One True Logic

Author : Owen Griffiths,A. C. Paseau
Publisher : Oxford University Press
Page : 336 pages
File Size : 54,6 Mb
Release : 2022-05-26
Category : Philosophy
ISBN : 9780192565242

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One True Logic by Owen Griffiths,A. C. Paseau Pdf

Logical monism is the claim that there is a single correct logic, the 'one true logic' of our title. The view has evident appeal, as it reflects assumptions made in ordinary reasoning as well as in mathematics, the sciences, and the law. In all these spheres, we tend to believe that there are determinate facts about the validity of arguments. Despite its evident appeal, however, logical monism must meet two challenges. The first is the challenge from logical pluralism, according to which there is more than one correct logic. The second challenge is to determine which form of logical monism is the correct one. One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. In particular, it generalises the Tarski-Sher criterion of logicality, provides a novel defence of this generalisation, offers a clear new argument for the logicality of infinitary logic and replies to recent pluralist arguments.

Author : JC Beall,Greg Restall
Publisher : Clarendon Press
Page : 152 pages
File Size : 42,6 Mb
Release : 2005-11-24
Category : Philosophy
ISBN : 9780191537141

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Logical Pluralism by JC Beall,Greg Restall Pdf

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them. In particular, they argue that broadly classical, intuitionistic, and relevant accounts of deductive logic are genuine logical consequence relations; we should not search for one true logic, since there are many. Their conclusions have profound implications for many linguists as well as for philosophers.

Author : Bernd Steinbach,Christian Posthoff
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 44,9 Mb
Release : 2009-01-29
Category : Computers
ISBN : 9781402095955

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Logic Functions and Equations by Bernd Steinbach,Christian Posthoff Pdf

Tsutomu Sasao – Kyushu Institute of Technology, Japan The material covered in this book is quite unique especially for p- ple who are reading English, since such material is quite hard to ?nd in the U.S. literature. German and Russian people have independently developed their theories, but such work is not well known in the U.S. societies. On the other hand, the theories developed in the U.S. are not conveyed to the other places. Thus, the same theory is re-invented or re-discovered in various places. For example, the switching theory was developed independently in the U.S., Europe, and Japan, almost at the same time [4, 18, 19]. Thus, the same notions are represented by di?- ent terminologies. For example, the Shegalkin polynomial is often called complement-free ring-sum, Reed-Muller expression [10], or Positive - larityReed-Mullerexpression [19].Anyway,itisquitedesirablethatsuch a unique book like this is written in English, and many people can read it without any di?culties. The authors have developed a logic system called XBOOLE.Itp- forms logical operations on the given functions. With XBOOLE, the readers can solve the problems given in the book. Many examples and complete solutions to the problems are shown, so the readers can study at home. I believe that the book containing many exercises and their solutions [9] is quite useful not only for the students, but also the p- fessors.

Author : Edwin Mares
Publisher : Cambridge University Press
Page : 282 pages
File Size : 40,5 Mb
Release : 2024-01-31
Category : Mathematics
ISBN : 9781009375290

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The Logic of Entailment and its History by Edwin Mares Pdf

What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

Author : Stewart Shapiro
Publisher : Unknown
Page : 235 pages
File Size : 44,9 Mb
Release : 2014
Category : Logic
ISBN : 9780199696529

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Varieties of Logic by Stewart Shapiro Pdf

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like "valid" and "logical consequence" are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the "debates" in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

Author : Theodore Sider
Publisher : Oxford University Press
Page : 305 pages
File Size : 55,5 Mb
Release : 2010-01-07
Category : Philosophy
ISBN : 9780192658814

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Logic for Philosophy by Theodore Sider Pdf

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 290 pages
File Size : 52,5 Mb
Release : 1997-08-07
Category : Mathematics
ISBN : 9780195094527

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Philosophy of Mathematics by Stewart Shapiro Pdf

Shapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Author : Raymond R. Smullyan
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642867187

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First-Order Logic by Raymond R. Smullyan Pdf

Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).

Author : Lizzie Susan Stebbing
Publisher : Routledge
Page : 372 pages
File Size : 55,5 Mb
Release : 2018-05-08
Category : Philosophy
ISBN : 9781351349079

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Revival: A Modern Introduction to Logic (1950) by Lizzie Susan Stebbing Pdf

As the author of this volume states, "the science of logic does not stand still." This book was intended to cover the advances made in the study of logic in the first half of the nineteenth century, during which time the author felt there to have been greater advances made than in the whole of the preceding period from the time of Aristotle. Advances which, in her eyes, were not present in contemporary text books. As such, this book offers a valuable insight into the progress of the subject, tracing this frenetic period in its development with a first-hand awareness of its documentary value.

Author : Neil Tennant
Publisher : Oxford University Press
Page : 360 pages
File Size : 44,8 Mb
Release : 2017-09-01
Category : Philosophy
ISBN : 9780191083655

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Core Logic by Neil Tennant Pdf

Neil Tennant presents an original logical system with unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. Core Logic, which lies deep inside Classical Logic, best formalizes rigorous mathematical reasoning. It captures constructive relevant reasoning. And the classical extension of Core Logic handles non-constructive reasoning. These core systems fix all the mistakes that make standard systems harbor counterintuitive irrelevancies. Conclusions reached by means of core proof are relevant to the premises used. These are the first systems that ensure both relevance and adequacy for the formalization of all mathematical and scientific reasoning. They are also the first systems to ensure that one can make deductive progress with potential logical strengthening by chaining proofs together: one will prove, if not the conclusion sought, then (even better!) the inconsistency of one's accumulated premises. So Core Logic provides transitivity of deduction with potential epistemic gain. Because of its clarity about the true internal structure of proofs, Core Logic affords advantages also for the automation of deduction and our appreciation of the paradoxes.

Author : Richard Whately
Publisher : Unknown
Page : 304 pages
File Size : 43,9 Mb
Release : 1857
Category : Logic
ISBN : UCAL:B3942517

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Elements of Logic by Richard Whately Pdf

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 54,8 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : C. Bohnet
Publisher : Springer
Page : 270 pages
File Size : 50,8 Mb
Release : 2015-06-11
Category : Mathematics
ISBN : 9781137521750

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Logic and the Limits of Philosophy in Kant and Hegel by C. Bohnet Pdf

This text examines the boundary between logic and philosophy in Kant and Hegel. Through a detailed analysis of 'quantity', it highlights the different ways Kant and Hegel handle this boundary. Kant is consistent in maintaining this boundary, but Hegel erases it and in the process transforms both logic and philosophy.

Author : Anil Nerode,Richard A. Shore
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781468402117

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Logic for Applications by Anil Nerode,Richard A. Shore Pdf

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

Author : Henry Aldrich
Publisher : Unknown
Page : 82 pages
File Size : 52,8 Mb
Release : 1843
Category : Electronic
ISBN : BL:A0018096549

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The Rudiments of the Art of Logic; literally translated ... with explanatory notes by Henry Aldrich Pdf