The purpose of this paper is to formulate first-order Peano arithmetic within the resources relevant logic, and demonstrate certain properties system thus formulated. Striking among these are facts that (1) it trivial absolutely consistent, but (2) classical straightforwardly contained in arithmetic. Under (1), I shall show particular 0 = 1 a non-theorem arithmetic; this, course, exactly...

Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour orthodoxy, and work Field, Warren Waxman, others suggests presumption its unjustified. This paper supports orthodoxy by establishing determinacy arithmetic well-motivated modal plural logic (Theorem 1). Recasting this result higher-order 13) reveals even nom...