A comprehensive introduction to formal logic, Logic and Philosophy: A Modern Introduction is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Abundant, carefully crafted exercise sets accompanied by a clear, engaging exposition build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, identity, relations, set theory, modal logic, and Aristotelian logic. And as its title suggests, Logic and Philosophy is devoted (...) not only to logic but also to the philosophical debates that led to the development of the field. Much new material has been added for the 13th edition. An introduction to set theory and its relationship to logic and mathematics, including philosophical issues, is now part of Chapter 13. Chapter 15 is an introduction to modal logic and Kripke semantics, concluding with a discussion of philosophical problems with any logical accommodation of modalities. Instructors who do not wish to present proof methods will find chapters on truth trees for both sentential and first-order logic, and a presentation of trees for modal logic. Special features of this text include presentations of the history of logic, alternatives to traditional methods of conditional and indirect proof, and a discussion of semantic problems with universal and existential instantiations. Throughout, the authors are sensitive to philosophical issues that arise from the relationship between ordinary language, symbolic logic, and justifications for the syntax and semantics of the various symbolic languages. Discussions range from the justification of the truth table for the sentential rendering of if... then statements to semantic and syntactic paradoxes, including some troubling paradoxes that arise in ordinary language (e.g., the so-called hangman or surprise quiz paradox). Logic and Philosophy includes ample material for a one-semester or two-semester course and provides a thorough preparation for more advanced logic courses. (shrink)

This paper introduces the special issue on Logic and Philosophy of Religion of the journal Sophia: International Journal of Philosophy and Traditions (Springer). The issue contains the following articles: Logic and Philosophy of Religion, by Ricardo Sousa Silvestre and Jean-Yvez Béziau; The End of Eternity, by Jamie Carlin Watson; The Vagueness of the Muse—The Logic of Peirce’s Humble Argument for the Reality of God, by Cassiano Terra Rodrigues; Misunderstanding the Talk(s) of the Divine: Theodicy (...) in the Wittgensteinian Tradition, by Ondřej Beran; On the Concept of Theodicy, by Ricardo Sousa Silvestre; The Logical Problem of the Trinity and the Strong Theory of Relative Identity, by Daniel Molto; Thomas Aquinas on Logic, Being, and Power, and Contemporary Problems for Divine Omnipotence, by Errin D. Clark. -/- . (shrink)

The interface of logic and philosophy is diverse, and has always been so. Understanding the interplay raises issues on which some philosophers have strong a priori views. My own preference as a working logician is to proceed by actual history of ideas, something still largely to be written for modern logic. I shall present a few lines connecting logic and philosophy around the theme of implication and consequence, and show how rich the agenda is as (...) it keeps evolving with contributions from many disciplines. This is a light survey paper, but I supply references for readers who want to see more of the nitty-gritty details. (shrink)

In Part 1 the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such (...) as truth, time, processes, knowledge and belief, obligation and permission. Accessible, authoritative, and assured, Modal Logics and Philosophy requires no more background than the completion of a standard introductory logic course. It will be welcomed not only by students looking for a bridge between introductory logic texts and the high-level technical literature but as a guide to, and exploration of, work at the forefront of logic and philosophy. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, (...) "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of (...) class='Hi'>logic contains many interesting thoughts that have gone widely unnoticed. (shrink)

Logic and philosophy of logic have increasingly become areas of research and great interest in Latin America and Spain, where significant work has been done and continues to be done in both of these fields. The goal of this volume is to draw attention to this work through a collection of original and unpublished papers by specialists from Latin America and Spain. Some of the papers are of importance for set-theory and model theory. They cover topics such (...) as the foundations of paraconsistency, the use of paraconsistent logic as a basis for set-theory, and the methodological aspects in both the justification of new axioms in set theory and the formalization of pre-theoretic notions. Other papers are related to epistemic logic. They deal with the issues of abduction and the choice of the simplest hypothesis, the definition of group probability, and the nature of explanation and understanding in such logic. There are also papers on logical paradoxes, the semantics of names (including fictional names), and the nature of relations. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the (...) work going on in our field—a book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

The problem of the relationship between formal logic and philosophy, which arose when formal logic arose, continues to concern both Soviet and foreign philosophers and logicians. Interest in this problem is traceable to a number of factors, among which, it should be noted at the outset, is the appearance of dialectical, logic. With the emergence of dialectical logic, the question of the relationship of formal logic to philosophy is posed anew. No matter how (...) we approach the question of the subject matter of dialectical logic, there is no doubt of the fact that, being logic, it is concerned with the investigation of philosophical problems. It follows that logic is at the same time philosophy or, at least, a portion of philosophy. (shrink)

Logic and philosophy of logic have increasingly become areas of research and great interest in Latin America and Spain, where significant work has been done and continues to be done in both of these fields. The goal of this volume is to draw attention to this work through a collection of original and unpublished papers by specialists from Latin America and Spain. Some of the papers are of importance for set-theory and model theory. They cover topics such (...) as the foundations of paraconsistency, the use of paraconsistent logic as a basis for set-theory, and the methodological aspects in both the justification of new axioms in set theory and the formalization of pre-theoretic notions. Other papers are related to epistemic logic. They deal with the issues of abduction and the choice of the simplest hypothesis, the definition of group probability, and the nature of explanation and understanding in such logic. There are also papers on logical paradoxes, the semantics of names, and the nature of relations. Max A. Freund is Professor of Logic and Philosophy at the University of Costa Rica and the National University of Costa Rica. He is co-author of the book Modal Logic its syntax and semantics, as well as the author of Judicial Logic, and of a forthcoming book The Logic of Sortals. Max Fernandez de Castro is Professor of Logic and Philosophy at the Autonomous Metropolitan University of Mexico. He is the author of the book Quine y la Ontologíaa and co-author of the books Lógica Matemática I: lógica proposicional, intuicionista y modal, Lógica Matemática II: clásica, intuicionista y modal, Teoría de Conjuntos, Lógica y Temas Afines I. Marco Ruffino is Professor of Philosophy at the University of Campinas and the editor of Manuscrito, the Brazilian international journal for Analytic Philosophy. He has many publications, in important philosophical journals, in the philosophy of language, of logic, and of mathematics; in the history of analytic philosophy, and on Frege and Wittgenstein. (shrink)

The Entretiens of the Institut International de Philosophie for 1978 were held in connection with the World Congress of Philosophy in Dusseldorf, from August 27 to September 1. The theme of the Entretiens was Logic and Philosophy. The undersigned, then President of LI.P., was responsible for the planning of the programme. The programme was designed to consist of four sections with the headings Classical and Intuitionist Logic, Modal Logic and its Applications, Inductive Logic and (...) its Applications, and Logic and Epistemology. The aim was also to convey to philosophers who are not experts in logic an informative and representative impression of some of the main sectors of the vast and rapidly expanding field of philosophical logic. At the same time it was thought that this impression should not be conveyed in the form of a series of survey papers but through presentations and discussions of specific topics falling under the main headings men tioned above. For each section a rapporteur was nominated to read a paper and an interlocuteur to comment on it. The programme chairman is grateful that he was able to engage a representative selection of front rank philosophi cal logicians to perform the various tasks. The papers and the comments are printed in this volume in the order in which they appeared in the Programme of the Entretiens. (shrink)

The new edition of this widely used and respected textbook includes three new chapters on conditional logic. Other chapters have been revised and updated, making the second edition a fully comprehensive introduction to modal logics and their application. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, Modal Logics and Philosophy focuses on showing how useful modal logic can be as a tool for formal philosophical analysis. In Part 1, the (...) reader is introduced to some standard systems of modal logic and provided with a series of exercises that encourage proficiency in manipulating these logics. Girle emphasizes possible world semantics for modal logics and its formal method, Jeffrey-style truth-trees, in which standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, and obligation and permission. (shrink)

Book Information Modal Logic and Philosophy. Modal Logic and Philosophy Roderic Girle Teddington Acumen 2000 198 Hardback 40 Paperback 16.95 By Roderic Girle. Acumen. Teddington. Pp. 198. Hardback: 40; Paperback: 16.95.

In the Western philosophical tradition logical investigation and philosophical advance have been inextricably linked, each having stimulated and shaped the other. In Logic and Philosophy William H. Brenner examines a broad range of logical concepts and methods as they relate to the larger context of philosophical investigation and thus bring to light the philosophical depth of logic and its relevance to philosophy in general.

This chapter begins with a discussion of humanist criticisms of scholastic logic. It then discusses the evolution of the scholastic tradition and the influence of Renaissance Aristotelianism, Descartes and his influence, the Port-Royal Logic, the emergence of a logic of cognitive faculties, logic and mathematics in the late 17th century, Gottfried Wilhelm Leibniz's role in the history of formal logic, and Kant's influence on logic.

We take into account two areas of the logical research of the Lvov-Warsaw School. First, we consider a new approach to research in the history of logic introduced and practiced by Łukasiewicz and some of his followers. In this style of doing history of logic, the knowledge of original philosophical and logical texts was combined with competence in modern logic. This method resulted in many important discoveries both in history and in logic and philosophy. At (...) the same time, we pay attention to contemporary historical research devoted to the logic created by the School itself. In this context, we present an overview of the six papers included in the special issue ‘Logic and its History in the Lvov-Warsaw School’. These papers were presented at an international symposium, ‘History in/of the Lvov-Warsaw School’, held in October 2022 in Warsaw, and they cover various aspects of historical-logical and logical achievements of the School. They concern topics from history of ancient logic, history of modern proof theory, and the issues of applying logic to philosophy and theology in the same way as the one implemented at the Lvov-Warsaw School. (shrink)

There is at this point no shortage of testimonials regarding the practice of philosophy for children. In addition, there have been a number of studies which give further support to the claim that philosophy for children is a valuable classroom practice. The idea that pre-college instruction in philosophy is beneficial is no longer in doubt, nor is there a significant lack of materials for use in philosophy for children programs. From Lewis Carroll to Matthew Lipman authors (...) constructed texts that go far in engaging children's philosophical inclinations. If there is any weakness in the practice of philosophy for children it is usually found in the individual classroom. (shrink)

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the title La géométrie dans le monde sensible in 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of (...) equivalence between theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (shrink)

Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their (...) reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one. (shrink)

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the titleLa géométrie dans le monde sensiblein 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of equivalence between (...) theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (shrink)

As the title suggests, this is a book devoted not merely to logic; students will also examine the philosophical debates that led to the development of the field.

This collection of 38 papers gives a cross-section of ongoing research in philosophy of science and philosophical logic. The papers, written by active researchers in the field and published here for the first time, are drawn from around 650 papers that were contributed to the 9th International Congress of Logic, Methodology and Philosophy of Science in Uppsala, Sweden, 1991. Some of the speakers whose contributions attracted special interest were invited to contribute their papers to this volume. (...) A few papers appear here more or less as they were presented at the Congress, whereas others are expansions or elaborations of the talks given. There is one section with five papers on philosophical logic. The other papers deal with many different aspects of philosophy of science, including general methodological questions, problems of probability, induction and decision theory, and ethics of science and technology, as well as foundational problems about particular sciences. Five special sections are concerned with logic, mathematics and computer science, the physical sciences, the biological sciences, cognitive science, and linguistics, respectively. Finally, there is one section on the history of logic, methodology and philosophy of science. The book will be of interest to philosophers of science and logicians, as well as to all researchers interested in the foundations of their disciplines. (shrink)

This anthology examines Love's Labours Lost from a variety of perspectives and through a wide range of materials. Selections discuss the play in terms of historical context, dating, and sources; character analysis; comic elements and verbal conceits; evidence of authorship; performance analysis; and feminist interpretations. Alongside theater reviews, production photographs, and critical commentary, the volume also includes essays written by practicing theater artists who have worked on the play. An index by name, literary work, and concept rounds out this valuable (...) resource. (shrink)

An analysis of the sources of Wittgenstein’s picture theory — which include not only his moment of insight on reading a magazine story about the use of models in a traffic court, but also the work of Russell, Hertz, and Boltzmann — provides the basis for an exploration of Wittgenstein’s articulation of a pictorial conception of representation in his wartime notebooks and its crystallization in the Tractatus. A discussion of Wittgenstein’s later criticism of the picture theory and his notion of (...) a “philosophical picture” illustrates the fundamental reversal in his transition to his later conception of philosophy: instead of taking literal pictures as a guide to the nature of meaning, he came to regard philosophical theories as akin to expressing an aesthetic preference for a certain style of representation. Wittgenstein’s treatment of factual language in the picture theory is related to his Tractarian approach to logical form, and the role of the show/say distinction in his early conception of logic and language. Particular attention is given to the difficulties generated by the idea that the conditions for the possibility of a given domain of discourse cannot be described in language, but must be shown by the form of words in question. (shrink)

Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a (...) variety of other responses and is shown to differ from all of them. (shrink)

The era in which Abū Naṣr al-Fārābī emerged as a canonical scientist significantly contributed to his education and shaped his scientific worldview. The formation of al-Farabi’s spiritual worldview and his ideas is directly associated with embracing the ancient philosophical tradition, more precisely, Aristotle’s philosophy and logic. The focus of the article is alFarabi’s analysis of Aristotle’s principles in the study of logic and their further development. Al-Farabi’s worldwide reputation as the Second Teacher after Aristotle, the First Teacher, (...) in the East is directly rooted in his mastery and advancement of the science of logic. In simple terms, the philosopher states that logic leads a person to a straight path to being capable of radically discerning between good and bad, truth and lies, and honesty and deceit. This, in turn, steers humanity away from succumbing to mistakes or getting into trouble. Al-Farabi constructs a comprehensive scientific analysis of the socio-cultural foundations of Aristotle’s doctrine of logic and the ability to adapt it in his unique way to society. The study of the theoretical basis of al-Farabi’s teachings on logic and its significance involves employing hermeneutic, comparative, and stylistic methods in the research of the texts. (shrink)

I argue that there is tension in Wittgenstein’s position on trivialities (i.e. tautologies and contradictions) in the Tractatus, as it contains the following claims: (A) sentences are pictures; (B) trivialties are not pictures; (C) trivialities are sentences. A and B follow from the “picture theory” of language which Wittgenstein proposes, while C contradicts it. I discuss a way to resolve this tension in light of Logicality, a hypothesis recently developed in linguistic research. Logicality states that trivialities are excluded by the (...) grammar, and that under the right analysis sentences which look trivial are in fact contingent. The tools necessary to support Logicality, I submit, were not available to Wittgenstein at the time, which explains his commitment to C. I end the paper by commenting on some points of contact between analytic philosophy and the generative enterprise in linguistics which are brought into relief by the discussion. (shrink)

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize (...) truth-value assignments to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework. (shrink)

Appropriate for upper-level undergraduates and graduate students, this volume includes a variety of Boole's writings on logical subjects, along with papers on related questions of probability. His earlier work, The Mathematical Analysis of Logic, appears here, together with an account of the notes Boole made on his own interleaved copy. In addition, the appendices contain relevant papers by contemporaries with whom the author engaged in discussion, making it possible to trace interesting developments in Boolean reasoning-particularly in regard to his (...) extended treatment of the relation between formal logic and the theory of probabilities. 1952 ed. (shrink)