An alien landed on Earth. Previously, she had already read a lot about us. In particular, she knew quite a bit about the history of science in general, and of mathematics in particular. First place she went to here on Earth was a room filled with a bunch of philosophers, in the building of a philosophy department in some random university (she was invisible to the naked eye, so the philosophers didn’t really realize she was there).
The philosophers were having quite a debate about the one true logic. “Huh?”, thought the alien in her own language (quotations of the alien’s thoughts are semantically transparent here, for I can’t really use the modes of presentation of her own thoughts). She was really puzzled about that discussion. She was well aware that for most of us logic, like mathematics, isn’t the type of thing that can be confirmed/disconfirmed through experience — or at least not with the same frequency, or not as easily as the natural sciences can be empirically confirmed/disconfirmed (“Those quineans …”, she also said to herself, “… I’m surprised it took them so long to arise in this planet”). She knew, that is, that there was a significant difference, if not as a matter of kind then as a matter of degree, between logic and mathematics on the one hand, and the natural sciences on the other.
“Why then…”, she wondered, “… why don’t they realize that the difference between different logics is much like the difference between different geometries?”. Her thought was roughly as follows: Euclidean geometry wasn’t shown to be false, it was just shown not to be applicable to other spatial structures but the initial, more canonical one; it does not compete with non-Euclidean geometry — they can peacefully live together in the same math department; maybe that is why people do not have as heated discussions about the one true geometry as they have about the one true logic; similarly, those particular logics (e.g. classical first-order logic, or strong-Kleene logic) are not show to be false when their laws do not match the properties of arguments/claims in natural language: it is just that they are not applicable to certain types of contents (even though they are applicable to other types of content).
She went back to her planet. But that issue still bewilders her. Fortunately, she still has access to our internet — and so she can read any comments we make about the error of her ways, or perhaps about the fact that she is right, even though that heated debate among philosophers is quite understandable given our psychology.
p iff p 