| Pure Hypothetical Syllogism:
| |
| If p, then q. | |
| If q, then r. | |
| If p, then r. | |
| Example: | |
| If all actions are causally determined, then no actions are free. | |
| If no actions are free, then no one is responsible for anything they do. | |
| If all actions are causally determined, then no one is responsible for anything they do. | |
| Disjunctive Syllogism: | |
| Either p or q. | |
| It is not the case that p. | |
| q. | |
| Example: | |
| Either my idea of God is generated from my own mind or something exists which is other than my mind. | |
| It is not the case that my idea of God is generated from my own mind. | |
| Something exists which is other than my mind. | |