Topics for test 1

The following are the topics to be covered. The proportion of the test covering each will approximate the proportion of the classes so far that have been devoted to that topic. Your homework and the collection of old tests will provide specific examples of the kinds of questions I might ask.

Basic concepts of deductive logic. You will be responsible for the concepts listed in appendix A.1. You should be able to define each in terms of possible worlds and truth values, and you should be prepared to answer questions about them, justifying your answer by reference to the definitions. Appendix A.1 includes relative exhaustiveness and all the concepts you’ve seen are special cases of it, so in principle, all are fair game. However, if I ask about something like mutual exclusiveness I’ll tell you how it is expressed using relative exhaustiveness. That does mean that you need to be able to understand how relative exhaustiveness is defined in special cases where there are no assumptions on the left of the arrow or no alternatives on the right; that means you need to know what it means to say, for example, that “φ, ψ ⇒.”

Implicature. Be able to define it and distinguish it from implication. Be able to give examples and explain them. Be ready to answer questions about it, justifying your answer by reference to its definition.

Analysis. Be able to analyze the logical form of a sentence as fully as possible using conjunction and present the form in both symbolic and English notation (that is, with the logical-and symbol ∧ and with the both-and way of expressing forms).

Synthesis. Be able to synthesize an English sentence that has a given logical form.

Derivations. Be able to construct derivations to show that entailments hold and to show that they fail. I may tell you in advance whether an entailment holds or leave it to you to check that using derivations. There may be some derivations where the rule Adj introduced in 2.4 would be convenient to use; but it is never necessary. You should be ready to use EFQ and ENV as well as Ext, Cnj, and QED; but derivations involving the latter three are much more likely.