The true modal logic (Q1181474)

This paper traces, in very nice detail, the reasoning that led Prior to propose his curious system \(\mathbf Q\) as the true quantified modal logic. Because a logic should make as few metaphysical commitments as possible, the true modal logic should avoid the necessitarian myth, to which classical quantified modal logic seems committed, that whatever exists exists necessarily. It should likewise eschew possibilism, the commitment to non-actual possibilia. \(\mathbf Q\) is intended to be a coherent actualist modal logic. To accomplish that, Prior denied the interdefinability of necessity and possibility and also the classical rule of necessitation. Without those the Barcan formula also goes. The author here is very sympathetic to Prior's intuitions and aims. Nevertheless, he sees problems lingering in \(\mathbf Q\), including its incompleteness. One way out is so-called haecceitism, but this is rejected as foreign to Prior's intuitions. The author here argues instead that an alternative is available which is true to Prior's program; all that is required is to modify the way one pictures what it is for a proposition to be possible. One may think of the world as the totality of facts, or as a maximal configuration of objects. The former picture leads to \(\mathbf Q\); the latter to the author's alternative \(\mathbf A\). \(\mathbf A\) is more conventional than \(\mathbf Q\), it is also provably complete. After an informal exposition of \(\mathbf A\), in which its fidelity to Prior's intentions is defended, \(\mathbf A\) is defined rigorously, both axiomatically and model-theoretically.