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What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind?
My mathematical skills are minimal, but it seems to me that the reason someone else would have discovered Pythagoras's theorem if Pythagoras hadn't is that the theorem formulates an observed and demonstrable set of relations. It may take imagination to discern that, but that doesn't make it a product of imagination in the sense that, say, a poem is.
The problem with this sort of thing is that it accepts the premise that utility is the foundation of value. Appreciating something for its own sake, rather for its usefulness, would seem a quintessentially human characteristic. That is why we call certain things the humanities. They may not help us get a job, but they can fulfill us as human beings.
The dangerous tendency of the Royal Society (founded in 1660) and of all subsequent forms of scientific materialism, from Darwin down to Dawkins and Dennett, is to deny the classic ideal of rationality and the residual momentum of human common sense that is its long-term, democratic-republican by-product. To say there is “Nothing in words” is of course a thematic-performative self-contradiction: It is asserted in words. But the aim is clear: to reduce a kind of wise traditional dualism — matter/mind, body/spirit, perception/conceptualization, sense experience/language — to a monistic materialism.
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