ABSTRACT
There are various kinds of logical inference that cannot be justiˆed on the basis of the propositional calculus; for example:
1. Any friend of Martin is a friend of John. Peter is not John’s friend. Hence, Peter is not Martin’s friend. 2. All human beings are rational. Some animals are human beings. Hence, some animals are rational. 3. The successor of an even integer is odd. 2 is an even integer. Hence, the successor of 2 is odd.
