Belief, Math, and Superman
This is the first in a series I am naming "Consider the Following Lecture a Bonus!", a quote taken from the illustrious Dr. John Zoidberg.
I have found that if you ask the average person "Is the number 51 prime or composite?" they will almost always say "prime."
In epistemology (a branch of philosophy that deals with belief, knowledge, and justification), there is a distinction between two different kinds of belief that is brought up a lot: de dicto belief vs. de re belief. De dicto is Latin for, loosely, "of the word." De re is Latin for, again loosely, "of reality."
So what the hell does that mean? Well, the example that I've heard most often to explain it involves Superman, of all things.
Imagine you want to figure out whether or not Lois Lane believes that Clark Kent can fly. On the one hand, Lois Lane believes that Clark Kent is an average person like herself, and so is not able to fly. This is what we would call the de dicto version of the belief: Lois believes that Clark Kent, her very normal co-worker, cannot fly. Reasonable enough.
But we know more, don't we? As a matter of fact (or rather, in reality), Clark Kent IS Superman. Lois Lane believes, obviously, that Superman can fly, so therefore she must also believe that Clark Kent can fly, as they are one and the same person. This is what we would call the de re version of her belief. While she would say "No" if you asked her the question, there is a sense in which she does in fact believe that Clark Kent can fly.
So, as a matter of chance, Lois believes de re that Clark Kent can fly, but she also believes de dicto that he can't.
This works because there is a piece of information which Lois Lane does not have available to her: the fact that Clark Kent is Superman. But what if a person had all of the relevant information directly available to them and still held contradicting de dicto and de re beliefs? How could that happen?
Well, is the number 51 prime or composite? If you are like most people I've met, you will believe that it is a prime number. But what if I were to ask you to tell me what 17 times 3 is?
Take a second if you need to...
Yeah, it's 51. So 51 is not a prime number. You've known all along how to multiply and divide numbers. In fact, you don't need to go out and look around for an answer to a math problem like that, you don't even need to use a calculator or a pencil (although they can save time). All of the math you are capable of doing is already in your head (or to put it the way a philosopher would: it is a priori knowledge). We have all of the relevant information available to us. As a matter of fact, 51=17x3, so we already know de re that 51 must be composite. Yet most of us believe de dicto that 51 is prime. Why?
My best guess: It sort of just feels prime, doesn't it?