Embedding \textit{if and only if} (Q427225)

Those who hold that indicative conditionals do not have truth values may regard their view as explaining why some left-nesting conditionals, as `If, if \(A\) then \(B\), then \(C\)', resist interpretation. (Contrary to their Note 1 on p. 450, an alternative formulation of this is not `If \(A\) if \(B\), then \(C\)', but rather `If \(B\) if \(A\), then \(C\)'). But a rejection of truth values for indicative conditionals should extend to rejection of truth values for indicative biconditionals, and these embed more successfully. The paper makes use of \textit{D. Lewis}'s results in his [``Probabilities of conditionals and conditional probabilities'', Philos. Rev. 85, No. 3, 297--315 (1976)].