## 1. Some Important Distinctions


### 1.1 Relevant Concepts of God



The term "God" is used with a wide variety of different
meanings. These tend to fall, however, into two main groups. On the
one hand, there are metaphysical interpretations of the term: God is
a prime mover, or a first cause, or a necessary being that has its
necessity of itself, or the ground of being, or a being whose essence
is identical with its existence. Or God is not one being among other
beings--even a supremely great being--but, instead, being
itself. Or God is an ultimate reality to which no concepts truly
apply.



On the other hand, there are interpretations that connect the term
"God" in a clear and relatively straightforward way with
religious attitudes, such as those of worship, and with very important
human desires, such as the desires that good will triumph, that
justice be done, and that the world not be one where death marks the
end of the individual's existence.



What properties must something have if it is to be an appropriate
object of worship, and if it is to provide reason for thinking that
there is a reasonable chance that the fundamental human desires just
mentioned will be fulfilled? A natural answer is that God must be a
person who, at the very least, is very powerful, very knowledgeable,
and morally very good. But if such a being exists, then it seems
initially puzzling why various evils exist. For many of the very
undesirable states of affairs that the world contains are such as
could be eliminated, or prevented, by a being who was only moderately
powerful, while, given that humans are aware of such evils, a being
only as knowledgeable as humans would be aware of their
existence. Finally, even a moderately good human being, given the
power to do so, would eliminate those evils. Why, then, do such
undesirable states of affairs exist, if there is a being who is very
powerful, very knowledgeable, and very good?



What one has here, however, is not just a puzzle, since the question
can, of course, be recast as an argument for the non-existence of
God. Thus if, for simplicity, we focus on a conception of God as
all-powerful, all-knowing, and perfectly good, one very concise way
of formulating such an argument is as follows:


1. If God exists, then God is omnipotent, omniscient, and morally
perfect.
2. If God is omnipotent, then God has the power to eliminate all
evil.
3. If God is omniscient, then God knows when evil exists.
4. If God is morally perfect, then God has the desire to eliminate
all evil.
5. Evil exists.
6. If evil exists and God exists, then either God doesn't have the
power to eliminate all evil, or doesn't know when evil exists, or
doesn't have the desire to eliminate all evil.
7. Therefore, God doesn't exist.



That this argument is valid is perhaps most easily seen by a
*reductio* argument, in which one assumes that the 
conclusion--(7)--is false, and then shows that the denial of (7),
along with premises (1) through (6), leads to a contradiction. Thus
if, contrary to (7), God exists, it follows from (1) that God is
omnipotent, omniscient, and morally perfect. This, together with (2),
(3), and (4) then entails that God has the power to eliminate all
evil, that God knows when evil exists, and that God has the desire to
eliminate all evil. But when (5) is conjoined with the reductio
assumption that God exists, it then follows via modus ponens from (6)
that either God doesn't have the power to eliminate all evil, or
doesn't know when evil exists, or doesn't have the desire to eliminate
all evil. Thus we have a contradiction, and so premises (1) through
(6) do validly imply (7).



Whether the argument is sound is, of course, a further question, for
it may be that one or more of the premises is false. The point here,
however, is simply that when one conceives of God as unlimited with
respect to power, knowledge, and moral goodness, the existence of
evil quickly gives rise to potentially serious arguments against the
existence of God.



Is the situation different if one shifts to a deity who is not
omnipotent, omniscient, and morally perfect? The answer depends on
the details. Thus, if one considers a deity who is omniscient and
morally perfect, but not omnipotent, then evil presumably would not
pose a problem if such a deity were conceived of as too remote from
Earth to prevent the evils we find here. But given a deity who falls
considerably short of omnipotence, omniscience, and moral perfection,
but who could intervene in our world to prevent many evils, and who
knows of those evils, it would seem that an argument rather similar
to the above could be formulated by focusing not on the mere
existence of evil, but upon the existence of evils that such a deity
could have prevented.



But what if God, rather than being characterized in terms of
knowledge, power, and goodness, is defined in some more metaphysical
way--for example, as the ground of being, or as being itself? The
answer will depend on whether, having defined God in such purely
metaphysical terms, one can go on to argue that such an entity will
also possess at least very great power, knowledge, and moral
goodness. If so, evil is once again a problem.



By contrast, if God is conceived of in a purely metaphysical way,
and if no connection can be forged between the relevant metaphysical
properties and the possession of significant power, knowledge, and
goodness, then the problem of evil is irrelevant. But when that is
the case, it would seem that God thereby ceases to be a being who is
either an appropriate object of religious attitudes, or a ground for
believing that fundamental human hopes are not in vain.


### 1.2 Incompatibility Formulations versus Inductive Formulations




The argument from evil focuses upon the fact that the world appears
to contain states of affairs that are bad, or undesirable, or that
should have been prevented by any being that could have done so, and
it asks how the existence of such states of affairs is to be squared
with the existence of God. But the argument can be formulated in two
very different ways. First, it can be formulated as a purely
deductive argument that attempts to show that there are certain facts
about the evil in the world that are logically incompatible with the
existence of God. One especially ambitious form of this first sort
of argument attempts to establish the very strong claim that it is
logically impossible for it to be the case both that there is any
evil at all, and that God exists. The argument set out in the
preceding section is just such an argument.



Alternatively, rather than being formulated as a deductive argument
for the very strong claim that it is logically impossible for both
God and evil to exist, (or for God and certain types, or instances,
or a certain amount of evil to exist), the argument from evil can
instead be formulated as an evidential (or inductive/probabilistic)
argument for the more modest claim that there are evils that actually
exist in the world that make it unlikely--or perhaps very 
unlikely--that God exists.



The choice between incompatibility formulations and evidential
formulations is discussed below, in section 2.


### 1.3 Abstract Versus Concrete Formulations




Any version of the argument from evil claims that there is some fact
concerning the evil in the world such that the existence of 
God--understood as at least a very powerful, very knowledgeable, and
morally very good person, and, ideally, as an omnipotent, omniscient,
and morally perfect person--is either logically precluded, or
rendered unlikely, by that fact. But versions of the argument often
differ quite significantly with respect to what the relevant fact is.
Sometimes, as in premise (5) in the argument set out above, the
appeal is to the mere existence of any evil whatever. Sometimes, on
the other hand, it is to the existence of a certain amount of evil.
And sometimes it is to the existence of evils of a certain specified
sort.



To formulate the argument from evil in terms of the mere existence
of any evil at all is to abstract to the greatest extent possible
from detailed information about the evils that are found in the
world, and so one is assuming, in effect, that such information
cannot be crucial for the argument. But is it clear that this is
right? For might one not feel that while the world would be better
off without the vast majority of evils, this is not so for absolutely
all evils? Thus some would argue, for example, that the frustration
that one experiences in trying to solve a difficult problem is
outweighed by the satisfaction of arriving at a solution, and
therefore that the world is a better place because it contains such
evils. Alternatively, it has been argued that the world is a better
place if people develop desirable traits of character--such as
patience, and courage--by struggling against obstacles, including
suffering. But if either of these things is the case, then the
prevention of all evil might well make the world a worse place.



It seems possible, then, that there might be evils that are
logically necessary for goods that outweigh them, and this possibility
provides a reason, accordingly, for questioning one of the premises
in the argument set out earlier--namely, premise (4), where it is
claimed that if God is morally perfect, then God has the desire to
eliminate all evil.



But there is also another reason why that claim is problematic,
which arises out of a particular conception of free will--namely, a
libertarian conception. According to this view of free will, and in
contrast with what are known as compatibilist approaches, free will
is incompatible with determinism, and so it is impossible even for an
omnipotent being to make it the case that someone freely chooses to
do what is right.



Many people claim, however, that the world is a better place if it
contains individuals who possess libertarian free will, rather than
individuals who are free only in a sense that is compatible with
one's actions being completely determined. If this claim can be made
plausible, one can argue, first, that God would have a good reason
for creating a world with individuals who possessed libertarian free
will, but secondly, that if he did choose to create such a world,
even he could not ensure that no one would ever choose to do
something morally wrong. The good of libertarian free will requires,
in short, the *possibility* of moral evil.



Neither of these lines of argument is immune from challenge. As
regards the former, one can argue that the examples that are
typically advanced of cases where some evil is logically necessary
for a greater good that outweighs the evil are not really, upon close
examination, convincing, while, as regards the latter, there is a
serious problem of making sense of libertarian free will, for
although there is no difficulty about the idea of actions that are
not causally determined, libertarian free will requires more than the
mere absence of determinism, and the difficulty arises when one
attempts to say what that something more is.



But although these challenges are important, and may very well turn
out to be right, it is fair to say, first, that it has not yet been
established that there is no coherent conception of libertarian free
will, and, secondly, that it is, at least, very doubtful that one can
establish that there cannot be cases where some evil is logically
necessary for a greater good that outweighs it without appealing to
some substantive, and probably controversial, moral theory.



The upshot is that the idea that either the actuality of certain
undesirable states of affairs, or at least the possibility, may be
logically necessary for goods that outweigh them, is not without some
initial plausibility, and if some such claim can be sustained, it
will follow immediately that the mere existence of evil cannot be
incompatible with the existence of an omnipotent, omniscient, and
morally perfect being.



How does this bear upon evidential formulations of the argument from
evil? The answer would seem to be that if there can be evils that are
logically necessary for goods that outweigh them, then it is hard to
see how the mere existence of evil--in the absence of further
information--can provide much in the way of *evidence* against
the existence of God.



What if one shifts to a slightly less abstract formulation of the
argument from evil that is based upon the premise that the world
contains a certain amount of evil, or upon the premise that the world
contains at least some natural evil? Then one is including marginally
more information. But one is still assuming, in effect, that most of
the detailed information about the evils found in the world is
completely irrelevant to the argument from evil, and a little
reflection brings out how very implausible this assumption is. So,
for example, consider a world that contains a billion units of natural
evil. Is this a good starting point for an argument from evil? The
answer is that, if either a deontological approach to ethics is
correct, or a form of consequentialism that takes the distribution of
goods and evils into account, rather than, say, simply the total
amount of goods and evils, whether this fact is an impressive reason
for questioning the existence of God surely depends on further details
about the world. If those billion units are uniformly distributed over
trillions of people whose lives are otherwise extremely satisfying and
ecstatically happy, it is not easy to see a serious problem of evil.
But if, on the other hand, the billion units of natural evil fell upon
a single innocent person, and produced a life that was, throughout,
one of extraordinarily intense pain, then surely there would be a very
serious problem of evil.



Details concerning such things as how suffering and other evils are
distributed over individuals, and the nature of those who undergo the
evils, are, then, of crucial importance. Thus it is relevant, for
example, that many innocent children suffer agonizing deaths. It is
relevant that animals suffer, and that they did so before there were
any persons to observe their suffering, and to feel sympathy for
them. It is also relevant that, on the one hand, the suffering that
people undergo apparently bears no relation to the moral quality of
their lives, and, on the other, that it bears a very clear relation
to the wealth and medical knowledge of the societies in which they
live.



The prospects for a successful abstract version of the argument from
evil would seem, therefore, rather problematic. It is conceivable,
of course, that the correct moral principles entail that there cannot
be any evils whose actuality or possibility makes for a better world.
But to attempt to set out a version of the argument from evil that
requires a defense of that thesis is certainly to swim upstream. A
much more promising approach, surely, is to focus, instead, simply
upon those evils that are thought, by the vast majority of people, to
pose at least a prima facie problem for the rationality of belief in
an omnipotent, omniscient, and morally perfect person.



Given that the preceding observations are rather obvious ones, one
might have expected that discussions of the argument from evil would
have centered mainly upon concrete formulations of the
argument. Rather surprisingly, that has not been so. Indeed, some
authors seem to focus almost exclusively upon very abstract versions
of the argument.



One of the more striking illustrations of this phenomenon is
provided by Alvin Plantinga's discussions of the problem of evil. In
*God and Other Minds*, in *The Nature of Necessity*,
and in *God, Freedom, and Evil*, for example, Plantinga,
starting out from an examination of John L. Mackie's essay "Evil
and Omnipotence" (1955), in which Mackie had defended an
incompatibility version of the argument from evil, focuses mainly on
the question of whether the existence of God is compatible with the
existence of evil, although there are also short discussions of
whether the existence of God is compatible with the existence of a
given quantity of evil, and of whether the existence of a certain
amount of evil renders the existence of God unlikely. (The latter
topic is then the total focus of attention in his long article,
"The Probabilistic Argument from Evil".)



That Plantinga initially focused upon abstract formulations of the
argument from evil was not, perhaps, surprising, given that a number
of writers--including Mackie, H. J. McCloskey (1960), and
H. D. Aiken (1957-58)--had defended incompatibility versions of
the argument from evil, and it is natural to formulate such arguments
in an abstract way, since although one may wish to distinguish, for
example, between natural evils and moral evils, reference to concrete
cases of evil would not seem to add anything. But once one shifts to
probabilistic formulations of the argument from evil, the situation is
very different: details about concrete cases of evil may be
evidentially crucial.



The problem, then, is that Plantinga not only started out by focusing
on very abstract versions of the argument from evil, but also
maintained this focus throughout. The explanation of this may lie in
the fact that Plantinga seems to have believed that if it can be shown
that the existence of God is neither incompatible with, nor rendered
improbable by, either (1) the mere existence of evil, or (2) the
existence of a specified amount of evil, then no philosophical problem
remains. People may find, of course, that they are still troubled by
the existence of specific evils, but this, Plantinga seems to be
believe, is a religious problem, and what is called for, he suggests,
is not philosophical argument, but "pastoral
care" (1974a,
63-4).[1]




Plantinga's view here, however, is very implausible. For not only can
the argument from evil be formulated in terms of specific evils, but
that is the natural way to do so, given that it is only certain types
of evils that are generally viewed as raising a serious problem with
respect to the rationality of belief in God. To concentrate
exclusively on abstract versions of the argument from evil is
therefore to ignore the most plausible and challenging versions of the
argument.


### 1.4 Axiological Versus Deontological Formulations



Consider, now, the following formulation of the argument from evil,
which, in contrast to the abstract version of the argument from evil
set out in section 1.1, focuses on quite concrete types of evil: 


1. There exist states of affairs in which animals die agonizing
deaths in forest fires, or where children undergo lingering suffering
and eventual death due to cancer, and that (a) are intrinsically bad
or undesirable, and (b) are such that any omnipotent person has the
power to prevent them without thereby either allowing an equal or
greater evil, or preventing an equal or greater good.
2. For any state of affairs (that is actual), the existence of that
state of affairs is not prevented by anyone.
3. For any state of affairs, and any person, if the state of affairs
is intrinsically bad, and the person has the power to prevent that
state of affairs without thereby either allowing an equal or greater
evil, or preventing an equal or greater good, but does not do so,
then that person is not both omniscient and morally perfect.



Therefore, from (1), (2), and (3):


4. There is no omnipotent, omniscient, and morally perfect
person.
5. If God exists, then he is an omnipotent, omniscient, and morally
perfect person.



Therefore:


6. God does not exist.


 
As it stands, this argument is deductively
valid.[2]
(Here is a 
proof.)
However it is likely to be challenged in various ways. In
particular, one vulnerable point is the claim, made in the last part
of statement (1), that an omnipotent and omniscient person could have
prevented those states of affairs without thereby either allowing an
equal or greater evil, or preventing an equal or greater good, and
when this is challenged, an inductive step will presumably be
introduced, one that moves from what we know about the undesirable
states of affairs in question to a conclusion about the overall value
of those states of affairs, all things considered--including things
that may well lie outside our ken. 



But the above argument is subject to a very different sort of
criticism, one that is connected with a feature of the above argument
which seems to me important, but which is not often commented 
upon--the fact, namely, that the above argument is formulated in terms of
*axiological* concepts, that is, in terms of the goodness or
badness, the desirability or undesirability, of states of
affairs. The criticism that arises from this feature centers on
statement (3), which asserts that an omniscient and morally perfect
being would prevent the existence of any states of affairs that are
intrinsically bad or undesirable, and whose prevention he could
achieve without either allowing an equal or greater evil, or
preventing an equal or greater good. For one can ask how this claim
is to be justified. One answer that might be offered would be that
some form of consequentialism is true--such as, for example, the
view that an action that fails to maximize the balance of good states
of affairs over bad states of affairs is morally wrong. But the
difficulty then is that any such assumption is likely to be a deeply
controversial assumption that many theists would certainly
reject.



The problem, in short, is that any axiological formulation of the
argument from evil, as it stands, is incomplete in a crucial respect,
since it fails to make explicit *how* a failure to bring about
good states of affairs, or a failure to prevent bad states of affairs,
entails that one is acting in a morally wrong way. Moreover, the
natural way of removing this incompleteness is by appealing to what
are in fact controversial ethical claims, such as the claim that the
right action is the one that maximizes expected value. The result, in
turn, is that discussions may very well become sidetracked on issues
that are, in fact, not really crucial--such as, for example, the
question of whether God would be morally blameworthy if he failed to
create the best world that he could.



The alternative to an axiological formulation is a deontological
formulation. Here the idea is that rather than employing concepts
that focus upon the value or disvalue of states of affairs, one
instead uses concepts that focus upon the rightness and wrongness of
actions, and upon the properties--rightmaking properties and
wrongmaking properties--that determine whether an action is one
that ought to be performed, or ought not to be performed, other
things being equal. When the argument is thus formulated, there is no
problematic bridge that needs to be introduced connecting the
goodness and badness of states of affairs with the rightness and
wrongness of actions.


## 2. The Choice between Incompatibility Formulations and Evidential Formulations



How is the argument from evil best formulated? As an
incompatibility argument, or as an evidential argument? In section
1.1, an incompatibility formulation of a very abstract sort was set
out, which appealed to the mere fact that the world contains at least
some evil. That formulation involved the following crucial
premise:


4. If God is morally perfect, then God has the desire to eliminate
all evil.


 
The problem with that premise, as we saw, is that it can be argued
that some evils are such that their actuality, or at least their
possibility, is logically necessary for goods that outweigh them, in
which case it is not true that a perfectly good being would want to
eliminate such evils.


 
In section 1.4, a much more concrete version of an incompatibility
argument was set out, which, rather than appealing to the mere
existence of some evil or other, appealed to specific types of 
evil--in particular, situations where animals die agonizing deaths in
forest fires, or where children undergo lingering suffering and
eventual death due to cancer. The thrust of the argument was then
that, first of all, an omniscient and omnipotent person could have
prevented the existence of such evils without thereby either allowing
equal or greater evils, or preventing equal or greater goods, and,
secondly, that any omniscient and morally perfect person will prevent
the existence of such evils if that can be done without either
allowing equal or greater evils, or preventing equal or greater
goods.


 
The second of these claims avoids the objections that can be
directed against the stronger claim that was involved in the argument
set out in section 1.1--that is, the claim that if God is morally
perfect, then God has the desire to eliminate all evil. But the
shift to the more modest claim requires that one move from the very
modest claim that evil exists to the stronger claim that there are
certain evils that an omniscient and omnipotent person could have
prevented the existence of such evils without thereby either allowing
equal or greater evils, or preventing equal or greater goods, and the
question arises as to how that claim can be supported. In
particular, can it be established by means of a purely deductive
argument?


 
Consider, in particular, the relevant premise in the more concrete
version of the argument from evil set out in section 1.4, namely:


1. There exist states of affairs in which animals die agonizing
deaths in forest fires, or where children undergo lingering suffering
and eventual death due to cancer, and that (a) are intrinsically bad
or undesirable, and (b) are such that any omnipotent person has the
power to prevent them without thereby either allowing an equal or
greater evil, or preventing an equal or greater good.


 
How would one go about establishing via a purely deductive argument
that a deer's suffering a slow and painful death because of a forest
fire, or a child's undergo lingering suffering and eventual death due
to cancer, is not logically necessary either to achieve a greater
good or to avoid a greater evil? If one had knowledge of the
totality of morally relevant properties, then it might well be
possible to show both that there are no greater evils that can be
avoided only at the cost of the evil in question, and that there are
no greater goods that are possible only given that evil. Do we have
such knowledge? Some moral theorists would claim that we do, and
that it is possible to set out a complete and correct moral theory.
But this is certainly a highly controversial metaethical claim, and,
as a consequence, the prospects for establishing a premise such as
(1) via a deductive argument do not appear promising, at least given the
present state of moral theory.



But if one cannot establish (1) via a deductive argument from one's
moral theory, cannot it be argued that that will lead to skepticism
about whether one can know what human actions are morally right and
morally wrong? This is a serious question, and it may well be that
such *knowledge* is ruled out. But as will become clear when we
consider evidential versions of the argument from evil, it may well be
that one can have *justified beliefs* about the rightness and
wrongness of actions.


 
If a premise such as (1) cannot, at least at present, be established
deductively, then the only possibility, it would seem, is to offer
some sort of inductive argument in support of the relevant premise.
But if this is right, then it is surely best to get that crucial
inductive step out into the open, and thus to formulate the argument
from evil not as a deductive argument for the very strong claim that
it is logically impossible for both God and evil to exist, (or for
God and certain types, or instances, of evil to exist), but as an
evidential (inductive/probabilistic) argument for the more modest
claim that there are evils that actually exist in the world that make
it unlikely that God exists.


## 3. Inductive Versions of the Argument from Evil


### 3.1 Arguments



If the argument from evil is given an evidential formulation, what
form should that take? There appear to be four main possibilities that
have been suggested in recent discussions. The first, which might be
called the *direct inductive* approach, involves the idea that
one can show that theism is unlikely to be true without comparing
theism with any alternative hypothesis, other than the mere denial of
theism. At the heart of this first approach, which was set out by
William Rowe, is the idea that one sound type of inductive inference
is what might be referred to as instantial generalization, where this
is a matter of projecting a generalization that has been found to hold
in all cases that have been so far examined to all cases whatever.


The second, which can be labeled the *indirect inductive*
approach, argues instead that theism can be shown to be unlikely to be
true by establishing that there is some alternative
hypothesis--other than the mere negation of theism--that is
logically incompatible with theism, and more probable than
theism. This approach, which was originally used by David Hume in one
of his arguments in his *Dialogues Concerning Natural
Religion*, and which has been set out and defended in a detailed
way by Paul Draper, can be viewed as involving an inference to the
best explanation, a type of inductive inference that was discovered by
C. S. Pierce, and which is now very widely accepted.


The third approach, which has been advanced by William Rowe,
involves what might be referred to as a *Bayesian* approach,
and it differs from the first two approaches in that it does not
involve either instantial generalization or inference to the best
explanation, or, indeed, any sort of inductive inference. The idea,
instead, is to start out from premises that are themselves substantive
probabilistic claims, and then to show that it follows deductively
from those premises, via axioms of probability theory, that it is
unlikely that God exists.


The fourth and final approach, which has been set out by Michael
Tooley, involves the idea of bringing a substantive theory of
inductive logic, or logical probability, to bear upon the argument
from evil, and then to argue that when this is done, one can derive a
formula giving the probability that God does not exist relative to
information about the number of apparent evils to be found in the
world.


These four approaches will be set out and considered in the sections that follow.



### 3.2 Direct Inductive Versions of the Evidential Argument from Evil


#### 3.2.1 A Concrete, Deontological, and Direct Inductive Formulation



The basic idea behind a direct inductive formulation of the argument
from evil is that the argument involves a crucial inductive step that
takes the form of an inductive projection or generalization in which
one moves from a premise concerning the known moral properties of some
state of affairs to a conclusion about the likely overall moral worth
of that state of affairs, given *all* its moral properties, both known
and unknown.



Such a direct inductive argument might, for example, take the following
form:


1. There are events in our world -- such as an animal's dying an
agonizing death in a forest fire, and a child's undergo lingering
suffering and eventual death due to cancer -- such that the
actions of allowing those events, when one could prevent them, both
(a) have very serious, known wrongmaking characteristics, and (b) have
no rightmaking characteristics of which we are aware that are
sufficient to balance out the known wrongmaking properties.



Therefore it is ***likely*** that:


2. For any such action, the totality of the wrongmaking
properties, ***both known and unknown***, outweighs the
totality of the rightmaking properties, ***both known and
unknown***.
3. Any action whose wrongmaking properties outweigh its rightmaking
properties is morally wrong.



Therefore, from (2) and (3) :


4. Such actions are morally wrong.
5. For any action whatever, an omnipotent and omniscient being is
capable of not performing that action.



Therefore, from (4) and (5):


6. If there is an omnipotent and omniscient being, then that being
performs some morally wrong actions.
7. A being that performs morally wrong actions is not morally perfect.



Therefore, from (6) and (7):


8. If there is an omnipotent and omniscient being, that being is not
morally perfect.
9. God is by definition an omnipotent, omniscient, and morally
perfect person.



Therefore, from (8) and (9):


10. God does not exist.



When the argument from evil is formulated in this way, it involves
five premises, set out at steps (1), (3), (5), (7) and (9). Statement
(1) involves both empirical claims, and moral claims, but the
empirical claims are surely true, and, setting aside the question of
the existence of objective rightmaking and wrongmaking properties, the
moral claims are surely also very plausible. The other four premises,
set out at steps (3), (5), (7) and (9), are plausibly viewed as
analytic truths.



As regards the logic of the argument, all of the steps in the
argument, other than the inference from (1) to (2), are deductive, and
are either clearly valid as they stand, or could be made so by trivial
expansions of the argument at the relevant points. The upshot,
accordingly, is that the above argument appears to stand or fall with
the defensibility of the inductive inference from (1) to (2). The
crucial questions, accordingly, are, first, exactly what the form of
that inductive inference is, and, secondly, whether it is sound.



#### 3.2.2 A Natural Account of the Logic of the Inductive Step



A familiar and very common sort of inductive inference involves
moving from information to the effect that all observed things of a
certain type have a certain property to the conclusion that absolutely
all things of the type in question have the relevant property. Could
the inductive step in the evidential argument from evil perhaps be of
that form?



One philosopher who has suggested that this is the case is William
Rowe, in his 1991 article, "Ruminations about Evil". Let us consider,
then, whether that view can be sustained.



In that article, Rowe formulates the premise of the crucial inference
as follows:



> 
> (P) No good state of affairs that we know of is such that an
> omnipotent, omniscient being's obtaining it would morally justify
> that being's permitting E1 or E2. (1991, 72)
> 
> 



(Here "E1" refers to a case of a fawn who dies in
lingering and terrible fashion as a result of a forest fire, and
"E2" to the case of a young girl who is brutally
raped, beaten, and murdered.)



Commenting on P, Rowe emphasizes that what proposition
P says is not simply that we cannot see how various goods
would justify an omnipotent, omniscient being's permitting
E1 or E2, but rather,



> 
> The good states of affairs I know of, when I reflect on them, meet
> one or both of the following conditions: either an omnipotent being
> could obtain them without having to permit either
> E1 or E2, or obtaining them wouldn't morally justify that being in permitting
> E1 or E2. (1991, 72)
> 



Rowe then goes on to say that:



> ... if this is so, I have reason to
> conclude that:
> 
>  
> > 
> > (Q) No good state of affairs is such that an omnipotent,
> > omniscient being's obtaining it would morally justify that
> > being's permitting E1 or E2.
> >  
> 
> 
> (1991, 72)
> 



Rowe uses the letter 'J' "to stand for the property
a good has just in case obtaining that good would justify an
omnipotent, omniscient being in permitting E1 or
E2" (1991, 73). When this is done, the above
inference can be compactly represented as follows:


* (P)

No good that we know of has J.



Therefore, probably:


* (Q)

No good has J.



Rowe next refers to Plantinga's criticism of this inference, and
he argues that Plantinga's criticism now amounts to the claim
that



> 
> we are justified in inferring Q (No good has J)
> from P (No good we know of has J) only if we have a
> *good reason* to think that if there were a good that has
> J it would be a good that we are acquainted with and could
> see to have J. For the question can be raised: How can we
> have confidence in this inference unless we have a good reason to
> think that were a good to have J it would likely be a good
> within our ken? (1991, 73)
> 



Rowe's response is then as follows:



> 
> My answer is that we are justified in making this inference in the
> same way we are justified in making the many inferences we constantly
> make from the known to the unknown. All of us are constantly inferring
> from the \(A\)s we know of to the \(A\)s we
> don't know of. If we observe many \(A\)s and note that
> all of them are \(B\)s we are justified in believing that
> the As we haven't observed are also
> \(B\)s. Of course, these inferences may be defeated. We may
> find some independent reason to think that if an \(A\) were a
> \(B\) it would likely not be among the \(A\)s we have
> observed. But to claim that we cannot be justified in making such
> inferences unless we already know, or have good reason to believe,
> that were an \(A\) not to be a \(B\) it would likely be
> among the As we've observed is simply to encourage
> radical skepticism concerning inductive reasoning in general. (1991,
> 73)
> 



Finally, Rowe points out that:



> 
> ... in considering the inference from
> P to Q it is very important to distinguish two
> criticisms:
> 
> 1. One is entitled to infer Q from P only if she
> has a good reason to think that if some good had J it would
> be a good that she knows of.
> 2. One is entitled to infer Q from P only if she
> has no reason to think that if some good had J it would
> likely not be a good that she knows of.
> 
> 
> 
> Plantinga's criticism is of type (A). For the reason given, it is
> not a cogent criticism. But a criticism of type (B) is entirely proper
> to advance against any inductive inference of the sort we are
> considering. (1991, 73-4)
> 
> 
> 



In view of the last point, Rowe concludes that "one important route
for the theist to explore is whether there is some reason to think
that were a good to have J it either would not be a good
within our ken or would be such that although we apprehend this good
we are incapable of determining that it has J," (1991, 74).


#### 3.2.3 An Evaluation of this Account of the Inductive Step



First, Rowe is right that a criticism of type (A) does involve
"radical skepticism of inductive reasoning in
general". But, secondly, having granted that point, how
satisfactory is Rowe's account of the reasoning involved? To answer
that question, what one needs to notice is that Rowe's claim that
"if we observe many \(A\)s and note that all of them are
\(B\)s we are justified in believing that the \(A\)s we
haven't observed are also \(B\)s" is somewhat ambiguous,
since while the claim that "we are justified in believing that
the \(A\)s we haven't observed are also \(B\)s" might
naturally be interpreted as saying


1. We are justified in believing that *all* the
\(A\)s that we haven't observed are also
\(B\)s



it is possible to construe it as making, instead, the following,
much weaker claim


2. We are justified in believing of *each* of the
\(A\)s that we haven't observed that that \(A\)
is also a \(B\).



Let us consider, then, the relevance of this distinction. On the one
hand, Rowe is certainly right that any criticism that claims that one
is not justified in inferring (2) unless one has additional
information to the effect that unobserved \(A\)s are not likely
to differ from observed \(A\)s with respect to the possession of
property \(B\) entails inductive skepticism. But, by contrast,
it is not true that this is so if one rejects, instead, the inference
to (1). For one might reject the latter inference on the ground that
while, given any particular \(A\), it is likely that ***that***
\(A\) is a \(B\), it is not likely that ***all*** \(A\)s are
\(B\)s. (Compare the situation with a very long conjunction: given any
particular conjunct, it may be likely that that conjunct is true,
while being very unlikely that every conjunct, and hence the
conjunction as a whole, is true.)



This is important, moreover, because it is (1) that Rowe needs, since
the conclusion that he is drawing does not concern simply *the
next* morally relevant property that someone might consider:
conclusion Q asserts, rather, that *all* further
morally relevant properties will lack property J. Such a
conclusion about all further cases is much stronger than a conclusion
about the next case, and one might well think that in some
circumstances a conclusion of the latter sort is justified, but that a
conclusion of the former sort is not.



One way of supporting the latter claim is by introducing the idea of
logical probability, where logical probability is a measure of the
extent to which one proposition supports another (Carnap, 1962,
19-51, esp. 43-7), and then arguing (Tooley, 1977,
690-3, and 1987, 129-37) that when one is dealing with an
*accidental generalization*, the probability that the
regularity in question will obtain gets closer and closer to zero,
without limit, as the number of potential instances gets larger and
larger, and that this is so regardless of how large one's
evidence base is. Is it impossible, then, to justify universal
generalizations? The answer is that if laws are more than mere
regularities--and, in particular, if they are second-order
relations between universals--then the obtaining of a law, and
thus of the corresponding regularity, may have a very high probability
upon even quite a small body of evidence. So universal generalizations
can be justified, *if* they obtain in virtue of underlying, governing
laws of nature.



The question then becomes whether Q expresses a law--or
a consequence of a law. If--as seems plausible--it does not,
then, although it is true that one in justified in holding, of any
given, not yet observed morally relevant property, that it is unlikely
to have property J, it may not be the case that it is
probable that no goodmaking (or rightmaking) property has property
J. It *may*, on the contrary, be probable that there
is *some* morally relevant property that does have property
J.



This objection could be overcome if one could argue that it is
unlikely that there are many unknown goodmaking properties. For if the
number is small, then the probability of Q may still be high
even if Q does not express a law, or a consequence of a
law. Moreover, I am inclined to think that it may well be possible to
argue that it is unlikely that there are many unknown, morally
relevant properties. But I also think that it is very likely that any
attempt to establish this conclusion would involve some very
controversial metaethical claims. As a consequence, I think that one
is justified in concluding that such a line of argument is not
especially promising.


### 3.3 Indirect Inductive Versions of the Evidential Argument from Evil



In his *Dialogues Concerning Natural Religion*, Hume contended
that it was not possible to arrive at the conclusion that the world
had a perfectly good cause--or a perfectly evil 
one--starting out simply from a world that consists of a mixture of good
and bad states of affairs:



> 
> There may *four* hypotheses be framed concerning the first
> causes of the universe: *that* they are endowed with perfect
> goodness, *that* they are endowed with perfect malice,
> *that* they are opposite and have both goodness and malice,
> *that* they have neither goodness nor malice. Mixed phenomena
> can never prove the two former unmixed principles. And the
> uniformity and steadiness of general laws seems to oppose the third.
> The fourth, therefore, seems by far the most probable. (1779, Part
> XI, 212)
> 



But if this is right, and the hypothesis that the first cause (or
causes) of the universe is neither good nor evil is more probable than
the hypothesis that the first cause is perfectly good, then the
probability of the latter must be less than one half.



Hume advanced, then, an evidential argument from evil that has a
distinctly different logical form from that involved in direct
inductive arguments, for the idea is to point to some proposition that
is logically incompatible with theism, and then to argue that,
given facts about undesirable states of affairs to be found in the
world, that hypothesis is more probable than theism, and, therefore,
that theism is more likely to be false than to be
true.[3]:



More than two centuries later, Paul Draper, inspired by Hume, set out
and defended this type of indirect inductive argument in a very
detailed way. In doing so, Draper focused upon two alternative
hypotheses, the first of which he referred to as "the Hypothesis of
Indifference," and which was as follows (1989,
13)[4]:


* (HI)

neither the nature nor the condition of sentient
beings on earth is the result of benevolent or malevolent actions
performed by nonhuman persons.



Draper then focused upon three sets of propositions about occurrences
of pleasure and pain, dealing, respectively, with (a) the experience
of pleasure and pain, by moral agents, which is known to be
biologically useful, (b) the experience of pleasure and pain, by
sentient beings that are not moral agents, which is known to be
biologically useful, and (c) the experience of pleasure and pain, by
sentient beings, which is not known to be biologically useful, and
Draper then argued that, where 'O' expresses the
conjunction of all those propositions, and 'T'
expresses the proposition that God exists, the probability that
O is the case given HI is greater than the
probability of O given T. It then follows, provided
that the initial probability of T is no greater than that of
HI, that T is more likely to be false than to be
true.



To set out Draper's argument in a little more detail, let us use
'\(\Pr(P \mid Q)\) ' to stand
for either the logical probability, or, as Draper (1996, 27) himself
does, the epistemic probability, that \(P\) is true, given that \(Q\) is true,
and then use the following instance of what is known as Bayes'
Theorem



\[
\tag{1}
\Pr(H \mid E) = \frac{\Pr(H) \Pr(E \mid H)}{\Pr(H)\Pr(E \mid H) + \Pr(J)\Pr(E \mid J)}
\]



This instance of Bayes' Theorem deals with the simple case where one
has two hypotheses H and J that are mutually exclusive and jointly
exhaustive, and where one is interested
in \(\Pr(H \mid E)\), that is, the
probability that H is true given evidence E. What this instance of
Bayes' Theorem does is provide one with a way of calculating that
probability, provided that one knows, first of
all, \(\Pr(H)\)
and \(\Pr(J)\)--that is, the a priori
logical probabilities of \(H\) and \(J\)--and also,
second, \(\Pr(E \mid H)\)
and \(\Pr(E \mid J)\)--that is, the
logical probability of \(E\) given, respectively, only \(H\) and only \(J\). 
By substitution in (1), we have:




\[
\tag{2}
\Pr(HI \mid O) = \frac{\Pr(HI)\Pr(O \mid HI)}{\Pr(HI)\Pr(O \mid HI) + \Pr(T)\Pr(O \mid T)}
\]


Similarly, by interchanging 'HI' and 'T', we also have:



\[
\tag{3}
\Pr(T \mid O) = \frac{\Pr(T)\Pr(O \mid T)}{\Pr(T)\Pr(O \mid T) + \Pr(HI)\Pr(O \mid HI)}
\]

If we then divide (2) by (3) we arrive at the following very useful equation:



\[
\tag{4}
\frac{\Pr(HI \mid O)}{\Pr(T \mid O)} = \frac{\Pr(HI)\Pr(O \mid HI)}{\Pr(T)\Pr(O \mid T)}
\]


So far, this is simply a matter of probability theory. But now Draper
introduces two substantive claims. The first is that the a priori
probability of the hypothesis of indifference is not less than the a
priori probability of theism, so that we have



\[
\tag{5}
\Pr(HI) \ge \Pr(T)
\]


Draper's second substantive claim is that the conjunction of
propositions about pleasure and pain to which Draper refers, and which
is represented by '\(O\)' is more likely to be true if the hypothesis of
indifference is true than if theism is true. So we have



\[
\tag{6}
\Pr(O \mid HI) \gt \Pr(O \mid T)
\]



But provided that \(\Pr(T)\) and \(\Pr(O \mid T)\) are not equal to zero--which is surely very reasonable--(5) and (6) can be rewritten as

 

\[
\tag{7}
\frac{\Pr(HI)}{\Pr(T)} \ge 1
\]


and




\[
\tag{8}
\frac{\Pr(O \mid HI)}{\Pr(O \mid T)} \gt 1
\]


It then follows, by multiplying (7) and (8), that



\[
\tag{9}
\frac{\Pr(HI)\Pr(O \mid HI)}{\Pr(T)\Pr(O \mid T)} \gt 1
\]


This, together with (4), then entails:



\[
\tag{10}
\frac{\Pr(HI \mid O)}{\Pr(T \mid O)} \gt 1
\]

 Finally, Draper assumes (as a substantive premise) that the
hypothesis of indifference is logically incompatible with theism:



\[
\tag{11}
HI \text{ entails } \negt T
\]


It then follows from (10) and (11) that



\[
\tag{12}
\Pr(\negt T \mid O) \gt \Pr(T \mid O)
\]


So we have the result that, given the facts about pleasure and pain
summarized by '\(O\)', theism is more likely to be false than to be
true.



There are various points at which one might respond to this
argument. First, it might be argued that the assumption that the
hypothesis of indifference is logically incompatible with theism is
not obviously true. For might it not be logically possible that there
was an omnipotent, omniscient, and morally perfect being who created a
neutral environment in which evolution could take place in a chancy
way, and who afterwards did not intervene in any way? But, if so,
then while \(T\) would be true, \(HI\) might also be
true--as it would be if there were no other nonhuman persons.
So, at the very least, it is not clear that \(HI\) entails
\(\negt T\).



Secondly, it might also be argued that the substantive premise
introduced at (5)--that is, \(\Pr(HI) \ge \Pr(T)\)-- is
open to
question. Draper supports it by arguing that whereas the hypothesis
of theism involves some ontological commitment, the Hypothesis of
Indifference does not. But, on the other hand, the latter involves a
completely universal generalization about the absence of any action
upon the earth by any nonhuman persons, of either a benevolent or
malevolent sort, and it is far from clear why the prior probability
of this being so should be greater than the prior probability of
theism.



Both of these objections can be avoided, however, by simply shifting
from \(HI\) to a different alternative hypothesis that Draper also
mentions, namely, "The Indifferent Deity Hypothesis":



> 
> There exists an omnipotent and omniscient person who created the
> Universe and who has no intrinsic concern about the pain or pleasure
> of other beings. (1989, 26)
> 



Thirdly, it can be objected that the argument does not really move far
beyond two of its three crucial assumptions--the assumptions set
out, namely, at steps (5) and (11), to the effect that
\(\Pr(HI) \ge \Pr(T)\),
and \(HI\) entails \(\negt T\). For given those assumptions,
it follows immediately that \(\Pr(T) \le 0.5\),
and so the rest of the argument merely moves from that conclusion to
the conclusion that \(\Pr(T) \lt 0.5\).



One response to this objection is that the move from
\(\Pr(T) \le 0.5\) to
\(\Pr(T) \lt 0.5\) is not insignificant, since it
is a move from a situation in which acceptance of theism may not be
irrational to one where it is certainly is. Nevertheless, the
objection does bring out an important point, namely, that the argument
as it stands says nothing at all about how much below 0.5 the
probability of theism is.


 
Fourthly, objections can be directed at the arguments that Draper
offers in support of a third substantive premise--namely, that
introduced at (6). Some of the objections directed against this
premise are less than impressive--and some seem very implausible
indeed, as in the case, for example, of Peter van Inwagen, who has to
appeal to quite an extraordinary claim about the conditions that one
must satisfy in order to claim that a world is logically possible:



> 
> One should start by describing in some detail the laws of nature
> that govern that world. (Physicists' actual formulations of quantum
> field theories and the general theory of relativity provide the
> standard of required "detail.") One should then go on to
> describe the boundary conditions under which those laws operate; the
> topology of the world's space-time, its relativistic mass, the number
> of particle families, and so on. Then one should tell in convincing
> detail the story of cosmic evolution in that world: the story of the
> development of large objects like galaxies and of stars and of small
> objects like carbon atoms. Finally, one should tell the story of the
> evolution of life. (1991, 146)



Such objections tend to suggest that any flaws in Draper's
argument in support of the crucial premise are less than obvious.
Nevertheless, given that the argument that Draper offers in support
of the premise at (6) involves a number of detailed considerations,
very careful scrutiny of those arguments would be needed before one
could conclude that the premise is justified.



Finally, rather than attacking the argument itself, one might
instead argue that, while it is sound, the conclusion is not really a
significant one. For what matters is not whether there is *some
evidence* relative to which it is unlikely that theism is true. What
matters is whether theism is improbable relative to our *total*
evidence. But, then, suppose that we introduce some different
observations--\(O^\*\)--such that it seems plausible that
\(O^\*\) is more likely to be the case if theism is true that if
the Hypothesis of Indifference is true. For example, \(O^\*\)
might be some proposition about the occurrences of experiences that
seem to be experiences of a loving deity. The question then is
whether the appropriate revision of the first substantive premise is
plausible. That is, do we have good reason for thinking that the
following statement is true:



\[
\tag{\(6^\&\)}
\Pr(O \amp O^\* \mid HI) \gt \Pr(O \amp O^\* \mid T) \, ?
\]


At the very least, it would seem that \((6^{\&})\) is much more
problematic than \((6)\). But if that is right, then the above,
Draper-style argument, even if all of its premises are true, is not
as significant as it may initially appear, since if \((6^{\&})\)
is not true, the conclusion that theism is more likely to be false
than to be true can be undercut by introducing additional evidence of
a pro-theist sort.



A Draper-style argument is one type of indirect inductive argument
from evil. It is important to notice, however, that in formulating an
indirect inductive argument from evil, one need not proceed along the
route that Draper chooses. This is clear if one focuses upon Hume's
formulation, and then thinks in terms of the idea of an inference to
the best explanation of the "mixed phenomena" that one
finds. If one explains the fact that the world contains an impressive
mixture of desirable and undesirable states of affairs by the
hypothesis that the creator of the world was an omnipotent,
omniscient, and indifferent deity, then nothing more needs to be
added. By contrast, if one wants to explain the mixed state of the
world by the hypothesis that the creator of the world was an
omnipotent, omniscient, and morally perfect deity, one needs to
postulate the existence of additional, morally significant properties
that lie beyond our ken, and ones, moreover, that are so distributed
that the mixed appearance does not correspond to what is really the
case. A theistic explanation is, accordingly, less simple than an
indifferent deity explanation, and therefore, provided that one can
argue that the *a priori* probability of the latter hypothesis
is not less than that of the former, one can appeal to the greater
simplicity of the latter in order to conclude that it has a higher
posterior probability than the theistic hypothesis. It then follows,
given that the two hypotheses are logically incompatible, that the
probability of the theistic hypothesis must be less than one half.


### 3.4 William Rowe's Bayesian-Style Probabilistic Versions of the Evidential Argument from Evil




We have just considered the Bayesian-style argument offered by Paul
Draper. Let us now turn to another.




In his 1996 paper, "The Evidential Argument from Evil: A Second
Look", Rowe set aside the problem of attempting to find a
satisfactory account of the inductive step involved in direct,
inductive formulations of the argument from evil in favor of a very
different, Bayesian formulation of the argument from evil. The latter
argument has been vigorously criticized by Plantinga (1998), but Rowe
(1998) has remained confident that the new argument is sound.


#### 3.4.1 A Summary of Rowe's Bayesian Argument



Rowe's new argument can be summarized as follows. First, its
formulation involves only three propositions, one of which is
proposition \(k\), which expresses, roughly, the totality of our
background knowledge, while the other two propositions are as
follows:


* \((P)\)

No good that we know of justifies an omnipotent,
omniscient, perfectly good being in permitting \(E\_1\) and \(E\_2\);
* \((G)\)

There is an omnipotent, omniscient, perfectly good being.



Secondly, the object of the argument as a whole is to start out from
some probabilistic assumptions, and then to move deductively, using
only axioms of probability theory, to the following two conclusions:



\[\begin{align}
\tag{C1} & \Pr(G \mid P \amp k) \lt \Pr(G \mid k) \\
\tag{C2} & \Pr(G \mid P \amp k) \lt 0.5 \,.
\end{align}\]


The first conclusion, then, is that the probability that God exists
is lower given the combination of \(P\) together with our background
knowledge than it is given our background knowledge alone. Thus
\(P\) disconfirms \(G\) in the sense of lowering the
probability of \(G\). The second conclusion is that \(P\)
disconfirms \(G\) in a different sense--namely, it, together
with our background knowledge, makes it more likely than not that
\(G\) is false.



Thirdly, in order to establish the first conclusion, Rowe needs only
the following three assumptions:



\[\begin{align}
\tag{1} & \Pr(P \mid \negt G \amp k) = 1 \\
\tag{2} & \Pr(\negt G \mid k) \gt 0 \\
\tag{3} & \Pr(P \mid G \amp k) \lt 1
\end{align}\]


Fourthly, all three assumptions, interpreted as Rowe does, are surely
eminently reasonable. As regards (1), it follows from the fact that
for any two propositions \(q\) and \(r\), if \(q\)
entails \(r\) then \(\Pr(r \mid q) = 1\), together with the fact 
that Rowe interprets \(P\) in such a
way that \(\negt G\) entails \(P\), since he interprets
\(P\) as saying that it is not the case that there is an
omnipotent, omniscient, and perfectly good being together with some
known good that justifies that being in allowing
\(E\_1\) and \(E\_2\).


As regards (2), it certainly seems plausible, assuming that the
existence of God is not logically necessary, that there is at least
some non-zero probability that God does not exist, given our
background knowledge. But one can derive (2), provided that one is
willing to accept the (not uncontroversial) principle that only
necessarily false propositions have a probability equal to zero. (This
principle is very plausible if one accepts the idea of
infinitesimals. If one does not, one may hold that some contingent
propositions have a probability equal to zero.) Given this assumption,
the reasoning is then that \(\Pr(\negt G \mid k)\) can be equal to
zero only if the conjunction \(\negt G \amp k\) is necessarily false,
which can be case only if either \(G\) is a necessary truth, or else
\(k\) entails \(G\), neither of which is the case.


Similarly, (3) also seems plausible, and here too one can derive
(3) provided that one is willing to accept the principle that only
necessarily false propositions have a probability equal to zero. Here
the reasoning will be that \(\Pr (P\mid G \amp k)\) can be equal to one
only if the conjunction \(\negt P \amp G \amp k\) is necessarily
false, which can be case only if either \(\negt P\) is necessarily
false, or the conjunction \(G \amp k\) entails \(P\), neither of which
is the case.



Secondly, if the existence of God is neither a
logically necessary truth nor entailed by our background knowledge,
and if the existence of God together with our background knowledge
does not logically entail that no good that we know of justifies an
omnipotent, omniscient, perfectly good being in permitting
\(E\_1\) and \(E\_2\), then one can
support (2) and (3) by appealing to the very plausible principle that
the probability of \(r\) given \(q\) is equal to one if and
only if \(q\) entails \(r\).



Finally, to establish the second conclusion--that is, that
relative to our background knowledge together with proposition
\(P\) it is more likely than not that God does not
exist--Rowe needs only one additional assumption:



\[
\tag{4}
\Pr(G \mid k) \le 0.5
\]


Given assumptions (1), (2), and (3), how does the argument for the first conclusion go? In outline, one first uses (1), (2), and (3) to prove that



\[
\notag
\Pr(P \mid k) \gt \Pr(P \mid G \amp k)
\
\]



It then follows very quickly that



\[
\notag
\Pr(G \mid k) \gt \Pr(G \mid P \amp k)
\
\]



Assumption (4) then allows one to conclude that



\[
\notag
\Pr(G \mid P \amp k)\lt 0.5\
\
\]


Here are the details.




The key starting point is with the following theorem of probability theory (Compare Draper, 1996, 268):



\[
\tag{5}
\Pr(P \mid k) = [\Pr(\negt G\mid k)\times \Pr(P \mid \negt G \amp k)] + [\Pr(G\mid k)\times \Pr(P \mid G \amp k)]
\]


Substituting into (5) using assumption (1) then gives one:



\[
\tag{6}
\Pr(P \mid k) = [\Pr(\negt G\mid k) \times 1] + [\Pr(G\mid k)\times \Pr(P \mid G \amp k)]
\]



Next, it is a truth of probability theory that



\[
\tag{7}
\Pr(G \mid k) = [1 - \Pr(\negt G \mid k)]
\]



Using (7) to substitute into (6) one has



\[\begin{align}
\tag{8}
 &\Pr(P \mid k) \\
\notag
 &= \Pr(\negt G\mid k) + [[1 - \Pr(\negt G \mid k)]\times \Pr(P \mid G \amp k)] \\
\notag 
 &= \Pr(\negt G\mid k) + \Pr(P \mid G \amp k) - [\Pr(\negt G \mid k)\times \Pr(P \mid G \amp k)] \\
\end{align}\]



Subtracting \(\Pr(P \mid G \amp k)\) from each side of (8) then gives one:



\[\begin{align}
\tag{9}
 &\Pr(P \mid k) - \Pr(P \mid G \amp k) \\
\notag
 &= \Pr(\negt G\mid k) - [\Pr(\negt G \mid k)\times \Pr(P \mid G \amp k)] \\
\notag
 &= \Pr(\negt G\mid k)\times [1 - \Pr(P \mid G \amp k)] 
\end{align}\]



But then in view of assumption (2) we have that \(\Pr(\negt G \mid k)
\gt 0\), while in view of assumption (3) we have that \(\Pr(P \mid G
\amp k) \lt 1\), and thus that \([1 - \Pr(P \mid G \amp k)] \gt 0\), 
so that it then follows from (9) that



\[
\tag{10}
\Pr(P \mid k) -\Pr(P \mid G \amp k) \gt 0.
\
\]



So one has



\[
\tag{11}
\Pr(P \mid k) \gt \Pr(P \mid G \amp k)
\
\]



The next stage involve showing that it follows from (11) that



\[
\notag
\Pr(G \mid P \amp k) \lt \Pr(G \mid k) 
\
\]


This is done as follows.


First, it follows from the definition of conditional probability one has



\[
\tag{12}
\Pr(P \amp G\amp k) = \Pr(G \mid P \amp k)] \times \Pr(P\mid k)
\]

and



\[
\tag{13}
\Pr(P \amp G\amp k) = \Pr(P \mid G \amp k)] \times \Pr(G\mid k)
\]


So we have



\[
\tag{14}
\Pr(G \mid P \amp k)] \times \Pr(P\mid k) = \Pr(P \mid G \amp k)] \times \Pr(G\mid k)
\]


Dividing both sides of (13) by \(\Pr(G \mid k) \times
\Pr(P \mid k)\) then gives one:



\[
\tag{15}
\frac{\Pr(G \mid P \amp k)}{\Pr(G \mid k)} = \frac{\Pr(P \mid G \amp k)}{\Pr(P \mid k)} 
\]



It then follows from (15) together with (11) that



\[
\tag{16}
\Pr(G \mid P \amp k) \lt \Pr(G \mid k) 
\]


Finally, it then follows from (16) together with (4) that



\[
\tag{17}
\Pr(G \mid P \amp k) \lt 0.5 
\]


#### 3.4.2 The Flaw in the Argument



Given the plausibility of assumptions (1), (2), and (3), together
with the impeccable logic, the prospects of faulting Rowe's
argument for his first conclusion may not seem at all promising. Nor
does the situation seem significantly different in the case of
Rowe's second conclusion, since assumption (4) also seems very
plausible, in view of the fact that the property of being an omnipotent, omniscient, and perfectly good being belongs to a family of properties, including the property of being an omnipotent, omniscient, and perfectly evil being, and the property of being an omnipotent, omniscient, and perfectly morally indifferent being, and, on the face of it, neither of the latter properties seems less likely to be instantiated in the actual world than the property of being an omnipotent, omniscient, and perfectly good being.



In fact, however, Rowe's argument is unsound. The reason is
connected with the point that while inductive arguments can fail, just
as deductive arguments can, either because their logic is faulty, or
their premises false, inductive arguments can also fail in a way that
deductive arguments cannot, in that they may violate a
principle--namely, the Total Evidence Requirement--which I
shall be setting out below, and Rowe's argument is defective in
precisely that way.



A good way of approaching the objection that I have in mind is by
considering the following, preliminary objection to Rowe's argument
for the conclusion that



\[
\notag
\Pr(G \mid P \amp k) \lt 0.5 \, .
\]


The objection is based on upon the observation that Rowe's argument
involves, as we saw above, only the following four premises:




\[\begin{align}
\tag{1} & \Pr(P \mid \negt G \amp k) = 1 \\
\tag{2} & \Pr(\negt G \mid k) \gt 0 \\
\tag{3} & \Pr(P \mid G \amp k) \lt 1 \\
\tag{4} & \Pr(G \mid k) \le 0.5
\end{align}\]


Notice now, first, that the proposition \(P\) enters only into
the first and the third of these premises, and secondly, that the
truth of both of these premises is easily secured. Thus, for the
first premise to be true, all that is needed is that \(\negt G\)
entails \(P\), while for the third premise to be true, all that
is needed, according to most systems of inductive logic, is that
\(P\) is not entailed by \(G \amp k\), since
according to most systems of inductive logic,
\(\Pr(P \mid G \amp k) \lt 1\) is
only false if \(P\) is entailed by \(G \amp k\).



Given assumptions (1), (2), and (3), how does the argument for the first conclusion go? In outline, one first uses (1), (2), and (3) to prove that
\(\Pr(P \mid G \amp k) \lt 1\)

 
Consider, now, what happens if, for example, Rowe's \(P\)
is replaced by:



> 
> Either God does not exist, or there is a pen in my pocket.
> 



Statements (1) and (3) will both be true given that replacement,
while statements (2) and (4) are unaffected, and one will be able to
derive the same conclusions as in Rowe's Bayesian argument. But
if this is so, then the theist can surely claim, it would seem, that
the fact that Rowe's '\(P\)' refers to evil in the world
turns out to play no crucial role in Rowe's new argument!



This objection, however, is open to the following reply. The reason
that I am justified in believing the proposition that either God does
not exist or there is a pen in my pocket is that I am justified in
believing that there is a pen in my pocket. The proposition that
either God does not exist or there is a pen in my pocket therefore
does not represent the total evidence that I have. But the argument in question
cannot be set out in terms of the proposition that, we can suppose, does in this case represent
one's total evidence--namely, the proposition that there is a
pen in my pocket--since *that* proposition is not entailed
by \(\negt G\).



The conclusion, in short, is that the above parody of Rowe's
argument doesn't work, since the parody violates the following
requirement:



> 
> **The Total Evidence Requirement**:   
> 
> For any proposition that is not non-inferentially justified, the
> probability that one should assign to that proposition's being true is
> the probability that the proposition has relative to one's total
> evidence.
> 



But this response to the above objection to the argument for the
conclusion that



\[
\notag
\Pr(G \mid P \amp k) \lt 0.5
\]


now makes it clear that there a *decisive objection* to the
argument as a whole. For notice that if \(P\)--the statement
that



> 
> No good we know of justifies an omnipotent, omniscient, perfectly
> good being in permitting \(E\_1\) and \(E\_2\)
> 



--is interpreted in such a way that \(\negt G\) entails
\(P\), it is then logically equivalent to the following
disjunctive statement:



\[
\notag
\negt G \text{ or } P^\*
\]


where \(P^\*\) is the proposition that Rowe sets out in footnote 8
of his article, namely:



> 
> No good we know of *would* justify God, (*if he
> exists*) in permitting \(E\_1\) and \(E\_2\) (1996, 283)
> 



Once this is noticed, it is clear that Rowe's argument is open
to precisely the same response as that used against the objection to
the parody argument just considered, since the justification that one
can offer for \(\negt G\) or \(P^\*\) is in fact just a
justification of the second disjunct--that is, \(P^\*\). This
means that in appealing to \(P\) (i.e., to \((\negt G)\) or
\(P^\*\)) one is not making use of one's total
evidence. So Rowe's argument, if it is to be sound, must instead
be formulated in terms of \(P^\*\).



But while \(\negt G\) entails \(P\), it does not entail
\(P^\*\). So the result of replacing '*P*' by
'*P*\*' in statement (1)--that is



\[
\tag{\(1^\*\)}
\Pr(P^\* \mid \negt G \amp k) = 1
\]


--will not be true, and so an argument of the form that Rowe offers
will not go through. Rowe's Bayesian argument is, therefore, unsound.


### 3.5 Inductive Logic and the Evidential Argument from Evil



In section 3.2.1, a concrete, deontological, and direct inductive
formulation of the argument from evil was set out. All of the steps
in that argument were deductive, except for the following crucial
inference:


1. There are events in our world -- such as an animal's dying an agonizing death in a forest fire, and a child's undergo lingering suffering and eventual death due to cancer -- such that the actions of allowing those events, when one could prevent them, both (a) have very serious, known wrongmaking characteristics, and (b) have no rightmaking characteristics of which we are aware that are sufficient to balance out the known wrongmaking properties.



Therefore it is *likely* that:


2. For any such action, the totality of the wrongmaking properties, *both known and unknown*, outweighs the totality of the rightmaking properties, *both known and unknown*.



The question, accordingly, is whether this inductive step is
correct.


Essentially, there are three ways in which one might attempt to
defend this inference. One is by treating it as a case of instantial
generalization. But as we saw in effect in section 3.2.3, when we
considered a formulation of the evidential argument from evil advanced
by William Rowe, it appears that the inductive step in the argument
from evil cannot be defended by appealing to instantial
generalization.


A second approach is to view that inductive step as a matter of
inference to the best explanation, and this is a more promising
possibility. That approach would lead to an argument of the general
form advanced by David Hume and Paul Draper, considered in
section.


There is, however, a third possibility, which is the focus of the
present section. Underlying this approach are two general ideas: the
first is that both induction via instantial generalization and
inference to the best explanation (abduction, the method of
hypothesis, hypothetico-deductive method) stand in need of
justification; the second idea is that at the heart of such a
justification will be the defense of an account of logical
probability.


The fundamental idea, accordingly, is that the way to determine
whether the inductive step that lies at the heart of the evidential
argument from evil is sound is by bringing serious inductive
logic--understood as a theory of logical probability--to
bear upon the question.


What is the appropriate theory of logical probability? Tooley
(2008 and 2012) employs a Carnapian theory in which the basic
equiprobability assumption is formulated in terms of what are called
'structure descriptions', and the fundamental postulate is that all
structure descriptions are equally likely. But if one holds, as Tooley
(1977 and 1987) does, that governing laws are logically possible, then
it is clear that the fundamental equiprobability assumption needs to
be formulated in terms of governing laws of nature. At present,
however, no detailed formulation of such an approach to logical
probability is available.


#### 3.5.1 An Illustration of the General Underlying Idea


 To establish that the inductive step in the version of the
evidential argument from evil set out above is sound requires a rather
technical argument in inductive logic. But one can gain an intuitive
understanding of the underlying idea in the following way. Suppose
that there is a rightmaking property of which we have no knowledge.
If an action of allowing a child to be brutally killed possessed that
property, then it might not be wrong to allow that action, depending
upon the weightiness of that unknown rightmaking property. But the
existence of unknown rightmaking properties is no more likely, a
priori, than of unknown wrongmaking properties. So let us suppose,
then, for this illustration, that there are two morally significant
properties of which we humans have no knowledge--a rightmaking
property \(R\), and a wrongmaking property \(W\). Let us
suppose, further, that these two properties are equally weighty,
since, a priori, there is no reason for supposing that one is more
significant than the other. Finally, let \(A\) be an action of
knowingly allowing a child to be brutally killed, and let us suppose
that the unknown morally significant rightmaking property \(R\)
is weightier than the wrongmaking property of knowingly allowing a
child to be brutally killed. One can then see that there are the
following four possibilities:


1. Action \(A\) has both unknown properties, \(R\) and
\(W\). In this case, those two unknown properties cancel one
another out, and action \(A\) will be morally wrong, all things
considered.
2. Action \(A\) has the unknown rightmaking property
\(R\), but not the unknown wrongmaking property \(W\). In
this case, action \(A\) may be morally permissible, all things
considered, on the assumption that property \(R\) is
sufficiently strong to outweigh the known wrongmaking property of
allowing a child to be brutally killed.
3. Action \(A\) has the unknown wrongmaking property
\(W\), but not the unknown rightmaking property \(R\). In
this case, action \(A\) is even more wrong, all things
considered, than it initially appeared to be.
4. Action \(A\) does not have either of the unknown, morally
significant properties, \(R\) and \(W\). In this case
action \(A\) is morally wrong to precisely the degree that it
initially appeared to be.



The upshot is that in this simplified example, at least three of the
four possibilities that we have considered are such that action
\(A\) turns out to be morally wrong, all things considered.


The intuitive idea, then, is that if one has an action that, given
only its known rightmaking and wrongmaking properties, is an action
that it would be morally wrong to perform, then it is more likely than
not it is also an action that it would be morally wrong to perform,
given the totality of its morally significant properties, *both
known and unknown*.


But what underlies this intuitive idea? The answer is a certain
very fundamental and very plausible equiprobability principle, to the
effect that if one has a family of mutually exclusive properties, and
if \(P\) and \(Q\) are any two members of that family, then
the *a priori* probability that something has property
\(P\) is equal to the *a priori* probability that that
thing has property \(Q\). For then given that principle, one can
consider the family of second order properties that contains the
second-order property of being a rightmaking property and the
second-order property of being a wrongmaking property, and then the
equiprobability principle in question entails that the *a
priori* probability that a given property \(P\) has the
second-order property of being a rightmaking property is equal to the
*a priori* probability that property \(P\) has the
second-order property of being a wrongmaking property. Similarly, if
one considers instead the family of properties that contains, for
example, the second-order property of being a rightmaking property of
weight \(W\) and the second-order property of being a wrongmaking
property of weight \(W\), the *a priori* probability that
a given property \(P\) has the first of those second-order
properties is equal to the *a priori* probability that property
\(P\) has the second of those properties.


The upshot is that given an action that would be morally wrong if
judged only by its known morally significant properties, every
possibility of a combination of unknown rightmaking and wrongmaking
properties that would make that action morally right all things
considered would be precisely counterbalanced by a combination of
unknown rightmaking and wrongmaking properties that would make that
action morally even more wrong, all things considered. But, in
addition, there can be combinations of unknown rightmaking and
wrongmaking properties that would move an action in *the
direction* of being morally right all things considered, but not
sufficiently far to make it morally right all things
considered. Finally, there is the possibility that the action has no
unknown morally significant properties.


 Consequently, if an action is one that it would be morally wrong
to perform, if judged only by its known morally significant
properties, then it is more likely than not that it is one that it is
morally wrong to perform given the totality of its morally significant
properties, both known and unknown.


Then, the probability that, judged in the light of all rightmaking
and wrongmaking properties, known and unknown, it would not be morally
wrong to allow the event in question must be less than \(\frac{1}{2}\).



The upshot is that the probabilistic inference that is involved in the
move from statement (1) to statement (2) in the argument set out above
in section 3.2.1 is inductively sound.



#### 3.5.2 The Formal Result


How is the formal calculation carried out? The answer is somewhat
complicated, and there are slightly different ways of doing it, as in
(Tooley 2008 and 2012b), with the method used in the latter case being
perhaps slightly more perspicuous, but with both methods generating
the same result. The key in both cases, moreover, is to make
assumptions that increase the probability that an action that is
morally wrong as judged only by its known rightmaking and wrongmaking
properties is morally right relative to the totality of its morally
significant properties, both known and unknown. In the absence of
those 'probability-increasing' assumptions, it is not at
all clear how the calculation could be carried out.


In the case where one focuses only upon a single action whose known
wrongmaking properties outweigh its known rightmaking properties, the
result is as one would expect, namely, that the probability that the
action in question is not morally wrong relative to the totality of
its morally significant properties, both known and unknown, must be
less than one half.


But what is the general result? Suppose, for example, that there
are \(n\) events, each of which is such that, judged simply by
known rightmaking and wrongmaking properties, it would be morally
wrong to allow that event. What is the probability that *none*
of those \(n\) events is such that it would be morally wrong to
allow that event, judged in the light of *all* rightmaking and
wrongmaking properties, both known and unknown?


The answer is arrived at by proving the following theorem dealing
with the case where there are precisely \(k\) unknown morally
significant properties:



> If there are \(k\) unknown morally significant properties,
> then given \(n\) events, each of which is such that, judged
> simply by known rightmaking and wrongmaking properties, it would be
> morally wrong to allow that event, the probability that none of those
> events is such that it is morally wrong to allow that event, judged in
> the light of *all rightmaking and wrongmaking properties, known and
> unknown*, must be less than 
> \[
> \notag
> \left( \dfrac{k}{k+1} \right) \left( \dfrac{1}{n+1} \right) \,.
> \]
> 


As one can see, this upper bound on the probability that it is not
morally wrong to allow any of the \(n\) events increases as \(k\),
the number of unknown morally significant properties, increases, and
as \(k\) increases without limit, it will tend to the limit of
\(\frac{1}{n+1}\).


One therefore has the following theorem:



> Given \(k\) events, each of which is such that,
> judged simply by known rightmaking and wrongmaking properties, it
> would be morally wrong to allow that event, the probability that none
> of those events is such that it is morally wrong to allow that event,
> judged in the light of *all rightmaking and wrongmaking properties,
> both known and unknown*, must be less than \(\frac{1}{n+1}\).
> 


#### 3.5.3 The Argument from Evil: A Quantitative Result


This approach arguably has two advantages over alternative accounts
of the inductive step that lies at the heart of the argument from
evil. One is that in bringing in an equiprobability principle, one is
approaching the issue at a more fundamental level than any approach
that appeals either to instantial generalization or inference to the
best explanation. The other is that this approach generates a result that enables
one not just to conclude that it is more likely than not that God does
not exist, but also to assign an upper bound to the probability that
God exists.


The upper bound, moreover, is surely very low indeed, for of the
billions of people and sentient non-persons who have existed, the
proportion who have had the good fortune never to have suffered in
ways such that the known wrongmaking properties of allowing such
suffering outweighed the known rightmaking properties must be small.
Accordingly, \(n\) must be extremely large, and thus the
probability that there is an omnipotent, omniscient, and morally
perfect person must be very low indeed.


## 4. Responses to the Argument from Evil: Refutations, Theodicies, and Defenses



Given an evidential formulation of the evidential argument from evil,
what sorts of responses are possible? A natural way of dividing up
possible responses is into what may be referred to as total
refutations, theodicies, and defenses. So let us begin by considering
what is involved in these three different, general types of
responses.



This threefold classification can be arrived at by the following line
of thought. An advocate of the argument from evil is claiming, in the
first place, that there are facts about the evils in the world that
make it *prima facie* unreasonable to believe in the existence
of God, and, in the second place, that the situation is not altered
when those facts are conjoined with all the other things that one is
justified in believing, both inferentially and non-inferentially, so
that belief in the existence of God is also unreasonable *relative
to the total evidence available, together with all relevant basis
states*. In responding to the argument from evil, then, one might
challenge either of these claims. That is to say, one might grant, at
least for the sake of argument, that there are facts about evil that,
other things being equal, render belief in God unreasonable, but then
argue that when those considerations are embedded within one's total
epistemic situation, belief in the existence of God can be seen to be
reasonable, all things considered. Alternatively, one might defend the
more radical thesis that there are no facts about evil in the world
that make it even *prima facie* unreasonable to believe in the
existence of God.



 
If the latter thesis is correct, the argument from evil does not even
get started. Such responses to the argument from evil are naturally
classified, therefore, as attempted, *total refutations* of
the argument.



The proposition that relevant facts about evil do not make it even
*prima facie* unreasonable to believe in the existence of God
probably strikes most philosophers, of course, as rather implausible.
We shall see, however, that a number of philosophical theists have
attempted to defend this type of response to the argument from
evil.



The alternative course is to grant that there are facts about
intrinsically undesirable states of the world that make it *prima
facie* unreasonable to believe that God exists, but then to argue
that belief in the existence of God is not unreasonable, all things
considered. This response may take, however, two slightly different
forms. One possibility is the offering of a complete
*theodicy*. As I shall use that term, this involves the
thesis that, for every actual evil found in the world, one can
describe some state of affairs that it is reasonable to believe
exists, and which is such that, if it exists, will provide an
omnipotent and omniscient being with a morally sufficient reason for
allowing the evil in question. 



It should be noted here that the term "theodicy" is
sometimes used in a stronger sense, according to which a person who
offers a theodicy is attempting to show not only that such morally
sufficient reasons exist, but that the reasons cited are in fact
*God's* reasons. Alvin Plantinga (1974a, 10; 1985a, 35) and
Robert Adams (1985, 242) use the term in that way, but, as has been
pointed out by a number of writers, including Richard Swinburne
(1988, 298), and William Hasker (1988, 5), that is to saddle the
theodicist with an unnecessarily ambitious program.



The other possibility is that of offering a defense. But what is a
defense? In the context of abstract, incompatibility versions of the
argument from evil, this term is generally used to refer to attempts
to show that there is no logical incompatibility between the
existence of evil and the existence of God. Such attempts involve
setting out a story that entails the existence of both God and evil,
and that is logically consistent. But as soon as one focuses upon
evidential formulations of the argument from evil, a different
interpretation is needed if the term is to remain a useful one, since
the production of a logically consistent story that involves the
existence of both God and evil will do nothing to show that evil does
not render the existence of God unlikely, or even very unlikely.



So what more is required beyond a logically consistent story of a
certain sort? One answer that is suggested by some discussions is
that the story needs to be one that is true for all we know. Thus
Peter van Inwagen, throughout his book *The Problem of Evil*,
frequently claims that various propositions are "true for all
we know," and in the "Detailed Contents" section at
the beginning of his book, he offers the following characterization
of the idea of a defense:



> 
> The idea of a "defense" is introduced: that is, the idea of
> a story that contains both God and all the evils that actually exist,
> a story that is put forward not as true but as "true for all anyone
> knows". (2006, xii)



It seems very unlikely, however, that its merely being the case that
one does not know that the story is false can suffice, since it may
very well be the case that, though one does not know that p
is false, one does have very strong evidence that it is. But if one
has strong evidence that a story is false, it is hard to see how the
story on its own could possibly counter an evidential argument from
evil.


 It seems, accordingly, that some claim about the probability of
the story's being true is needed. One possibility, suggested by some
discussions, is that one might claim that rather than the story's
being a remote possibility that has only a minuscule chance of being
true, the story represents "a real possibility", and so
has a substantial chance of being true. Thus, while Peter van Inwagen
usually talks about his stories' being true for all anyone knows, he
also introduces the distinction between remote possibilities, and real
possibilities (2006, Lecture 4, esp. pp. 66-71).



It is also hard to see, however, how this can be sufficient either.
Suppose, for example, that one tells a story about God and the
Holocaust, which is such that if it were true, an omnipotent being
would have been morally justified in not preventing the Holocaust.
Suppose, further, that one claims that there is a twenty percent
chance that the story is true. A twenty percent chance is certainly
a real possibility, but how would that twenty percent chance
undermine a version of the argument from evil whose conclusion was
that the probability that an omnipotent being would be justified in
allowing the Holocaust was very low?



Given the apparent failure of the previous two suggestions, a natural
conclusion is that the story that is involved in a defense must be
one that is likely to be true. But if this is right, how does a
defense differ from a theodicy? The answer is that while a theodicy
must specify reasons that would suffice to justify an omnipotent and
omniscient being in allowing all of the evils found in the world, a
defense need merely show that it is likely that there are reasons
which would justify an omnipotent and omniscient being in not
preventing the evils that one finds in the world, even if one does
not know what those reasons are. A defense differs from a theodicy,
then, in that a defense attempts to show only that some
God-justifying reasons probably exist; it does not attempt to specify
what they are.



There is, however, one final possibility that needs to be considered.
This is the idea that what is needed in a defense is not a story that
can be shown to be likely to be true, but, rather, a story that, for
all we know, is not unlikely. The thought here is that, even if
there is some probability that the story has relative to our
evidential base, we may not be able to determine what that
probability is, or even any reasonably delimited range in which that
probability falls. If so, it cannot be shown that the story is likely
to be true, but neither can it be shown that the story is unlikely to
be true.



The question that immediately arises is whether a proposition that
would undercut an inductive argument from evil if one knew it were true can
undercut the argument if one is unable to assign any probability to the
proposition's being true, and if so, how. One thought might be that
if one can assign no probability to a proposition, one should treat
it as equally likely to be true as to be false. But propositions
vary dramatically in logical form: some are such as might naturally
be viewed as atomic, others are sweeping generalizations, others are
complex conjunctions, and so on. If one treated any proposition to
which one could not assign a probability as equally likely to be true
as to be false, the result would be an incoherent assignment of
probabilities. On the other hand, if one adopts this idea only in
the case of atomic propositions, then given that stories that are
advanced in defenses and theodicies are typically quite complex,
those stories will wind up getting assigned low probabilities, and it
is then unclear how they could undercut an inductive argument from
evil. 


## 5. Attempted Total Refutations



There are at least three main ways in which one might attempt to show
that the argument from evil does not succeed in establishing that
evil is even *prima facie* evidence against the existence of
God, let alone that the existence of God is improbable relative to
our total evidence. The first appeals to human epistemological
limitations; the second, to the claim that there is no best of all
possible worlds; and the third, to the ontological argument.


### 5.1 Human Epistemological Limitations



The most popular attempt at a total refutation of the argument from
evil claims that, because of human cognitive limitations, there is no
sound inductive argument that can enable one to move from the premise
that there are states of affairs that, taking into account only what
we know, it would be morally very wrong for an omnipotent and
omniscient person to allow to exist, to the conclusion that there are
states of affairs such that it is likely that, all things considered,
it would be morally very wrong for an omnipotent and omniscient
person to allow those states of affairs to exist.



The appeal to human cognitive limitations does raise a very important
issue, and we have seen that one very natural account of the logical
form of the inductive step in the case of a direct inductive argument
is not satisfactory. But, as we have seen in sections 3.3 and 3.4,
there are other accounts of the type of reasoning involved in the
crucial inductive step in evidential forms of the argument from
evil. First of all, the appeal to human cognitive limitations does
not itself show that there is anything wrong either with the
reasoning that Draper offers in support of the crucial premise in his
indirect inductive version of the argument from evil, or with the
inference to the best explanation type of reasoning employed in the
updated version of Hume's indirect inductive formulation of the
argument from evil. Secondly, the appeal to human cognitive
limitations provides no reason at all for rejecting the version of
the argument from evil that appeals to fundamental equiprobability
principles of inductive logic, principles that arguably must obtain
if any sort of induction is ever justified.



Short of embracing compete inductive skepticism, then, it would seem
that an appeal to human cognitive limitations cannot provide an
answer to evidential versions of the argument from evil.


### 5.2 The 'No Best of All Possible Worlds' Response



A second way of attempting to show that the argument from evil does
not even get started is by appealing to the proposition that there is
no best of all possible worlds. Here the basic idea is that if for
*every* possible world, however good, there is a better one,
then the fact that this world could be improved upon does not give
one any reason for concluding that, if there is an omnipotent and
omniscient being, that being cannot be morally perfect.


 This response to the argument from evil has been around for quite
a while. In recent years, however, it has been strongly advocated by
George Schlesinger (1964, 1977), and, more recently, by Peter Forrest
(1981)--though Forrest, curiously, describes the defense as one
that has been "neglected", and refers neither to
Schlesinger's well-known discussions, nor to the very strong
objections that have been directed against this response to the
argument from evil.



The natural response to this attempt to refute the argument from evil
was set out very clearly some years ago by Nicholas La Para (1965)
and Haig Khatchadourian (1966) among others, and it has been
developed in an especially forceful and detailed way in an article by
Keith Chrzan (1987). The basic thrust of this response is that the
argument from evil, when properly formulated in a
*deontological* fashion, does not turn upon the claim that
this world could be improved upon, or upon the claim that it is not
the best of all possible worlds: it turns instead upon the claim that
there are good reasons for holding that the world contains evils,
including instances of suffering, that it would be morally wrong, all
things considered, for an omnipotent and omniscient being to allow.
As a consequence, the proposition that there might be better and
better worlds without limit is simply irrelevant to the argument from
evil, properly formulated.


 If one accepts a deontological approach to ethics, this response
seems decisive. Many contemporary philosophers, however, are
consequentialists, and so one needs to consider how the 'no best
of all possible worlds' response looks if one adopts a
consequentialist approach.


 Initially, it might seem that by combining the 'no best of
all possible worlds' response with consequentialism, one can construct
a successful, total refutation. For assume that the following things
are true:


1. An action is, by definition, objectively morally right if and only if it is,
among the actions that one could have performed, at least one of the actions that
produces at least as much value as every alternative action;
2. An action is objectively morally wrong if and only if it is not objectively morally
right;
3. One is morally blameworthy only if one performs some objectively wrong action when one could instead have performed an objectively right action;
4. If one is an omnipotent and omniscient being, then for any action
whatever, there is always some other action that produces greater
value.



Then it follows that it is impossible for an omnipotent and
omniscient being to perform a morally wrong action, and therefore
that the failure of such a being to prevent various evils in this
world cannot be morally wrong.



Consider an omnipotent and omniscient being that creates a world with
zillions of innocent persons, all of whom endure extraordinarily
intense suffering forever. If (1), (2), and (3) are right, then such
a being does not do anything morally wrong. But this conclusion,
surely, is unacceptable, and so if a given version of
consequentialism entails this conclusion, then that form of
consequentialism must be rejected.


 Can consequentialism avoid this conclusion? Can it be formulated
in such a way that it entails the conclusion that allowing very great,
undeserved suffering is morally very different, and much more serious,
than merely refraining from creating as many happy individuals as
possible, or merely refraining from creating individuals who are not
as ecstatically happy as they might be? If it cannot, then it would
seem that the correct conclusion to draw is that consequentialism is unsound.
On the other hand, if consequentialism can be so formulated that this
distinction is captured, then an appeal to consequentialism, thus
formulated in a sound way, will not enable one to avoid the crucial objection to the
'no best of all possible worlds' response to the argument
from evil.


### 5.3 The Appeal to the Ontological Argument



A final way in which one could attempt to show that facts about evil
cannot constitute even *prima facie* evidence against the
existence of God is by appealing to the ontological
argument. Relatively few philosophers have held, of course, that the
ontological argument is sound. But there have certainly been notable
exceptions--such as Anselm and Descartes, and, in the last
century, Charles Hartshorne (1962), Norman Malcolm (1960), and Alvin
Plantinga (1974a, 1974b)



If the ontological argument were sound, it would provide a rather
decisive refutation of the argument from evil. For in showing not
merely that there is an omnipotent, omniscient, and morally perfect
being, but also that it is necessary that such a being exists, it would
entail that the proposition that God does not exist must have
probability zero on any body of evidence whatever.


 The only question, accordingly, is whether the ontological
argument is sound. The vast majority of present-day philosophers
believe that it is not, and one way of arguing for that view is by
appealing to strengthened Gaunilo-type objections--where the idea
behind a strengthened Gaunilo-type objection is that, rather than
merely paralleling the ontological argument, as Gaunilo did in responding to
Anselm, in order to show that there is an overpopulation problem for
reality in the form of perfect islands, perfect unicorns, and so on,
one can instead construct versions that lead to mutually incompatible
conclusions, such as the conclusion that there is a perfect solvent,
together with the conclusion that there is a perfectly insoluble
substance (Tooley, 1981). But if the logical form of the ontological
argument is such that arguments of precisely the same form generate
contradictions, then the ontological argument must be unsound.


 A more satisfying response to the ontological argument would, of
course, show not merely that the ontological argument is unsound, but
also precisely why it is unsound. Such a response, however, requires a
satisfactory account of the truth conditions of modal
statements--something that lies outside the scope of this
article


## 6. Attempted Defenses



In this section, we shall consider three attempts to show that it is
reasonable to believe that every evil is such that an omnipotent and
omniscient person would have a morally sufficient reason for not
preventing its existence, even if one is not able to say, in every
case, what that morally sufficient reason might be.


### 6.1 The Appeal to Positive Evidence for the Existence of God



If a given, concrete formulation of the argument from evil appeals to
cases of intrinsically undesirable states of affairs that give rise
only to evidential considerations, rather than to an incompatibility
conclusion, then, although the existence of God may be improbable
relative to that evidence, it may not be improbable relative to one's
total evidence. Theists, however, have often contended that there
are a variety of arguments that, even if they do not prove that God
exists, provide positive evidence. May not this positive evidence
outweigh, then, the negative evidence of apparently unjustified
evils?



Starting out from this line of thought, a number of philosophers have
gone on to claim that in order to be justified in asserting that
there are evils in the world that establish that it is unlikely that
God exists, one would first have to examine *all* of the
traditional arguments for the existence of God, and show that none of
them is sound. Alvin Plantinga, for example, says that in order for
the atheologian to show that the existence of God is improbable
relative to one's total evidence, "he would be obliged to
consider all the sorts of reasons natural theologians have invoked
*in favor of* theistic belief--the traditional
cosmological, teleological and ontological arguments, for
example." (1979, 3) And in a similar vein, Bruce Reichenbach
remarks:



> 
> With respect to the atheologian's inductive argument from evil,
> the theist might reasonably contend that the atheologian's
> exclusion of the theistic arguments or proofs for God's
> existence advanced by the natural theologian has skewed the
> results. (1980, 224)
> 



Now it is certainly true that if one is defending a version of the
argument from evil that supports only a probabilistic conclusion, one
needs to *consider* what sorts of positive reasons might be
offered in support of the existence of God. But Plantinga and
Reichenbach are advancing a rather stronger claim here, for they are
saying that one needs to look at all of the traditional theistic
arguments, such as the cosmological and the teleological. They are
claiming, in short, that if one of those arguments turned out to be
defensible, then it might well serve to undercut the argument from
evil.



But this view seems mistaken. Consider the cosmological argument. In
some versions, the conclusion is that there is an unmoved mover. In
others, that there is a first cause. In others, that there is a
necessary being, having its necessity of itself. None of these
conclusions involves any claims about the moral character of the
entity in question, let alone the claim that it is a morally perfect
person. But in the absence of such a claim, how could such
arguments, even if they turned out to be sound, serve to undercut the
argument from evil?



The situation is not essentially different in the case of the
argument from order, or in the case of the fine-tuning argument. For
while those arguments, if they were sound, would provide grounds for
drawing some tentative conclusion concerning the moral character of
the designer or creator of the universe, the conclusion in question
would not be one that could be used to overthrow the argument from
evil. For given the mixture of good and evil that one finds in the
world, the argument from order can hardly provide support even for
the existence of a designer or creator who is very good, let alone
one who is morally perfect. So it is very hard to see how any
teleological argument, any more than any cosmological, could overturn
the argument from evil.



A similar conclusion can be defended with respect to other arguments,
such as those that appeal to purported miracles, or religious
experiences. For while in the case of religious experiences it might
be argued that personal contact with a being may provide additional
evidence concerning the person's character, it is clear that the
*primary* evidence concerning a person's character must
consist of information concerning what the person does and does not
do. So, contrary to the claim advanced by Robert Adams (1985, 245),
even if there were veridical religious experiences, they would not
provide one with a satisfactory defense against the argument from
evil.



A good way of underlining the basic point here is by setting out an
alternative formulation of the argument from evil in which it is
granted, for the sake of argument, that there is an omnipotent and
omniscient person. The result of doing this is that the conclusion at which one *initially* arrives is not that there is no omnipotent, omniscient, and morally perfect person, but rather that, although there is an omnipotent and omniscient person, that person is not morally perfect, from which it then follows that that there is no omnipotent, omniscient, and morally perfect person.



When the argument from evil is reformulated in that way, it becomes
clear that the vast majority of considerations that have been offered
as reasons for believing in God can be of little assistance to the
person who is trying to resist the argument from evil. For most of
them provide, at best, very tenuous grounds for *any*
conclusion concerning the moral character of any omnipotent and
omniscient being who may happen to exist, and almost none of them
provides any support for the hypothesis that there is an omnipotent
and omniscient being who is also morally perfect.



The ontological argument is, of course, a notable exception, and,
consequently, the advocate of the argument from evil certainly needs
to be able to show that it is unsound. But almost all of the other
standard arguments are simply not to the point.


### 6.2 Belief in the Existence of God as Non-Inferentially Justified




What if, rather than holding that there is positive evidence that
lends support to the existence of God, one holds instead that the
belief that God exists is non-inferentially justified? The claim in
question is an interesting one, and a thorough evaluation of it would
involve consideration of some deep issues in epistemology.
Fortunately, it does not seem to make any real difference in the present
context whether or not the claim is true.



The reason emerges if one considers the epistemology of perception.
Some philosophers hold that some beliefs about physical objects are
non-inferentially justified, while others hold that this is never so,
and that justified beliefs about physical states of affairs are
always justified via an inference to the best explanation that starts
out from beliefs about one's experiences. But direct realists as
much as indirect realists admit that there can be cases where a
person would be justified in believing that a certain physical state
of affairs obtained were it not for the fact that he has good
evidence that he is hallucinating, or else subject to perceptual
illusion. Moreover, given evidence of the relevant sort, it makes no
difference whether direct realism is true, or indirect realism: the
belief in question is undermined to precisely the same extent in
either case.



The situation is the same in the case of religious experience. If,
as was argued in the previous section, the primary evidence
concerning a person's character consists of what the person does or
fails to do in various circumstances, and if, as a consequence,
conclusions concerning the character of a deity based upon religious
experience can be undercut by the argument from evil, then nothing is
changed if one holds that the having of religious experiences, rather
than providing one with evidence for the existence of God, makes it
the case that one is non-inferentially justified in believing in the
existence of God. The non-inferential justification is merely a
*prima facie* justification, and one that is undercut by
evidence bearing upon a person's character that deals with what the
person does and does not do.


### 6.3 Induction Based on Partial Success


 Swinburne (1988, 297-8) argued in support of the conclusion that
theism does need a theodicy. In doing so, however, he noted one minor
qualification--namely, that if one could show, for a sufficiently
impressive range of evils that initially seemed problematic, that it
was likely that an omnipotent and omniscient person would be morally
justified in not having prevented them, then one might very well be
justified in believing that the same would be true of other evils,
even if one could not specify, in those other cases, what the morally
sufficient reason for allowing them might be.


 What Swinburne says here is surely very reasonable, and I can see
no objection in principle to a defense of this sort. The problem with
it is that no theodicy that has ever been proposed has been successful
in the relevant way--that is, there is no impressive range of
undesirable states of affairs where people initially think that the
wrongmaking properties of allowing such states of affairs to exist
greatly outweigh any rightmaking properties associated with doing so,
but where, confronted with some proposed theodicy, people come to
believe that it would be morally permissible to allow such states of
affairs to exist. Indeed, it is hard to find *any* such cases, let alone
an impressive range.


## 7. Theodicies


 What are the prospects for a complete, or nearly complete
theodicy? Some philosophers, such as Swinburne, are optimistic, and
believe that "the required theodicy can be provided"
(1988, 311). Others, including many theists, are much less
hopeful. Plantinga, for example remarks:



> 
> ... we cannot see *why* our world, with all its ills, would
> be better than others we think we can imagine, or *what*, in
> any detail, is God's reason for permitting a given specific and
> appalling evil. Not only can we not see this, we can't think of
> any very good possibilities. And here I must say that most attempts
> to explain *why* God permits evil--*theodicies*, as
> we may call them--strike me as tepid, shallow and ultimately
> frivolous. (1985a, 35)
> 



What types of theodicies that have been proposed? An exhaustive
survey is not possible here, but among the most important are
theodicies that appeal, first, to the value of acquiring desirable
traits of character in the face of suffering; secondly, to the value
of libertarian free will; thirdly, to the value of the freedom to
inflict horrendous evils upon others; and fourthly, to the value of a
world that is governed by natural laws.


### 7.1 A Soul-Making Theodicy



One very important type of theodicy, championed especially by John
Hick, involves the idea that the evils that the world contains can be
seen to be justified if one views the world as designed by God to be an
environment in which people, through their free choices, can undergo
spiritual growth that will ultimately fit them for communion with
God:



> 
> The value-judgement that is implicitly being invoked here is that one
> who has attained to goodness by meeting and eventually mastering
> temptation, and thus by rightly making responsibly choices in concrete
> situations, is good in a richer and more valuable sense than would be
> one created *ab initio* in a state either of innocence or of virtue. In
> the former case, which is that of the actual moral achievements of
> mankind, the individual's goodness has within it the strength of
> temptations overcome, a stability based upon an accumulation of right
> choices, and a positive and responsible character that comes from the
> investment of costly personal effort. (1977, 255-6)
> 



Hick's basic suggestion, then, is that soul-making is a great good,
that God would therefore be justified in designing a world with that
purpose in mind, that our world is very well designed in that regard,
and thus that, if one views evil as a problem, it is because one
mistakenly thinks that the world ought, instead, to be a hedonistic
paradise.


 Is this theodicy satisfactory? There are a number of reasons for
holding that it is not. First, what about the horrendous suffering
that people undergo, either at the hands of others--as in the
Holocaust--or because of terminal illnesses such as cancer? One
writer--Eleonore Stump--has suggested that the terrible
suffering that many people undergo at the ends of their lives, in
cases where it cannot be alleviated, is to be viewed as suffering that
has been ordained by God for the spiritual health of the individual in
question (1993b, 349). But given that it does not seem to be true
that terrible terminal illnesses more commonly fall upon those in bad
spiritual health than upon those of good character, let alone that
they fall only upon the former, this 'spiritual
chemotherapy' view seems quite hopeless. More generally, there
seems to be no reason at all why a world must contain horrendous
suffering if it is to provide a good environment for the development
of character in response to challenges and temptations.



Secondly, and is illustrated by the weakness of Hick's own discussion (1977, 309-17), a soul-making theodicy provides no justification for the existence of any animal pain, let alone for a world where
predation is not only present but a major feature of non-human animal
life, and has been so for millions of years. The world could perfectly well have contained only human persons, or only human persons plus herbivores.



Thirdly, the soul-making theodicy also provides no account of the suffering that young, innocent children endure, either because of terrible diseases, or at the hands of adults. For here, as in the case of animals, there is no soul-making purpose that is served.



Finally, if one's purpose were to create a world that would be a good
place for soul-making, would our earth count as a job well done? It
is very hard to see that it would. Some people die young, before they
have had any chance at all to master temptations, to respond to
challenges, and to develop morally. Others endure suffering so great
that it is virtually impossible for them to develop those moral
traits that involve relationships with others. Still others enjoy
lives of ease and luxury where there is virtually nothing that
challenges them to undergo moral growth.


### 7.2 Free Will



A second important approach to theodicy involves the following ideas:
first, that libertarian free will is of great value; secondly, that
because it is part of the definition of libertarian free will that an
action that is free in that sense cannot be caused by anything
outside of the agent, not even God can cause a person to freely do
what is right; and thirdly, that because of the great value of
libertarian free will, it is better that God create a world in which
agents possess libertarian free will, even though they may misuse it,
and do what is wrong, than that God create a world where agents lack
libertarian free will.



One problem with an appeal to libertarian free will is that no
satisfactory account of the concept of libertarian free will is yet
available. Thus, while the requirement that, in order to be free in
the libertarian sense, an action not have any cause that lies outside
the agent is unproblematic, this is obviously not a sufficient
condition, since this condition would be satisfied if the behavior in
question were caused by random events within the agent. So one needs
to add that the agent is, in some sense, the cause of the action. But
how is the causation in question to be understood? Present accounts
of the metaphysics of causation typically treat causes as states of
affairs. If, however, one adopts such an approach, then it seems that
all that one has when an action is freely done, in the libertarian
sense, is that there is some uncaused mental state of the agent that
causally gives rise to the relevant behavior, and why freedom, thus
understood, should be thought valuable, is far from clear.


 The alternative is to shift from event-causation to what is
referred to as 'agent-causation'. But then the question is
whether there is any satisfactory account of causation where causation
is not a relation between states of affairs. Some philosophers, such
as Timothy O'Connor (1995, 1996, 2000a, 2000b, and 2002) and Randolph
Clarke (1993, 1996, and 2003) have claimed that such an account can be
given, but their suggestions have not been widely accepted. 



But even if the difficulty concerning the nature of libertarian free
will is set aside, there are still very strong objections to the
free-will approach. First, and most important, the fact that
libertarian free will is valuable does not entail that one should
never intervene in the exercise of libertarian free will. Indeed,
very few people think that one should not intervene to prevent
someone from committing rape or murder. On the contrary, almost
everyone would hold that a failure to prevent heinously evil actions
when one can do so would be seriously wrong.



Secondly, the proposition that libertarian free will is valuable does
not entail that it is a good thing for people to have the power to
inflict great harm upon others. So individuals could, for example,
have libertarian free will, but not have the power to torture and
murder others.



Thirdly, many evils are caused by natural processes, such as
earthquakes, hurricanes, and other weather conditions, and by a wide
variety of diseases. Such evils certainly do not appear to result
from morally wrong actions. If that is right, then an appeal to free
will provides no answer to an argument from evil that focuses upon
such evils.


 Some writers, such as C. S. Lewis and Alvin Plantinga, have
suggested that such evils may ultimately be due to the immoral actions
of supernatural beings (Lewis, 1957, 122-3; Plantinga, 1974a, 58). If
that were so, then the first two objections mentioned above would
apply: one would have many more cases where individuals were being
given the power--much greater than the power that any human
has--to inflict great harm on others, and then were being allowed
by God to use that power to perform horrendously evil actions leading
to enormous suffering and many deaths. In addition, however, it can
plausibly be argued that, though it is possible that earthquakes,
hurricanes, cancer, and the predation of animals are all caused by
malevolent supernatural beings, the probability that this is so is
extremely low.


### 7.3 The Freedom to Do Great Evil


 The fact that agents could be free in a libertarian sense even if
they did not have the power to inflict great harm upon others has led
at least one philosopher--namely, Richard Swinburne--to
argue that, while free will is valuable, precisely how valuable it is
depends upon the range of actions open to one. Swinburne's idea is
that if the possible actions that are open to one vary enormously in
moral worth, then libertarian free will is very valuable indeed,
whereas if the variation in the moral status of what one can do is
very limited, then libertarian free will adds much less to the world:
one has what has been characterized as a 'toy world', where one has
very little responsibility for the well-being of others.


This variant on the appeal to libertarian free will is also open to
a number of objections. First, as with free will theodicies in
general, this line of thought provides no justification for the
existence of occurrences that not only appear, upon cursory
inspection, to be natural evils, uncaused by any agents, but where, in
addition, the very closest scientific examination supports the
conclusion that there are no grounds for postulating anything beyond
purely physical events as the causes of the occurrences in
question.


Secondly, if what matters is simply the existence of alternative
actions that differ greatly in moral value, this can be the case even in a
world where one lacks the power to inflict great harm on others, since
there can be actions that, rather than inflicting great suffering on
others, would instead benefit others enormously, and which one could
either perform or intentionally refrain from performing.


Thirdly, what exactly is the underlying line of thought here? In
the case of human actions, Swinburne surely holds that one should
prevent someone from doing something that would be morally horrendous,
if one can do so. Is the idea, then, that while occasional prevention
of such evils does not significantly reduce the extent of the moral
responsibility of others, if one's power were to increase, a point
would be reached where one should sometimes refrain from preventing
people from performing morally horrendous actions? But why should this
be so? One answer might be that if one intervened too frequently,
people would come to believe that they did not have the ability to
perform such actions. But, in the first place, it is not clear why
that would be undesirable. People could still, for example, be
thoroughly evil, for they could still very much wish that they had the power to
perform such terrible actions, and be disposed to perform such actions
if they ever came to have the power. In the second place, prevention
of deeply evil actions could take quite different forms. People could,
for example, be given a conscience that led them, when they had
decided to cause great injury to others, and were about to do so, to
feel that what they were about to do was too terrible a thing, so that
they would not carry through on the action. In such a world, people
could surely still feel that they themselves were capable of
performing heinously evil actions, and they would contemplate
performing such actions, but in the end their sense of the great
wrongness of the actions would triumph over their selfish reasons for
wanting to perform the actions in question.



### 7.4 The Need for Natural Laws


A final important theodicy involves the following ideas: first, it
is important that events in the world take place in a regular way,
since otherwise effective action would be impossible; secondly, events
will exhibit regular patterns only if they are governed by natural
laws; thirdly, if events are governed by natural laws, the operation
of those laws will give rise to events that harm individuals; so,
fourthly, God's allowing natural evils is justified because the
existence of natural evils is entailed by natural laws, and a world
without natural laws would be a much worse world.


This type of theodicy is also exposed to serious objections. First
of all, the occasional occurrence of miraculous intervention,
including events that clearly appeared contrary to natural laws, would
not render effective human action impossible, since humans would see
that such miraculous occurrences were extremely rare.


Secondly, and relatedly, consider a world where the laws of
physics, rather than being laws that admit of no exceptions, are
instead probabilistic laws. Effective human action would still be
possible in such a world, provided that the relevant probabilities
were sufficiently high. But if so, then effective human action would
be no less possible in a world with non-statistical laws where there
were occasional miraculous interventions.


Thirdly, many of the greatest evils could have been prevented by
miraculous interventions that would not have been detected. Consider,
for example, interventions to prevent natural disasters such as
volcanic eruptions, or earthquakes, including the earthquake in China
in 1556 that killed around 800,000 people, or tsunamis, such as the
one in 2004 that hit 12 Asian countries, and killed over 200,000
people. Or consider the interventions that would be needed to prevent
pandemics, such as the Black Death in the Middle Ages, which is
estimated to have killed between 75 million and 200 million people, or
the 1918 flu pandemic, which killed between 50 million and 100 million
people. Similarly, consider great moral evils, such as the
Holocaust. A small intervention by an omnipotent, omniscient, and
perfectly good being could have allowed one of the many failed attempts
to assassinate Hitler to succeed, or a small mental nudge could have
resulted in Hitler's realizing the error in his virulent
anti-Semitism.


Fourthly, what natural evils a world contains depends not just on
the laws, but also on the initial, or boundary conditions. Thus, for
example, an omnipotent being could create *ex nihilo* a world
which had the same laws of nature as our world, and which contained
human beings, but which was devoid of non-human carnivores. Or the
world could be such that there was unlimited room for populations to
expand, and ample natural resources to support such populations.


Fifthly, many evils depend upon *precisely* what laws the world
contains. An omnipotent being could, for example, easily create a
world with the same laws of physics as our world, but with slightly
different laws linking neurophysiological states with qualities of
experiences, so that extremely intense pains either did not arise, or
could be turned off by the sufferer when they served no purpose. Or
additional physical laws of a rather specialized sort could be
introduced that would either cause very harmful viruses to
self-destruct, or prevent a virus such as the avian flu virus from
evolving into an air-born form that has the capacity to kill hundreds
of million people.


Finally, this theodicy provides no account of moral evil. If other
theodicies could provide a justification for God's allowing moral
evil, then, of course, moral evil would not be a problem. But, as we
have seen, no satisfactory justification appears to be available.



### 7.5 Religious Theodicies


The four types of theodicies considered so far all appeal to
beliefs and evaluative claims that the theodicist thinks should be
acceptable, upon careful reflection, to anyone, including those who
are not religious. But if one thinks that one's religious beliefs are
ones that it is reasonable to accept, what is wrong with a theodicy
that appeals to some of one's religious beliefs? Of course, if the
religious beliefs to which one appeals, taken together, entail the
existence of an omnipotent, omniscient, and morally perfect person,
such a theodicy would be question-begging. But one can choose a subset
that, even if it entails the existence of a very powerful and
knowledgeable creator--or even an omnipotent and omniscient
one--does not entail the existence of God.


There are many religions, and even within a given religion, very
significant differences in the religious beliefs of people, and very
different beliefs to which one might appeal, so there are many
different religious theodicies that can be constructed. Here I shall
focus only on one general type. I think, however, that it will
illustrate the kinds of objections that arise.


The religious theodicy in question is as follows. First, human
beings, rather than having arisen through a process of natural
evolution, were brought into existence by the creator of the
universe. He placed the first two human beings in a perfect world,
free of suffering and death. Those human beings, however, freely chose
to disobey a command of the creator, and the result was the Fall of
mankind, which meant not only that the first two humans became subject
to suffering and death, but that all of their descendants did so as
well. The creator, however, lovingly engaged, several generations
later, in a rescue operation, in which he, in the person of his son,
became incarnated as a human being, and by undergoing a sacrificial
death, made it possible for the creator to forgive every human who
accepted this sacrifice, and who would then enjoy eternal beatitude living in the
presence of the creator.


This type of religious theodicy has been advanced by a number of
Christians, with a variant of it being found, for example, in Peter
van Inwagen's book, *The Problem of Evil* (2006, 85ff.). It is
not, of course, a full theodicy, since it does not account for the
suffering of non-human animals, at least before the Fall. So let us
focus on it simply as offering an account of God's justification for
allowing human suffering. Thus viewed, how successful is it?


To be successful, a theodicy must appeal only to beliefs that it is
reasonable to accept. Do the beliefs involved in the above story
qualify? It would seem not. First of all, among the crucial beliefs
is the belief that human beings, rather than coming into being via a
natural process of evolution, were specially created. In setting out
the story, I have not specified how that was done. Traditionally
Christians believed, either that Adam and Eve were created *ex
nihilo*, as the story of creation in Genesis 1 seems to say, or
else, as the creation story in Genesis 2 says, that Adam was created
out of the dust of the earth, and then Eve was formed, sometime later,
out of one of Adam's ribs.


There are very good reasons for rejecting both of these accounts,
since the evidence that humans are descended from earlier primates is
extremely strong indeed. Especially impressive is the evidence
provided by DNA studies, described by Daniel J. Fairbanks his book
*Relics of Eden*, and which includes such as things as the
evidence that human chromosome number two resulted by fusion from two
primate chromosomes, together with facts about (1) transposable
elements, including retroelements, (2) pseudogenes, and (3)
mitochondrial DNA.


In the light of such evidence, it is not surprising that many
Christian philosophers have accepted the hypothesis of common descent,
and have adopted some form of theistic evolution, in which the creator
intervened at some point to transform some earlier primates into
members of a new species, Homo sapiens. But while this version of
special creation is an improvement, given the very close relations
between human and chimpanzee DNA, and the fact that known mechanisms
of chromosome rearrangement render the transition from some non-human
species to Homo sapiens not at all improbable, the postulation of
divine intervention at that particular point does not seem
plausible.


It would be a different matter, of course, if humans had immaterial
minds, but there is very strong empirical evidence against that view,
including such things as the effects of a blow to the head and brain
damage of different sorts, the effects of diseases such as
Alzheimer's, the decline of mental capacities with aging, the
relations between the mental development of children and the growth of
neural circuitry, the inheritance of personality traits, the different
correlations in the case of identical twins versus fraternal twins
with regard to such traits as intelligence, the effects of
psychotropic drugs, such as Prozac, and so on (Tooley, 2012,
42-4).


Secondly, the story postulates not just a special creation, but
also a special creation in which humans, initially, were not subject
to suffering or death. Given, among other things, that that period was
a very short one, one cannot offer positive historical evidence again
the existence of such a short period that involved only two
humans. But the belief is surely a remarkable one that can be viewed
as likely only if it is supported by evidence. The evidence that can
be offered, however, consists entirely of the creation story in
Genesis, so that question is, how reliable is such evidence? To answer
that question, one can see what other stories one finds in
Genesis. One striking story is that of Noah--who apparently lived
around 4500 years ago--according to which there was a worldwide
flood that killed all animals on Earth, except for those that were on
the ark. But there are excellent reasons for believing that such a
story is very unlikely to be true, both in the light of the number of
animal species that currently exist, and in the light of the
evidence--attempts by authors such as Whitcomb and Morris in
their book *The Genesis Flood: The Biblical Record and its
Scientific Implications* (1966) to argue otherwise
notwithstanding--that there has not been any world-wide flood in
the past 5000 years.


In addition, those who view Genesis as a source of important truths
do so because it is part of the Bible. So one can also ask about the
reliability of the Bible when it testifies to remarkable events. In
many cases, of course, there is no way of checking whether those remarkable events actually took place, but when there is, one finds that there is good reason to believe that the event in
question did not take place. Thus, for example, there is the story of
the sun's standing still for about a day during Joshua's battle at
Jericho, the story of the slaughter of all of the Egyptian first-born
children, and the story of the graves being opened and the dead
walking around the city at the time of Jesus's death (Matthew 27:
52-53). One would surely expect non-Biblical records of such events if
they had really taken place, but there are none.


Finally, the religious theodicy that we are considering also
involves a number of very problematic moral claims. First, we are
asked to believe that there is nothing morally problematic about a
morally good deity making it the case that if one of the first two
humans disobeys some command, all of the many billions of descendants
of that human will, as a consequence, be subject to suffering and
death to which they would not otherwise be exposed. Secondly, we are
also asked to believe that a morally good deity is unable to forgive
people their misdeeds unless he becomes incarnate in the form of his
son and suffers a sacrificial death. Thirdly, while, according to this story,
those who accept the sacrifice made on their behalf have all their
tears wiped away and enjoy eternal happiness in the presence of God,
those who do not accept the sacrifice fare considerably less well, and
suffer eternal torment in hell. So we are being asked to believe that
such eternal punishment is not morally problematic.


In short, the religious theodicy that we have been considering in
this section is very implausible, not only on scientific and
historical grounds, but on moral grounds as well. The question,
accordingly, is whether there is some religious theodicy that is not
exposed to scientific, or historical, or moral objections.


## 8. More Modest Variants on Defenses and Theodicies


 In section 1.3, it was argued that concrete formulations of the
argument from evil, which focus upon specific evils, or else upon
narrowly defined types of evils, are superior to abstract formulations
of the argument from evil, which start out from very general
statements concerning evil--such as that there is evil in the
world, or that there are natural evils, or that there is an enormous
amount of evil, and so on. Consider, then, an evidential argument
from evil that focuses upon Rowe's famous case of Sue--a young
girl who was brutally beaten, raped, and murdered. Confronted with
such a case, it is natural to think that a satisfactory response will
involve arguing that it is plausible that the terrible occurrence in
question itself has some hidden property that makes it the case that
allowing it to happen is not morally wrong all things considered.


 But as Peter van Inwagen has argued--most recently in *The
Problem of Evil*--there is a very different possibility, and one
that he thinks is much more promising. The basic idea is as follows.
First of all, one begins by focusing upon abstract formulations of the
argument from evil, and one attempts to put forward a story that makes
it plausible that the existence of, say, a great amount of horrendous
suffering in the world, is actually desirable because there is some
great good that outweighs that suffering, and that can only be
achieved if that amount of suffering is present, or some greater evil
that can only be avoided if that amount of suffering is present. (This
story might either be a theodicy-style story that specifies the great
good in question, or a defense-style story, which does not do so.)
Secondly, if that story provides a satisfactory answer to an abstract
version of the argument from evil that focuses upon the existence of
horrendous suffering, one can then turn to concrete versions of the
argument from evil, and there the idea will be that God had good
reason to allow a certain amount of horrendous suffering, and the
terrible case of Sue is simply one of the cases that he allowed. It
is not that Sue's suffering itself had some property that made its
occurrence good all things considered. God could very well have prevented it, and had he done so, he would have eliminated an
occurrence that was bad in itself, all things considered. But had he
done so, he would have had to have allowed some other horrendous evil
that, as things stand, he prevented, and the reason that he would have
had to do that would be to ensure that the global property of there
being a certain amount of horrendous evil in the world was
instantiated--something that was necessary to achieve a greater
good, or to avoid a greater evil.


 In short, defenses and theodicies that are based upon this idea,
rather than appealing to the idea that apparent evils are not evils in
themselves, all things considered, once all local properties--all
properties that those events themselves have--are taken into
account, appeal, instead, to the idea that there are global properties
whose instantiation is important, and that can only be instantiated if
there are events that are evil in themselves.


Does this shift from local properties to global properties help? It
would seem that it cannot. Consider against the case of Sue. An
advocate of the evidential argument from evil claims that no matter
how carefully one examines the case, and thinks about it, considering,
as one does, all of the rightmaking and wrongmaking properties of
which one has any knowledge, the conclusion is that the wrongmaking
properties of allowing what happened to Sue clearly outweigh any
rightmaking properties of allowing that event. The advocate of a
global property approach then suggests the possibility that there is
some global rightmaking property that involves the world's having a
certain amount of evil, or a certain amount of a certain kind of evil,
and that if someone had intervened to prevent the rape and murder of
Sue, this would have changed the world from one that did have the
desired amount of evil, or evil of the type in question, to one that
does not, and that when this property is taken into account, it turns
out that it would have been wrong to prevent Sue's being raped and
murdered--unless one was going to allow some compensating evil
elsewhere.


But what exactly is the global wrongmaking property in question?
Does one know, or even have any reason at all for believing, that
bringing it about that the amount of evil of kind \(K\) is less than some
specific amount \(T\) is a wrongmaking property of actions? The answer,
surely, is that no one has knowledge of any such wrongmaking
property. Moreover, anyone who claimed to have such knowledge would
also have to claim also to know that if an omnipotent and omniscient
being had prevented the rape and murder of Sue, without also allowing
some other, compensating evil action, that would have caused the
amount of evil of type \(K\) to dip below level \(T\).


One need not, of course, advance a principle involving some
specific value of \(T\). One could, instead, make the existential claim
that there is some level \(T\) such that, first, it is a wrongmaking
property of an action to cause the amount of evil of type \(K\) to dip
below level \(T\), and, second, that if an omnipotent and omniscient being
had intervened to prevent the rape and murder of Sue, that would, in
the absence of some compensating action, have caused the amount of
evil of type \(K\) to dip below level \(T\). But surely no one knows, or even
has any reason for believing, that this is the case.


The situation as regards an appeal to global properties is, in
short, as follows. An advocate of the argument from evil points to
various events, such as the rape and murder of Sue, and claims that no
matter how carefully one considers the case, one's conclusion is that
the known wrongmaking properties of not preventing that occurrence
outweigh any rightmaking properties that not preventing the occurrence
is known to have had. In response, the possibility of a relevant,
morally significant global property is introduced. But this is a mere
possibility, since there is no relevant morally significant global
property of which one has knowledge, let alone which one has good
reason to believe is present in the case in question. So the
possibility of a relevant global property is simply that: a mere
possibility, and as such it gets dealt with in the way that all
unknown morally significant properties, both rightmaking and
wrongmaking, and both local and global, are dealt with in, for example,
the logical probability version of the evidential argument from evil
set out above in section 3.5.