The Neo-Fregean seeks to defend arithmetical platonism and logicism by taking a different tack: Hume's Principle by itself is taken to provide a contextual definition of numbers.  The viability of this approach is secured by the result now called Frege's Theorem: Hume's Principle, when added to a suitable system of second-order logic, suffices for the proof of the basic laws of arithmetic, Peano's axioms (see Wright 1983: 158–69). Arithmetical logicism is secured if Hume's Principle can be shown to be analytic in an appropriate sense. Arithmetical platonism, with numbers as logical objects, is secured because, when logical truths are substituted for the right-hand side of Hume's Principle, the resulting instance on the left-hand side is also logically true, and explicitly refers to numbers.