Department of Philosophy (PHI)
Conditionals: Theme and Variations (all are equivalent)
| If B then D | "If Rolf is a beagle then he is a dog." |
| D if B | "Rolf is a dog if he is a beagle." |
| B only if D | "Rolf is a beagle only if he is a dog." |
| Only if D, B | "Only if Rolf is a dog is he a beagle." |
| If not D then not B | "If Rolf isn't a dog then he isn't a beagle." |
| Not B if not D | "Rolf isn't a beagle if he isn't a dog." |
| Not D only if not B | "Rolf isn't a dog only if he isn't a beagle." |
| Only if not B, not D | "Only if Rolf isn't a beagle is he not a dog." |
| Either not B or D | "Either Rolf isn't a beagle or he is a dog." |
| Not B unless D | "Rolf isn't a beagle unless he's a dog." |
| Either D or not B | "Either Rolf is a dog or he isn't a beagle." |
| D unless not B | "Rolf is a dog unless he's not a beagle." |
| Not both B and not D | "Rolf is not both a beagle and a non-dog." |
| Not both not D and B | "Rolf is not both a non-dog and a beagle." |
NOTE: switching B and D, or negating both, will change any of these statements to one that is not equivalent to the original.