ABSTRACT
Philosophers, mathematicians, and developmental psychologists often assume that the earliest number concepts we develop are concepts of natural number. Furthermore, it is widely claimed that the conceptualizations we develop are consistent with Peano-like axioms—a starting element and a one-to-one successor function that generates the infinite set of natural numbers. Are these claims warranted? Here we present empirical evidence that, challenging this view, suggests that even highly educated adults routinely conceptualize the natural numbers in ways that are radically different from, or even at odds with, Peano-like characterizations. We argue that the collection of counting numbers differs in important ways from the formal mathematical set of natural numbers, such that natural number concepts may not arise naturally from our counting experience.
