Argument against impossible powers

Last revised: 03/15/25

These are in progress and subject to revision. Feedback welcomed.

Definitions: Power is the capacity to act or to produce an effect. Capacity is what a thing can do. Logically impossible refers to what cannot happen or be the case (whether or not anything has the capacity for it).

First argument

1. Something has no capacity to act or to produce an effect if and only if it is not a category or instance of power. (¬P ↔ ¬Q)

2. Whatever is logically impossible has no capacity to act or to produce an effect. (¬P)

3. Therefore, whatever is logically impossible is not a category or instance of power. (¬Q Definitional Modus Ponens)

Second argument

1. If there is no possibility for the existence of something, then there is zero capacity for the existence of it.

2. There is no possibility for the existence of logically impossible effects.

3. Therefore, there is zero capacity for the existence of logically impossible effects. (Definitional Substitution on #1-2)

4. If there is zero capacity for a given effect, then lacking capacity for that given effect takes nothing away from another entity’s causal proficiencies.

5. Therefore, lacking capacity for the existence of a logically impossible state of affairs takes nothing away from another entity’s causal proficiencies. (Definitional Substitution on #4-5)

6. If true, then an entity that is lacking capacity for the existence of a logically impossible state of affairs is not lacking a causal proficiency in that given respect.

7. Therefore, an entity that is lacking capacity for the existence of a logically impossible state of affairs is not lacking a causal proficiency in that given respect. (Modus Ponens on #5-6)

8. If true, then an entity that is lacking capacity only for the existence of a logically impossible state of affairs has casual proficiency in all given respects.

9. An entity that has casual proficiency in all given respects is omnipotent.

10. Therefore, an entity that is lacking capacity only for the existence of a logically impossible state of affairs is omnipotent. (Definitional Substitution on #8-9)