Logic Plural Word
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Plural Logic
Author: Alex Oliver
language: en
Publisher: Oxford University Press
Release Date: 2016-11-04
Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). Current logic is singularist: its terms 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. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The authors' approach is an attractive blend of no-nonsense argumentative directness and open-minded liberalism, and they convey the exciting and unexpected richness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book. This second edition includes a greatly expanded treatment of the paradigm empty term zilch, a much strengthened treatment of Cantorian set theory, and a new chapter on higher-level plural logic.
Words without Objects
A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of two main targets of Henry Laycock's book; for it is seriously incomplete. The picture, he argues, leaves no space for stuff like air and water. With discrete objects, we may always ask 'how many?', but with stuff the question has to be 'how much?' Within philosophy, stuff of certain basic kinds is central to the ancient pre-Socratic world-view; but it also constitutes the field of modern chemistry and is a major factor in ecology. Philosophers these days, in general, are unlikely to deny that stuff exists. But they are very likely to deny that it is ('ultimately') to be contrasted with things, and it is on this account that logic and semantics figure largely in the framework of the book. Elementary logic is a logic which takes values for its variables; and these values are precisely distinct individuals or things. Existence is then symbolized in just such terms; and this, it is proposed, creates a pressure for 'reducing' stuff to things. Non-singular expressions, which include words for stuff, 'mass' nouns, and also plural nouns, are 'explicated' as semantically singular. Here then is the second target of the book. The posit that both mass and plural nouns name special categories of objects (set-theoretical 'collections' of objects in the one case, mereological 'parcels' or 'portions' of stuff in the other) represents, so Laycock urges, the imposition of an alien logic upon both the many and the much.
Handbook of Cognitive Linguistics and Second Language Acquisition
This cutting-edge volume describes the implications of Cognitive Linguistics for the study of second language acquisition (SLA). The first two sections identify theoretical and empirical strands of Cognitive Linguistics, presenting them as a coherent whole. The third section discusses the relevance of Cognitive Linguistics to SLA and defines a research agenda linking these fields with implications for language instruction. Its comprehensive range and tutorial-style chapters make this handbook a valuable resource for students and researchers alike.