 Given the discussion so far, it seems reasonable to suggest that concepts \(F\) and \(G\) will be equinumerous whenever the number of objects falling under \(F\) is identical to the number of objects falling under \(G\). This suggestion will be codified by Hume’s Principle. However, before discussing this principle, the reader should convince him- or herself of the following four facts: (1) that the material equivalence of two concepts implies their equinumerosity, (2) that equinumerosity is reflexive, (3) that equinumerosity is symmetric, and (4) that equinumerosity is transitive. In formal terms, the following facts are provable: