Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 A simple formal language
- 2 Predicates and functors
- 3 The isomorphism problem
- 4 Quantification
- 5 Transmundism
- 6 Putnam's ‘Meaning of “meaning”’
- 7 Lewis on languages and language
- 8 Causation and semantics
- 9 Belief–desire psychology
- 10 Direct knowledge
- References
- Index
1 - A simple formal language
Published online by Cambridge University Press: 01 October 2009
- Frontmatter
- Contents
- Preface
- Introduction
- 1 A simple formal language
- 2 Predicates and functors
- 3 The isomorphism problem
- 4 Quantification
- 5 Transmundism
- 6 Putnam's ‘Meaning of “meaning”’
- 7 Lewis on languages and language
- 8 Causation and semantics
- 9 Belief–desire psychology
- 10 Direct knowledge
- References
- Index
Summary
This book is concerned with what makes one interpretation of a language the correct one and another the wrong one. I will be discussing this problem in the context of possible-worlds semantics and so, in order to set the scene, and by way of introduction for those who have not come across possible-worlds semantics for natural languages, I shall, in the first two chapters, set out a simple fragment so that we can see what is going on.
I hope that most of you will have a familiarity with at least the language of the first-order predicate calculus. (sometimes called the lower predicate calculus or LPC). I shall set out here a simple version of this, but without quantifiers, which I can generalize to a language rich enough for the points I want to make. So here is a language ℒ
Sentences or well-formed formulae of ℒ are finite sequences of what are called symbols. Although, in logical languages, symbols are often represented by letters, it is best to think of them as corresponding to words in natural language rather than letters. The sentences of ℒ are those allowed by the formation rules. The formation rules are sensitive to the syntactic category of each symbol. It is time to be specific.
ℒ contains a category of names. Let these be Adriane, Bruce, Julie and David.
ℒ contains a category of predicates. Let these be runs, whistles and sees.
ℒ contains a category of sentential functors (sometimes called connectives). Let these be not, and and if.
ℒ contains a left parenthesis, (, and a right parenthesis,).
Categories (2) and (3) may be further subdivided.
- Type
- Chapter
- Information
- Language in the WorldA Philosophical Enquiry, pp. 5 - 19Publisher: Cambridge University PressPrint publication year: 1994