Incompatible-Properties Arguments: A Survey

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The phrase "Three O Paradox" is probably a shorthand reference to the statement that a being cannot simultaneously be omniscient, omnipresent, and omnipotent.

In this article, I will list a number of incompatible-properties arguments discussed by Theodore Drange in his article ‘Incompatible-Properties Arguments: A Survey’. Drange discusses objections in his articles, so I advise anyone interested to read it. I will not discuss any of them here. In some cases, individual articles will discuss them more in-depth.

Incompatible-Properties Arguments- The Drange article.

A. The Perfection vs. Creation Argument, Version 1

1. If God exists, then he 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).

B. The Perfection vs. Creation Argument, 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).

C. The Immutability vs. Creation Argument

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)

D. The Immutability vs. Omniscience Argument

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).

E. The Immutable vs. All-Loving Argument

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).

F. The Transcendence vs. Omnipresence Argument

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).

Therefore, it is impossible for God to exist (from 1, 2, and 5).

G. The Transcendence vs. Personhood Argument

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).

H. The Nonphysical vs. Personal Argument

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).

I. The Omnipresence vs. Personhood Argument

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).

J. The Omniscient vs. Free Argument

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).

K. The Justice vs. Mercy Argument

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).

Drange’s arguments are varied. Some of them only apply to the Christian god, some apply to all. Some are more soldly argued than others. Nevertheless, his collection was worthy of putting on our list simply because of its exhaustive nature.


See also


v · d Arguments against the existence of god
Existential arguments   Argument from nonbelief · Who created God? · Turtles all the way down · Problem of non-God objects · Argument from incompatible attributes · No-reason argument · Santa Claus argument
Arguments from the Bible   Failed Prophecy · Biblical contradictions
Reasonableness arguments   Occam's Razor · Outsider test · Argument from locality · Argument from inconsistent revelations
Moral arguments   Euthyphro dilemma · Problem of evil · Problem of evil (evidential) · Moral argument
Other arguments   Emotional pleas against the existence of God
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