The philosophy of logic

Postprin

Logic and Philosophy of Religion

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

Introduction

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book

To Teach Modal Logic: An Opinionated Survey

I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy, which do not stem mainly from mathematical issues, but which is motivated by central problems of philosophy and language. I will point out some themes to start elaborating a guide for a more comprehensive approach to teach modal logic, and consider the contributions of dual-process theories in cognitive science, in order to explore a pedagogical framework for the proposed point of view.Comment: Proceedings of the Fourth International Conference on Tools for Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M. Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat, Fran\c{c}ois Schwarzentrube

Causal Theory of Reference of Saul Kripke

Since the 1960s, Kripke has been a central figure in several fields related to mathematical logic, language philosophy, mathematical philosophy, metaphysics, epistemology and set theory. He had influential and original contributions to logic, especially modal logic, and analytical philosophy, with a semantics of modal logic involving possible worlds, now called Kripke semantics. In Naming and Necessity, Kripke proposed a causal theory of reference, according to which a name refers to an object by virtue of a causal connection with the object, mediated by the communities of speakers. DOI: 10.13140/RG.2.2.26557.2096

Greek and Roman Logic

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

The Logic of Time: from Aristotle to Computer Science

Charla tipo conferencia-seminario dada para alumnos de un másterThis short course will explore that continuous thread which connects the discussion about time in philosophy with the modern use of temporal logic in computer science. It will go through the history of temporal logic to show how ideas developed by ancient and medieval philosophy have been rediscovered in modern times and applied to solve relevant problems in computer science. Part 1: An historical perspective on temporal logic • Synthesis: the nature of time is a central issue of classical and medieval phylosophy • Downfall: in the Renaissance the subject loses interest and is removed from the philo- sophical discussion • Rediscovery: in the 19th and 20th centory temporal logic become a central issue again Part 2: Time in Computer Science • Algorithms, states and computations • Imperative programs and Reactive programs • Temporal Logic for Computer Science: CTL and LTL • The satisfiability problem • The model checking problemUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Teaching Peirce to Undergraduates

Fourteen philosophers share their experience teaching Peirce to undergraduates in a variety of settings and a variety of courses. The latter include introductory philosophy courses as well as upper-level courses in American philosophy, philosophy of religion, logic, philosophy of science, medieval philosophy, semiotics, metaphysics, etc., and even an upper-level course devoted entirely to Peirce. The project originates in a session devoted to teaching Peirce held at the 2007 annual meeting of the Society for the Advancement of American Philosophy. The session, organized by James Campbell and Richard Hart, was co-sponsored by the American Association of Philosophy Teachers

Language Idling and Language in Use Wittgenstein on Following Rules

This paper has a simple goal: it aims to present the difference between static logic and dynamic grammar. At the same time I will stress another difference which traverses logic and grammar: the difference between language idling and language in use. There is a development from static logic to dynamic grammar in Wittgenstein"s philosophy from early to late, whereas the difference between language idling and language in use pervades the whole oeuvre. Therefore I shall distinguish between four different conditions pertaining to the attempt to render the relations that hold language together. We find in early Wittgenstein "idle static logic" and "static logic in use," and in late Wittgenstein "idle dynamic grammar" and "dynamic grammar in use." This four-fold distinction serves to emphasize that the crucial shift to "use," which is usually claimed to be a feature of the Philosophical Investigations, already takes place in the Tractatus. A negligence of this "double shift" from logic to grammar and from idle language to language in use brought about a vast amount of misapprehensions of Wittgenstein"s philosophy, especially of the account of rule following