A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

The present volume stems from a book-proposal made about two years ago to College Publications, London. The main idea was that of illustrating the interplay between the contemporary work in logic and the mainstream mathematics. The division of the volume in two sections - topics in 'logic' vs topics in 'computing' - is more or less conventional. Some contributions are focussed on historical and technical details meant to put in perspective the impact of the work of some outstanding mathematicians (...) and philosophers on the contemporary research in logic and computing science. Some other papers, also with a historical flavour, were supposed to evidentiate punctual methods of research and specific concepts or topics, as, e.g., decidability, computability, randomness, and computational or descriptive complexity. In general, the papers were intended as specific surveys of results. Other volumes - to be issued subsequently in the same series - will hopefully delineate aspects of the contemporary logic landscape that have not been illustrated here. The intended audience of the book includes graduate students in mathematical logic, foundations of matematics, and computing science, as well as philosophers, mathematicians, and, possibly, other scientists interested in the recent research on logic and computing. (shrink)

Computer Science and Artificial Intelligence will be the twenty-first century logic development of the main power source, and in the twenty-first century will largely determine the face of logic. At least in the early twenty-first century, logic will focus on the following topics: how to deal with common sense reasoning in the logic of Eph coordination, non-monotonic and fault tolerance factors? how to make robots with human intelligence and creativity, as established from the empirical evidence used to guide future action (...) in the induction of judgments can be wrong? how the knowledge representation and knowledge reasoning, in particular, is based on the existing knowledge base and between the cognitive subject knowledge and the reasoning? how contextual factors, combined with a variety of natural language understanding and reasoning, so that intelligent robots to employing natural language for successful communication with people? . . . . And so on. (shrink)

As used by professional logicians today, is the name of their chosen subject singular or plural, "logic" or "logics"? This is a special case of a more general question. For instance, an algebraist might write a book entitled "Algebra", which is about algebras. Though many mathematicians are not aware of it, logic today most decidedly has its plural aspect. Indeed, it always did. Classical logic, which mathematicians often tend to identify with the entirety of logic, was in place roughly (...) by the beginning of the twentieth century. Since then a wide range of so-called non-classical logics have been developed. But indeed, before the creation of classical logic, there were multiple versions of logic, some of them more-or-less formalized. The current growing interest in medieval and ancient European and Asian logics has brought much of this back to modern awareness. Perhaps a later volume in this series will look at the history from a contemporary viewpoint. But that is not our task here. This is the second volume in a series called Landscapes in Logic. The intention of the series is to present reports illustrating the interplay between contemporary work in logic and mainstream mathematics. Of course this is both vague and overly ambitious, and must result in heterogeneous collections. The first volume in the series, Contemporary Logic and Computing, appeared in 2020. The contents divided plausibly into topics from contemporary logic, and from contemporary computing. The present volume is more diverse, and includes articles about both classical and non-classical logics, sometimes from the semantic side and sometimes from the proof-theoretic side. Some articles are primarily technical, often algebraic, while others are more philosophical in nature. Many fit into multiple categories. This multiplicity should not be seen as a defect. The papers here do not just explore logics house by house, but say something about their general neighborhoods as well. (shrink)

In this paper I consider Hegel’s idea of logic in different passages of his work (in the Introduction to the Science of Logic, in the Vorbegriff of the Encyclopaedia Logic, in the Lectures on the History of Philosophy), and I compare it with some contemporary conceptions of logic. In my view, such a comparison is relevant in at least two senses. First, it makes possible to address the controversial question: «what kind of logic is Hegel’s logic?». Second, it allows (...) to locate Hegel’s view within contemporary debates, assessing its actuality. In this perspective, Hegel’s reflections reveal to be crucial in order to deal with some questions at the very core of contemporary debates in the philosophy of logic. (shrink)

There is a certain dominant tradition, school, ambiance or intellectual community in contemporary philosophy of science which can conveniently be labelled logical empiricism. Now a curious and (I believe) hitherto unremarked change occurred in the accepted methodology of logical empiricism shortly after the end of World War II. Before then accepted forms of argument for philosophical theses about the logic, analysis, or rational reconstruction of science fell into two main categories. Some arguments appealed to familiar or historically attestable facts (...) about the development of science, the declared aims of scientists, etc. in certain areas. Others appealed to criteria of generality, clarity, accuracy, consistency, simplicity, and similar considerations of a systematic nature in the construction of philosophical analyses. Appeals were rarely, if ever, made at that time to intuition. If an intuitive idea was mentioned at all, it was mentioned as something that might suggest a starting-point of enquiry but could not be relied upon, even presumptively, as the ground for a conclusion. But this situation changed markedly from the late '40's onwards. Many arguments came to be rested, quite explicitly, on the alleged intuitive acceptability of certain premisses. In the Carnapian school, for example, the guiding objective of an inductive logician seems no longer to be the rational reconstruction of scientific reasoning but rather the axiomatisation of his own intuitions by the most sophisticated methods available. (shrink)

This is a very rewarding topic when we consider the history of dialectical logic, although it may seem to be unrewarding if it is formal logic that is under discussion. We are familiar with Hegel's hypercritical writings on this subject, with his evaluation of the use of symbols in cognition as "empty play," and with his — to say the least — skeptical reaction to early attempts at the mathematization of logic. He characterized the construction of calculi as "reduction" of (...) logic to a mechanical level lower than that it had already attained. Leibniz's feat in the realm of "logic" was condemned by the great dialectician, and a subsequent experiment in the improvement of logic through mathematics, undertaken by a follower of Leibniz, Ploucquet, was described by Hegel as a transformation of the process of inference into an "utterly contentless" manipulation of sentences . The fact is, however, that Ploucquet anticipated Lambert and Hamilton in constructing a table of propositions in which not only subjects but predicates were quantified, thus opening the road to the future algebraization of logic. (shrink)

[This book offers] compilation of examples from TV, newspapers, magazines, advertisements, and our nation's political dialogue.

An introduction to informal logic, critical thinking and rhetoric utilizing actual public discourse .

Originally written in 1956 and revised in 1972, this book explores the work of many of the most important thinkers of the 20th century, including Ayer, ...

This logic book puts critical-thinking skills into a context that you'll remember and use throughout your life.

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention (...) that it can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his (...) understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

This collection of essays reexamines the origins of logical empiricism and offers fresh insights into its relationship to contemporary philosophy of science.

Descartes’ Rules for the direction of the mind presents us with a theory of knowledge in which imagination, considered as an “aid” for the intellect, plays a key role. This function of schematization, which strongly resembles key features of Proclus’ philosophy of mathematics, is in full accordance with Descartes’ mathematical practice in later works such as La Géométrie from 1637. Although due to its reliance on a form of geometric intuition, it may sound obsolete, I would like to show that (...) this has strong echoes in contemporary philosophy of mathematics, in particular in the trend of the so called “philosophy of mathematical practice”. Indeed Ken Manders’ study on the Euclidean practice, along with Reviel Netz’s historical studies on ancient Greek Geometry, indicate that mathematical imagination can play a central role in mathematical knowledge as bearing specific forms of inference. Moreover, this role can be formalized into sound logical systems. One question of general epistemology is thus to understand this mysterious role of the imagination in reasoning and to assess its relevance for other mathematical practices. Drawing from Edwin Hutchins’ study of “material anchors” in human reasoning, I would like to show that Descartes’ epistemology of mathematics may prove to be a helpful resource in the analysis of mathematical knowledge. (shrink)

Jaina philosophy provides a very distinctive account of logic, based on the theory of ?sevenfold predication?. This paper provides a modern formalisation of the logic, using the techniques of many-valued and modal logic. The formalisation is applied, in turn, to some of the more problematic aspects of Jaina philosophy, especially its relativism.

In Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy , edited by Admir Skodo, an array of historical and philosophical chapters decenter the idea of formal logic as the most accurate, timeless, and abstract description of all thought and reasoning.

"Philosophical logic" describes two distinct areas: the investigation of the fundamental concepts of logic, the formal investigation of alternatives and extensions to classical logic. The first is a philosophical discipline, concerned with notions like truth, propositions, necessity, logical consequence, vagueness, and reasoning. The second is a technical discipline, devoted to developing formal logical systems-modal logics, second-order logics, intuitionistic logics, relevance logics, logics of vagueness and conditionals-and proving things about them. Most texts in philosophical logic focus (...) on one of these areas, but in this book John MacFarlane treats them together in an integrated way, showing how philosophical considerations motivate the technical projects, and how the constraints revealed by the technical projects illuminate the philosophical issues. Topics covered include quantifiers, modal logic, indicative conditionals, model-theoretic and proof-theoretic characterizations of logical consequence, intuitionistic logic, fundamental logical disagreement, relevance logic, the relation of logic and reasoning, and vagueness. Each chapter is organized around suggested readings and includes exercises. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Written by a leading authority on logicism and logical form and a successful expositor and teacher Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter. (shrink)

Recanati takes for granted the conveyance conception of linguistic communica- tion, although it is not very clear exactly where he lies on the spectrum of possible variations. Even if we disavow all such conceptions of linguistic communication, there will be a place for semantic theory in articulating normative concepts such as logical consistency and logical validity. An approach to semantics focused on such normative concepts is illustrated using the example of ““It’’s raining””. It is argued that Recanati’’s conception of semantics (...) as involving the pragmatics of saturation and modulation cannot account for the logical properties of ““It’’s raining”. (shrink)

In a case study, the mechanism of decomposition of diazonium ions in solution is discussed; the reasonable mechanism brought forward in 1940 was not refuted until 1973, in spite of experimental results published in 1952 that were not consistent with the proposed mechanism. A new mechanistic hypothesis, mentioned in the literature in 1973, was in contradiction to the paradigm that nitrogen molecules do not react with organic reagents in solution. After a psychologically explainable crisis the new hypothesis was tested experimentally (...) and the paradigm mentioned was falsified for this case. In the analysis it is shown that Pop-perian logic was commingled with Kuhn’s cycle of normal science, crisis, and revolution, as well as with a psychological barrier. Joint investigations of modern problems by chemists and philosophers of science are encouraged because they may elucidate how progress in scientific discoveries takes place at the present time. (shrink)

This book is concerned with the connection between the formal structure of agency and the formal structure of genocide. The contributors employ philosophical approaches to explore the idea of genocidal violence as a structural element in the world. Do mechanisms or structures in nation-states produce types of national citizens that are more susceptible to genocidal projects? There are powerful arguments within philosophy that in order to be the subjects of our own lives, we must constitute ourselves specifically as national subjects (...) and organize ourselves into nation states. Additionally, there are other genocidal structures of human society that spill beyond historically limited episodes. The chapters in this volume address the significance--moral, ethical, political--of the fact that our very form of agency suggests or requires these structures. The contributors touch on topics including birthright citizenship, contemporary mass incarceration, anti-black racism, and late capitalism. Logics of Genocide will be of interest to scholars and advanced students working in philosophy, critical theory, genocide studies, Holocaust and Jewish studies, history, and anthropology. (shrink)

This is a review of A. Skodo (ed.) "Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy".

The aim of this paper will be to show how significant the logical theories of judgement which were worked out at the end of the nineteenth century have been for the ontological thought during the twentieth century. Against the classical - Aristotelian and Scholastic - analysis of predicative judgement, Franz Brentano on one hand and Gottlob Frege on the other hand have leveled two different criticisms, which then generated two radically divergent ontological paradigms. On one side, despite Brentano’s own nominalistic (...) stands, there was a tremendous extension of the general category of “object” as well as of the notion of “being” with, as a consequence, the exceptionnally luxuriant ontologies of Brentano’s heirs. On the other side, notwithstanding Frege’s own Platonistic affinities, there was a drastic deflation of the realm of objects to the benefit of the realm of concepts taken as classifying functions, and therefore a strong nominalistic trend among Frege’s heirs. The development of quantified modal logics at the middle of twentieth century however forced contemporary ontology to reconsider this simple alternative in order to give place to some hybrid entities such as individual concepts or other kinds of “intensional objects”. (shrink)

In theology, by W.L. Rowe.--Divine foreknowledge and human freedom, by A. Kenny.--Some puzzles concerning omnipotence, by G.I. Mavrodes.--The paradox of the stone, by C.W. Savage.--Creation ex nihilo, by J. Donnelly.--The miraculous, by R.F. Holland.--On miracles, by P.J. Dietl.--The tacit structure of religious knowing, by J.H. Gill.--On the observability of the self, by R.M. Chisholm.--Re-examining Kierkegaard's "Teleological suspension of the ethical," by J. Donnelly.

The gene is one of the most fundamental concepts in life sciences, having been developed in the mold of the Mendelian paradigm of heredity, which shaped genetics across 150 years. How could Mendel possibly be so prophetic in the middle of 19th century, using only the small garden of the monastery as his experimental breeding field? I believe that we are indebted to Mendel's mastery of the scientific method, which was far ahead of his time. Although his experimental technology was (...) literally garden‐variety, Mendel's excellence in the method of science, algebra, and logical analysis helped him in designing the right experiment and in interpreting the results insightfully. This may be valuable to recall in today's technology‐focused culture, where the center of interest tends to be on the generation and description of high‐throughput datasets from specialized genomics screens. As Mendel's story suggests, progress in 21st century genetics may also depend on the development of robust concepts and generalizations. (shrink)