before any argument or proof becomes possible. When some of them have been granted, others can be proved, though these others, so long as they are simple, are just as obvious as the principles taken for granted. For no very good reason, three of these principles have been singled out by tradition under the name of “Laws of Thought.”
They are as follows:
- The law of identity : “Whatever is, is.”
- The law of contradiction : “Nothing can both be and not be.”
- The law of excluded middle : “Everything must either be or not be.”
These three laws are samples of self-evident logical principles, but are not really more fundamental or more self-evident than various other similar principles: for instance, the one we considered just now, which states that what follows from a true premise is true. The name “laws of thought” is also misleading, for what is important is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them; in other words, the fact that when we think in accordance with them we think truly . But this is a large question, to which we must return at a later stage.
In addition to the logical principles which enable us to prove from a given premise that something is certainly true, there are other logical principles which enable us to prove, from a given premise, that there is a greater or less probability that something is true. An example of such principles—perhaps the most important example is the inductive principle, which we considered in the preceding chapter.
One of the great historic controversies in philosophy is the controversy between the two schools called respectively “empiricists” and “rationalists.” The empiricists—who are best represented by the British philosophers, Locke, Berkeley, and Hume—maintained that all our