Why did humans develop precise systems for measuring experience, like numbers, clocks, andcalendars? I argue that precise representational systems were constructed by earlier generationsof humans because they recognized that their noisy perceptual systems were not capturingdistinctions that existed in the world. Abstract symbolic systems did not arise from perceptualrepresentations, but instead were constructed to describe and explain perceptual experience. Byanalogy, I argue that when children learn number words, they do not rely on noisy perceptualsystems, but instead acquire these words as units in a broader system of procedures, whosemeanings are ultimately defined by logical relations to one another, not perception.