Knowledge from Pebbles: What Can Be Counted, and What Cannot

T here is an idea , powerful across the long history of formation of much of what we take to be knowledge, that the objects of our thought can best be understood as pebbles. By way of explaining this cryptic point, let us remind you of one of Borges’s last stories, “Tigres azules” (Blue tigers). Its narrator, Alexander Craigie, was a Scottish philosopher whomade a living teaching “occidental logic” at Lahore (modern Pakistan) circa 1900. Professor Craigie was in every way an apostle of reason, except that since his earliest childhood he had been fascinated by tigers, which even populated his dreams (already we should feel a slight tension between ways of knowing). Toward the end of 1904 Craigie read somewhere the surprising news that a blue variant of the species had been sighted. He dismissed the report as product of error or linguistic confusion, but eventually even the tigers in his dreams turned blue. Unable to resist his curiosity, he set off toward the sources of the rumor. When he arrived at a Hindu village mentioned in some of the reports and told thevillagerswhathewas looking for, he found that they becamequite guarded, but they claimed to knowof this blue tiger, and