The Incompatible Properties Argument(s) by T.M. Drange

[This article was originally published by Dr. Theodore Drange in Philo 1998 (2), pp. 49-60. It has been re-purposed here, eliminating most of Drange’s accompanying comments to anticipated objections. The intention here is just to provide the outlines of his argument(s) in their logical form(s) and promote awareness of the argument’s overall strength.]

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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).

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).

  1. 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)

  1. 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).

  1. 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).

  1. 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).

  1. 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).

  1. 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).


  1. 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).


  1. 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).

  1. 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).

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. -T.M.D.


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.ffrf.org/fttoday/august97/barker.html&gt;.

[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.

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