Our project: propositional logic

Now we can set out the project we’re going to pursue for the rest of this course. We’re going to look at the logic of some key expressions which play a crucial role in a huge range of arguments. We’re going to look at four important sentence-connectives in English: ‘and’, ‘it is not the case that’, ‘or’, and ‘if … then … ’.

The logic of these connectives is called Propositional Logic, because it concerns structures made up from sentential clauses (which express propositions—that is, claims) and sentence connectives.

In each case, we’ll introduce a truth-functional sentence connective in our formal language (giving a clear and precise definition of the meaning of that connective in each case) which at least seems to correspond reasonably closely to the natural-language connective we’re interested in. Then we’ll explore how and to what extent we can capture what’s going on in claims and arguments involving the natural-language connective using the connectives of our formal language.

By the end of the course, you’ll see how we’re able to clarify and evaluate arguments expressed in natural language by using our formal language.

Working this way—with precisely defined connectives in a formal language—has a number of advantages. As we’ve noted already, we can specify very precisely what we mean by expressions in our formal language. Another useful feature of our formal language is that it helps us to be clear about the distinction between the original expression of a claim or argument in natural language and ideas about what (more precisely) is being expressed.

If we’re going to use our formal language to clarify what’s going on in claims and arguments expressed in natural language, we need to be able to test suggested representations of claims expressed in natural language in our formal language. This is what we’ll look at next.