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A Structuralist Theory of Logic
Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics.
Anachronisms in the History of Mathematics
Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.
Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language
This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.
Doctors, Politics and Society: Historical Essays
The great British reformer Jeremy Bentham wrote that 'the art of legislation is but the art of healing practised upon a large scale'. He added that 'It is the common endeavour of both to relieve men from the miseries of life. But the physician relieves them one by one: the legislator by millions at a time'. Bentham raised the question of the interplay of medicine with politics. It forms an important topic with powerful contemporary overtones. This volume, containing eleven essays plus a lengthy introduction, seeks to explore it historically. It takes a long perspective, covering the last two centuries and also an international viewpoint, examining Britain in detail but also containing contributions dealing with the United States, Germany, Russia and France.
Ernst Mach’s World Elements
By exploring Mach's views on science as well as philosophy, this book attempts to wrest him free from his customary association with logical positivism and to reinterpret him on his own terms as a natural philosopher and naturalist about human knowledge. Physicists, psychologists, philosophers of science, historians of twentieth-century thought and culture, and educators will find this volume a valuable help in interpreting Mach's ideas.
Philosophical and Foundational Issues in Measurement Theory
Measurement theory has only recently become recognized as a legitimate, specialized field of inquiry. This text covers a wide range of issues of central concern to contemporary measurement theorists, and a broad range of philosophical perspectives are represented. The formalist, representationalist approach defines measurement as the assignment of numbers to entities and events to represent their properties and relations. It also states that measurement theory is supposed to analyze the concept of a scale of measurement, describe various types of scales and their uses, and formulate the conditions required for the existence of scales of various types. Since this approach dominates contemporary measurement theory, the volume begins with essays by some of its leading architects. In order to allow for diverse points of view, the book also includes articles that attempt to broaden this approach, and several that even criticize the approach.
Sense, Reference, and Philosophy
Sense, Reference, and Philosophy develops the far-reaching consequences for philosophy of adopting non-Fregean intensionalism, showing that long-standing problems in the philosophy of language, and indeed other areas, that appeared intractable can now be solved. Katz proceeds to examine some of those problems in this new light, including the problem of names, natural kind terms, the Liar Paradox, the distinction between logical and extra-logical vocabulary, and the Raven paradox. In each case, a non-Fregean intentionalism provides a philosophically more satisfying solution.
Laws and Explanations; Theories and Modal Possibilities
The book has two parts: In the first, after a review of some seminal classical accounts of laws and explanations, a new account is proposed for distinguishing between laws and accidental generalizations (LAG). Among the new consequences of this proposal it is proved that any explanation of a contingent generalization shows that the generalization is not accidental. The second part involves physical theories, their modality, and their explanatory power. In particular, it is shown that (1) Each theory has a theoretical implication structure associated with it, such that there are new physical modal operators on these structures and also special modal entities that are in these structures. A sp...
Knowledge and Reference in Empirical Science
Knowledge and Reference in Empirical Science is a fascinating study of the bounds between science and language: in what sense, and of what, does science provide knowledge? Is science an instrument only distantly related to what's real? Can the language of science be used to adequately describe the truth? In this book, Jody Azziouni investigates the technology of science - the actual forging and exploiting of causal links, between ourselves and what we endeavor to know and understand.
