A relevant theory of conditionals

Williamson on Counterpossibles

“…One usual approach to nonvacuism (see for example [8,10,28,30] amongst others) is to retain the contours of the orthodox account, while dropping the restriction to possible worlds. On such an approach, (1) can be false in the way any false counterfactual is: by having its consequent false at some of the closest worlds where its antecedent is true.…”

A reason maintenance perspective on relevant Ramsey conditionals

“…A possible starting point is the work of Mares and Fuhrmann on relevant conditionals [31]. Their account, however, is truth conditional.…”

“…Restricting the scope of admissible conditionals to only relevant ones allows us to reject examples like (4) and (5) as reported in [31]: (4) If someone were to create a square circle, then we would not be amazed.…”

“…In most accounts of conditionals [43, 27, 24, 25, 34, for example] (but notably not in [31]), (4) and (5) will come out as acceptable counterfactuals. Assuming that axioms of geometry hold in all possible worlds, the first will be trivially acceptable since the antecedent is contradictory.…”

“…The SNePS reasoning system is a natural deduction system of relevance logic [2]. Hence, the account of conditionals provided is not susceptible to the fallacies of relevance and, thus, avoids irrelevant conditionals along the lines of [31].…”