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otherwise, so long as the probability of God ’ s existence is greater than 0. |
It is foolish not to lead the Christian life. |
Parts of the wager argument – whether in Pascal ’ s own version or this |
modern one – are best presented using a device called a “ decision table ” |
(below). The words at the top of each column describe a possible state of |
the world or universe. There are just two, and each one has some chance |
or probability of being the truth. We can ’ t eliminate either, according to |
Pascal. Each box tells the result you get if the state named in the column |
is true and you make the choice in the row. So, for example, the result for |
you if the Christian God exists and you lead the Christian life and believe |
this God exists is a gain or benefi t of all – in Pascal ’ s words – or infi nite |
positive value – in the words of the modern argument – and a loss of either |
nothing – which seems to be what Pascal thinks – or something very small, |
some worldly pleasure – as the modern argument has it. Pascal doesn ’ t |
explicitly tell us what goes into some of the boxes. For example, he doesn ’ t |
say what the results for you are if the Christian God exists but you don ’ t |
believe this. The modern statement of the wager fi lls this in for us. |
The third and fourth premises of the argument below are implicit or |
hidden. This argument is certainly deductively valid once these hidden |
premises are added. Each simple step in the reasoning in the argument is |
truth - functionally valid. So any criticism of the argument must tell us that |
one or more of the premises are false. Here are some examples of |
criticisms: |
(a) The fi rst premise says that anyone who leads the Christian life and |
believes, no matter why he does this, gets the benefi t. That ’ s what is |
in Table 1 and the fi rst premise tells us that everything in the table is |
true. But it ’ s false. The Christian God would not reward someone who |
believes or leads the life of a believer solely in order to gain the benefi t |
of infi nite happiness. |
(b) According to the reasoning, the table completely describes the possible |
states of the world and says what will result in each of these states if |
you do believe and lead an appropriate life or you don ’ t believe and |
do not lead the Christian life. But is that correct? Suppose, when the |
Christian God doesn ’ t exist, it is also true that another type of god |
does. This god punishes severely those who believe in the Christian |
God or lead a Christian life. This is a possibility; it is not ruled out by |
logic any more than the existence of the Christian God is ruled in or |
out by logic. If that happens, then what is said in Table 1 down column |
2 aren ’ t certain results. They are merely one among many possible sets |
of results. These are the results that would happen when the Christian |
30 Leslie Burkholder |
God doesn ’ t exist and no other god does either. What is said about |
the state when the Christian God doesn ’ t exist also holds for when |
that God does exist. Other kinds of gods could possibly exist as well, |
even when the Christian God exists. The results listed in column 1 of |
the table are only the ones that happen when the Christian God exists |
and no other kind of god does. So either premise 1 is false because |
what the table states is that the results are really only one of indefi nitely |
many possible results, or premise 2 is false because the columns do |
not cover all the possibilities. They only really cover the case when the |
Christian God exists and no other does and the case when the Christian |
God does not exist and no other does either. |
(c) Suppose that there is no problem with either premise 1 or premise 2. |
Then there is a problem with the implicit or hidden premise 3. |
According to the table, the benefi t gained from believing in the case |
when the Christian God exists is infi nitely positive and the loss from |
not believing in this case is infi nitely negative. Using these facts and |
the rest in the table, we are supposed to be able to calculate that we |
are better off believing in the existence of the Christian God than not |
believing. But there is no way to make sound calculations involving |
infi nite gains and losses. So premise 3 may be false – or at least it is |
very uncertain that it is true. |
God is, or He is not. Reason can decide nothing here. [ . . . ] A game is |
being played at the extremity of this infi nite distance where heads or tails will |
turn up. [ . . . ] Which will you choose then? [ . . . ] Let us weigh the gain and |
the loss in wagering that God is. [ . . . ] If you gain, you gain all; if you lose, |
you lose nothing. Wager, then, without hesitation that He is. ( § 233) |
P1. The information in Table 1 is true. |
P2. The information in Table 1 is complete. |
C1. The information in Table 1 is true and the information in Table 1 |
is complete (conjunction, P1, P2). |
Table 1 |
Christian God exists |
(Prob > 0) |
Christian God doesn ’ t |
exist (Prob > 0) |
Lead Christian life |
and believe |
Christian God exists |
Gain = all, infi nite |
good; loss = small |
or nothing |
Gain = nothing; |
loss = small or nothing |
Don ’ t lead Christian |
life and believe |
Christian God exists |
Gain = nothing; |
loss = all, infi nite bad |
Gain = nothing; |
loss = nothing |
Pascal’s Wager 31 |
P3. If the information in Table 1 is true and the information in Table 1 is |
complete, then you are better off having the life of a believer and believing |
in the Christian God than not doing so. |
C2. You are better off having the life of a believer and believing in the |
Christian God than not doing so ( modus ponens , C1, P3). |
P4. If you are better off having the life of a believer and believing in the |
Christian God than not doing so, then you logically should choose the |
Christian kind of life and believe in God. |