From: morgan@sitka.triumf.ca (Morgan Burke)
Subject: bug in FAQ file
Organization: TRIUMF, Vancouver BC
Date: Wed, 16 Sep 1992 00:14:23 GMT

I am convinced that there is a flaw in the logic of one of the
rebuttals to Pascal's Wager in the alt.atheism FAQ file.

From the alt.atheism FAQ file:

>8. "If you believe in God and turn out to be incorrect, you have lost nothing
>     -- but if you don't believe in God and turn out to be incorrect, you will
>     go to hell.  Therefore it is foolish to be an atheist."
>
[ valid rebuttals deleted ]
>
>     Formally speaking, the argument consists of four statements:
>
>       1. One does not know whether God exists.
>       2. Not believing in God is bad for one's eternal soul if God does
>          exist.
>       3. Believing in God is of no consequence if God does not exist.
>       4. Therefore it is in one's interest to believe in God.
>
>     One problem with this argument, in the abstract, is that it creates
>     information from no information.  This is considered invalid in
>     information theory.  Statement 1 indicates one has no information about
>     God -- but statements 2 and 3 indicate that beneficial information can be
>     gained from the absolute lack of information about God.  This violates
>     information entropy -- information has been extracted from no
>     information, at no "cost".

Before I get into details, let me present a few counter-examples.

        I am late for my bus.  I can take a short cut through the
        neighbour's yard, but this will result in being attacked
        by a 200-pound pit bull if the dog is in the yard.  Since
        I cannot tell whether the dog is in the house or yard, I
        decide it is safest to avoid the yard.

Although this seems like a well-reasoned decision, according to the
FAQ file it is irrational, since it is based on the lack of knowledge
regarding the whereabouts of the pit bull.  A more quantitative example:

        int odd(n)   /* return an odd number       */
            int n;   /* arbitrary integer argument */
        {
          /* assume n is even */
          return 2 * n - 1;
        }

This programmer calculated that it is beneficial (ie. computationally
more efficient) to assume that n is even than to check first as to
whether it might already be odd.  Again, this type of decision is
apparently irrational, since it indicates "that beneficial information
can be gained from the absolute lack of information about" n.  Simple
computational analysis show that the programmer is correct, however.

It seems evident that the FAQ claim that "information has been extracted
from no information" is false.  In fact, each of the above decisions was
reached based on the following pieces of information:

        -- the consequence of being right
        -- the consequence of being wrong

WRT Pascal's Wager, we _know_ that in the Christian worldview, believers
benefit and unbelievers burn.  This information is sufficient to allow
limited powers of deduction.  Note that it does not allow us to
conclude whether we are right or wrong in our belief, only what the
consequences of this belief will be.

It should also be said that the FAQ statement "that beneficial
information can be gained from the absolute lack of information
about God" is misleading;  in fact, "beneficial" information is being
gained from knowledge of the consequences of believing/rejecting God.

So, contrary to the FAQ list, the logic behind Pascal's Wager can be
soundly applied to at least some scenarios.  On the other hand, there
are variants of Pascal's Wager that are obviously ridiculous.  For
example, how can one choose between the following two wagers:

        A homocidal maniac may be standing outside my door, waiting
        to cut me into bits with his chainsaw when I leave.  If I am
        correct, then I better stay here.  Even if I am wrong, staying
        here does no harm.  Either way, staying put is the best course
        of action.

        A homocidal maniac may be just about to rush in and cut me to
        bits with his chainsaw.  If I am correct, then I better get
        out of here.  Even if I am wrong, leaving does no harm.  Either
        way, leaving is the best course of action.

Evidently, Pascal's Wager is valid in some circumstances, and not in
others.  The only difference that I can see is the relative probabilities
that people assign to the core assumptions.  In the last two cases,
most would consider the presence of the maniac to be highly unlikely,
and reject both wagers on those grounds.  In the earlier case of the
pit bull, the presence of the dog is a real possibility, so that wager
seems acceptable.  In the case of the odd/even numbers, it is reasonable
to assume a 50-50 chance of each, so the programmer's wager is definitely
valid.

In the case of God, believers obviously assign Him a high probability
of existing;  they therefore have no problem with the Wager.  Atheists,
however, rank Him as somewhere below "unlikely";  to them the wager
is absurd.  If the validity of Pascal's Wager is a function of one's
belief, then obviously it is useless as an objective measure of the
value of faith.

Perhaps the FAQ should be corrected to reflect these points.

-- Morgan Burke (morgan@reg.triumf.ca)
Newsgroups: alt.atheism