Philosophy of Religion 30: 159-168, 1990.
9 1991 Kluwer Academic Publishers. Printed in the Netherlands.
On Rescher On Pascal's Wager
G R A H A M OPPY
Department of Philosophy, RSSS, Australian National University,
Canberra, ACT 2601
In Pascal's Wager: A Study Of Practical Reasoning In Philosophical
Theology, 1 Nicholas Rescher aims to show that, contrary to received
philosophical opinion, Pascal's Wager argument is "the vehicle of a
fruitful and valuable insight - one which not only represents a milestone in
the development of an historically important tradition of thought but can
still be seen as making an instructive contribution to philosophical
theology. ''2 In particular, Rescher argues that one only needs to adopt a
correct perspective in order to see that Pascal's Wager argument is a good
argument. Moreover, there seems to be a certain amount of contemporary
support for Rescher's claim that Pascal's Wager argument can be seen to
be a good argument when properly construed. 3 However, despite this
recent trend to adopt a more sympathetic stance towards Pascal's Wager
argument, I propose to defend the traditional view that Pascal's Wager
argument is almost entirely worthless - at least from the theological
standpoint. (No doubt, it has historical significance from the standpoint of
decision theory; but that's a separate matter.)
This paper is divided into two sections. I begin, in section 1, by outlining the defence of Pascal's Wager argument which is given by Rescher in
Pascal's Wager. Then, in section 2, I explain why this defence fails.
.
As Rescher emphasises, Pascal's Wager argument unfolds against a
background of scepticism about the powers of theoretical reason. "Pascal
holds, with the Renaissance skeptics, that our human resources for
securing knowledge by inquiring reason are wholly inadequate to the
demands of apologetics. ''4 Indeed - and this is a point which will be
160
important later on - Rescher is at pains to note that Pascal insists that
theoretical reason is "utterly impotent" in the context of the assessment of
the question of God's existence. Consequently, the Wager argument is
forced to appeal to a further species of "reasons", viz: practical reasons.
According to Rescher, the core of Pascal's Wager argument - at least
from a logical point of view - lies in decision theory (i.e. in the theory of
decision-making in situations of uncertainty about outcomes). We can
illuminate this basic argument by referring to the following table:
Options
Returns to the chooser
God Exists
(Prob=p)
God does not exist
(Prob= 1 - p)
Bet on God
oo (-B)
-13
Bet against God
little or nothing
(perhaps negative)
0
The idea is that, in deciding whether or not to bet on God - i.e. in deciding
whether or not to believe in God - what we do is to consider the expected
return for each of these options. Moreover, we suppose: (i) that the cost of
making the bet is B; (ii) that the subjective probability which we assign to
the claim that God exists is p; and (iii) that the returns on our decision are
as outlined in the above table. (Note that, if we bet on God, and it turns out
that God exists, then our return is infinite - for the value of oo--B is just
oo.) But now we note that: (a) the expected return of a bet on God is
oo.p + ( - B ) . ( 1 - p ) which is oo provided that p is finite; and (b) that the
expected return of a bet against God is (little or nothing).p + 0 . ( 1 - p )
which is little or nothing (and quite likely negative). So - according to
Pascal's Wager argument - it is reasonable to conclude that our expected
return is infinite in the case that we bet on God, and little or nothing in the
case that we do not bet on God; and hence it is reasonable to conclude that
one ought to bet on God.
Now, of course, there are a number of assumptions which are required
by this argument. It is immediately apparent that, in order to reach the
conclusion that one ought to bet on God, one needs to defend the
following claims:
1.
It is reasonable to suppose that the value of a bet on God, in the
case in which God exists, is 0o.
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2.
3.
4.
5.
It is reasonable to assign a finite value to p (i.e. to the probability
that God exists).
It is reasonable to suppose that there are only two options between
which one is to choose, viz: (i) a universe which includes the
traditional Christian God; and (ii) a universe without deities (or
transcendent beings) of any sort.
It is reasonable always to act so as to maximise expected utility.
It is reasonable to suppose that there are no theoretical considerations which can decide the question whether God exists.
Consequently, it is plain that there are a number of types of persons who
will be untouchedby this argument. Among these - as Rescher notes - are
the following: (i) convinced atheists, who set the value of p to zero; (ii)
those, such as out-and-out hedonists who live for the pleasure of the
moment alone, who set the value of future benefits to zero; (iii) those,
such as all-trusting disbelievers who hold that if God did exist He would
be bound to be all-forgiving, who maintain that one would get the future
benefits whether or not one believed; (iv) radical sceptics who hold that
both knowledge and reasonable conviction are impossible; (v) noncalculating sceptics who, for one reason or another, are not prepared to
perform the sort of self-interested calculation which the argument requires; and (vi) non-Christian theists (e.g. Zoroastrians) who have very
different ideas about the rewards of belief. 5
However, Rescher does not suppose that the fact that the argument will
not touch some people points to a defect in the argument. Indeed, it is one
of the main themes of Rescher's book that Pascal's Wager has been
persistently misunderstood by philosophers who (he claims) have supposed that the argument is meant to provide reasons which would persuade any rational person that s/he ought to believe in God. Not so,
according to Rescher. Rather, what the argument is intended to do - in
Rescher's view - is to persuade any person who thinks that there is a finite
probability that the Christian God exists, who holds "standard views"
about the nature of that God, and who is always prepared to make decisions on the basis of considerations of maximum expected utility:
"Pascal's discussion is directed at t'homme moyen sensuel, the ordinary,
self-centred, "man of the world" preoccupied with his own well-being and
his own prudential interests. Pascal does not address the already converted, but the glib worldly cynic - the free thinking libertin of his day,
the sort of persons who populated the social circle in which Pascal himself
moved prior to his conversion. ''6
So, Rescher's assessment of the worth of Pascal's Wager argument is
this: The argument is intended to be directed towards people who already
hold certain assumptions, and to convince these people that they ought to
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believe in God. Moreover, given this intention, it is clear that the argument
is a good one - i.e. it is clear that people who hold the assumptions in
question ought to be persuaded by the argument to believe in God.
.
There is a logical (or perhaps mathematical) error in Rescher's version of
Pascal's Wager argument which - on the face of it - completely
invalidates the argument. This error stems from the fact that Rescher
throughout supposes that there are only two types of values which the
probability of the proposition God exists can take: zero, orfinite.
(To see that Rescher does repeatedly make this assumption, consider
the following extracts from his book:
All that matters for [Pascal's] reasoning is that [the probability of
God's existence] is non-zero. As long as there is a finite chance of
God's existence - no matter how small - the expectation of the "betand-believe" alternative outweighs that of its rival. 7
Pascal's reasoning is only in a position to persuade someone who
believes that God may exist. 8
A gamble is advantageous on the basis of [the] expected-value
standard whenever:
chance of winning
cost of stake
potential loss
chance of losing
size of prize
potential gain
And if the potential gain is infinite, this standard favours the gamble as
long as the chance of winning is non-zero. 9
[The argument] will certainly fail to touch the convinced atheist.
Someone who sets the probability of God's existence at zero will
obviously not arrive at the argument's conclusion. 1~
Pascal's argument is simply addressed to those who see the existence
of the Christian God as a real possibility to which they are prepared to
accord a nonzero probability (however "imponderable" they may deem
this quantity to be in other regards). Apart from this the numerical
status of this probability - even its having a definite and stable value is quite irrelevant.ll
Everything turns on what we are (responsibly) prepared to deem to
be real possibilities, those having probabilities at any rate greater than
zero (no matter how low we may think them to be). 12
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It is obvious from these remarks that Rescher supposes that either the
probability that God exists is zero (in which case it is impossible that God
exists), or else that the probability that God exists is finite).
However, it is incorrect to suppose that "non-zero" and "finite" are coextensive; for it is epistemically possible that the probability that God
exists is infinitesimal. Moreover, when this is recognised, it is also
immediately apparent that the calculation of the expected return of a bet
on God is no longer as straightforward as the initial argument suggested.
For, of course, the value of oo.p + (-B).(1 - p) can take any value greater
than ( - B ) . ( 1 - p ) depending upon the exact values of oo and p.13 And
so, plainly, the argument from expected utility does not go through
in all cases; it depends upon the particular values of oo and p which are
involved. I4
Now, to this, it may be objected that the essence of Rescher's version of
Pascal's Wager argument is untouched. True, Rescher does overlook the
fact that "non-zero" and "finite" are not coextensive - but all this shows
that the class of people who will be untouched by the argument must be
extended to include: (vii) cautious sceptics who are not prepared to assign
a finite value to the probability th~it the Christian God exists. That is, can't
Rescher reply that - although his own presentation of the argument is
slightly flawed - it is nonetheless true that the argument can still succeed
in achieving its Apologetic aim? After all, if we grant the piece of reasoning which we presented initially is cogent, then it is still true that we must
grant that mayone who accepts the assumptions 1.-5. listed above is
required to accept the conclusion that God exists,
This reply will not do. The claim that Pascal's motives are entirely
Apologetic - i.e that he only seeks to address people who already hold
certain views - is plainly not as significant as Rescher supposes. For,
while it might be true that "Pascal's Wager" is best interpretted as a sort of
consistency argument ("if you believe those things, then you must believe
in God, on pain of inconsistency"), it is clear that what one of Pascal's
targets ought to do, on learning of his/her (apparent) inconsistency, is to
examine all of the beliefs which s/he has which are relevant to the generation of the inconsistency. But then s/he will be faced with the question of
whether s/he ought to accept the (apparently) dubitable assumptions which
are central to the argument. Perhaps we can grant that anyone who accepts
the assumptions 1.-5. is required to accept the conclusion that God exists but ought one to accept all of these assumptions?
(Here is a parallel case: Suppose that I know someone who (somewhat
confusedly) believes (i) that if there is no God, then morality has no
objective foundation; (ii) that morality has an objective foundation; and
(iiP that it is quite unclear whether or not there is a God. I can point out to
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this person that it follows logically from (i) and (ii) that there is a God but, of course, it doesn't follow from this that they have good reason to
believe that there is a God! For it might be that they have very good
independent reasons for believing (iii), and very weak reasons for believing (i) or (ii) (or both). The most that a consistency argument can do is to
show that I need to revise some of my beliefs - but it alone cannot tell me
which beliefs need to be adjusted.)
The point which I have just made can be summarised in the claim that it
is important to distinguish two senses in which Rescher could be taken to
be saying that Pascal's Wager is successful. (i) On the one hand, it could
be that Rescher is saying that the argument is successful because it shows
that any persons who accept 1.-5. ought to believe in the Christian God, on
pain of logical contradiction. But, on this construal, there is the underlying assumption that persons who accept 1.-5., and who learn that they are
thus committed to belief in the existence of God, won't then choose to
modify themselves in such a way that they no longer accept one (or more)
of 1.-5. (ii) On the other hand, it could be that Rescher is saying that the
argument is successful because it shows that any persons who accept 1.-5.
ought to believe in the Christian God, because that is overall the most
rational thing for them to do. And, on this construal, it would no longer be
true that there is an underlying assumption that persons who accept 1.-5.
won't choose to modify themselves in such a way that they no longer
accept one (or more) of 1.-5.
Perhaps it can be granted that the Wager argument is a successful piece
of Apologetic argumentation in sense (i). (Of course, it is crucial to this
concession that the people to whom it is directed assign a finite probability
to the claim that God exists.) However, it is important to note how weak
this claim is - for it says nothing about the overall rationality of the
situation in which these people are placed. Surely l'homme moyen sensual
ought, upon being informed of Pascal's argument and the nature of his
own beliefs, to ask whether it is reasonable to continue to accept each of
1.-5. But if it is quite clear that it is not at all rational to subscribe to all of
1.-5.
then it is hard to see that there is any great merit in the argument,
even as an instrument of Apologetics. (What's so great about getting very
stupid people to believe in God? It's probably easier to do that by telling
them stories about hellfire and damnation.) What would be an achievement would be to produce an argument which was successful in sense (ii)
- but it remains to be argued that Pascal's Wager argument even comes
close to achieving this.
So far, then, I have suggested that Rescher's appeat to the nature of the
Apologetic task for which Pascal's Wager argument is designed does not
manage to evade the question of the soundness of that argument. What
165
Rescher suggests is that the validity of the argument suffices to show that
it is a good argument when directed to people who accept all of the
premises of that argument. However, it is important to note that, from this
perspective, any valid argument which has the conclusion that one ought
to believe that God exists will be just as good as Pascal's Wager argument.
In order to determine whether there is a more substantial sense in which
Pascal's Wager argument is a good argument, we need to consider the
question whether it is reasonable to accept all of the premises of the
argument. So let's see.
We have already noted that it is a crucial assumption of the argument
that there are really only two alternatives between which reason is impotent to decide, viz: (a) that there is a God who rewards all those who
believe in Him with eternal and infinite happiness; and (b) that life ends
with death. But it seems to me that there are infinitely many other alternatives between which Pascal's homme moyen sensual ought to say that
reason is equally impotent to decide. Among these possibilities are: (c)
that there is a God who has predetermined our final destiny, so that what
we do in this life has no consequences for our fortune in the next llfe - in
which case it seems that we ought to do all that we can to make this life as
pleasant as possible; (d) that there is a God who looks with great favour on
agnostics and atheists because they have proportioned their belief to the
evidence, and have not engaged in a mercenary manipulation of their own
understanding; (e) that there is a God who is not satisfied by mere belief in
his existence, and who only rewards those who subscribe to the principles
of the one true faith (be it Catholicism, Methodism, Anglicanism, Presbyterianism, Congregationalism, Greek Orthodoxy, Mormonism, Seventh
Day Adventism, Jim-And-Tammy Bakkerism, Judaeism, Islam, Hinduism,
or the worship of Kali or Odin); (f) that there is a committee of gods who
have different desiderata for permission to enter the next life, and who
alternate in making decisions (so that there is no consistent basis upon
which decisions are made); and so on. 15
Now, perhaps, it will be objected that, although this argument does
show that there are further possibilities which Pascal ought not to have
discounted, nonetheless it does not serve to establish that there is really an
infinite set of possible deities. No matter; we can establish this quite
directly. For consider the following:
1. For each natural number n there is the deity S n who is much like the
traditional Christian God, except that s/he rewards all and only
those people who live for exactly n years (rounded down to the
nearest whole year).
2. For each natural number n there is the deity T n who is much like the
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traditional Christian God, except that s/he rewards all and only
those who are among the first n people to die.
. For each natural number n there is the deity U n who is much like
the traditional Christian God, except that s/he rewards all and only
those who are not among the fn'st n people to die.
Apart from these rather arbitrary (not to say whimsical) deities, there are
also some other deities (in other worlds) who are guided by slightly more
substantial considerations, e.g.:
. For each natural number n, there is a world W n in which there are n
deities (all much like the Christian God) who reward all and only
those people who believe that there are n deities who are much like
the Crhistian God.
And so on. (It doesn't require much imagination to multiply these examples. The way in which these possible deities differ from the traditional
Christian God - by which I mean, at a minimum, a being who satisfies the
description "the unique omnipotent, omniscient, eternal, and wholly good
creator of the world ex nihilo" - is in their moral qualities. But, while
these beings are not wholly good, I do not see that this fact provides any
reason to suppose that the existence of these beings is somehow more
improbable than the existence of the more traditional Christian God.)
I would be prepared to argue that the available evidence does not
support the existence of any one of the deities which I have mentioned in
the two preceding paragraphs to a greater extent than each of the other
deities mentioned there. Moreover, I would also be prepared to argue that
anyone who is even moderately sceptical about the abilities of theoretical
reason to reach conclusions about the nature and existence of transcendent
entities will agree in this judgement. However - as an anonymous
reviewer of this paper pointed out to me - for the purposes of the present
argument it is sufficient to note that one who holds that theoretical reason
is "utterly impotent" when it comes to transcendental questions can hardly
have good reason to suppose that some of these hypotheses are more likely
than others. In other words: Pascal's l ' h o m m e m o y e n sensual ought to hold
that there is an infinite range of possible deities about whose existence he
acknowledges that his reason is impotent to decide. But, if this is so, then
surely l ' h o m m e moyen sensual ought to assign no more than an infinitesimal value to the subjective probability that any one of these deities
exists. And so it seems that there is good reason for l ' h o m m e m o y e n
sensual to claim that a thorough scepticism about the ability of theoretical
reason to decide the question of the existence of God will lead to the
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conclusion that it is not reasonable to assign a finite value to the probability that the standard Christian God exists - and also that it is not
reasonable to suppose that there are only two alternatives between which
one must choose.
To sum up the argument: Rescher's version of Pascal's Wager argument has a very peculiar status. For, on the one hand, it is supposed to be
directed towards people who are very sceptical about the ability of
theoretical reason to establish the existence of "transcendent entities". Yet,
on the other hand, it also presupposes that the people to whom it is
directed will concede that there are only two live options (either the
Christian God exists, or no transcendent beings exist), and that these
people will assign a finite probability to the claim that the Christian God
exists. But these people - if there are any such people - are in a very
uncomfortable epistemic situation; for their alleged scepticism about the
abilities of theoretical reason seems to be in considerable tension with the
further claims which they wish to make. But, given this fact, what these
people need to do is to examine the beliefs which they already have in
order to modify (or perhaps discard) some of the discordant beliefs.
Moreover, it is certainly not the case that these people can reasonably use
the whole set of these discordant beliefs in order to arrive at further
beliefs.
Finally, it should be noted that it could be argued that there is something repugnant about the idea that one might make use of Rescher's
version of Pascal's Wager argument in the service of apologetics. The
reason for this claim is that, in order to use the argument as a tool of
apologetics, we do not need to suppose that it is a good argument in the
second of the two senses distinguished earlier in this paper. If the point is
just to get people to believe in God, then it doesn't matter whether it is
overall most reasonable for these people to believe in God - and so we
could, quite cynically, make full use o f the Wager argument against not
terribly bright people in fuil knowledge of the fact that the argument is
defective (i.e. in full knowledge of the fact that it is not reasonable to
accept all of the premises of the argument). However, if we care about
what it is most rational for people to believe (in the light of the evidence
which they currently possess, and in light of the cognitive abilities which
they enjoy), then it would be irresponsible (and indeed immoral) for us to
use the Wager argument on the sorts of people in whom it could
reasonably be expected to bring about belief. (If we think that there are
independent means of showing that God exists, then we should appeal to
those means. If we think there are no such independent arguments, then
perhaps we should question our own belief that God exists.)
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Notes
1. University of Notre Dame Press, Notre Dame, 1985.
2. Ibid., p.x
3. Cf. C.D. Kay, "Review of N. Rescher's Pascal's Wager," International
Journal for Philosophy of Religion 22 (1987): 112-113; and G. Brown, "A
Defence of Pascal's Wager," RS 20 (1985): 465-479.
4. Ibid., p. 5
5. Ibid., pp. 24-25
6. Ibid., pp. 26-27
7. Ibid., p. 15
8. Ibid.,p. 16
9. Ibid., pp. 16-17
10. Ibid., p. 24
11. Ibid., p. 35
t2. Ibid., p. 93
13. I have mentioned the "value of ~ " here, because - as Cantor first noted there are actual many different infinities, of differing magnitudes. I shan't
worry about the comp!ications to which this distinction gives rise in this
paper.
14. Note, by the way, that it is no objection to observe that infinitesimals are
somewhat dubious entities. The same point could be made in the language of
measure theory - i.e. in the mathematical theory which is appropriate for
dealing with probabilities in the case in which there are infinitely many
options. The set of worlds in which the Christian God exists may have
measure zero, and yet be non-empty.
15. Cf. J.L. Mackie, The Miracle of Theism. Oxford: Oxford University Press
(1982): p. 203.