My analysis here is an attempt to bring out the main through-line in the development of Bulgarian philosophy of law today. A proper account of Bulgarian philosophy of law in the 20th century requires an attempt to find, on the one hand, a solution to epistemological and methodological problems in law and, on the other, a clear-cut influence of the Kantian critical tradition. Bulgarian philosophy of law follows a complicated path, ranging from acceptance and revision of Kantian philosophy (...) to the development of interesting theories on the logic of legal reasoning. (shrink)

Three early 20th-century attempts at unifying separate areas of biology, in particular development, genetics, physiology, and evolution, are compared in regard to their success and fruitfulness for further research: Jacques Loeb’s reductionist project of unifying approaches by physico-chemical explanations; Richard Goldschmidt’s anti-reductionist attempts to unify by integration; and Sewall Wright’s combination of reductionist research and vision of hierarchical genetic systems. Loeb’s program, demanding that all aspects of biology, including evolution, be studied by the methods of the experimental sciences, (...) proved highly successful and indispensible for higher level investigations, even though evolutionary change and properties of biological systems up to now cannot be fully explained on the molecular level alone. Goldschmidt has been appraised as pioneer of physiological and developmental genetics and of a new evolutionary synthesis which transcended neo-Darwinism. However, this study concludes that his anti-reductionist attempts to integrate genetics, development and evolution have to be regarded as failures or dead ends. His grand speculations were based on the one hand on concepts and experimental systems that were too vague in order to stimulate further research, and on the other on experiments which in their core parts turned out not to be reproducible. In contrast, Sewall Wright, apart from being one of the architects of the neo-Darwinian synthesis of the 1930s, opened up new paths of testable quantitative developmental genetic investigations. He placed his research within a framework of logical reasoning, which resulted in the farsighted speculation that examinations of biological systems should be related to the regulation of hierarchical genetic subsystems, possibly providing a mechanism for development and evolution. I argue that his suggestion of basing the study of systems on clearly defined properties of the components has proved superior to Goldschmidt’s approach of studying systems as a whole, and that attempts to integrate different fields at a too early stage may prove futile or worse. © 2011 Elsevier Inc. (shrink)

As indicated by its title, this book provides an overview of philosophy of science in the twentieth century. It focuses mostly on post-WWII philosophy of science, but it discusses earlier developme...

The first beginnings of modern logic in Croatia are recognizable as early as in the middle of the 19th century in Vatroslav Bertić. At the turn of the 20th century, Albin Nagy, who was teaching in Italy, made contributions to algebraic logic and to the philosophy of logic. At that time, a distinctive author Mate Meršić stood out, also working on algebraic logic. In the Croatian academic philosophy, until the publication of Gajo Petrović's (...) textbook (1964) and the contributions by Heda Festini, a critical or indifferent attitude toward modern logic prevailed. The first comprehensive modern logic textbook in Croatian was written by mathematician Vladimir Devidé (1964), known, for example, for his axiomatizations of natural numbers and classical propositional logic. In the Croatian philosophy of the 1980s and 1990s, influential logicians are Goran Švob and mathematician Zvonimir Šikić. At the turn of the 21st century, logical investigations are being intensified and extended to various branches of the contemporary logic. (shrink)

The book deals with the reception and critique of symbolic logic among German-speaking philosophers at the turn of the 20th century. The first part discusses the period from the late 1870s up to the end of the 19th century. The main issue is the arrival of the Boolean algebra of logic in Germany and Austria. It examines also the reasons why Gottlob Frege was so unsuccessful in his attempts to draw the attention of philosophers to (...) his logicist programme. The second part deals with the first two decades of the 20th century. Its main topic of inquiry is the reception of Bertrand Russell's and Louis Couturat's ideas in the German-speaking world. In particular, it concentrates on the relationship between Russell and neo-Kantians. (shrink)

The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.

After Poland gained independence in 1918, logic developed very quickly both as a scientific direction and as a taught discipline. This introduction to the special issue “Logic in Poland in the 20th Century,” published in Volume 13:1 (2024) and Volume 13:2 (2024), provides the historical context for the development of logic in the interwar period.

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical (...) development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided: 1. What were the reasons for the philosophers' lack of interest in formal logic? 2. What were the reasons for the mathematicians' interest in logic? 3. What did "logic reform" mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic? 4. Was mathematical logic regarded as art, as science or as both? (shrink)

The article discusses the formation of the philosophical concept of Leonid Evgenievich Gabrilovich (1878–1953), a Russian thinker of the first half of the 20th century. In the Rus­sian period of creativity, i.e. until 1918, as it is shown in the article, in his philosophi­cal development Gabrilovich experienced the influence of such fundamental theories as the philosophy of normative, immanent philosophy of W. Schuppe and phenomenology of E. Husserl. The article studies the following articles by L.E. Gabrilovich of the (...) first, “Russian” period: “On the concepts of truth and reliability in the theory of knowledge” 1908, “On two scientific concepts of thinking (to justify one dativist logic)” 1909, “On the meaning and essence of elementary concepts (an attempt at a new development of the problem of universal concepts)” 1910, as well as some others. It is shown that in his philosophical work L.E. Gabrilovich consistently and purposefully followed the de­velopment of his own concept, the nature of which makes it possible to attribute his phi­losophy to the logical and epistemological direction in Russian philosophy of the 20th cen­tury. The article proves that according to their ideas and structure, the analyzed texts of Gabrilovich revealed the themes of mathematical formalism, dativist logic, at the same time they were the main stages in the development of his own logical and epistemological concept as mathematical thinking and the actual form. L.E. Gabrilovich outlined the re­sults of these developments in the book “On Mathematical Thinking and the Concept of the Actual Form”, a 1914 essay written by him in German. It is concluded that the con­cept of “dativist logic”, developed by Gabrilovich in articles of 1909 and 1910, will later result in his theory of “actual forms”. (shrink)

Poincaré’s conventionalism has thoroughly transformed both the philosophy of science and the philosophy of mathematics. Not only proponents of conventionalism, such as the logical positivists, were influenced by Poincaré, but also outspoken critics of conventionalism, such as Quine and Putnam, were inspired by his daring position. Indeed, during the twentieth century, most philosophers of mathematics and of science engaged in dialogue with conventionalism. As is often the case with such complex clusters of ideas, there is no consensus about the (...) meaning of conventionalism in general, and Poincaré’s original version of it, in particular. Nonetheless, notions such as the under-determination, empirical equivalence, implicit definition, holism and conceptual relativity, all of which can be linked to Poincare's writings have become central to philosophy. This essay explores the impact of some of these notions on twentieth century philosophy of science. In addition to inspiration based on Poincare's actual views, it emphasizes directions based on misreading and unjustified appropriations of Poincaré. (shrink)

The most prominent “schools” or programs for the foundations of mathematics that took shape in the first third of the 20th century emerged directly from, or in response to, developments in mathematics and logic in the latter part of the 19th century. The first of these programs, so-called logicism, had as its aim the reduction of mathematics to purely logical principles. In order to understand properly its achievements and resulting problems, it is necessary to review the (...) background from that previous period. (shrink)

The book is comprised of three components. The first component analyses the creative contribution to the theory of imperatives and norms provided by 20th-century Polish researchers. The second component summarizes their reflections and considerations. The third component is an anthology of the classic writings of Polish authors of the time; it constitutes an illustration of the first part and indicates that their research covered practically the whole scope of this theory. Author Jacek Jadacki (born 1946) is professor at (...) Warsaw University. His scholarly production includes approximately hundred works spanning almost every domain in philosophy: from logic, through ontology, epistemology, aesthetics and ethics, to the history of these disciplines. Among his more than twenty books are Possible Ontologies (with Zdzislaw Augustynek; 1993), From the Viewpoint of the Lvov-Warsaw School (2003), and Polish Analytical Philosophy (2009). His pupils include such well-known figures of modern Polish thought as Anna Brozek, Mariusz Grygianiec, Joanna Odrowaz-Sypniewska, and Mieszko Talasiewicz. (shrink)

Semiotic and linguistic studies of the 20th century have been important mostly in two senses — (1) they have opened a road for comparative research on the origin and development of language and other systems of signs adding a new dimension to the history of culture; (2) they have shown a possibility of uniting different fields of humanities around semiotics suggesting a way to trespass separation and atomisation of different trends in investigating culture. In the 21st century (...) one may hope for closer integration of semiotics and exact and natural sciences. The points of intersection with the mathematical logic, computer science and information theory that already exist might lead to restructuring theoretical semiotics making it a coherent and methodologically rigid discipline. At the same time, the continuation of neurosemiotic studies promises a breakthrough in understanding those parts of the work of the brain that are most intimately connected to culture. From this point of view semiotics may play an outstanding role in the synthesis of biological science and humanities. In my mind that makes it a particularly important field of future research. (shrink)

B a c k g r o u n d. The current research focuses on Ukraine's academic philosophical culture in the second half of the 20th century during the Soviet era, emphasising the historical and methodological bases of truth interpretation by its representatives. Using descriptive methodology and comparative analysis, it was found that the Ukrainian academic philosophy of this period, represented here by the legacy of recognised figures often referred to in the philosophical literature as the Kyiv School (...) of Philosophy, is a revival of philosophy in Ukraine based on so-called "authentic" Marxism-Leninism. M e t h o d s. In particular, to analyse the concept of truth, representatives of the Ukrainian academic philosophical culture of the studied period employed the dialectical method, which is interpreted in dialectical materialism through the concept of the "development" of the material universe. Specifically, within this dialectics of nature, dialectical negation is considered a stage of object development in which the achievements of the earlier stages are not eliminated but rather "removed" – contained within it. R e s u l t s. The interpretation of logic as a theoretical reflection of historical patterns in theoretical form enabled them to define truth as correspondence to reality and analyse it through the lens of the dialectical inter-transformation of the categories of subjective and objective, relative and absolute. The application of the dialectical method to the concepts of "relative" and "absolute" resulted in the identification of "relatively absolute," "absolutely relative" truth, and the opposition of the "relatively absolute truth" to the "absolutely absolute truth." They regard the latter – absolutely absolute truth – as an unreachable ideal that serves as a regulative principle, the pursuit of which promotes cognitive progress through the accumulation of partial, relative truths. C o n c l u s i o n s. Thus, in the second half of the 20th century, during the Soviet era, representatives of Ukraine's academic philosophical culture employed dialectical materialism methodology to define the concept of truth, allowing them to justify the process of cognition as complex and endless. At the same time, as representatives of that era's academic philosophy have emphasised, on the path to achieving relative truths, in addition to objective dialectical contradictions, there are also subjective formal-logical errors and mistakes that can only be distinguished from objective contradictions through practical verification. (shrink)

Esej pojednává o koncepci poznání, již zformuloval významný český filosof a ekonom Karel Engliš (1880-1961) a nejuceleněji uložil do monumentálního spisu Velká logika. Toto teprve nyní publikované dílo obsahuje enormně bohatý materiál, a proto se přítomná studie soustředila na několik myšlenkových motivů, jejichž prostřednictvím lze konkrétně posoudit přínos i možnosti Englišova konceptu tří myšlenkových řádů (ontologicko-kauzálního, teleologického a normologického). Jsou to témata lidské vůle a možné svobody, rozlišení logických a empirických poznávacích prostředků a problém účelnosti a užitečností poznání. Tyto tematické (...) okruhy bylo možno zvažovat u Englišovy kritiky představitelů různých filosofických směrů – osvícence Voltaira, voluntaristy Schopenhauera a pragmatisty W. Jamese. Konfrontace jejich názorů s koncepcí myšlenkových řádů dokládá možné kritické použití Englišovy optiky. (shrink)

This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic (...) semantics so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

The global crisis that erupted in 2008 has left unmistakably deep scars in architectural culture. But what is happening now is not solely attributable to what began as a mortgage crisis; many of the causes lie deeper, and go back further than a few years. In a way, the recession has simply accelerated, and exacerbated, various pre-existing trends. Without overstating the case, the West, and above all Europe, is undergoing such major change at the beginning of the twenty-first century (...) that it is no longer logical to expect the future to be simply an extrapolation and continuation of the recent past. And this could well have far-reaching consequences for architecture. Of course, this is not the first time that people have declared that things will never be the same again. And up to now reality has usually turned out to be a good deal better than predicted. But there are reasons why architects in Europe should consider the possibility that this time it really might turn out differently. (shrink)

Current debate in metaethics includes the question of objectivity. What does it mean for a moral prescription to be objective? It is easy to see how matters of fact are objective, and it is also easy to see how matters of taste are subjective. But what about matters of morality? Given the diversity in moral beliefs and practices it appears these cannot be matters of fact. Are they thus matters of taste? If so, we are left with the unlivable conclusion (...) that all moral prescriptions are beyond rational scrutiny. David Hume expressed these problems in a way that continues to be influential today: ‘Tis as little contrary to reason to prefer even my own acknowled'd lesser good to my greater’ (Hume, 2003: 2.III.ii). Resolving problems about moral objectivity is further complicated by the philosophical presuppositions of analytic philosophy that have dominated the 20th century, initiated in the work of G.E. Moore, and promulgated in theories such as logical positivism and ordinary language philosophy. Contemporary thinkers from both the cognitivist and the non‐cognitivist camps have tried to demonstrate that moral claims are objective in the sense of being subject independent. By considering contemporary appeals to the ideally rational self to establish objectivity, and objections to rationality as a ground for objectivity, it will be argued that objectivity can be grounded in the good which in turn is grounded in human nature. This approach can be found in the Socratic denial of knowingly doing evil, and out of this a foundation for moral objectivity can be developed that does not require an appeal to the individual's mental state and which preserves individual responsibility for knowing the good. (shrink)

The widespread impression that recent philosophy of science has pioneered exploration of the “social dimensions of scientific knowledge” is shown to be in error, partly due to a lack of appreciation of historical precedent, and partly due to a misunderstanding of how the social sciences and philosophy have been intertwined over the last century. This paper argues that the referents of “democracy” are an important key in the American context, and that orthodoxies in the philosophy of science tend to (...) be molded by the actual regimes of science organization within which they are embedded. These theses are illustrated by consideration of three representative philosophers of science: John Dewey, Hans Reichenbach, and Philip Kitcher.Author Keywords: Social dimensions of science; Logical positivism; Democracy; Context of discovery/justification; Goals of science. (shrink)

Among the political changes brought about by the First World War was the formation of new countries, including Latvia. This in turn resulted in a strong need for the first national legislative acts and thus a substantial amount of effort to develop Latvian legal terminology which dates back to the beginning of the 19th century. The purpose of the paper is to study the development of Latvian terminology of marriage in the 20th century through analysis of the (...) relevant body of laws. The paper focuses on marriage-related terms extracted from the major legislative acts governing the institution of marriage in the 20th century. The present study adopts the qualitative research approach which constitutes data collection and data analysis. For the purposes of a comprehensive and efficient analysis of the extracted legal terms, marriage terms are divided into the following five thematic groups: 1) engagement; 2) entering into marriage; 3) nullity of marriage; 4) dissolution of marriage ; and 5) consequences of dissolution or nullity of marriage. The paper suggests that the core of the Latvian terminology of marriage has remained stable, as entering into marriage is a solid procedure where two interested parties give notice to a public or religious institution in order to officially register their relationship. Similarly, both parties often feel the need to terminate this relationship just as officially. This stability of fundamental processes contributes to terminological continuity. (shrink)

This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic (...) semantics so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

Preface. Almost fifty years ago, in 1948, when I was an undergraduate at Queens College in New York and a student of Carl G. Hempel's, I received from his hands an offprint of his now-classic but then just-published paper “Studies in the Logic of Explanation”, written in collaboration with Paul Oppenheim and then just published in Philosophy of Science.1 This paper greatly impressed me—and I was not alone. We have here one of those unusual publications that sets the agenda (...) for a whole generation of investigators. It set in train an enormous body of discussions and publications which shaped the course of deliberations about scientific explanation over the next decades—an effort to which my own work also made some contributions. However my present aim is not to consider what came out of the Hempel-Oppenheim paper but what went into it. I want, in sum, to consider the prehistory of that era of scientific explanation studies—and to look more closely at the background ramifications of this paper that launched a thousand others. (shrink)

This paper discusses the problems of an ontological value of the variable in Russell’s philosophy. The variable is essential in Russell’s theory of denotation, which among other things, purports to prove Meinongian being outside of subsistence and existence to be logically unnecessary. I argue that neither Russell’s epistemology nor his ontology can account for the ontological value of the variable without running into qualities of Meinongian being that Russell disputed. The problem is that the variable cannot be logically grounded by (...) Russell’s theory of denotation. As such, in so far as being is concerned, Meinong and Russell’s theories are much closer than is typically thought. The arguments are supported with concerns raised by Russell, Frege, and Moore regarding the ontological value of the variable. The problem can be summarised as follows: the variable is the fundamental denoting-position of a formal theory that is meant to explain the structure of the ontological. If such a formal theory is meant to ground the ontological, then the formal must also represent the actual structure of the ontological. Yet the variable, the fundamental symbol of denotation in a theory that defines objects, is ontologically indefinable. (shrink)

The vicissitudes of mathematical reason in the 20th century Content Type Journal Article Pages 1-6 DOI 10.1007/s11016-011-9556-y Authors Thomas Mormann, Department of Logic and Philosophy of Science, University of the Basque Country UPV/EPU, Donostia-San Sebastian, Spain, Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

For the purpose of contributing to a clarification of the term process, different kinds of musical processes are investigated: A rule-determined phase shifting process in Steve Reich's Piano Phase (1966), a model for an indeterminate composition process in John Cage's Variations II (1961), a number of evolution processes in György Ligeti's In zart fliessender Bewegung (1976), and a generative process of fractal nature in Per Nørgård's Second Symphony (1970). In conclusion I propose that six process categories should be included in (...) a typology of processes: Rule-determined, goal-directed and indeterminate transformation processes, and rule-determined, goal-directed and indeterminate generative processes. (shrink)

Tian Yu Cao has written a serious and scholarly book covering a great deal of physics. He ranges from classical relativity theory, both special and general, to relativistic quantum …eld theory, including non-Abelian gauge theory, renormalization theory, and symmetry-breaking, presenting a detailed and very rich picture of the mainstream developments in quantum physics; a remarkable feat. It has, moreover, a philosophical message: according to Cao, the development of these theories is inconsistent with a Kuhnian view of theory change, and supports (...) better a quali…ed realism. (shrink)

Gersonides' Afterlife is the first full-scale treatment of the reception of one of the greatest scientific minds of medieval Judaism: Gersonides (1288-1344). An outstanding representative of the Hebrew Jewish culture that then flourished in southern France, Gersonides wrote on mathematics, logic, astronomy, astrology, physical science, metaphysics and theology, and commented on almost the entire bible. His strong-minded attempt to integrate these different areas of study into a unitary system of thought was deeply rooted in the Aristotelian tradition and yet (...) innovative in many respects, and thus elicited diverse and often impassionate reactions. For the first time, the twenty-one papers collected here describe Gersonides' impact in all fields of his activity and the reactions from his contemporaries up to present-day religious Zionism. (shrink)

Gersonides' Afterlife is the first full-scale treatment of the reception of one of the greatest scientific minds of medieval Judaism: Gersonides (1288-1344). An outstanding representative of the Hebrew Jewish culture that then flourished in southern France, Gersonides wrote on mathematics, logic, astronomy, astrology, physical science, metaphysics and theology, and commented on almost the entire bible. His strong-minded attempt to integrate these different areas of study into a unitary system of thought was deeply rooted in the Aristotelian tradition and yet (...) innovative in many respects, and thus elicited diverse and often impassionate reactions. For the first time, the twenty-one papers collected here describe Gersonides' impact in all fields of his activity and the reactions from his contemporaries up to present-day religious Zionism. (shrink)

The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding (...) of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. -/- The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege. (shrink)

This volume has two primary aims: to trace the traditions and changes in methods, concepts, and ideas that brought forth the logical empiricists’ philosophy of physics and to present and analyze the logical empiricists’ various and occasionally contrary ideas about the physical sciences and their philosophical relevance. These original chapters discuss these developments in their original contexts and social and institutional environments, thus showing the various fruitful conceptions and philosophies behind the history of 20th-century philosophy of science. Logical (...) Empiricism and the Natural Sciences is divided into three thematic sections. Part I surveys the influences on logical empiricism’s philosophy of science and physics. It features chapters on Maxwell’s role in the worldview of logical empiricism, on Reichenbach’s account of objectivity, on the impact of Poincaré on Neurath’s early views on scientific method, Frank’s exchanges with Einstein about philosophy of physics, and on the forgotten role of Kurt Grelling. Part II focuses on specific physical theories, including Carnap’s and Reichenbach’s positions on Einstein’s theory of general relativity, Reichenbach’s critique of unified field theory, and the logical empiricists’ reactions to quantum mechanics. The third and final group of chapters widens the scope to philosophy of science and physics in general. It includes contributions on von Mises’ frequentism; Frank’s account of concept formation and confirmation; and the interrelations between Nagel’s, Feigl’s, and Hempel’s versions of logical empiricism. (shrink)

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and (...) the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic’s coming of age in the 20th century: Godel’s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs. (shrink)

This article is a theoretical study of the relations between logic and Anglo-American cognitive science. It uses temporal, historical, and intentional evidence, and it is based on two consequential assumptions: (a) between the late 19th century and the first decades of the 20th century, some logical systems attempted to explain the foundations of mathematics and (b) since the 1940s and 1950s, these same systems became implicit sources of contents and methods of the rising Cognitivism. This study (...) produces an important conclusion: Anglo-American cognitive science partly derives from logic and partly shares many similarities with this science. (shrink)

"The Art of Logical Thinking" is a book written by William Walker Atkinson, an American attorney, merchant, publisher, and author in the late 19th and early 20th centuries. The book was first published in 1909 under the pseudonym Theron Q. Dumont, one of Atkinson's many pen names. The primary focus of "The Art of Logical Thinking" is to provide readers with insights into developing and refining their logical thinking abilities. Atkinson explores various aspects of logical reasoning and critical thinking, (...) aiming to guide readers in making better decisions, solving problems, and approaching issues with a more rational mindset. Key topics covered in the book include: The Nature of Thought: Atkinson delves into the fundamentals of thought processes, examining how ideas are formed and how the mind operates in its thinking capacity. Logical Analysis: The book provides techniques for breaking down complex problems into smaller, more manageable components, facilitating a systematic and logical approach to problem-solving. Deductive and Inductive Reasoning: Atkinson discusses both deductive and inductive reasoning, explaining their principles and applications. Deductive reasoning involves drawing specific conclusions from general principles, while inductive reasoning involves deriving general principles from specific observations. (shrink)

John Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in 'What are logical notions?' (1986) breathed new life into (...) this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. (shrink)

Logic is concerned with the design or structure of arguments. It describes the forms of valid argument and is concerned with the public presentation and reception of arguments. Hence it has a close connection with politics and the public sphere, and with rhetoric as the science of persuasion. Philosophers have analysed the objective conditions of validation, that is, the justifiability of assertions about the world. This quest for objective and scientific validity in argumentation about the nature of reality dominated (...) much of the development of logic in the 20th century. Logical arguments are held to be successful as a result of the ‘force of reason’ rather than because one's opponents have been bribed or coerced. Logic involves the study of the abstract, deductive moves in argumentation rather than an empirical study of how actual arguments are conducted. However, there is also a tension between rhetoric and philosophy; Plato drew a clear distinction between knowledge and persuasion. Logic is intended to give security to the former. The historical drift of logic is towards abstraction, especially the use of mathematical forms of representation. The study of logic is an important component of any project on encyclopaedic knowledge, that is, with knowledge that circulates in the public sphere, but the globalization of culture has raised an important problem about the universalistic claims of traditions of logic, namely, are there different forms of logical reasoning? (shrink)

The decisive role played by Ortega and his “School of Madrid” in modernizing the 20th century Spanish thinking is widely accepted, but their contribution to bring our logic up to day was rather unfortunate: far from backing the introduction or reception of modern logic, the “School of Madrid” attempted an alternative logic, the so-called ‘logic of vital reason’, non-viable. As it is a symptomatic failure, I’ll give a broader account of it starting from, and (...) going through, a confrontation in this respect between the “School of Madrid” and its contemporary “School of Barcelona”. (shrink)

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that (...) they are founded on only one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today. (shrink)

This paper deals with Aristotelian and Stoic logic. In the first part the author writes about the history of logic and shows, why Stoic logic had not been studied properly from the Middle Ages up to the beginning of the 20th century, when an increasing interest in the study of Stoic logic is visible. The paper describes the character of Aristotelian and Stoic logic respectively. Stoic logic is first introduced as a system (...) of propositional logic. On this basis a complementarity between the two logical systems of Antiquity is stated. The ways to support the thesis that Stoic logic involved some features of predicative logic are shown at the end of the first part. The ways in which the two rival logical systems were perceived by the authors of the first centuries A. D., namely Galen and Boethius, is described in the second part. Galen is seen as the first to develop an objective synthesis of the two systems. In his Eisagogé dialektiké he tries to show the goals of both rival logical systems. Boethius, in his De hypotheticis syllogismis, is also combining the Aristotelian and the Stoic logic. However, his synthesis is different from Galen's because Boethius probably forms the synthesis unknowingly and indirectly through compiling his confused sources. (shrink)

This book revives inductive logic by bringing out the underlying epistemology. The resulting structural reliabilist theory propounds the view that justification supervenes on syntactic and semantic properties of sentences as justification-bearers. It is claimed to set up a genuine alternative to the prevailing theories of justification. Kawalec substantiates this claim by confronting structural reliabilism with a number of epistemological problems. While the book is addressed to both professionals and students of philosophical logic, probability, epistemology, and philosophy of science, (...) it also surveys ideas central to the development of philosophy in the 20th century. It will be a valuable companion to multifarious graduate and postgraduate courses. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic (...) and mathematics. It argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

This book collects most of the invited papers presented at the 12th International Congress of Logic, Methodology and Philosophy of Science in Oviedo, August 2003. It contains state of the art accounts of ongoing work by a selection of the most renowned researchers in the field. The papers in the Logic section deal with topics in mathematical logic, as well as philosophical logic, and the area of logic and computation. The section on General Methodology contains (...) articles on models, theories, probability, induction, causation, and other topics. A number of papers discuss Philosophical Issues of Particular Sciences, such as mathematics, physics, linguistics, psychology, biology, and medicine. There is also a section on Ethics of Science, and papers from a special symposium on the Emergence of Scientific Medicine in the 19th-20th Century. (shrink)

Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical (...) means. As a result formallogic was taken over by mathematics in the beginning of the 20th century as is shown by sketching the German example. (shrink)