A general recipe for classical recapture

Abstract In this essay, I prove two general recapture theorems (the GRT and the $$\textbf{GRT}^\textsf{Dual}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>GRT</mml:mi> <mml:mi>Dual</mml:mi> </mml:msup> </mml:math> ). Each of these states that any sub-logic of classical logic that is closed under six rules of inference is equivalent, in the relevant sense, to classical logic. After proving in each case that the six rules in question are independent of one another, and exploring a number of possible modifications or extensions of these results, I compare the results to Jc Beall’s recapture results in Beall (2011), Beall (2013a) and Beall (2013b). The GRT (and $$\textbf{GRT}^\textsf{Dual}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>GRT</mml:mi> <mml:mi>Dual</mml:mi> </mml:msup> </mml:math> ) are shown to be more powerful and general than Beall’s more piecemeal approach.