Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

Sorensen here offers a unified solution to a large family of philosophical puzzles and paradoxes through a study of "blindspots": consistent propositions that cannot be rationally accepted by certain individuals even though they might by true.

If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

Roy Sorenson offers a unique exploration of an ancient problem: vagueness. Did Buddha become a fat man in one second? Is there a tallest short giraffe? According to Sorenson's epistemicist approach, the answers are yes! Although vagueness abounds in the way the world is divided, Sorenson argues that the divisions are sharp; yet we often do not know where they are. Written in Sorenson'e usual inventive and amusing style, this book offers original insight on language and logic, the way world (...) is, and our understanding of it. (shrink)

There was once a land inhabited by many tribes. For a long time, each of the tribes was isolated from all the rest. When they finally made contact, all were amazed to discover how similar they were to one another. All of them spoke languages with exactly the same syntax— that of English. Nevertheless, it soon became clear that there were systematic behavioral differences among the tribes. These differences were reflected in the tribespeoples’ reactions to..

Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms -- such as 'tall', 'red', 'bald', and 'tadpole' -- have borderline cases ; and they lack well-defined extensions. The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate.This anthology collects for the first time the most important papers in the field. After a substantial introduction that surveys (...) the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent the best recent work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity. (shrink)

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

The argument proceeds by exploiting the gradually decreasing vagueness of a certain sequence of predicates. the vagueness of 'vague' is then used to show that the thesis that all vague predicates are incoherent is self-defeating. a second casualty is the view that the probems of vagueness can be avoided by restricting the scope of logic to nonvague predicates.

There was once a land inhabited by many tribes. For a long time, each of the tribes was isolated from all the rest. When they finally made contact, all were amazed to discover how similar they were to one another. All of them spoke languages with exactly the same syntax— that of English. Nevertheless, it soon became clear that there were systematic behavioral differences among the tribes. These differences were reflected in the tribespeoples’ reactions to..

Semantic indeterminacy is the ether of philosophy of language. It fills the interstices of our intentions and pervades accounts of presupposition, tense, fiction, translation, and especially, vagueness. Yet semantic indeterminacy is as impossible as ectoplasm. Indeed, more so! The demonstration need only borrow a few assumptions used elsewhere in widely accepted impossibility results. Since an impossibility is never a necessary condition for anything actual, semantic indeterminacy must be superfluous. Language is no more explained by semantic indeterminacy than calculus is explained (...) by (pre-Robinsonian) infinitesimals. (shrink)