believing in God: even under the assumption that God's existence is
unlikely, the potential benefits of believing are so vast as to make
betting on theism rational.
Critics in turn have raised a number of now-classic challenges.
According to intellectualism, deliberately choosing which beliefs to
hold is practically impossible; according to the many-gods objection,
Pascal's wager begs the question and hence is irrational; according to
evidentialism, Pascalian reasoning is epistemically irresponsible and
hence immoral; and according to various paradoxes, reference to
infinite values is decision-theoretic non-sense.
1. A Reason for Believing in God
There are two kinds of argument for theism. Traditional, epistemic
arguments hold that God exists; examples include arguments from
cosmology, design, ontology, and experience. Modern, pragmatic
arguments hold that, regardless of whether God exists, believing in
God is good for us, or is the right thing to do; examples include
William James's will to believe and Blaise Pascal's wager.
Pascal — French philosopher, scientist, mathematician and probability
theorist (1623-1662) — argues that if we don't know whether God exists
then we should play it safe rather than risk being sorry. The argument
comes in three versions (Hacking 1972), all of them employing decision
theory.
For those who are unfamiliar with decision theory, the idea can be
illustrated by considering a lottery. Suppose there are 100 tickets at
$1 each and a jackpot of $1000. Is it rational to play? If you total
the earnings and the expenses for all the tickets ($1000 – $100), then
divide by the number of tickets, you find that on average each ticket
nets $9. In comparison, not playing involves zero expense and zero
payoff. Since $9 is preferable to $0, it is rational to play.
Alternately, suppose there are 1000 tickets costing $2 each, a grand
prize of $1000, and a consolation prize of $500. Then the total
earnings and expenses ($1500 – $2000), divided by the number of
tickets, yields a net loss of fifty cents for the average ticket. In
this case, unless you have some reason to believe that a given ticket
is not average, playing the game is irrational.
To put the matter more generally: a given action (say, buying a
ticket) is associated with a set of possible outcomes (say, winning
the grand prize, winning the consolation prize, or losing); each
outcome has a certain value or "utility" (the utility of winning might
be the value of the prize minus the cost of the ticket); the
"expectation" for each outcome is equal to its utility multiplied by
the probability of its happening; the expectation for a given action
is the sum of the expectations for each possible associated outcome.
The course of action having the maximum expectation is the rational
one to follow.
a. The Super-Dominance Argument
Pascal begins with a two-by-two matrix: either God exists or does not,
and either you believe or do not.
–Table I– God exists God does not exist
You believe in God (a) infinite reward (c) 250 utiles
You do not believe in God (b) infinite punishment (d) 200 utiles
If God exists then theists will enjoy eternal bliss (cell a), while
atheists will suffer eternal damnation (cell b). If God does not exist
then theists will enjoy finite happiness before they die (say 250
units worth), and atheists will enjoy finite happiness too, though not
so much because they will experience angst rather than the comforts of
religion. Regardless of whether God exists, then, theists have it
better than atheists; hence belief in God is the most rational belief
to have.
b. The Expectations Argument
What if the atheist is a happy hedonist, or if the theist is a
miserable puritan? In that case the value of cell (d) is greater than
that of (c), and the dominance argument no longer works. However, if
there is a 50-50 chance that God exists then we can calculate the
expectations as follows:
–Table II– God exists God does not exist
You believe in God +infinity something finite
You do not believe in God -infinity something finite
The expectation for believing in God = positive infinity x ½ plus
something finite x ½ = positive infinity; the expectation for not
believing = negative infinity x ½ plus something finite x ½ = negative
infinity. Hence it is rational to believe in God.
c. The Dominating Expectations Argument
It's unlikely that the probability of God's existing is exactly
one-half, but this does not matter. Due to the infinite value in cell
(a), if God's existence has any finite probability then the
expectation for believing in God will be infinite. Furthermore, this
infinity will swamp the values in cells (b), (c), and (d), so long as
(c) is not infinitely negative and neither (b) nor (d) is infinitely
positive.
2. The Intellectualist Objection: Is Belief a Matter of Choice?
According to doxastic voluntarism, believing and disbelieving are
choices that are up to us to make. Intellectualists deny this; they
say it's impossible to adopt a belief simply because we decide to. If
I offered to pay you $1000 for believing the sky is green, for
instance, could you sincerely adopt this belief simply by wishing to?
Evidently not. Therefore, some say, Pascal's wager does not give
legitimate grounds for believing in God.
But although we cannot adopt a belief simply by deciding to, the same
is true for other actions. For instance, we cannot go to school simply
by deciding to; rather, we have to wake up by a certain time (which
may mean first developing a certain kind of habit), we must get
dressed, we must put one foot in front of another, etc. Then if we are
lucky we will end up at our destination, though this is far from
guaranteed. Likewise for any other endeavor in life: one chooses to
become a doctor, or to marry by age 30, or to live in the tropics —
the attainment of such goals can be facilitated, though not purely
willed, by appropriate micro-steps that are more nearly under
voluntary control. Indeed, even twitching your little finger is not
entirely a matter of volition, as its success depends on a functioning
neural system running from your brain, through your spine, and down
your arm. Your minutest action is a joint product of internal volition
and external contingencies. The same applies to theistic belief:
although you cannot simply decide to be a theist, you can choose to
read one-sided literature, you can choose to join a highly religious
community, you can try to induce mystical experiences by ingesting
LSD, and you can choose to chant and pray. No mere exercise of will
can guarantee that you will end up believing in God, but neither can
any exercise of will guarantee that you succeed in doing anything else
you decide to do. If there is a difference between our ability to
voluntarily believe something and our ability to voluntarily wiggle
our toe, it is a difference in degree of likely success, and not a
difference in logical kind.
Yet a difference in degree may be significant, and it's worth noting
that theists and atheists may disagree on the power of prayer to
change one's beliefs. Theists generally think that prayer tends to
bring one into contact with God, in which case one is likely to
notice, recognize, and believe in God's existence. Atheists, on the
other hand, have no particular reason to think that mere praying
should notably effect conversion. An agnostic would do well then to
try; for it would be precisely in the case where success matters that
trying is likely to be most efficacious.
Indeed, it might not matter whether we can choose to have the beliefs
we have. If Tables I or II be right then the fact would remain that it
is pragmatically better to believe in God than not, insofar as
theists, taken across all possible worlds, are on average better off
than atheists. It doesn't matter whether theism results from personal
will-power, God's grace, or cosmic luck — regardless, being better off
is being better off. Thus, Pascal's wager need not succeed as a tool
of persuasion for it to serve as a tool of assessment (Mougin & Sober
1994).
3. The Many-Gods Objection: Do Rival Religious Options Undermine Each Other?
Pascal's compatriot Denis Diderot replied to the wager that an
ayatollah or "imam could just as well reason the same way." His point
is that decision theory cannot decide among the various religions
practiced in the world; it gives no warrant for believing in Pascal's
Catholicism, or even in a generic Judeo-Christianity. The reason is
that Tables I and II beg the question in favor of a certain kind of
theism; a more complete matrix must consider at least the following
possibilities.
–Table III– Yahweh exists Allah exists
You worship Yahweh infinite reward infinite punishment
You worship Allah infinite punishment infinite reward
In reply, Pascalians offer a number of defenses.
a. Genuine Options
Some Pascalians insist that only certain theological possibilities
count as "genuine options" (James 1897, Jordan 1994b), although this
notion is never clearly defined. Perhaps a proposition P is a genuine
option for some subject S only if S is likely to succeed in believing
P, should S choose to. However, the relevance of volition is
questionable, as discussed in the previous section. Alternatively,
perhaps P is a genuine option for S unless P strikes S as "bizarre" or
untraditional (Jordan 1994b). The difficulty here lies in
distinguishing this position from emotional prejudice (Saka 2001).
Finally, it may be that a genuine option is one that possesses
sufficient evidential support, in which case it can then participate
in a run-off decision procedure.
b. Run-off Decision Theory
Some Pascalians propose combining pragmatic and epistemic factors in a
two-stage process. First, one uses epistemic considerations in
selecting a limited set of belief options, then one uses prudential
considerations in choosing among them (Jordan 1994b). Alternatively,
one first uses prudential considerations to choose religion over
non-religion, and then uses epistemic considerations to choose a
particular religion (Schlesinger 1994, Jordan 1993).
In order to be at all plausible, this approach must answer two
questions. First, what is the justification for deliberately excluding
some possibilities, no matter how improbable, from prudential
reasoning? It seems irrational to dismiss some options that are
acknowledged to be possible, even be they unlikely, so long as the
stakes are sufficiently high (Sorensen 1994). Second, can epistemic
considerations work without begging the question? Schlesinger argues
that the Principle of Sufficient Reason gives some support for
believing in God, but in a Pascalian context this is questionable. If
you subscribe to a suitable form of the Principle of Sufficient Reason
(one that leads to a given kind of theism), you are likely to be a
theist already and hence Pascal's wager does not apply to you; on the
other hand, if you do not believe in the right kind of Principle of
Sufficient Reason then you will not think that it makes theism more
probable than atheistic Buddhism, or anthropomorphic theism more
probable than deism. Other epistemic considerations, such as
Schlesinger's appeal to testimony, simplicity, and sublimity, meet
with analogous challenges (Amico 1994, Saka 2001).
c. Relativism
Some Pascalians, while acknowledging that the Wager might be unsound
for today's multi-culturally sophisticated, maintain that the Wager is
sound relative to Pascal and his peers in the 1600s, when Catholicism
and agnosticism were the only possibilities (Rescher 1985, Franklin
1998). But the Crusades in the 1100s taught the French of Islam, the
Renaissance in the 1400s taught the French of Greco-Roman paganism,
the discoveries of the 1500s taught the French of new-world paganism,
and several wars of religion taught the French of Protestantism. To
claim that the educated French of the 1600s rightfully rejected alien
beliefs without consideration appears to endorse rank prejudice.
d. Generic Theism
Some acknowledge that Pascal's wager cannot decide among religions,
yet maintain that "it at least gets us to theism" (Jordan 1994b,
Armour-Garb 1999). The idea is that Catholics, Protestants, Jews,
Moslems, and devil-worshippers can all legitimately use decision
theory to conclude that it's best to believe in some supreme being.
Against this there are two objections. First, it disregards
theological possibilities such as the Professor's God. The Professor's
God rewards those who humbly remain skeptical in the absence of
evidence, and punishes those who adopt theism on the basis of
self-interest (Martin 1975, 1990; Mackie 1982). Second, the claim that
Pascal's wager yields generic theism assumes that all religions are
theistic. But consider the following sort of atheistic Buddhism: if
you clear your mind then you will attain nirvana and otherwise you
won't — i.e. if you fill your mind with thoughts and desires, e.g. if
you believe that God exists or if you love God, then you will not
attain salvation (Saka 2001).
4. The Evidentialist Objection: Is Prudential Reasoning Ethical
There are two versions of this objection that need to be kept
distinct. The first one suggests that Pascalian reasoners are
manipulative egoists whom God might take exception to, and they won't
be rewarded after all (Nicholl 1978). Schlesinger 1994 responds by
saying that any reasoning that gets us to believe in God, if God
exists, can't be bad. But this argument seems to depend on the nature
of God. If God holds that results are all that matter, that the ends
justify the means, then Schlesinger is right. But maybe God holds that
true beliefs count as meritorious only if they are based on good
evidence; maybe God rewards only evidentialists. In short, this form
of the objection is just another version of the many-gods objection.
Another form of evidentialism refers not to God's character but to our
own. Regardless of how God might or might not reward our decisions, it
may be categorically, epistemically or otherwise wrong — "absolutely
wicked", in the words of GE Moore — for us to base any belief on
decision-theoretic self-interest (Clifford 1879, Nicholls 1978).
Since utilitarians would tend to favor Pascalian reasoning while
Kantians and virtue ethicists would not, the issue at stake belongs to
a much larger debate in moral philosophy.
5. The Paradox Objection: Is Decision Theory Coherent?
a. The Equi-utility Paradox
If you regularly brush your teeth, there is some chance you will go to
heaven and enjoy infinite bliss. On the other hand, there is some
chance you will enjoy infinite heavenly bliss even if you don't brush
your teeth. Therefore the expectation of brushing your teeth (infinity
plus a little extra due to oral health = infinity) is the same as that
of not brushing your teeth (infinity minus a bit due to cavities and
gingivitis = infinity), from which it follows that dental hygiene
isn't a particularly prudent course of action. In fact, as soon as we
allow infinite utilities, decision theory tells us that any course of
action is as good as any other (Duff 1986). Hence we have a reductio
ad absurdum against decision theory, at least when it's extended to
infinite cases. In reply to such difficulties, Jordan 1993 proposes a
run-off decision theory as described above.
b. The St. Petersburg Paradox
Imagine tossing a coin until it lands heads-up, and suppose that the
payoff grows exponentially according to the number of tosses you make.
If the coin lands heads-up on the first toss then the payoff is $2; if
it takes two tosses then the payoff is $4; if it takes three tosses
then the payoff is $8; and so forth, ad infinitum. Now the odds of the
game ending on the first toss is 1/2; of ending on the second toss,
1/4; on the third, 1/8; and so forth. Since there is a one-half chance
of winning $2, plus a quarter chance of winning $4, plus a one-eighth
chance of winning $8… your expectation for playing the game is (1/2 x
$2) + (1/4 x $4) + (1/8 x $8) +… i.e. $1 + $1 + $1… = infinity! It
follows you should be willing to pay any finite amount for the
privilege of playing this game. Yet it clearly seems irrational to pay
very much at all. The conclusion is that decision theory is a bad
guide when infinite values are involved (for discussion of this very
old paradox, see Sorensen 1994). Byl 1994 points out that instead of
referring to infinite payoffs we can speak of arbitrarily high ones.
No matter how improbable be the existence of God, it is still
decision-theoretically rational to believe in God if the reward for
doing so is sufficiently, yet only finitely, high. However, this does
not address the heart of the problem, for the St. Petersburg paradox
too may be cast in terms of an arbitrarily high limit. Intuitively,
one would not be willing to pay a million dollars, say, for the
privilege of playing a game capped at one-million-and-one coin tosses,
and it's not just because of the diminishing value of money. There is
something unsettling about decision theory, at least as applied to
extreme cases, and so we might be skeptical about using it as a basis
for religious commitment.
6. References and Further Reading
The best known defense of Pascal is Lycan & Schlesinger 1989; for
responses see Amico 1994 and Saka 2001. A good sourcebook is Jordan
1994a.
* Amico, Robert (1994) "Pascal's wager revisited", International
Studies in Philosophy 26:1-11.
* Armour-Garb, Bradley (1999) "Betting on God", Religious Studies 35:119-38.
* Byl, John (1994) "On Pascal's wager and infinite utilities",
Faith & Philosophy 11:467-73.
* Clifford, William (1879) "The ethics of belief", Lectures &
Essays, Macmillan.
* Duff, Anthony (1986) "Pascal's wager and infinite utilities",
Analysis 46:107-09.
* Franklin, James (1998) "Two caricatures, I: Pascal's wager",
International Journal for Philosophy of Religion 44:115-19.
* Hacking, Ian (1972) "The logic of Pascal's wager", reprinted in
Jordan 1994a.
* James, William (1897) "The will to believe", reprinted in The
Will to Believe and Other Essays, Dover.
* Jordan, Jeff (1991) "The many-gods objection and Pascal's
wager", International Philosophical Quarterly 31:309-17.
* Jordan, Jeff (1993) "Pascal's wager and the problem of infinite
utilities", Faith & Philosophy 10:49-59.
* Jordan, Jeff, editor (1994a) Gambling on God, Lanham MD: Rowman
& Littlefield.
* Jordan, Jeff (1994b) "The many-gods objection", in Jordan 1994a;
a restatement of Jordan 1991.
* Lycan, William & George Schlesinger (1989) "You bet your life",
in Reason & Responsibility, 7th edition (ed. Joel Feinberg, Belmont
CA: Wadsworth). Also in the 8th, 9th, 10th editions; in Philosophy and
the Human Condition, 2d edition (ed. Tom Beauchamp et al., Englewood
Cliffs NJ: Prentice Hall, 1989); and in Contemporary Perspectives on
Religious Epistemology (ed. Douglas Geivet & Brendan Sweetmar, Oxford,
1993). See also Schlesinger 1994.
* Mackie, J.L. (1982) The Miracle of Theism, Oxford, pp. 200-03.
* Martin, Michael (1975) "On four critiques of Pascal's wager",
Sophia 14:1-11.
* Martin, Michael (1990) Atheism, Philadelphia: Temple University
Press, pp. 229-38.
* Mougin, Gregory & Elliott Sober (1994) "Betting on Pascal's
wager", Nous 28:382-95.
* Nicholl, Larimore (1978) "Pascal's wager: the bet if off",
Philosophy & Phenomenological Research 39:274-80.
* Pascal, Blaise (composed in 1600s, first published in 1800s)
Pensees, section 343; translated & reprinted by Penguin and many
others.
* Rescher, Nicholas (1985) Pascal's Wager, University of Notre Dame Press.
* Saka, Paul (2001) "Pascal's wager and the many gods objection",
Religious Studies 37:321-41.
* Schlesinger, George (1994) "A central theistic argument", in
Jordan 1994a; a restatement of Lycan & Schlesinger 1989.
* Sorensen, Roy (1994) "Infinite decision theory", in Jordan 1994a.
See also: Faith and Reason
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