It is widely agreed that contraposition, strengthening the antecedent and hypothetical syllogism fail for subjunctive conditionals. The following putative counter-examples are frequently cited, respectively:1
If John had made a mistake, it would not have been a big mistake.
Therefore, if John had made a big mistake, he would not have made a mistake.
If this match had been struck, it would have lit.
Therefore, if this match had been soaked in water overnight and struck, it would have lit.
If J. Edgar Hoover had been a communist, he would have been a traitor.
If he had been born a Russian, he would have been a communist.
Therefore, if he had been born a Russian, he would have been a traitor.
The standard account of subjunctives – it is alleged – explains why these classical inference rules fail.2 On...