From my paper "Miracles and the Case for Theism."
It is true that in order for miraculous occurrences to play a role
in a case for theism, it must be the case that such events contradict
naturalistic expectations. But it does not follow that, from the point
of view of naturalism, these events have to be maximally improbable.
Other events that contradict naturalistic expectations to a greater degree
can be passed off as mere anomalies because no plausible theistic
explanation is available to tempt the naturalist to alter his beliefs about
the way the world works. Paul Horwich gives an account of what it is
for an event to be surprising that may shed some light on this matter.
He claims that it is necessary to distinguish between unlikely events
and surprising events, since many unlikely events do not surprise us.
If I were to flip a coin 100 times and get heads every time it would
surprise me, even though any other sequence of heads and tails would
be equally unlikely. What distinguishes surprising events from other
unlikely events is the presence of an alternative account of the circumstances
under which the event occurred, an account not previously
accepted, that would diminish the improbability of the event in
question. Thus in the coin-tossing case the possibility that the coin
might not be fair causes me to wonder if the world is in fact the way
I, who am accustomed to coins being fair, previously thought it to be.
This explains why it would not be surprising if Jones were to win a
lottery amongst a billion people, but it would be surprising if Smith
were to win three lotteries amongst a thousand people, even though it
is more probable that Smith should win his three thousand-person
lotteries than that Jones should win a billion-person lottery. This is
because the Smith case gives me reason to change my background
assumption about the fairness of the lotteries in a way that the Jones
case does not. Thus surprisingness, for Horwich, does not vary with
improbability, it varies with the degree to which events force us to
change our hypotheses about how things happen in the world. 21 In
cases where there is evidence that a miracle has occurred, it is the
combination of natural improbability and the availability of supernatural
explanation that makes the evidence surprising from the point
of view of naturalism, not the improbability alone. So perhaps we can
attribute Mackie's insistence that miracles are maximally improbable
for atheists to the fact that good evidence for miracles would be maximally
surprising for atheists; for persons with a naturalistic bent the
acceptance of miracles requires a thorough revision of their view of
the world. (Miracles would also surprise theists, if they were not expecting
God to act in the way he did and would find it necessary to
change their view about what God is like). However, as Horwich has
shown, surprisingness is not strictly a function of improbability; therefore
Mackie is mistaken in assuming that since miracles are maximally
surprising they must also be maximally improbable.
It is true that in order for miraculous occurrences to play a role
in a case for theism, it must be the case that such events contradict
naturalistic expectations. But it does not follow that, from the point
of view of naturalism, these events have to be maximally improbable.
Other events that contradict naturalistic expectations to a greater degree
can be passed off as mere anomalies because no plausible theistic
explanation is available to tempt the naturalist to alter his beliefs about
the way the world works. Paul Horwich gives an account of what it is
for an event to be surprising that may shed some light on this matter.
He claims that it is necessary to distinguish between unlikely events
and surprising events, since many unlikely events do not surprise us.
If I were to flip a coin 100 times and get heads every time it would
surprise me, even though any other sequence of heads and tails would
be equally unlikely. What distinguishes surprising events from other
unlikely events is the presence of an alternative account of the circumstances
under which the event occurred, an account not previously
accepted, that would diminish the improbability of the event in
question. Thus in the coin-tossing case the possibility that the coin
might not be fair causes me to wonder if the world is in fact the way
I, who am accustomed to coins being fair, previously thought it to be.
This explains why it would not be surprising if Jones were to win a
lottery amongst a billion people, but it would be surprising if Smith
were to win three lotteries amongst a thousand people, even though it
is more probable that Smith should win his three thousand-person
lotteries than that Jones should win a billion-person lottery. This is
because the Smith case gives me reason to change my background
assumption about the fairness of the lotteries in a way that the Jones
case does not. Thus surprisingness, for Horwich, does not vary with
improbability, it varies with the degree to which events force us to
change our hypotheses about how things happen in the world. 21 In
cases where there is evidence that a miracle has occurred, it is the
combination of natural improbability and the availability of supernatural
explanation that makes the evidence surprising from the point
of view of naturalism, not the improbability alone. So perhaps we can
attribute Mackie's insistence that miracles are maximally improbable
for atheists to the fact that good evidence for miracles would be maximally
surprising for atheists; for persons with a naturalistic bent the
acceptance of miracles requires a thorough revision of their view of
the world. (Miracles would also surprise theists, if they were not expecting
God to act in the way he did and would find it necessary to
change their view about what God is like). However, as Horwich has
shown, surprisingness is not strictly a function of improbability; therefore
Mackie is mistaken in assuming that since miracles are maximally
surprising they must also be maximally improbable.
