Ockham discusses terms in great detail, and he goes on to discuss propositions and arguments. He was concerned primarily with formal syllogistic reasoning, but he did make a number of observations that impinge on the areas we know in symbolic logic as the propositional calculus and modal logic. Among other things, he discussed the truth conditions of conjunctive and disjunctive propositions, reduced “neither-nor” to “and” and “not,” discussed valid arguments of the form “*p* and *q*, therefore *p*,” “*p*, therefore *p* or *q*,” and “*p* or *q*, not *p*, therefore *q*,” pointed out the related fallacies, and stated Augustus De Morgan’s laws explicitly.

At the end of his treatment of inference, he discussed some very general nonformal rules of inference. Assuming in appropriate cases that we are speaking about a valid argument, they are as follows:1. if the antecedent is true the conclusion cannot be false 2. the premises may be true and the conclusion false 3. the contradictory of the conclusion implies the contradictory of the premise or conjunction of premises 4. whatever is implied by the conclusion is implied by the premises 5. whatever implies the premises implies the conclusion 6. whatever is consistent with the premises is consistent with the conclusion 7. whatever is inconsistent with the conclusion is inconsistent with the premises 8. a contingent proposition cannot follow from a necessary one 9. a contingent proposition cannot imply a contradiction 10. any proposition follows from a contradiction 11. a necessary proposition follows from any proposition

He illustrated the last two with these examples: “You (a man) are a donkey, therefore you are God,” and assuming God is necessarily triune, “You are white, therefore God is triune.” Ockham concluded his discussion by saying that because these rules are not formal they should be used sparingly.