Towards a Finite Pascalian Wager

In this article I consider the Many God’s Objection to

Pascal’s Wager. This objects to “transfinite” versions of

the wager. That is, to say, it is an objection to

versions of the wager that argue that it’s always decision

theoretically rational to wager that God exists. More

particularly, it objects to the principle that an

infinite utility multiplied by any probability, provided

that it has a non-zero value, amounts to infinite

expected utility. It notes, moreover, that there are an

innumerable number of different theologies, each of which

make use of infinite utilities. Hence it’s reasoned that

if we permit that transfinite versions of the wager are

sound, we would have pragmatic reason to adopt not just

Christian theology, but also a vast range of alternative

theologies. I attempt to re-enforce this objection by

arguing that since we do not permit the use of infinite

utilities in other contexts, it is special pleading to

use it in relation to Pascal’s Wager. However, I argue

that the wager can be re-stated in such a way that it

circumvents these difficulties. In particular, I attempt

to develop a wager that eschews the use of infinite

utilities. This revisionist wager makes the probability

of God’s existence much more important than it is in

transfinite versions. I then note that provided that

theism is approximately as probable as atheism, this

finite wager circumvents the Many Gods objection. Notice

the limitations on my thesis:

(1). It is beyond the scope of this essay to argue that

the probability of theism is approximately equal to

that of atheism. My contention is purely

conditional. If theism is approximately as probable

as atheism, then the Many God’s Objection can be

avoided.

(2). I am not arguing that if the probability of theism

is approximately equal to that of atheism, then a

finite Pascalian Wager succeeds. Rather, the claim

is just that, in such circumstances, we avoid one

particular objection i.e. the Many God’s Objection.

I proceed in four major sections. In the first section, I

briefly sketch out what the Wager is and what it aims to

do. In the second section, I delve into an explanation of

some of the decision theory that underpins the Wager,

noting how protean it (the Wager) is. In the third

section, I introduce and attempt to re-enforce the Many

God’s Objection. In the fourth and final section, I

attempt to develop a revisionist finite version of the

wager.

Traditionally, Pascal’s Wager is thought to be a

‘pragmatic argument’ for belief in God. That is to say,

it is an argument for belief in God that does not attempt

to argue that there is any epistemic reason to believe

that there is in-fact a God. Rather, it attempts simply

to show that it is in our interests to believe in God.i

Hence unlike traditional Natural Theological arguments,

Pascal’s Wager does not attempt to argue that there is

any evidence for the being of God as conceived of in the

Abrahamic traditions. It is understandable then, why it

is that there’s long tradition of philosophers who have

taken the Wager to be inconsistent with evidentialist

conceptions of epistemic justification. It’s worth noting

however, that like many of the traditional Natural

Theological arguments, the Wager is very protean, and

recent modifications to the wager have been made which

establish that is not at all inconsistent with an

evidentialism that affirms the evidential value of

religious experience. For instance, although he does not

explicitly claim that his model is a version of Pascal’s

Wager, Timothy Mawson has developed what I would call a

‘Pascalian Wager’ that does precisely this. Mawson

argues, rightly or wrongly, that an atheist who meets

certain criteria is under a prima facie obligation to

pray to God to find out if He is there.ii Mawson’s

criteria are as follows:

(1). They assign a non-negligible probability to the

existence of God,

(2). They think that the existence of God is an important

issue

(3). They aren’t in possession of a compelling argument

that makes them believe that praying would lead them

to false positives. iii

(Incidentally, Mawson goes so far as to argue that

atheists who meet these criteria ought to pray to God

that they stop being an atheist). Mawson’s suggestion is

that were God to respond positively, this subsequent

religious experience would qualify as a piece of evidence

that justifies religious belief. So on this model, the

Wager itself is not what justifies belief. Rather, it

provides agents with prudential reason to act as if on

the assumption that God exists with the hope that if He

does He might choose to make Himself known to the

believer.

Following Jeffrey Jordan, it’s helpful to distinguish

between two different sub-categories of ‘pragmatic

argument’ for belief in God. The first are what we will

call “Truth Dependent” pragmatic arguments whilst the

second are what we will call “Truth Independent”

pragmatic arguments. In the first instance, “Truth

Dependent” pragmatic arguments are arguments that suggest

that belief in God is prudentially rational because of

the benefits enjoyed if the belief is true. The benefits, in

other words, accrue only on the condition that theism is

true. By contrast, “Truth Independent” pragmatic arguments

are arguments that appeal to the good effects of theistic

belief even if theism is false. As Jordan notes, for

instance, in Hume’s Dialogues Concerning Natural

Religion, Cleanthes (the philosophical theist) seems to

suggest that belief in God, in particular, belief in a

future afterlife, is necessary to ensure moral behavior.

The Decision Theory

Before we can assess the merits of Pascal’s Wager, it

would help if we had a basic grasp of the decision theory

that underpins the Wager. In a nutshell, once we plug in

what it is that we value, decision theory tells us how it

is that we ought to act when we have limited knowledge.

This limited knowledge includes, in particular, a limited

knowledge and ability to calculate the probability of any

given state of the world.iv In decision theory, there are

five relevant factors to consider:

(1). States of the world i.e. ways in which the world

might be,

(2). Actions i.e. the different alternative courses of

action that we might take,

(3). Outcomes. These are the effects that we expect to

occur as a result of performing a given action if a

particular state of the world were to obtain.

(4). Utilities. These are the outcomes that we value or

dis-value. Decision Theory effectively tells us how

we can maximize what it is that we value while

reducing the risk of dis-value/loss. The final

factor to consider is

(5). The probabilities. These are the probabilities that

we attach to any given state. That is the

probability, given our background evidence, of any

given state obtaining. In the Wager, for instance,

the relevant probability is the probability that God

exists.v

The probabilities are important in decision theory

inasmuch as they help us to calculate the most prudent

course of action. When we multiply the probabilities by

the associated utilities and subtract any costs, we get

the “Expected Utility” of each of the outcomes. The

“Expectation Rule” then dictates that we ought to pursue

that course of action that has the greatest ‘Expected

Utility’. Formally stated, the “Expectation Rule”

(hereafter ER) states that:

(ER) For any person S, and any number of alternative actions, α and β,

available to S, if α has a greater expected utility than does β, S should

choose αvi

Thus we can diagrammatically represent a decision with

the following matrix

States of the World

State 1

State 2

Action 1 Outcome 1 Outcome 2

Action 2 Outcome 3 Outcome 4

As I mentioned earlier, to calculate the “Expected

Utility”, we simply multiply the utilities by the

probabilities and subtract any costs. So suppose we’re

deliberating whether or not to take a warm coat. Suppose

moreover, that the probability of it being cold today is

50%. Let us also stipulate that we would prefer, if

possible, not take a warm jacket. Nevertheless, we would

prefer to carry a warm jacket when we don’t have to, to

being cold. We can thus represent the deliberative

process with the following decision matrix (let the

numbers in the cells designate our agents preference

ordering).

It will be cold

today (50%)

It won’t be cold

today (50%)

Take a warm jacket Outcome 1: Keep

warm

20

Outcome 2:

Needlessly carry a

warm jacket

4

Don’t take a warm

jacket

Outcome 3: Get Outcome 4: Don’t

have to needlessly

cold

2

carry a warm

jacket

10

In this case, the Expectation Rule dictates that we ought

to take a warm coat. After all:

(1). EU (take a warm jacket) = EU(Outcome 1) + EU(Outcome

2)

Which becomes,

(2). EU (take a warm jacket) = ½(20) + ½(4)

(3). EU (don’t take a warm jacket) = EU(Outcome 3) +

EU(Outcome 4)

Which becomes,

(4). EU (don’t take a warm jacket) = ½(2) + ½(10)

(5). (½(20) + ½(4)) > (½(2) + ½(10))

So,

(6). EU (take a warm jacket) > EU (don’t take a warm

jacket)

This is known as “decision under risk”, that is

deliberating when we know the relevant probabilities of

each of the states. By contrast, deliberating when we

lack knowledge of the relevant probabilities is known as

“decision under uncertainty”.vii One way to think about

decision under uncertainty is to think about the role

that the veil of ignorance plays in Rawlsian political

theory. The thought is this: suppose that you task is to

develop the ‘basic structure’ of society, but from behind

a veil of ignorance. That is from a position in which we

have no knowledge of what position it is that we will

take once the veil has been lifted. We are ‘uncertain’,

that is, of how it is that our lives will go once we

enter the society that we have constructed for ourselves.

The decision we face under such circumstances is a

‘decision under uncertainty’.viii

There are a number of different rules that can be adopted

when we face ‘decisions under uncertainty’. These rules

are as follows:

Maximin:

Effectively, this rule tells us that we ought to ‘play it

safe’, and pursue that course of action whose worst

outcome is better than the worst outcomes of the other

available actions.ix

Maximax:

This rule simply tells us to throw caution to the wind as

it were, and to simply pursue that course of action that

has the greatest expected utility. Unlike the Maximin

rule, this rule effectively tells us to ignore the

potential loss if things go badly.x

The Indifference Rule

This rule instructs us to proceed as if each state is

equi-probable and then simply applies the expectation

rule. In other words, the expected utility of any two

actions A and B is given simply by multiplying the

utility of relevant states by 50%. In effect, rule would

reduce decision under uncertainty to decision under

risk.xi

Strong Dominance Rule: When some action A always has

better outcomes than rival actions, then A strongly

dominates. In other words, if A has better outcomes

regardless of what state obtains, A strongly dominatesxii

Weak Dominance Rule: Some action A weakly dominates if

there is some state S in which A has better outcomes than

the alternatives. The dominance is weak inasmuch as it

occurs with some outcomes, but not others.xiii

Satisfactory Act Rule: Consider two actions A and B. If

some person S can ‘live with’ each of the outcomes of A,

but B contains some outcomes that are ‘intolerable’, then

A is said to be ‘satisfactory’ and S should pursue A.xiv

It seems fairly clear that there is the potentiality for

Pascalian-type Wagers that would correspond to each of

these rules. For instance, from the way Pascal himself

set it up, we might think of it in terms of strong

dominance. But the general concept of the wager is by no

means committed to strong dominance. Insofar as we might

think that we lose something if we incorrectly wager that

God exists, we might just think of the wager in terms of

Weak Dominance. This gives us some idea of just how

protean the wager is.

Pascal’s Wager Summarized:If you recall, I distinguished in the first section

between truth dependent and truth independent pragmatic

reasons. Pascal’s Wager is an example of a “truth

dependent” pragmatic argument. The best summary of the

wager comes from its author, Blaise Pascal. He writes:

Let us examine this point and declare: “Either God is or He is not.” But to

which view shall we incline? Reason cannot decide this question. Infinite

chaos separates us. At the extremity of this infinite distance a game is in

progress, where either heads or tails may turn up. How will you wager?

… Let us weigh the gain and the loss involved by wagering that God

exists. Let us assess the two cases: if you win, you win all; if you lose, you

lose nothing. Do not hesitate then, wager that He does exist.

On canonical versions of the wager, the thought is that

we ought to wager that God does exist, because if we are

right, then our gain is supposed to be infinite. Since if

we correctly wager that God exists, we would enjoy the

unending good of a personal and loving relationship with

God in the afterlife. But if, on the other hand, we

incorrectly wager that God does not exist, then our loss

is infinite. After all we then lose out on the never

ending Good of a personal and loving relationship with

God.xv Nevertheless, it seems that if we wager that God

exists and we’re wrong, we make a loss, since it would

mean a life spent in pursuit of a relationship with a God

that doesn’t exist. It means that we lose out on the

other valuable things that we could have pursued if we

hadn’t wagered that God exists. However, if we wager that

God does not exist, even if it turns out that, in the

final analysis, we were right, we have taken a

significant risk for a relatively small gain. For the

sake of simplicity, we might refer to this version of the

wager as a “transfinite wager” as distinct from “finite

wagers”. As their names suggest, whereas transfinite

wagers make use of infinite utilities, finite wagers only

make use of finite utilities. One of the distinctive

features of transfinite wagers is that if they are sound,

then it is always decision theoretically rational to wager

that God exists. After all, an infinite utility

multiplied by any probability, provided that it has a

non-zero value, always equals an infinite expected

utility. In other words, regardless of how low the

probability of theism is, the expected utility of

wagering that God exists always swamps the expected

utility of other actions.xvi

We can summarize the decision process with the following

matrix.xvii

God exists God does not exist

Believe that God

exists

Infinite gain Small loss

Believe that God

does not exist

Infinite loss Small gain

We can further break the decision down into its

constituent parts:

The Act: The relevant ‘act’ in this context is either

believing or failing to believe that God exists.

The State: The relevant ‘state’ here, is it being the

case that either God does or does not exist.

The Outcomes: The relevant ‘outcome’ here is either

enjoying or failing to enjoy the allegedly infinite

benefit of a loving, personal relationship with God.

The Utilities:

(1) The allegedly infinite benefit of a personal

and loving relationship with God if we correctly

believe that God exists.

(2) The gain of not having lived our lives in

pursuit of a relationship with a God that doesn’t

exist should it be the case that we correctly

believe that God does not exist.

Presumably, the dis-utilities are:

(1) The allegedly infinite loss if we incorrectly

believe that God does not exist and

(2) The small loss if we incorrectly believe that God

does exist.

The probabilities: The probability that God does or

does not exist

The Many God’s Objection

As we noted earlier, transfinite versions of Pascal’s

Wager claim that it is always decision theoretically

rational to wager that God exists because an infinite

utility multiplied by any probability, however low, is an

infinite expected utility. In other words, the

transfinite wager is underpinned by a principle that

permits the use of infinite utilities. The Many God’s

Objection rightly objects that if we permit this

principle with respect to Pascalian Wagers, we have

pragmatic reason to embrace not just Christian theology,

but also Muslim and certain forms of Hindu theology.xviii

In-fact, if it were sound it we would give us pragmatic

reason to embrace any logically possible theology that

involves the potential for an infinite return.1 Thus

leaving us with rational indeterminacy at best, and a

contradiction at worst! 1 If some hypothesis H is even logically possible, it follows that Pr(H) > 0 since if Pr(H) = 0, then H is logically impossible

In its most basic form, the Many God’s Objection claims

that transfinite versions of the Wager are flawed

because, given that Christianity and atheism are not

jointly exhaustive of the betting options, it cannot

recommend any single theology.xix In-fact, given that the

probabilities are irrelevant to transfinite versions of

the wager, such wagers would recommend that we embrace

all logically possible theologies that involve an

infinite payout for right belief, thereby leaving us with

rational indeterminacy.2 xx By way of illustration, pick

any conceivable theology T that offers infinite payout

for right belief. Since an infinite utility multiplied by

any probability, however low, always equals an infinite

expected utility, it follows that we have a transfinite

wager for T. We can repeat this for any other theology

that we might dream up. Michael Martin for instance,

envisages a deity that he calls the “Perverse Master” who

“punishes with infinite torment those that believe in

God” whilst rewarding atheists with infinite bliss.xxi

2 By ‘rational indeterminacy’ I just mean that no single course of action is uniquely rational.

Again, given that the expected utility of doubting this

deity’s being is infinite, a Pascalian-like wager would

recommend inculcating disbelief.

In-fact, things are worse for the transfinite wager than

merely landing us with rational indeterminacy. If it’s

sound, the transfinite wager implies a contradiction. To

see this, consider that part of what the wager draws on

to get going is the idea that God requires right belief.

Christian doctrine, for instance, requires that we

believe in an explicitly Christian doctrine and

disbelieve any rival theological doctrine such as Islam.

Likewise Islamic theology requires that we believe an

explicitly Islamic doctrine, and disbelieve rival

theologies e.g. Christianity. If the expected utility of

these theologies is infinite, then the transfinite wager

would provide us with a pragmatic reason to believe both

Islamic doctrine and Christian doctrine. In other words,

it recommends both that we believe and disbelieve

Christian doctrine.

This point is seems sufficient to show that there

something must be wrong with the use of infinite

utilities. After all, part of what seems to give rise to

the Many God’s Objection is the fact that the infinite

utilities make the probability of each of the states

irrelevant. However, it seems to me that we can further

re-enforce this point by considering the implications of

the use of infinite utilities in other areas of decision-

making. If it turns out that the use of infinite

utilities leads to similar absurdities in other areas,

then it is even more implausible, special pleading in-

fact, to insist on the use of infinite utilities with

respect to the transfinite wager.

Re-enforcing the objection

To illustrate the absurdities that arise when you use

infinite utilities, suppose that some person Sam attaches

lexical priority to the continuation of his life over the

assumption of any additional risk. To illustrate this

idea: suppose that I have a 100-barrel revolver, and only

one of the chambers is loaded, but I don’t know which

one. Sam, who is seated in front of me, really values

roses, but he also really values the continuation of his

life. Suppose that I offer Sam a whole load of roses in

exchange for the opportunity to point my revolver at him,

and pull the trigger. In other words, I’m offering him a

whole load of roses in exchange for an extra 1% chance of

dying. Since Sam places lexical priority on the value of

his life over the assumption of any additional risk, he

wouldn’t take any number of roses in exchange for an

extra 1% chance of death.

Suppose that Sam just gotten into his car, and he’s

considering the possibility that whilst he’s been out,

someone has rigged my car with a bomb that will explode

when he turns the key. Now in-spite of his strange views

about the lexical value of his life, Sam is a well-liked

individual, and it strikes him as vastly improbable that

this has occurred. But it is nevertheless possible that his

car has been rigged, and hence there is some associated

risk. The fact that Sam attaches lexical priority to the

continuation of his life over any chance that he might

die just is to say that he is unwilling to accept any

additional risk of death. Hence the expected utility of

checking his car for explosives will always be greater

than the expected utility of not checking. In-fact it

gets worse than this. Suppose that Sam has a particularly

fancy car which has been designed in such a way that the

engine shuts off when he’s sitting at traffic lights, and

then turns back on as soon as he takes his foot off the

break. Now it’s possible that each time the engine shuts

off, a computerized car bomb has been activated, which

has been programmed to detonate when he takes his foot of

the break. Given that he attaches lexical priority to the

continuation of his life over the assumption of any

additional risk, the expected utility of checking for

explosives before proceeding will always be greater than

the expected utility of not checking. In-fact so long as

he allows that states which are no more than logically

possible to factor into his decision making, why not

consider the possibility that as he’s walking down the

road, there is always an invisible man in-front of him

who is waiting for the opportune time to lay an invisible

mine in his path. Given that he places lexical priority

to the continuation of his life, Sam is forced to consider

this possibility because the expected utility of checking

for invisible mines will always outweigh the expected

utility of not checking. We can keep multiplying these

sorts of examples ad nausea. In-fact, we could repeat

such examples for any logically possible state that might

result in Sam dying by explosive device so long as he

attaches lexical priority to the continuation of his life

over the assumption of additional risk. In other words,

if we allow a principle that permits the use of infinite

utilities, we get an explosion (no pun intended) of

actions that are supposed to be decision theoretically

rational but which are, intuitively speaking, sub-par. By

‘sub-par’ here, I really mean that they are the sorts of

actions that would unreasonably restrict how we act.

Notice that Sam has effectively made use of an infinite

utility. After all, part of what he is saying when he

says that the continuation of his life has lexical

priority over the assumption of any additional risk, is

that the expected utility of his continued life is always

greater than the expected utility that might be gained by

accepting some additional risk of death. Moreover, the

only way for the expected utility of his continued life

to always outweigh the expected utility of some scenario

in which he accepts some additional risk is if his

continued life is infinitely more valuable to him than

any utility that might be gained by accepting additional

risk. By contrast, if he were to place only finite

utility on the value of his continued life, it follows

that there is some hypothetical scenario in which either

the probability of things going badly is low enough that

he would be prepared to accept the associated risk, or

else the expected utility is so great as to overwhelm the

expected utility of his continued life.

So when we conjoin the expectation rule with the use of

infinite utilities, we get counter-intuitive

consequences. But for all we know at this point it may

that the problem might lie with the Expectation Rule

rather than the use of infinite utilities. However,

eschewing the Expectation Rule is implausible. Consider

someone who faces a forced choice between two products.

Both products are of comparable quality, but one product

is double the price of the other. If this person prefers

to retain as much money as possible, it seems

straightforwardly irrational for him to buy the more

expensive product. But if we eschew the Expectation Rule,

we cannot say that this person has acted irrationally.

Moreover, part of what seems to fuel the intuition that

the explosion of actions that Sam faces are ‘sub-par’ is

that, by attaching such high utilities to the value of

his life, he isn’t maximizing expected utility. It would

be self-defeating to assume the use of the expectation

rule to eschew the expectation rule.

This suggests that we ought to qualify our use of the

expectation rule. Principally it suggests that the use of

infinite utilities is implausible. This requires however,

that we place greater importance on the probabilities. To

illustrate, consider Pascal’s Wager. If the expected

utility of theism is finite, it follows that in order to

ensure that the expected utility of theism is higher than

the expected utility of atheism the probability of theism

must be at least approximately equal to that of atheism.

After all if Pr(~G)>>Pr(G), then EU(atheism) >

EU(theism). Where ‘G’ designates the proposition that God

exists. In other words, if the probability of God’s non-

existence is vastly greater than the probability of Gods

existence, then the expected utility of atheism is

greater than the expected utility of theism

Circumventing the Many God’s Objection

Towards the end of the last section, I suggested that if

we eschew the use of infinite utilities, we place greater

importance on the probability of God’s existence, since

if Pr(~G)>>Pr(G), then EU(atheism)>EU(theism). Hence it

is not enough that it is merely logically possible that God

exist. Rather, theism must have a ‘positive probability’.

As we will go on to see, this has important implications

for how it is that we might circumvent the Many God’s

Objection.

As we saw earlier, the Many God’s Objection objects to

transfinite wager on the grounds that the use of infinite

utilities make any question of probability or prior

evidence for theism irrelevant. As I began to hint at

toward the end of the last section, this suggests that

one possible way to circumvent the Many God’s Objection

would to eschew the use of infinite utilities. By doing

this, the probabilities become much more important, since

if the utility of theism is finite, and the probability

of atheism is sufficiently high, the expected utility of

atheism will outweigh the expected utility of theism.

Thus to ensure that the expected utility of theism is

greater than the expected utility of atheism, theism

needs to be is at least approximately as probable as

atheism. But if theism is at least approximately as equal

as probable as atheism, a finite wager will not provide

us with a pragmatic reason to adopt just any theology.

Rather, it will only recommend those whose probability is

sufficiently high. For instance, if the Christian

apologist prefaces his discussion of Pascal’s Wager with

a presentation of evidence sufficient to (a) make

Christian doctrine equi-probable with atheism and (b)

render rival theologies e.g. Islam improbable, then the

wager will recommend acting as though Christian doctrine,

but it will not recommend acting as though rival

doctrines are true. After all in such circumstances, the

prior probability of Christianity is higher than the

prior probability of rival theologies such that when we

then multiply the probabilities by the relevant

utilities, the expected utility of Christianity turns out

to be greater than the expected utilities of rival

theologies. In other words, we should think of Pascal’s

Wager a tiebreaker in the sense that it applies only when

there is an evidential stalemate between theism and

atheism. Thus one way to circumvent the many God’s

Objection is to start by arguing that Pr(G)≈Pr(~G) where

‘G’ designates the proposition that God exists.

We should keep in mind however, that such a wager is not

necessarily a tiebreaker. If the utility of theism is finite

but vast, it might be the case that

EU(theism)>EU(atheism) even if the probability of atheism

is slightly greater than the probability of theism. To see

this, suppose for the sake of argument that Pr(~G)>Pr(G)

& ~Pr(~G)>>Pr(G). In other words, the probability of

God’s non-existence is greater the probability of God’s

existence, but it’s not the case that the probability of

God’s non-existence is vastly greater than the

probability of God’s existence. More particularly,

suppose that Pr(~G) = 0.75 and Pr(G) = 0.25. Suppose

moreover, that the utility of atheism is 5 utils. In that

case, EU(atheism) = 375. But suppose that the utility of

theism is 16 utils. In that case, EU(theism) = 400. Thus

under the stipulated conditions EU(theism)>EU(atheism)

even though atheism is, on the background evidence, more

likely than theism.

So can we construct a finite version of the wager? In

effect, the question concerns whether or not it’s

possible to maintain a finite but vast expected utility

for theism that is consistent with Abrahamic theology.

After all, given that the Wager is most frequently

deployed within the context of an apology for Judaism,

Christianity and/or Islam, it will be of little interest

to us if the wager we develop comes at the cost of

Abrahamic theology. I suggest that, on reflection, it

isn’t difficult to construct a wager consistent with

Abrahamic theology. Keep in mind that what does the work

in making the expected utility of theism infinite in

transfinite versions of the wager is the value/utility of

theistic afterlife. Indeed without a highly valuable

theistic afterlife, it’s difficult to see how the

expected utility of theism would be so much greater than

the expected utility of atheism.

So what would a finite but vastly valuable afterlife look

like? One way to think about it would be to start by

noting that on any standard conception of Christian

afterlife, humans never come to be like God. In other

words, humans retain their finitude in the sense that

they do not ever come to be omnipotent or omniscient.xxii

This is relevant from the point of view that it entails

that however saturated with joy and rapture the afterlife

might be, human ability to actually perceive that joy is

limited. In-fact, as Jordan notes, this concept seems to

be fairly familiar: suppose, by way of illustration, that

you really enjoy Coke. Suppose I start handing you cans

of Coke. From the first, second and third Cokes you might

derive great satisfaction. But suppose that I keep

handing them to you. At some point the addition of an

extra Coke is not going to increase your utility level

any higher. In-fact were I to keep handing them to you,

there would come a point at which you would come to

experience dis-utility where you would be burping and

farting from having consumed too much Coke. To put it

simply, there is what we might call a “saturation level”

at which the addition of any extra Coke makes no

difference to your satisfaction levels. This is what

economists call the “law of diminishing marginal

utility”. Likewise, there might come a point at which

additional exposure to God’s presence does not make

humans any happier. However, we need to note the

limitations of this analogy. I don’t want to suggest that

there comes a point at which humans begin to experience

dis-utility in the presence of God. All I want to suggest

is that the human ability to perceive the joy of heaven

is limited by their finite size, and hence we cannot

continue to make a human’s life better simply by

continually adding more of whatever it is that we find to

be constitutive of happiness.

In their article “Betting Against Pascal’ Wager”, Sober

and Mougin’s object that if the utility of theistic

afterlife is enormous but finite, then it follows that:

If Pr(P)<1, then EU(theism)>EU(atheism) if and only

if Pr(G&P)>Pr(X)xxiii

Where ‘P’ designates traditional Pascalian theology. This

holds that theists go to heaven whilst atheists go to

hell, and X designates some aberrant theology such that

atheists are sent to heaven whilst theists go to

heaven.xxiv However, as they note, traditional formulations

of Pascal’s wager take it for granted that, on the

background evidence Pr(G)<<0.5 i.e. the probability of

God’s existence is very low.xxv As a result, Pr(G&P) will

be very low even if Pr(P) is very high. In other words,

the probability of the conjunction of God’s existence

with Pascalian theology will be very low even if the

probability of Pascalian theology is very high. This is

because the probability of theism would drag down the

otherwise high probability of Pascalian theology. In such

circumstances it is possible that the probability of the

deviant theology might be greater than the probability of

the conjunction of God’s existence with Pascalian

theology even if, by itself, the deviant theology is

highly improbable. Put simply, if Pr(G&P)<<0.5, then it’s

possible that Pr(G&P)<Pr(X) even if Pr(X)<<0.5.xxvi

It seems to me that the seeds for the most promising

means of escaping this objection are already present in

the solution that I offered to the Many God’s Objection.

As you’ll recall, I argued that the best solution to the

Many God’s Objection was to think of the Wager as a

‘tiebreaker’. But the very notion of a tiebreaker

requires that Pr(G)≈Pr(~G). In other words, it requires

that the probability of God’s existence be roughly equal

with the probability of God’s non-existence. If it’s the

case that Pr(G)≈Pr(~G), the probability of God’s

existence does not drag the probability of (G&P) down as

far. Thus if we think of the finite wager not as an

attempt to argue that it’s always rational to wager that

God exists, but as a tiebreaker, it would seem that we

have a potential strategy for circumventing the

difficulties that Sober and Mougin raise. However, as

with my response to the Many God’s Objection, the success

of this strategy would hinge on the ability of the

Natural Theologian to present sufficient evidence to

think that the existence of God is at least roughly as

probable as God’s non-existence.

Wrapping up:To conclude, we saw first that by developing a finite

Pascalian wager, we place much greater significance on

the probability of God’s existence. This suggests that if

the Christian apologist prefaces his discussion of the

wager with evidence sufficient to make Christianity (or

theism) at least approximately as probable as atheism,

then his wager will recommend inculcating Christian

belief, but it won’t necessarily recommend inculcating

rival theologies. As I mentioned at the beginning, it is

beyond the scope of this essay to argue that

theism/Christianity is approximately as probable as

atheism. But it does offer a potential escape route for

the proponent of Pascal’s Wager.

We also noted that by eschewing the assumption of

traditional Pascalian wagers that Pr(G) << ½ , and by

thinking of it instead as ‘tiebreaker’, we have a

potential escape route from the objection that Sober and

Mougin’s for finite wagers. In particular, we noted that

if Pr(G)≈Pr(~G), then the probability of God’s existence

does not drag down the probability of (G&P).

Thus based on one simple move, i.e. eschewing the

assumption that Pr(G) << ½ we saw a route of escape first

from the Many God’s Objection, and then from Sober and

Mougin’s criticism of finite Pascalian Wagers.

References

i Jordan, Jeffrey. “Pragmatic Arguments”. A Companion to the Philosophy of Religion: Second Edition. Edited by Charles Taliaferro, Paul Draper and Phillip Quinn. Blackwell Publishing. 2010. Blackwell Reference Online. 10/06/2013. Section title “Pascal’s Wager”.

ii Mawson, TJ. “Praying to Stop Being an Atheist”. International Journal for Philosophy of Religion. Vol. 67, No. 3 (June 2010), pp. 173-186. pp 174

iii Ibid.

iv Jordan, Jeffrey. “Pascal’s Wager: Pragmatic Arguments and Belief in God”. Oxford Scholarship Online. January 2007. DOI: 10.1093/acprof:oso/9780199291328.001.0001. Chapter “Pascal’s Wager”. pp 4

v Ibid.

vi Ibid. pp 5

vii Ibid. pp 6

viii Freeman, Samuel. “Original Position”. The Stanford Encyclopedia of Philosophy. Accessed 11/06/13. http://plato.stanford.edu/entries/original-position/#ArgMaxCriTJSec2628. Section 6.1 “Argument from the Maximin Criterion”

ix Jordan, Jeffrey. “Pascal’s Wager: Pragmatic Arguments and Belief in God”. Oxford Scholarship Online. January 2007. DOI: 10.1093/acprof:oso/9780199291328.001.0001. Chapter “Pascal’s Wager”. pp 7

x Ibid. pp 8

xi Ibid. pp 7

xii Ibid.

xiii Ibid.

xiv Ibid.

xv Jordan, Jeffrey. “Pragmatic Arguments”. A Companion to the Philosophy of Religion: Second Edition. Edited by Charles Taliaferro, Paul Draper and

Phillip Quinn. Blackwell Publishing. 2010. Blackwell Reference Online. 10/06/2013. Section title “Pascal’s Wager”.

xvi Ibid.

xvii Martin, Michael. “Pascal’s Wager as an Argument for not believing in God”. Religious Studies. Vol 19. No 1. 1983. pp 57-64. pp 58

xviii Ibid. pp 2 xix Ibid.

xx Jordan, Jeffrey. “Pascal’s Wager: Pragmatic Arguments and Belief in God”. Oxford Scholarship Online. January 2007. DOI: 10.1093/acprof:oso/9780199291328.001.0001. Chapter “An Embarrassment of Riches?”. pp 4

xxi Martin, Michael. “Pascal’s Wager as an Argument for not believing in God”. Religious Studies. Vol 19. No 1. 1983. pp 57-64. pp. 59-60

xxii Adams, Marilyn Mccord. “Sin as Uncleanness”. In “A Reader in Contemporary Philosophical Theology”. Edited by Oliver Crisp. pp 254-273.New York. T&T Clark. 2009. pp 272

xxiii Mougin, Gregory and Elliot Sober. “Betting Against Pascal’s Wager”. Nous. Vol. 28. No 3. 1994. pp 382-395. pp 386

xxiv Ibid. pp 384

xxv Ibid. pp 386

xxvi Ibid.

Bibliography Adams, Marilyn Mccord. “Sin as Uncleanness”. In “A Reader in

Contemporary Philosophical Theology”. Edited by Oliver Crisp. pp 254-273. New York. T&T Clark. 2009.

Freeman, Samuel. “Original Position”. The Stanford Encyclopedia of Philosophy. Accessed 11/06/13. http://plato.stanford.edu/entries/original-position/#ArgMaxCr

iTJSec2628.

Jordan, Jeffrey. “Pascal’s Wager: Pragmatic Arguments and Belief in God”.Oxford Scholarship Online. January 2007. DOI: 10.1093/acprof:oso/9780199291328.001.0001.

Jordan, Jeffrey. “Pragmatic Arguments”. A Companion to the Philosophy of Religion: Second Edition. Edited by Charles Taliaferro, Paul Draper and Phillip Quinn. Blackwell Publishing. 2010. Blackwell Reference Online. 10/06/2013

Martin, Michael. “Pascal’s Wager as an Argument for not believing in God”. Religious Studies. Vol 19. No 1. 1983. pp 57-64

Mawson, TJ. “Praying to Stop Being an Atheist”. International Journal for Philosophy of Religion. Vol. 67, No. 3 (June 2010), pp. 173-186.

Mougin, Gregory and Elliot Sober. “Betting Against Pascal’s Wager”. Nous. Vol. 28. No 3. 1994. pp 382-395.