Incompatible-Properties Arguments: A Survey
by Theodore M. Drange
The following article is from Philo,
Volume 1, Number 2.
Abstract: Ten arguments for the nonexistence of God are
formulated and discussed briefly. Each of them ascribes to God a pair
of properties from the following list of divine attributes: (a)
perfect, (b) immutable, (c) transcendent, (d) nonphysical, (e)
omniscient, (f) omnipresent, (g) personal, (h) free, (i) all-loving,
(j) all-just, (k) all-merciful, and (1) the creator of the universe.
Each argument aims to demonstrate an incompatibility between the two
properties ascribed. The pairs considered are: 1. (a-1), 2. (b-1), 3.
(b-e), 4. (b-i), 5, (c-f), 6. (c-g), 7. (d-g), 8. (f-g), 9. (e-h), and
10. (j-k). Along the way, several other possible pairs are also
mentioned and commented upon.
Atheological arguments (arguments for the nonexistence of God) can be
divided into two main groups. One group consists of arguments which aim
to show an incompatibility between two of God's properties. Let us call
those "incompatible-properties arguments." The other group
consists of arguments which aim to show an incompatibility between God's
existence and the nature of the world. They may be called "God-vs.-world
arguments." A prime example of one of those would be the Evidential
Argument from Evil. This paper will survey only arguments in the first
group. Arguments in the second group are discussed elsewhere.[1]
To generate incompatible-properties arguments, it would be most
helpful to have a list of divine attributes. I suggest the following.
God is:
(a) perfect
(b) immutable
(c) transcendent
(d) nonphysical |
(e) omniscient
(f) omnipresent
(g) personal
(h) free |
(i) all-loving
(j) all-just
(k) all-merciful
(1) the creator of the universe |
This is certainly not a complete list, for there are other properties
that have been ascribed to God. For example, the list excludes
omnipotence. Furthermore, I am not claiming here that there is any one
person who has ascribed all of these properties to God. I would say,
though, that each of the properties has been ascribed to God by someone
or other.
It would be of interest to consider whether there are pairs of
properties from the given list which are incompatible with each other.
For each such pair, it would be possible to construct an
incompatible-properties argument for God's nonexistence. The present
essay aims to study that issue in the style of a survey. It will not go
into the relevant philosophical issues in any great depth. Nor will it
consider the further matter of whether anyone has actually claimed the
existence of a being which possesses any of the incompatible pairs. It
is assumed in the background, however, that there are indeed such
people. Let us proceed, then, to consider various possible
incompatible-properties arguments.
1. The Perfection-vs.-Creation Argument
Consider the pair a-l, which takes God to be perfect and also to be
the creator of the universe. It seems that those properties might be
shown to be incompatible in two different ways. The first way is as
follows:
Version 1
1. If God exists, then he is perfect.[2]
2. If God exists, then he is the creator of the universe.
3. A perfect being can have no needs or wants.
4. If any being created the universe, then he must have had some need
or want.
5. Therefore, it is impossible for a perfect being to be the creator
of the universe (from 3 and 4).
6. Hence, it is impossible for God to exist (from 1, 2, and 5).
Premise 3 might be challenged on the grounds that a perfect being,
full of love, could desire to share his love with others. Thus, a
perfect being could have a want, which would make premise 3 false. I
suppose the only problem with this is that, if a being wants something
that he does not have, then he cannot be perfect, for he would be in a
certain way incomplete. Whether or not this adequately defends premise 3
is hard to say. There is a certain unclarity, and perhaps subjectivity,
in the idea of "perfection" which poses an obstacle to any
sort of rigorous reasoning about the concept.[3]
Premise 4 might also be challenged. Perhaps God created the universe
accidentally. For example, he "slipped and fell," thereby
creating a mess, which turned out to be our universe. In that case, God
would not have had any need or want in creating the universe, and
premise 4 would be false. There are difficulties with this, however.
First, almost every theist who takes God to have created the universe
takes it to have been done deliberately, not accidentally. And second,
if the creation were accidental, then that in itself would imply that
God is imperfect (since perfect beings do not have accidents), and that
would be another basis for the Perfection-vs.-Creation Argument. Thus,
this sort of challenge to premise 4 itself runs into problems.
Version 2
1. If God exists, then he is perfect.
2. If God exists, then he is the creator of the universe.
3. If a being is perfect, then whatever he creates must be perfect.
4. But the universe is not perfect.
5. Therefore, it is impossible for a perfect being to be the creator
of the universe (from 3 and 4).
6. Hence, it is impossible for God to exist (from 1, 2, and 5).
The usual reply to this line of thought is that, whatever
imperfections the universe may contain, they are the fault of mankind,
not God. Thus, the universe was indeed perfect when God first created
it, but it later became imperfect because of the actions of humans. This
could be taken as an attack on the argument's premise 3, construed to
imply that what is perfect must remain so indefinitely. I shall not
pursue the many twists and turns that this issue might take. It is
essentially the same as what is called the "Deductive Argument from
Evil," which is a topic beyond the scope of the present survey. Let
us instead move on to a new argument.
2. The Immutability-vs.-Creation Argument
Let us now consider the pair b-l, which takes God to be immutable
(unchangeable) and also the creator of the universe. This argument, too,
comes in different versions.[4] However, I shall
consider just one of them here:
1. If God exists, then he is immutable.
2. If God exists, then he is the creator of the universe.
3. An immutable being cannot at one time have an intention and then at
a later time not have that intention.
4. For any being to create anything, prior to the creation he must
have had the intention to create it, but at a later time, after the
creation, no longer have the intention to create it.
5. Thus, it is impossible for an immutable being to have created
anything (from 3 and 4).
6. Therefore, it is impossible for God to exist (from 1, 2, and 5).
Premise 3 might be challenged on the grounds that the loss of an
intention through the satisfaction of it is not a genuine change in a
being. If a man wants something, X, and then obtains it, he has not
thereby changed his attitude towards X. It is not that he once had a
pro-attitude towards X but now he has a con-attitude towards it. So long
as he is satisfied with X, his attitude remains unchanged. This may very
well be true, but why claim that the only genuine change there can be in
a being is a change in attitude? Why not allow that there can be other
sorts of genuine change, and one of them is the loss of an intention
through the satisfaction of it? Until some clear answer to this question
is given, premise 3 seems to have some merit.
Premise 4 might be attacked in at least two different ways. It has
been claimed that both the concept of "prior to the existence of
the universe" and the concept of "God existing within
time" are bogus. Time is a part or aspect of the universe itself
and so there cannot be a time "before the universe." And God
is a timeless being, so the idea of God having a certain property at one
time but lacking it at a later time is misguided. Since God is not
within time, he cannot have properties at particular times.
My response to both objections is that creation is a temporal
concept. This is built into the very definition of "create" as
"to cause to come into being." X cannot cause Y to come into
being unless X existed temporally prior to Y. Thus, if indeed there was
no time prior to the existence of the universe, then it is logically
impossible for the universe to have been created. In that case, there
could not possibly be a creator of the universe. And, furthermore, if
indeed God does not exist within time, then he could not have been the
creator of the universe, because, by the very concept of creation, if
the universe was created at all, then its creator must have existed
temporally prior to it. So if God, being timeless, did not exist
temporally prior to anything, then God cannot have been the creator of
the universe.
There is another objection to premise 4 which is similar to one we
considered in relation to argument 1. It is that 4 would be false if the
universe were created unintentionally. Again, it should be mentioned
that people who believe that the universe was created also believe that
it was created intentionally. But I would like to point out another
possible response here. In place of the concept of intention, it would
be possible to appeal to some other concept in the construction of
argument 2. One candidate for that would be the concept of performing an
action. In order for someone to create something, even if it is done
unintentionally, the creator must perform an action, and that action
must take time. Thus there must be a time during which a creator is
performing a certain action and a later time (after the action has been
performed) during which he is no longer performing that action. It could
be argued that this, too, represents a change in the being who is
performing the action. Thus, this would be another reason for
maintaining that an immutable being cannot create anything (whether
intentionally or not).
3. The Immutability-vs.-Omniscience Argument
This argument is based on an alleged incompatibility between
attributes (b) and (e) on our list. It, too, comes in different
versions, one of which is the following[5]:
1. If God exists, then he is immutable.
2. If God exists, then he is omniscient.
3. An immutable being cannot know different things at different times.
4. To be omniscient, a being would need to know propositions about the
past and future.
5. But what is past and what is future keep changing.
6. Thus, in order to know propositions about the past and future, a
being would need to know different things at different times (from 5).
7. It follows that, to be omniscient, a being would need to know
different things at different times (from 4 and 6).
8. Hence, it is impossible for an immutable being to be omniscient
(from 3 and 7).
9. Therefore, it is impossible for God to exist (from 1, 2, and 8).
The usual place at which this argument is attacked is its premise 4.
It is claimed that a timeless being can know everything there is to know
without knowing propositions about the past and future. Consider the
following two propositions as examples:
A. The origin of the planet Earth is in the past.
B. The end (or destruction) of the planet Earth is in the future.
The claim is that a timeless being need not know propositions A and B
in order to know everything there is to know, because such a being could
know the exact dates of both the origin and the end of the earth and
that would suffice for complete knowledge. That is, A and B would be
"covered," and so it would not be necessary for the omniscient
being to know A and B in addition to those dates.
But, of course, this claim can be challenged. To know the dates of
the origin and the end of the earth does not entail knowing propositions
A and B. To know A and B requires being situated within time (somewhere
between the origin and end of the earth), so they are not anything that
a timeless being could know. However, they certainly are things that an
omniscient being must know. Thus, the given objection to premise 4 of
the argument above is a failure.
It should be noted that a somewhat different incompatible-properties
argument could also be constructed using the divine attribute of
transcendence instead of immutability. The argument would focus on the
point that a transcendent being must be timeless and a timeless being
cannot know propositions about the past and future. However, an
omniscient being, as shown above, must know propositions about the past
and future. Therefore, it is impossible for a transcendent being to be
omniscient. The incompatibility would be between attributes (c) and (e)
on our list. Such an argument could be called "the Transcendence-vs.-Omniscience
Argument." The same issues would be raised in it as were raised,
above, in connection with the Immutability-vs.-Omniscience Argument.
4. The Immutability-vs.-All-Loving Argument
Here the alleged incompatibility is between attributes (b) and (i).
The argument may be expressed as follows:
1. If God exists, then he is immutable.
2. If God exists, then he is all-loving,
3. An immutable being cannot be affected by events.
4. To be all-loving, it must be possible for a being to be affected by
events.
5. Hence, it is impossible for an immutable being to be all-loving
(from 3 and 4).
6. Therefore, it is impossible for God to exist (from 1, 2, and 5).
To be affected is to be changed in some way, so premise 3 is pretty
much true by definition. Premise 4 might be challenged, but when the
nature of love is contemplated, it is seen that 4 must also be true. The
concept of love that is relevant here is that of agape, which is
the willingness to sacrifice oneself for the sake of others. If events
were to call for some sacrifice on God's part, then, to be loving in the
relevant sense, he must go ahead and perform the sacrifice. Since that
requires being affected, the truth of premise 4 is assured.
This argument is a particularly forceful one. There is another
argument which is very similar to it, which pits immutability against
the property of being a person (property [g] on our list). It
could be called the "Immutability-vs.-Personhood Argument."
The basic idea behind it would be that in order to genuinely be a person
(or personal being), it is necessary that one be capable of being
affected by what happens. I think that that one, too, is quite forceful,
but I shall not pursue it here. (For a similar argument, see section 6
below.) We have done quite enough with the divine attribute of
immutability.
5. The Transcendence-vs.-Omnipresence Argument
Here the incompatibility is between properties (c) and (f). The
argument may be formulated as follows:
1. If God exists, then he is transcendent (i.e., outside space and
time).
2. If God exists, then he is omnipresent.
3. To be transcendent, a being cannot exist anywhere in space.
4. To be omnipresent, a being must exist everywhere in space.
5. Hence, it is impossible for a transcendent being to be omnipresent
(from 3 and 4).
6. Therefore, it is impossible for God to exist (from 1, 2, and 5).
The usual place at which this argument is attacked is premise 3. It
is claimed that to transcend space does not entail being totally outside
space. A being could be partly inside space and partly outside. Consider
the Flatland analogy: a three-dimensional object transcends Flatland,
and yet it exists within the Flatland dimensions (as well as outside).
So, God could be like that. He exists within space (and, indeed,
everywhere in space!) but he also exists outside space, the latter
feature being what warrants calling him "transcendent."
My only objection here is that the Flatland analogy does not quite
make the idea of transcendence intelligible. We understand perfectly
well how a three-dimensional object might "transcend" Flatland
while still being (partly) within it. However, this is still talking
about objects in space. To try to extend the analogy so as to talk about
something that is "outside space as well as within it" is
unsuccessful. That is something that we are totally unable to
comprehend. In the end, the very concept of transcendence that is
appealed to here is incoherent. This illustrates the point that defenses
against incompatible-properties arguments may very well lead to
incoherence or other objections to theism.
6. The Transcendence-vs.-Personhood Argument
This is an even better argument for bringing out the relevant
incoherence. It pits property (c) against property (g), instead of
against (f):
1. If God exists, then he is transcendent (i.e., outside space and
time).
2. If God exists, then he is a person (or a personal being).
3. If something is transcendent, then it cannot exist and perform
actions within time.
4. But a person (or personal being) must exist and perform actions
within time.
5. Therefore, something that is transcendent cannot be a person (or
personal being) (from 3 and 4).
6. Hence, it is impossible for God to exist (from 1, 2, and 5).
Again, premise 3 might be challenged on the grounds that a
transcendent being could be both partly inside time and partly outside
time, with the latter feature being what warrants the label
"transcendent." That is, God is said to perform actions within
time but also to have a part or aspect that extends outside time.
However, this notion of "partly inside time and partly
outside" is definitely incoherent. No one has a clue what that
might mean. To pursue such a line of thought might evade the charge of
"incompatible properties," but it leads directly to the charge
of incoherence, which is just as bad, if not worse.
Premise 4 might also be challenged. It might be said that its concept
of personhood is too limited and that persons (or personal beings) could
exist totally outside time. I am inclined to resist this sort of
conceptual expansion. If the concept of personhood is extended that far,
then it ceases to do the work that it was supposed to do, which was to
make God into a more familiar figure. Furthermore, if persons (or
personal beings) can exist totally outside of time, then it becomes
unclear what it might mean to speak of "persons" (or
"personal beings") at all. The boundaries of the class become
so blurred that the concept becomes vacuous.
Closely related to the concept of personhood is the concept of being
free, which is property (h) on our list. An argument similar to 6,
above, one which might be called the "Transcendent-vs.-Free
Argument," could be constructed, pitting property (c) against
property (h). In its corresponding premise 4, the point would be made
that, in order for a being to be free, it must exist and perform
actions within time. Otherwise, there would be no way for any freedom to
be manifested. Almost all theists, it should be noted, accept the idea
that God is a free agent, and thus are inclined to say of him that he
(at least occasionally) performs actions within time. If they call God
"transcendent" at all, then they would aim to attack premise 3
of the arguments in question, not premise 4. Of course, as pointed out
above, to attack premise 3 leads one to make incoherent statements, so
such a maneuver cannot be regarded to be successful.
7. The Nonphysical-vs.-Personal Argument
Let us consider pitting property (d) against property (g). Then we
get an argument which might be formulated in a very short way, as
follows:
1. If God exists, then he is nonphysical.
2. If God exists, then he is a person (or a personal being).
3. A person (or personal being) needs to be physical.
4. Hence, it is impossible for God to exist (from 1-3).
Premise 3 has been advocated by Kai Nielsen, who wrote: "we have
no understanding of 'a person' without 'a body' and it is only persons
that in the last analysis can act or do things."[6] But
not all nontheists would accept premise 3. One who does not is J. L.
Mackie.[7] This argument turns on the issue of whether
the idea of a "bodiless person" is consistent and coherent.
That is a difficult and highly controversial issue, and I shall not
pursue it here in this survey.[8]
It should be noted that the divine attribute of being nonphysical
might also be taken to be incompatible with still other divine
attributes, such as being free and being all-loving, which would give
rise to slightly different incompatible-properties arguments. All such
arguments, though, would lead into the same sort of difficult and
controversial issues as does the Nonphysical-vs.-Personal Argument, and
so should not be regarded to be among the most forceful of the various
atheological arguments available.
8. The Omnipresence-vs.-Personhood Argument
Similar considerations arise when we pit property (f) against
property (g). The argument may again be formulated in a brief way, as
follows:
1. If God exists, then he is omnipresent.
2. If God exists, then he is a person (or a personal being).
3. Whatever is omnipresent cannot be a person (or a personal being).
4. Hence, it is impossible for God to exist (from 1-3).
The point of premise 3 is similar to that for the
previous argument. When we contemplate what it means to be a person (or
a personal being), we see that it conflicts with being omnipresent. What
sorts of things might be omnipresent, anyway? Perhaps a gravitational
field would serve as an example. They would all appear to be items in a
different category from persons, so to try to assimilate them
would be to commit a category mistake. Persons can no more be
omnipresent than they can be odd or even (in the mathematical sense).
9. The Omniscient-vs.-Free Argument
We now come to a more complicated argument, which pits
property (e) against (h). One way of formulating it is presented by Dan
Barker.[9] A slightly different version may be
formulated as follows:
1. If God exists, then he is omniscient.
2. If God exists, then he is free.
3. An omniscient being must know exactly what actions he will and will
not do in the future.
4. If one knows that he will do an action, then it is impossible for
him not to do it, and if one knows that he will not do an action, then
it is impossible for him to do it.
5. Thus, whatever an omniscient being does, he must do, and whatever
he does not do, he cannot do (from 3 and 4).
6. To be free requires having options open, which means having the
ability to act contrary to the way one actually acts.
7. So, if one is free, then he does not have to do what he actually
does, and he is able to do things that he does not actually do (from
6).
8. Hence, it is impossible for an omniscient being to be free (from 5
and 7).
9. Therefore, it is impossible for God to exist (from 1, 2, and 8).
Some have denied that omniscience entails knowing all
about the future. They say that omniscience only entails knowing what
there is to know. But the future actions of free persons are open, and
not there to be known about. Thus, not even an omniscient being could
know about them. This may provide a basis for rejecting premise 3 of the
argument.
This sort of objection to 3 can be attacked in many
different ways. One way would be to affirm that an omniscient being
would indeed need to know all about the future. All propositions about
the future are either true or false, and an omniscient being, by
definition, must know the truth of any proposition that is in fact true.
Furthermore, theists, often following the Bible on this point, commonly
attribute unrestricted knowledge of the future to God.[10]
Indeed, if God does not know the future actions of any free beings, then
there is very little, if any, pertaining to the future about which he
can be certain. For no matter what the situation may be, there is always
a chance that it will be affected by such actions.
Another way to attack the given objection is to
maintain that, even if God does not know about the future actions of other
free agents, he must know about his own future actions. One
reason for this is that God's actions are all based on perfect justice
and immutable law. There is never any caprice in them. His purposes and
intentions have remained steadfast from all eternity, so anyone who
totally understands God's purposes and intentions, as he himself does,
would be able to infallibly predict his actions. It follows that God
must know what he himself will and will not do in the future, which
would establish the truth of premise 3 if it is taken to refer to God.
Premise 4 is a consequence of the definition of
knowledge. If a proposition is known to be true, then it must be true
and cannot be false. So, if X knows that Y will do Z, then it is
impossible for Y not to do Z. And this is so even where X and Y are the
same person.
Premise 6 says that a free agent can do what he
doesn't do. That may sound odd at first, but when it is understood
correctly, it seems correct. Suppose we identify what Y does as
"act Z." Then in order for Y to be free, prior to doing Z, it
must have been possible for Y to do Z and it must also have been
possible for Y not to do Z. If it were not possible for Y not to do Z,
then Y's doing of Z could not be regarded as a free act. Free acts are
avoidable. You can't be free if you had to do the thing that you
did. This seems intuitively right, though some forms of compatibilism
might reject it. It is not a totally settled issue in philosophy. I
leave it to the reader to ascertain whether or not premise 6 is correct.
If it is, then I think the argument goes through.
10. The Justice-vs.-Mercy Argument
The last argument to be considered in this survey pits
property (j) against property (k). It may be formulated as follows:
1. If God exists, then he is an all-just judge.
2. If God exists, then he is an all-merciful judge.
3. An all-just judge treats every offender with exactly the severity
that he/she deserves.
4. An all-merciful judge treats every offender with less severity than
he/she deserves.
5. It is impossible to treat an offender both with exactly the
severity that he/she deserves and also with less severity than he/she
deserves.
6. Hence, it is impossible for an all-just judge to be an all-merciful
judge (from 3-5).
7. Therefore, it is impossible for God to exist (from 1, 2, and 6).
I have heard it said by Christians that the way God
judges offenders depends on whether or not they are true believers. If
they are, then he is lenient with them, but if they are not, then he
treats them with exactly the severity they deserve (which can be pretty
bad). By this Christian way of speaking, God is said to be both an
all-just and an all-merciful judge. He is all-just in giving everyone an
equal opportunity to become a true believer and thereby come to receive
leniency, but he is also all-merciful in that every true believer,
without exception, receives mercy. This way of viewing matters would be
an attack on both premise 3 and premise 4, above.
I would respond by maintaining that premises 3 and 4
come closer to capturing ordinary language than the given Christian way
of speaking. According to the latter, God treats some offenders more
leniently with regard to what they deserve than he does other offenders.
It does not seem that such a judge would (or should) be called
"all-just." And similarly, since he does not treat all
offenders less severely than they deserve, he would not (and should not)
be called "all-merciful" either. Instead of being both
all-just and all-merciful, the Christian God, as described, would be
neither.
As with many of the previous attacks on the
incompatible-properties arguments, this one turns on semantical issues.
In a sense, it is all a matter of semantics, for the issue of whether or
not certain property ascriptions conflict with certain other property
ascriptions depends very much on what exactly they mean. Theists could
defend against the arguments by denying that the property terms in
question mean what the proponents of the arguments claim they mean.
Often such denials lead to still other difficulties for the theist. A
full presentation and defense of incompatible-properties arguments
should explore such implications and fully pursue the many issues,
whether semantical or not. That project is beyond the scope of the
present essay.
My aim was simply to survey several of the more common
(and a few not so common) incompatible-properties arguments for the
nonexistence of God. Just which of those arguments are sound and which
of them are most effective in discussions and debates with theists are
further issues that are certainly worth pursuing.
References
1. See, especially, Theodore M.
Drange, Nonbelief and Evil: Two Arguments for the Nonexistence of God
(Amherst, N.Y.: Prometheus Books, 1998).
2. Following tradition, and for
simplicity, I use the male personal pronoun for God. My apologies to
anyone who finds that linguistic practice offensive.
3. This obstacle applies to any
version of the Ontological Argument.
4. See, especially, Richard M. Gale, On
the Nature and Existence of God (Cambridge: Cambridge University
Press, 1991), chapter 2. The versions of the argument discussed by Gale
are different from the one taken up in the present essay.
5. Gale, On the Nature and
Existence of God, chapter 3.
6. Kai Nielsen, An Introduction to
the Philosophy of Religion (New York: St. Martin's Press, 1982), p.
36.
7. See J. L. Mackie, The Miracle
of Theism (Oxford: Oxford University Press, 1982), pp. 1-2.
8. For reasons that support the
incoherence of "disembodied persons," see Nonbelief and
Evil, appendix E, section 2.
9. See his Web essay "The
Freewill Argument for the Nonexistence of God" at the following
address: <http://www.infidels.org/org/ffrf/fttoday/august97/barker.html>.
10. For a long list of biblical
references to God's knowledge of the future free actions of humans, see Nonbelief
and Evil, appendix B, section 2.
Theodore M. Drange is Professor of Philosophy at West Virginia
University.
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