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Author: Colin R. Caret Publisher: Mind Association Occasional ISBN: 0198715692 Category : Mathematics Languages : en Pages : 368
Book Description
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
Author: Colin R. Caret Publisher: Mind Association Occasional ISBN: 0198715692 Category : Mathematics Languages : en Pages : 368
Book Description
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
Author: Matthew W. McKeon Publisher: Peter Lang ISBN: 9781433106453 Category : Philosophy Languages : en Pages : 180
Book Description
The Concept of Logical Consequence is a critical evaluation of the model-theoretic and proof-theoretic characterizations of logical consequence that proceeds from Alfred Tarski's characterization of the informal concept of logical consequence. This study evaluates and expands upon ideas set forth in Tarski's 1936 article on logical consequence, and appeals to his 1935 article on truth. Classical logic, as well as extensions and deviations are considered. Issues in the philosophy of logic such as the nature of logical constants, the philosophical significance of completeness, and the metaphysical and epistemological implications of logic are discussed in the context of the examination of the concept of logical consequence.
Author: James Allard Publisher: Cambridge University Press ISBN: 9781139442459 Category : Philosophy Languages : en Pages : 270
Book Description
This book is a major contribution to the study of the philosopher F. H. Bradley, the most influential member of the nineteenth-century school of British Idealists. It offers a sustained interpretation of Bradley's Principles of Logic, explaining the problem of how it is possible for inferences to be both valid and yet have conclusions that contain new information. The author then describes how this solution provides a basis for Bradley's metaphysical view that reality is one interconnected experience and how this gives rise to a new problem of truth.
Author: Luis M Augusto Publisher: ISBN: 9781848902367 Category : Languages : en Pages : 228
Book Description
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications. Both deductive and non-deductive consequence are discussed. The starting point is classical deductive consequence: classical logic is the reference system, and the non-classical deductive systems are seen as extensions, deviations, or variations thereof. The discussion of non-classical deductive consequence focuses on many-valued, intuitionistic, modal, paraconsistent, and substructural logical consequences. The topic of non-deductive consequence is elaborated on from the viewpoints of abductive, inductive, and probabilistic logics. All in all, the major contemporary (classes of) logical systems are here discussed. The approach is mathematical in essence, and the mathematical background, mainly founded on order relations, is treated thoroughly and in an accessible way for the non-mathematician.
Author: Stewart Shapiro Publisher: Clarendon Press ISBN: 0191524018 Category : Mathematics Languages : en Pages : 302
Book Description
The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.
Author: Antoni Ligeza Publisher: Springer ISBN: 3540324461 Category : Technology & Engineering Languages : en Pages : 312
Book Description
Thinking in terms of facts and rules is perhaps one of the most common ways of approaching problem de?nition and problem solving both in everyday life and under more formal circumstances. The best known set of rules, the Ten Commandments have been accompanying us since the times of Moses; the Decalogue proved to be simple but powerful, concise and universal. It is logically consistent and complete. There are also many other attempts to impose rule-based regulations in almost all areas of life, including professional work, education, medical services, taxes, etc. Some most typical examples may include various codes (e.g. legal or tra?c code), regulations (especially military ones), and many systems of customary or informal rules. The universal nature of rule-based formulation of behavior or inference principles follows from the concept of rules being a simple and intuitive yet powerful concept of very high expressive power. Moreover, rules as such encode in fact functional aspects of behavior and can be used for modeling numerous phenomena.
Author: JC Beall Publisher: Oxford University Press ISBN: 0199288402 Category : Philosophy Languages : en Pages : 152
Book Description
Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.
Author: Maria van der Schaar Publisher: Springer Science & Business Media ISBN: 9400751370 Category : Philosophy Languages : en Pages : 172
Book Description
This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic.
Author: Colin R. Caret
Author: Colin R. Caret
Author: John Etchemendy
Author: Matthew W. McKeon
Author: James Allard
Author: Luis M Augusto
Author: Stewart Shapiro
Author: Antoni Ligeza
Author: Rudolf Carnap
Author: JC Beall
Author: Maria van der Schaar