3.03 We cannot think anything illogical, because we would then have to think illogically.

Cf. 5.4731. "Thinking illogically" is a contradiction in terms if "thinking" is understood as Wittgenstein means it. That is why we cannot do it. There is no such thing to do. And so what is illogical is utterly inconceivable. There cannot, as a matter of logic, of sense, be an illogical state of things. The word "cannot" here sounds metaphysical, but it can't be. It would be absurd to say that that which is unthinkable or inconceivable cannot occur in the world. Why on earth not, after all? And what are we talking about? What is the reference of "the unthinkable"? Asking this starts to sound metaphysical and mystical, but here that is plainly a mistake. “Thinking illogically” is self-contradictory, neither possible nor impossible, that is why we ‘cannot’ “think anything illogical,” because that too is, or implies, a contradiction. What could it mean to have a thought of “an illogical state of things”? It would mean to have a logical picture, a kind of copy or representation of, the logic of an illogical thing, the internal structure of something with no internal structure. This is, again, neither possible nor impossible but sheer nonsense.