The first thing to realize about grading as a psychological process is that it precedes measurement and counting. Judgments of the type “A is larger than B” or “This can contains less milk than that” are made long before it is possible to say, e.g., “A is twice as large as B” or “A has a volume of 25 cubic feet, B a volume of 20 cubic feet, therefore A is larger than B by 5 cubic feet,” or “This can (...) contains a quart of milk, that one 3 quarts of milk, therefore the former has less milk in it.” In other words, judgments of quantity in terms of units of measure or in terms of number always presuppose, explicitly or implicitly, preliminary judgments of grading. The term four means something only when it is known to refer to a number which is “less than” certain others, say five, six, seven, arranged in an ordered series of relative mores and lesses, and “more than” certain others, say one, two, three, arranged in an ordered series of relative mores and lesses. Similarly, a foot as a unit of linear measure has no meaning whatever unless it is known to be more than some other stretch, say an inch, and less than a third stretch, say a yard. (shrink)

Structures for Semantics offers an advanced course in logical and mathematical techniques and structures that are used in semantics, in relation to their semantic applications. The book helps students with a background in semantics to develop their skills of formalization and it makes research in semantics accessible. Workers in other disciplines will use it to discover more about the role of formal modelling in current semantic research, and about semantics itself. Following a chapter on logic and set theory there are (...) three parts of chapters: two pairs of chapters on partial order and equivalence relations in relation to semantic analyses of tense, partial information and vagueness; two chapters on methods for creating ordered structures in relation to intervals, events, and the semantics of change; two chapters on lattices and Boolean algebras in relation to types for noun phrases and verbs, and the semantics of plurals and mass nouns. For upper-level undergraduate students and graduate students in semantics: theoretical linguists, logicians, philosophers of language, computer scientists interested in natural language semantics. (shrink)

This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horn's masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the book's original publication.