A Note on Goddard and Routley's Significance Logic

The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics (namely, logics able to handle nonsignificant sentences) with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this essay we show that with the aid of plurivalent semantics it is possible to straightforwardly instantiate Goddard and Routley’s understanding of how the connectives should work within significance logics.