HOW TRUTH-FUNCTIONAL CONNECTIVES WORK

We have now defined conjunction, disjunction, and negation. That, all by it- self, is sufficient to complete the branch of modern logic called propositional logic. The definitions themselves may seem peculiar. They do not look like the definitions we find in a dictionary. But the form of these definitions is impor- tant, for it tells us something interesting about the character of such words as “and,” “or,” and “not.” Two things are worth noting: (1) These expressions are used to construct a new proposition from old ones; (2) the newly constructed proposition is always a truth function of the original propositions—that is, the

4. p q q

~p

These forms of argument are invalid. This can be shown by the following single instance:

She is either using her modem or talking on the phone. She is using her modem.

She is not talking on the phone.

This argument might seem valid if one assumes that she cannot talk on the phone while using her modem. The premises, however, do not specify that she has only one phone line. If she talks on one phone line while using her modem on a different phone line, then the premises are true and the conclusion is false. Because this is possible, the argument is invalid, and so is its form, 3. Moreover, this argument would remain invalid if the disjuncts were listed in a different order, so that the argument took the form of 4. Thus, affirming a disjunct is a fallacy.