Book contents
- Frontmatter
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Mathematical Prolegomenon
- Part I Propositional Logic
- 1 Classical Logic and the Material Conditional
- 2 Basic Modal Logic
- 3 Normal Modal Logics
- 4 Non-normal Modal Logics; Strict Conditionals
- 5 Conditional Logics
- 6 Intuitionist Logic
- 7 Many-valued Logics
- 8 First Degree Entailment
- 9 Logics with Gaps, Gluts and Worlds
- 10 Relevant Logics
- 11 Fuzzy Logics
- 11a Appendix: Many-valued Modal Logics
- Postscript: An Historical Perspective on Conditionals
- Part II Quantification and Identity
- Postscript: A Methodological Coda
- References
- Index of Names
- Index of Subjects
11 - Fuzzy Logics
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Mathematical Prolegomenon
- Part I Propositional Logic
- 1 Classical Logic and the Material Conditional
- 2 Basic Modal Logic
- 3 Normal Modal Logics
- 4 Non-normal Modal Logics; Strict Conditionals
- 5 Conditional Logics
- 6 Intuitionist Logic
- 7 Many-valued Logics
- 8 First Degree Entailment
- 9 Logics with Gaps, Gluts and Worlds
- 10 Relevant Logics
- 11 Fuzzy Logics
- 11a Appendix: Many-valued Modal Logics
- Postscript: An Historical Perspective on Conditionals
- Part II Quantification and Identity
- Postscript: A Methodological Coda
- References
- Index of Names
- Index of Subjects
Summary
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.
- Type
- Chapter
- Information
- An Introduction to Non-Classical LogicFrom If to Is, pp. 221 - 240Publisher: Cambridge University PressPrint publication year: 2008