Logic and contingent existence

It is argued here that Prior's non-standard modal system Q, and the Parry–Dunn system of analytic implication, though entirely independent and independently motivated systems, together provide a rationale for explicating the concept of validity in a non-standard way; their implications are explored for the theory of natural deduction as well as for modal logic and the concept of entailment. I give an account of formal logic from this non-standard viewpoint, together with an informal presentation of the system that unites the insights of Prior (drawing on Russell) and, Parry (drawing on Kant), and the motivations for both in the concept of the contingent existence – as opposed to the contingent truth or falsehood – of a proposition.