This month, we discuss conditionals with Anthony (Thony) Gillies, Professor of Philosophy at Rutgers University. Click here to listen to our conversation.
Lately, philosophers have resurrected interest in formal theories of what’s meant by conditional statements, or if-then statements. Conditionals are basic, because they relate conditions – knowns and unknowns, actions and results, etc. But how do they relate them? Let’s examine one simple example that turns out to complicate this question.
First, let’s say someone murdered the owner of the mansion. Now suppose we are told that are two suspects:
Either the butler did it, or the gardener did it.
Therefore: If the butler didn’t do it, then the gardener did.
This seems like a completely valid inference – it’s impossible for the first statement to be true and the second statement false. And yet, the philosopher Robert Stalnaker argued that if that is a valid inference, then the following two statements have to be synonymous:
if X is the case, then Y is the case
either X isn’t the case or Y is the case
The trouble is that, for other reasons, there really seems to be no way that those two statements can be synonymous. For example, if they were synonymous, then ‘If George Washington was born in 1998, then he wasn’t born in 1998’ would be true! Why? It would just mean ‘Either George Washington wasn’t born in 1998 or he wasn’t.’ And he wasn’t! So thinking that those two things are synonymous really leads to absurd consequences.
So what do we do? It’s not clear that we can reject the first inference, because it really seems to be completely perfect. And thinking that ‘if X then Y’ means ‘either not X or Y’ leads to absurdity. And Stalnaker’s argument is difficult to argue against. Uh-oh.
Tune in to hear how our guest negotiates these extremely subtle logical waters!
Dominic Surya