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Question Is there really a strong distinction between understanding what a proposition means and believing or disbelieving it? It strikes me that if I believe a proposition while my opponent does not, one way to explain the disagreement is to say that he misunderstands either that proposition or some related proposition. And so if we really did both understand all of the propositions in question, we'd have to agree about them as well.

Accepted:
July 10, 2016

Comments

I'd say that in many cases

I'd say that in many cases there's indeed a difference between grasping a proposition and believing the proposition, i.e., believing it to be true. To take a well-known example from mathematics, Georg Cantor believed that the Continuum Hypothesis is true, whereas Kurt Gödel believed it's false. Both were brilliant mathematicians; I see no reason to think that their disagreement arose from either man's misunderstanding the proposition in question or some related proposition.

But not all cases are like that. Consider the proposition that all bachelors are unmarried. Anyone who fails to believe that proposition, I'd say, fails to grasp it, because grasping the proposition implies believing the proposition. At any rate, I can't make sense of the idea that someone could grasp that proposition without believing it.