*Alex Oliver and Timothy Smiley*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199570423
- eISBN:
- 9780191755866
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570423.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This book aims to be the natural point of entry to what will be a new subject for most readers. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate ...
More

This book aims to be the natural point of entry to what will be a new subject for most readers. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII’s wives’, ‘the real numbers’, ‘√−1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration.Less

This book aims to be the natural point of entry to what will be a new subject for most readers. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote *Principia Mathematica*’, ‘Henry VIII’s wives’, ‘the real numbers’, ‘√−1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration.

*Alex Oliver and Timothy Smiley*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199570423
- eISBN:
- 9780191755866
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570423.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

The notion of a plural term is spelled out using the relation of plural denotation. This chapter investigates whether plural denotation is distributive or collective. Different authors—Peter Simons, ...
More

The notion of a plural term is spelled out using the relation of plural denotation. This chapter investigates whether plural denotation is distributive or collective. Different authors—Peter Simons, Keith Hossack, Mark Sainsbury, Byeong-uk Yi—have argued for one or other answer, but their arguments are unsound. The conclusion is that plural denotation is indeterminate in this respect, since both kinds of denotation—distributive and collective—produce the same correct truth conditions for plural predications. Five ways of formulating truth conditions are investigated, including those featuring so-called free relatives, such as the multiply ambiguous what-phrase in ‘F(a) is true iff F is true of what a denotes’.Less

The notion of a plural term is spelled out using the relation of plural denotation. This chapter investigates whether plural denotation is distributive or collective. Different authors—Peter Simons, Keith Hossack, Mark Sainsbury, Byeong-uk Yi—have argued for one or other answer, but their arguments are unsound. The conclusion is that plural denotation is indeterminate in this respect, since both kinds of denotation—distributive and collective—produce the same correct truth conditions for plural predications. Five ways of formulating truth conditions are investigated, including those featuring so-called free relatives, such as the multiply ambiguous what-phrase in ‘*F*(*a*) is true iff *F* is true of what *a* denotes’.

*Alex Oliver and Timothy Smiley*

- Published in print:
- 2016
- Published Online:
- February 2017
- ISBN:
- 9780198744382
- eISBN:
- 9780191843877
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198744382.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

The notion of a plural term is spelled out in this chapter using the relation of plural denotation. The chapter investigates whether plural denotation is distributive or collective. Different ...
More

The notion of a plural term is spelled out in this chapter using the relation of plural denotation. The chapter investigates whether plural denotation is distributive or collective. Different authors—Peter Simons, Keith Hossack, Mark Sainsbury, Byeong-uk Yi—have argued for one or other answer, but their arguments are unsound. The conclusion is that plural denotation is indeterminate in this respect, since both kinds of denotation—distributive and collective—produce the same correct truth conditions for plural predications. Five ways of formulating truth conditions are investigated, including those featuring so-called free relatives, such as the multiply ambiguous what-phrase in ‘F(a) is true iff F is true of what a denotes’.Less

The notion of a plural term is spelled out in this chapter using the relation of plural denotation. The chapter investigates whether plural denotation is distributive or collective. Different authors—Peter Simons, Keith Hossack, Mark Sainsbury, Byeong-uk Yi—have argued for one or other answer, but their arguments are unsound. The conclusion is that plural denotation is indeterminate in this respect, since both kinds of denotation—distributive and collective—produce the same correct truth conditions for plural predications. Five ways of formulating truth conditions are investigated, including those featuring so-called free relatives, such as the multiply ambiguous what-phrase in ‘*F*(*a*) is true iff *F* is true of what *a* denotes’.

*Alex Oliver and Timothy Smiley*

- Published in print:
- 2016
- Published Online:
- February 2017
- ISBN:
- 9780198744382
- eISBN:
- 9780191843877
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198744382.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII's wives’, ‘the real numbers’, ‘√—1’, ‘they’); plural predicates ...
More

This book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII's wives’, ‘the real numbers’, ‘√—1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration. A system of higher-level plural logic is then outlined. It bears a striking similarlty to the set theory.Less

This book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote *Principia Mathematica*’, ‘Henry VIII's wives’, ‘the real numbers’, ‘√—1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration. A system of higher-level plural logic is then outlined. It bears a striking similarlty to the set theory.