Handbook of the History of Logic: - Fordham University Faculty

Logic in the 14 th Century after Ockham 481
for as-of-now consequences are to be found in Buridan and Pseudo-Scotus (cf.
[Pozzi, 1978, 69]).
‘If the antecedent must be conceded, so must be the consequent.’
⇒ A A ⇒ B
⇒ B
‘If the consequent must be denied, so must be the antecedent.’
⇒¬B A ⇒ B
⇒¬A
‘From the contradictory of the consequent the contradictory of the antecedent
follows’: contraposition [Ockham, 1974, 728].
A ⇒ B
¬B ⇒¬A
‘Whatever follows from the contradictory of the antecedent follows from the
contradictory of the consequent.’
A ⇒ B ¬A ⇒ C
¬B ⇒ C
‘Whatever is antecedent to the contradictory of the consequent is antecedent to
the contradictory of the antecedent.’
A ⇒ B C ⇒¬B
C ⇒¬A
‘From a conjunction to one of its parts constitutes a valid consequence.’
A&B ⇒ A
‘From one of its parts to the whole disjunction constitutes a valid consequence.’
A ⇒ A ∨ B
‘From a conditional with its antecedent to its consequent constitutes a valid
consequence.’ 50
A → B,A ⇒ B
Now something perhaps slightly surprising for the modern reader: rules for
consequences that do not obtain (which I represent by ‘⇒’). In modern systems
50Here again it is clear that our authors were very much aware of the distinction between
conditionals and consequences.