Graeme (R.) Forbes

Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a special appendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, Modern Logic gives equal weight to semantics and proof theory and explains their relationship, and develops in detail techniques for symbolizing natural language in first-order logic. After a general introduction featuring the notion of logical form, the book offers sections on classical sentential logic, monadic predicate logic, and full first-order logic with identity. A concluding section deals with extensions of and alternatives to classical logic, including modal logic, intuitionistic logic, and fuzzy logic. For students of philosophy, mathematics, computer science, or linguistics, Modern Logic provides a thorough understanding of basic concepts and a sound basis for more advanced work.

A verb is transitive iff it usually occurs with a direct object, and in such occurrences it is said to occur transitively . Thus ‘ate’ occurs transitively in ‘I ate the meat and left the vegetables’, but not in ‘I ate then left’ (perhaps it is not the same verb ‘left’ in these two examples, but it seems to be the same ‘ate’). A verb is intensional if the verb phrase (VP) it forms with its complement is anomalous in at least one of three ways: (i) interchanging expressions in the complement referring to the same entity can change the truth-value of the sentence embedding the VP; (ii) the VP admits of a special “unspecific” reading if it contains a quantifier, or a certain type of quantifier; and (iii) the normal existential commitments of names and existential quantifiers in the complement are suspended even when the embedding sentence is negation-free.

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives.

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes (2000b). In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. (This paper is an abridged version of Forbes (2001a); the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives