Douglas Hofstadter (Gödel, Escher, Bach, p. 99), discussing whether mathematics would be the same in all conceivable worlds, writes: “[I]t seems that if we want to be able to communicate at all, we have to adopt some common base, and it pretty well has to include logic.”

I sympathize with Hofstadter, here. A conceivable world seems to imply that we can hold it in our minds and make some sense of it. However, this sentence does not recommend Hofstadter as a careful observer of human communication.

Or, if we hold Hofstadter’s viewpoint steady and see human communication in its light, we might conclude that the daily experience of the average human is to live in an inconceivable world. That’s an interesting idea to ponder, at least for as long as one can take it seriously rather than succumbing to a cynical, but superficial and uninteresting, interpretation. It is hard to doubt that we hold at least a little of the world in our minds. How much? What’s the SI unit for conceivability? Does a feeling of understanding use the same units, or another?

As a narrower and more straightforward subset we might look at dreams, which routinely violate any standard of coherence one might apply. Nonetheless, they occupy our consciousnesses for a substantial portion of every night and, although some of the content of dreams seems to defy translation into language, we don’t find ourselves incapable of communicating about dreams.

We could also rephrase Hofstadter’s point more narrowly. The phrase “communicate at all” might be a bit of hyperbole. I think he is making as an unstated assumption that we wish our communications on mathematics, conceivable worlds, and so forth to rise to some standard of clarity and comprehensibility. If we make the unstated assumption more explicit, we might say, “If we want to have conversations that are logical, we have to adopt some common base that includes logic.” A true enough statement, and perhaps not as vacuously tautological as it first appears.