Introduction

11.1.1 In this chapter we look at fuzzy logic, that is, logic in which sentences can take as a truth value any real number between 0 and 1.

11.1.2 We look at one of the major motivations for such a logic: vagueness. We also show some of the connections between fuzzy logic and relevant logics.

11.1.3 Finally, fuzzy logic gives a very distinctive account of the conditional, since modus ponens may fail. The chapter examines what fuzzy conditionals are like.

Sorites Paradoxes

11.2.1 Suppose that Mary is aged five, and hence is a child. If someone is a child, they are a child one second later: there is no second at which a person turns from a child to an adult. (We are talking about biological childhood here, not legal childhood. The latter does terminate at the instant someone turns eighteen, in many jurisdictions.) So in one second's time, Mary will still be a child. Hence, one second after that, she will still be a child; and one second after that; and one second after that … Hence, Mary will be a child after any number of seconds have elapsed. But this is, of course, absurd. After an appropriate number of seconds have elapsed, so have thirty years, by which time Mary is thirty-five, and so certainly not a child.

11.2.2 The argument of 11.2.1 is known as a sorites paradox. It arises because the predicate ‘is a child’ is vague in a certain sense.