOTES
(2) The universe is a member of the class of Chevrolets plus the universe.
So
(3) probably the universe is the product of intelligent design.
7 A similar argument shows that what is wrong with the pseudo-argument cited in
note 6 is that there are some members of the class of Chevrolets plus the universe
(namely, the random configurations cited above) about which we know that they
are not the products of design; so we know that there is no nomic connexion
between being a member of that class and being designed.
CHAPTER 4
I Kurt Baier, The Moral Point of View, abridged edition (New York: Random House,
1965), p. 150.
2 Ibid., p. 156.
3 Actually, things are a bit more complicated. The suicidally depressed patient
harms himself by committing suicide if, even though he does not desire continued
life at the time of his suicide, he would, in the normal course of events, have come
to desire (and acquire) continued life in the future. Hence the reader should add
to my subsequent definition of 'hedonist', "a person about whom it is false that he
would have come to desire (and acquire) moral innocence, were it not for his
present misdeeds". Whether there are in fact such people is not crucial to my
central argument, for a reason which will shortly emerge.
4 The entailment does not go the other way. A child is not harmed by the boredom
which sometimes accompanies his piano practice, even though he strongly desires
its absence as an end-in-itseIf.
5 See David K. Lewis, Counterfactuals (Cambridge: Harvard University Press,
1973), pp. 24-26.
I have in mind Lewis's possible world analysis of counterfactuals. See the book
6
referred to in the preceding note.
7 According to The Compact Edition of the Oxford English Dictionary (p. 1964),
'oblige' means "to bind by ... a moral ... tie, to render liable ... ".
According to The Random House Dictionary oft he English Language (p. 917), 'oblige'
means (1) "to require or constrain" and (2) "to bind morally ... ".
There are, of course, other senses of 'oblige'. The latter dictionary gives these
alternative senses: "(a) to make (an action, policy, etc.) necessary ... : 'Your
recalcitrance obliges firmness on my part'; (b) to place under a debt of gratitude:
obligate; (c) to favor or accommodate: 'Mr. Weems will oblige us with a song'; (d)
to be kindly accommodating; help out).
It is plain, however, that none of these alternative senses is at all a plausible
candidate for the meaning of 'morally oblige(d)'. A review of various major
dictionaries reveals no ambiguity in the term 'morally obliged' which is analogous