Numbers as Properties Melisa Vivanco September, 2023 [Draft] Abstract Although number sentences are ostensibly simple, familiar, and applicable, the justifcation for our arithmetical beliefs has been con- sidered mysterious by the philosophical tradition. In this paper, I ar- gue that such a mystery is due to a preconception of two realities, one mathematical and one nonmathematical, which are alien to each other. My proposal shows that the theory of numbers as properties en- tails a homogeneous domain in which arithmetical and nonmathemat- ical truth occur. As a result, the possibility of arithmetical knowledge is simply a consequence of the possibility of ordinary knowledge 1 . 1 Introduction There are numerous reasons to affrm that mathematical knowledge is possi- ble. Nonetheless, the feasibility of a satisfactory explanation of mathematical knowledge has been seriously questioned in the specialized literature. On the one hand, in contrast to other knowledge domains, mathematics enjoy a high applicability rate. On the other hand, our perceptual limitations concerning the content of mathematical statements have induced several diffculties in 1 Acknowledgments: Versions of this material were presented at MIT, UNAM, University of Miami, Vienna (at the “What in the World(s)?!” conference), Prague (at the 16th CLMPST), and elsewhere. I especially thank Mario Gomez–Torrente, Otávio Bueno, Max Fernandez, Carmen Curcó, Simon Evnine, Stephen Yablo, Agustín Rayo, Milo Phillips– Brown, and Curtis Miller for the insightful and stimulating exchange of ideas that led to the results presented in this work. 1