The Naive Perspective: Numbers as Symbols and Quantities

This is the first paper in a six-part series, plus synthesis, on what we call the Univalent Correspondence: six perspectives on what a natural number "is". We treat numerals as syntax and the underlying number as semantics, tracing this distinction through the historical arc running from Mill's empiricism, Husserl's phenomenology of arithmetic, and Frege's critique of psychologism, into Benacerraf's identification problem. We show that the naive level is simultaneously insufficient—due to symbol/object confusion and foundational underdetermination—and indispensable, as the interface where embodied counting and culturally transmitted numeral systems anchor mathematical content in human cognition.