Here’s a claim that many philosophers make or would like to make as if it were certain:
“I can think whatever I want as long as I do not contradict myself.” (B XXVII)
This particular formulation is owed to Kant. But, that is irrelevant. Similar claims, as I said, appear everywhere in the tradition: Descartes surely would accept it, and certainly also would Chalmers. I think the claim is false. I’m sure my mind is limited and that this limits do not correspond with my capricious whims. So not everything I want is something I can think of (unless of course we understand ‘wanting’ as ‘thinking’, but then the claim is ridiculous, not certain). Yet, even if you agree that you can think of everything you want, there’s a further, more substantial, problem with this claim.
If it is true, then there’s a limit to what we can think of: contradictions. How can we, even with great Cartesian powers, know this? How can we know that contradictions cannot be thought of? How can the content of any mental state be the representation “that contradictions cannot be thought of”? It seems that the content itself is a thought about contradictions. So it cannot, itself, be the content of a thought.
Here’s another way to make the same point. If we are to know that contradictions cannot be thought of, we better know what contradictions are. Otherwise, we don’t know what we are talking about when we say that contradictions cannot be thought of. Suppose we know what contradictions are, perhaps because we can identify them. Doesn’t this presuppose that contradictions can be thought of? For how can we identify something without even thinking of it? Is it that as soon as we understand that, say, representation “R” is a contradiction it magically pops out of mental existence? That seems odd, if not ridiculous.
No matter what we take contradictions to be, if we are to claim that the very notion plays any useful role, it better be that we are able to have thoughts about them. The problem, then, with having thoughts the content of which is a contradiction is not their impossibility, but something else.
Here’s what, I believe, is a more useful way to understand contradictions. Take the contents of thoughts to be something like recipes for mental movement. There are, as with cooking, several different kinds of recipes. Some are good for several different contexts, others aren’t. Some are tastier than others, some are more boring than others, some are fun, some are dumb. Yet, they all get us to move somehow. Contradictions are a special recipe for thinking: they ask us to move one way and then move back to the same spot. They are, in this sense, absolutely useless. They are neither tasty, fun, or boring. They are, more likely, quite frustrating. But we can still have thoughts with them as content.
I think a lot of us do have those thoughts more often than not.