We cannot verify your location
Browse Book and Journal Content on Project MUSE
OR

The Connectives

Lloyd Humberstone

Publication Year: 2011

A comprehensive investigation of the sentence connectives--and, or, if, not--with special attention to their logical properties.

Published by: The MIT Press

Title Page, Copyright, Dedication

pdf iconDownload PDF (42.8 KB)
 

Contents

pdf iconDownload PDF (112.0 KB)
pp. vii-xii

read more

Preface and Navigation Guide

pdf iconDownload PDF (143.3 KB)
pp. xiii-xviii

This book is about the semantics and pragmatics of natural language sentence connectives and about the properties of and relations between analogous devices in the formal languages of numerous systems of propositional (or sentential) logic. And the intended readership is: all who find connectives, and the conceptual issues ...

read more

0. Preliminaries

pdf iconDownload PDF (467.5 KB)
pp. 1-46

Given n non-empty sets S1, . . . , Sn and a relation RS1 × · · · × Sn, we call the structure (R, S1, . . . , Sn an n-ary relational connection. When siSi (for i = 1, . . . , n) we often write Rs1, . . . , sn for s1, . . . , snR, using the familiar ‘infix’ notation s1Rs2 for the case of n = 2. ...

read more

1. Elements of Sentential Logic

pdf iconDownload PDF (1.0 MB)
pp. 47-194

This chapter and the next present some basic material in sentential logic. The intention is to stress those topics of particular relevance to what follows later, as well as to highlight the way individual connectives fare in the general development. We begin our discussion of logical matters by introducing the idea of a formal language. ...

read more

2. A Survey of Sentential Logic

pdf iconDownload PDF (1.2 MB)
pp. 195-374

There are two related respects in which our treatment of semantic matters up to this point might be generalized. As has been remarked, our boolean valuations are homomorphisms from the language on which we concentrated in §1.1 (with connectives ∧, ∨, ¬, ⊤, ⊥) to the two-element boolean algebra. ...

read more

3. Connectives: Truth-Functional, Extensional, Congruential

pdf iconDownload PDF (994.5 KB)
pp. 375-510

This chapter introduces and compares the three properties of connectives listed in its title. As they appear in the list, these properties go from the strongest, truth-functionality—the topic of the present section—to the weakest, congruentiality, to be reviewed in §3.3, via an interestingly intermediate property called here extensionality (§3.2). ...

read more

4. Existence and Uniqueness of Connectives

pdf iconDownload PDF (864.3 KB)
pp. 511-630

In this chapter, we will discuss the existence (§4.2) and uniqueness (§4.3) of sentential connectives in the sense of connective in which connectives are not simply syntactic operations, but operations building formulas with certain inferential properties and relationships (as in 1.19). ...

read more

5. “And”

pdf iconDownload PDF (959.1 KB)
pp. 631-766

Before passing to the three aspects of the study of natural language alluded to in the title of this subsection, a word by way of reminder should be said on the subject of logic. Here syntactic and semantic considerations also arise, in the shape of proof-theoretic or formal conditions on (generalized) consequence relations and of conditions on valuations. ...

read more

6. “Or”

pdf iconDownload PDF (1.1 MB)
pp. 767-924

Before beginning with an introduction proper, giving a brief overview of this section and of the rest of the chapter, we offer, by way of an hors d’oeuvres – an “Or” d’oeuvres, we might say – a glimpse at a problem besetting studies of this most intriguing of the sentence connectives, the word or. ...

read more

7. “If”

pdf iconDownload PDF (1.4 MB)
pp. 925-1162

This chapter addresses not only some of logical and semantic issues raised by ‘if__ then. . . ’, but also the behaviour of related connectives which have been proposed to formalize various special relations of implication and entailment. We associate the label conditionals with the former project ...

read more

8. “Not”

pdf iconDownload PDF (908.8 KB)
pp. 1163-1286

For a direct parallel with the preceding three chapters, we should open with an extended discussion of the points at which the treatment of negation in formal logic has been held inadequately to represent the behaviour of not (or it is not the case that) in English or corresponding locutions in other natural languages. ...

read more

9. Universally Representative and Special Connectives

pdf iconDownload PDF (453.6 KB)
pp. 1287-1336

This chapter introduces and compares two properties a connective may have or lack in a logic: the property of being ‘universally representative’ and the property of being what we shall call ‘special’. It will be sufficient to treat logics as individuated by the set of sequents they contain. ...

References

pdf iconDownload PDF (543.5 KB)
pp. 1337-1439

Index

pdf iconDownload PDF (366.2 KB)
pp. 1440-1492


E-ISBN-13: 9780262298834
Print-ISBN-13: 9780262016544

Page Count: 1512
Publication Year: 2011

Recommend

UPCC logo

Subject Headings

  • Logic.
  • Grammar, Comparative and general -- Connectives.
  • Language and logic.
  • You have access to this content
  • Free sample
  • Open Access
  • Restricted Access