This is a very well formed list of arguments against the existence of God. It was originally written by Theodore M. Drange. It was originally posted in the magazine Philo in 1998. I retrieved it from the site Infidels.org
Link: http://infidels.org/library/modern/theodore_drange/incompatible.html

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 only survey 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 (g) personal
(b) immutable (h) free
(c) transcendent (i) all-loving
(d) nonphysical (j) all-just
(e) omniscient (k) all-merciful
(f) omnipresent (l) 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[2] is perfect.
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 Immutable-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 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: .

[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.