What can we know about that which we cannot even imagine?

In this essay I will consider a sequence of questions, ending with one about the breadth and depth of the epistemic limitations of our our science and mathematics. I will then suggest a possible way to circumvent such limitations. I begin by considering questions about the biological function of intelligence. This will lead into questions concerning human language, perhaps the most important cognitive prosthesis we have ever developed. While it is traditional to rhapsodize about the perceptual power provided by human language, I will emphasize how horribly limited – and therefore limiting – it is. This will lead to questions of whether human mathematics, being so deeply grounded in our language, is also deeply limited. I will then combine all of this into a partial, sort-of, sideways answer to the guiding question of this essay: what we can ever discern about all that we cannot even conceive of?

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