The aim of this book is to introduce students to the ideas and techniques of symbolic logic. Logic is the study of arguments. After working through this book the reader should be in a position to identify and evaluate a wide range of arguments.

Once an argument has been identified, we need to determine whether it is a good argument or a bad one. By ‘good argument’ we mean a valid argument; by ‘bad argument’ we mean an invalid argument. Our primary method for determining validity will be natural deduction proofs, but we also use the (simpler but more cumbersome) method of truth-trees. In addition, we briefly show how truth-tables can also be used to test for validity.

Elementary logic studies arguments, and, in doing so, it studies the logical or inferential properties of the so-called logical connectives: ‘and’, ‘if … then …’, ‘or’, ‘not’ and ‘if and only if’. We use these logical words much of the time, even if we might find it hard to say what they mean. In logic, however, these key words have a clear and explicit meaning.

SOME KEY TERMS AND IDEAS

Premises and conclusion

In elementary logic, the premises and conclusion of an argument are all declarative sentences; that is, they are sentences that are either true or false. There are only two truth-values and each declarative sentence has one and only one of them. ‘The cat is on the mat’, ‘no one loves Raymond’ and ‘all bachelors are bald’ are examples of declarative sentences.