Introduction

In this chapter we explore how we know the principles of deductive logic. We could also discuss the principles of induction and abduction, but these topics are extremely complicated and I do not want to dedicate the rest of this book to discussion of the principles of reasoning.

Systems of deductive logic – such as the ones most undergraduate philosophy students learn in their first or second year – typically have two sorts of principles. First, there are the laws of the logical system. These laws are sometimes called “theorems” or, in the case of standard propositional logic, “tautologies”. Laws are statements. In formal logical systems, these statements are formulas of various sorts. But we shall not be using the language of formal logic here. Instead, we shall write our laws in English or in a schematic form of English, writing, for example, “either S1 or S2” to stand for disjunctive statements such as “either it is going to rain soon or it will remain humid all afternoon” or “either dogs hate cats or dogs are afraid of cats”.

A law of logic is a necessarily true statement. It is true in all possible worlds (see Chapter 2). Some philosophers think that laws of logic must have other characteristics as well. For example, some think that a law of logic must be necessarily true by virtue of its form. For example, the statement “red is a colour” is necessarily true. Red cannot be anything other than a colour.