Logic, Epistemology, and the Unity of Science – Serie

their communication abilities? The ?rst part of the book,Reason, - tion and Communication, contains a general philosophicaldiscussion of these important questions. In Chapter 2,The Balance ofReason, Dascal discusses the ideal of aperfectly reliable balance of reason, an ideal challenged by scepticism. He shows that the balance metaphor is compatible with two di?erent conceptions of rationality which are both present in Western thought. The ?rst conception expects the balance of reason to provide conclusive decisionsin every rational deliberation. Thesecond conception ackno- edges the limits of human reason. It is clearly more appropriate for h- dling uncertainty, revision of intentions and more apt to face scepticism. Leibnitz, one of the most eminent rationalist philosophers, made a s- stantial contribution to both conceptions of rationality. Dascal discusses in detailhis ideas. He shows how Leibnizcameto grips with the balance metaphor. Thestateof equilibrium of thescalesof a balancemirrorsthe equilibriumofindi?erence betweentheargumentsforandthearguments against a belief, a decision or an action. Yet an indi?erence of that kind seems to model arbitrariness rather than rationality.Leibniz, as Dascal stresses, was well aware oftheproblem. Heacknowledged that the b- ance of reason, when it is conceived as a metric and digital balance, lies open to the objection raised above, but he worked out another version of the balance of reason to circumvent this. We can conceive of a balance which permits us to directly compare the "values" of what is placed on the scales without reducing them to universal measuring units.

The aim of the series Logic, Epistemology, and the Unity of Science, of which this is the first volume, is to take up anew the challenge of considering the scientific enterprise in its entirety in light of recent developments in logic and philosophy. Developments in logic are especially relevant to the current situation in philosophy of science. At present, there is no single logic, single approach to semantics or well-defined conception of scientific method dominating the philosophy of science. At the same time, questions concerning linguistic, reductionist and foundationalist approaches to epistemology, the analytic and synthetic distinction as well as disputes concerning semantics and pragmatics have been illuminated by recent developments in logic. Given the power of such developments, discussions of the unity of science are even more intriguing and urgent than in the 20th century. The first title in this new series aims to explore, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The present volume contains essays from some of the most important and influential philosophers in contemporary philosophy, discussing a range of topics such as philosophy of science, epistemology, philosophy of logic and game theoretical approaches. It will be of great interest to philosophers, computer scientists and all others interested in the scientific rationality.

One of the most basic problems in the philosophy of science involves determining the extent to which nature is governed by laws. This volume presents a wide-ranging overview of the contemporary debate and includes some of its foremost participants. It begins with an extensive introduction describing the historical, logical and philosophical background of the problems dealt with in the essays. Among the topics treated in the essays is the relationship between laws of nature and causal laws as well as the role of ceteris paribus clauses in scientific explanations. Traditionally, the problem of the unity of science was intimately connected to the problem of understanding the unity of nature. This fourth volume of Logic, Epistemology, and the Unity of Science tackles these problems as part of our consideration of the most fundamental aspects of scientific understanding.

In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature of the interplay between logic and science. It presents contributions from the world's leading scholars under the following headings:- Proof, Knowledge and Computation- Truth Values beyond Bivalence- Category-Theoretic Structures- Independence, Evaluation Games, and Imperfect Information- Dialogue and Pragmatics.The contents exemplify the liveliness of modern perspectives on the philosophy of logic and mathematics and demonstrate the growth of the discipline. It describes new trends, possible developments for research and new issues not normally raised in the standard agenda of the philosophy of logic and mathematics. It transforms rigid classical partitions into a more open field for improvisation.

Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

This interdisciplinary volume reflects on the effects of recent discoveries in genetics on a broad range of scientific fields. It shows the way in which those discoveries influence genetics itself and many other fields, and explains the impact of genetics on contemporary culture. The volume contains the most recent views of the Nobel Laureate Francois Jacob on genetics and the nature of living things.

Perhaps one of the most striking characteristics of later medieval philosophy and science is the remarkable unity with which the different fields of investigation were articulated to each other, in particular with respect to the methodology used. While it is fair to say that current science is characterized by a plurality of methodologies and by a high degree of specialization in each discipline, in the later medieval period there was one fundamental methodology being used across disciplines, namely logic. One can say without hesitation that logic provided unity to knowledge and science in the later medieval times. Logic (which was then understood more broadly than it is now, including semantics and formal epistemology) was one of the first subject-matters in the medieval curriculum; it was thought that the knowledge of logic was a necessary, methodological requirement for a student to move on to the other disciplines. And indeed, the widespread use of this logical and semantic methodology can be perceived in disciplines as diverse as natural philosophy (physics), theology, ethics and even medicine. Besides the fact that medieval logic provided unity to science then, while modern logic does not play the same role now (if anything at all, it is mathematics that might be considered as the fundamental methodology for current investigations), it is also widely acknowledged that the medieval and modern traditions in logic are very d- similar in many other respects.

The idea of the present volume emerged in 2002 from a series of talks by Frank Stephan in 2002, and John Case in 2003, on developments of algorithmic learning theory. These talks took place in the Mathematics Department at the George Washington University. Following the talks, ValentinaHarizanovandMichèleFriendraised thepossibility ofanexchange of ideas concerning algorithmic learning theory. In particular, this was to be a mutually bene?cial exchange between philosophers, mathematicians and computer scientists. Harizanov and Friend sent out invitations for contributions and invited Norma Goethe to join the editing team. The Dilthey Fellowship of the George Washington University provided resources over the summer of 2003 to enable the editors and some of the contributors to meet in Oviedo (Spain) at the 12th International Congress of Logic, Methodology and Philosophy of Science. The editing work proceeded from there. The idea behind the volume is to rekindle interdisciplinary discussion. Algorithmic learning theory has been around for nearly half a century. The immediate beginnings can be traced back to E.M. Gold’s papers: “Limiting recursion” (1965) and “Language identi?cation in the limit” (1967). However, from a logical point of view, the deeper roots of the learni- theoretic analysis go back to Carnap’s work on inductive logic (1950, 1952).

This research is the result of a fruitful connection and provides a sign- cant link between two topics of a logical and philosophical enquiry. It tries to provide a solution to the problem of analyticity: with this expression I understand, on the one hand, the essential nature of analytic truths and, on the other, the related explanation of the analytic nature of logical inference. The connection between these two sides of what will be referred to as the Analyticity Principle, can be brie?y explained as follows: by analytic truth one understands in general a sentence whose content is logically true; by logically true one understands moreover truth independent from matters of fact or empirical data, a truth which is therefore established by logical criteria only. On this basis, it follows that a logical inference represents a purely analytic process, in opposition to its property of being able to produce knowledge, a situation which is exempli?ed by the con?icting - tions of validity and utility. The question-begging topic of this research is therefore that of analyticity, the inspiring problem for which a solution is formulated in the present book. If analyticity represents the starting point of this research, the other part of its content is the result of a far more complex question; to represent the notion of Information in the context of logical calculi.

Accordingly, the sociological and historical interpretation - volves in fact two kinds of discontinuity which are closely related: the discontinuity of science as such and the discontinuity of the more inclusive political and social context of its development.

Andinmy haste, I said: “Allmenare Liars” 1 —Psalms 116:11 The Original Lie Philosophical analysis often reveals and seldom solves paradoxes. To quote Stephen Read: A paradox arises when an unacceptable conclusion is supported by a plausible argument from apparently acceptable premises. [...] So three di?erent reactions to the paradoxes are possible: to show that the r- soning is fallacious; or that the premises are not true after all; or that 2 the conclusion can in fact be accepted. There are sometimes elaborate ways to endorse a paradoxical conc- sion. One might be prepared to concede that indeed there are a number of grains that make a heap, but no possibility to know this number. However, some paradoxes are more threatening than others; showing the conclusiontobeacceptableisnotaseriousoption,iftheacceptanceleads to triviality. Among semantic paradoxes, the Liar (in any of its versions) 3 o?ers as its conclusion a bullet no one would be willing to bite. One of the most famous versions of the Liar Paradox was proposed by Epimenides, though its attribution to the Cretan poet and philosopher has only a relatively recent history. It seems indeed that Epimenides was mentioned neither in ancient nor in medieval treatments of the Liar 1 Jewish Publication Society translation. 2 Read [1].

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.

Gottfried Wilhelm Leibniz was an outstanding contributor to many fields of human knowledge. The historiography of philosophy has tagged him as a "rationalist". But what does this exactly mean? Is he a "rationalist" in the same sense in Mathematics and Politics, in Physics and Jurisprudence, in Metaphysics and Theology, in Logic and Linguistics, in Technology and Medicine, in Epistemology and Ethics? What are the most significant features of his "rationalism", whatever it is? For the first time an outstanding group of Leibniz researchers, some acknowledged as leading scholars, others in the beginning of a promising career, who specialize in the most significant areas of Leibniz's contributions to human thought and action, were requested to spell out the nature of his rationalism in each of these areas, with a view to provide a comprehensive picture of what it amounts to, both in its general drive and in its specific features and eventual inner tensions.The chapters of the book are the result of intense discussion in the course of an international conference focused on the title question of this book, and were selected in view of their contribution to this topic.They are clustered in thematically organized parts. No effort has been made to hide the controversies underlying the different interpretations of Leibniz's "rationalism" -- in each particular domain and as a whole. On the contrary, the editor firmly believes that only through a variety of conflicting interpretive perspectives can the multi-faceted nature of an oeuvre of such a magnitude and variety as Leibniz's be brought to light and understood as it deserves.

OndrejMajer,Ahti-VeikkoPietarinen,andTeroTulenheimo 1 Games and logic in philosophy Recent years have witnessed a growing interest in the unifying methodo- gies over what have been perceived as pretty disparate logical ‘systems’, or else merely an assortment of formal and mathematical ‘approaches’ to phi- sophical inquiry. This development has largely been fueled by an increasing dissatisfaction to what has earlier been taken to be a straightforward outcome of ‘logical pluralism’ or ‘methodological diversity’. These phrases appear to re ect the everyday chaos of our academic pursuits rather than any genuine attempt to clarify the general principles underlying the miscellaneous ways in which logic appears to us. But the situation is changing. Unity among plurality is emerging in c- temporary studies in logical philosophy and neighbouring disciplines. This is a necessary follow-up to the intensive research into the intricacies of logical systems and methodologies performed over the recent years. The present book suggests one such peculiar but very unrestrained meth- ological perspective over the eld of logic and its applications in mathematics, language or computation: games. An allegory for opposition, cooperation and coordination, games are also concrete objects of formal study.

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics.From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements.The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way.Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.

This book examines the role of acts of choice in classical and intuitionistic mathematics.

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics. It addresses one of the central issues in the epistemology and philosophy of mathematics, namely the relationship between phenomenological meaning constitution and constructive semantics. Contributing authors explore deep structural connections and fundamental differences between phenomenology and constructivism. Papers are drawn from contributions to a prestigious workshop held at the University of Friedrichshafen.Readers will discover insight into structural connections between the phenomenological concept of meaning constitution and constructivist concepts of meaning. Discussion ranges from more specific conceptualizations in the philosophy of logic and mathematics to more general considerations in epistemology, inferential semantics and phenomenology. Questions such as a possible phenomenological understandingof the relationship between structural rules and particle rules in dialogical logic are explored. Significant aspects of both phenomenology and dialectics, and dialectics and constructivism emerge.Graduates and researchers of philosophy, especially logic, as well as scholars of mathematics will all find something of interest in the expert insights presented in this volume.

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics.

The book provides a historical (with an outline of the history of the concept of truth from antiquity to our time) and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas (pro and contra) as well as points out various applications of the semantic theory of truth to philosophical problems (truth-criteria, realism and anti-realism, future contingents or the concept of correspondence between language and reality).

The book provides a historical (with an outline of the history of the concept of truth from antiquity to our time) and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s.

This volume aims to provide the elements for a systematic exploration of certain fundamental notions of Peirce and Husserl in respect with foundations of science by means of drawing a parallelism between their works. Tackling a largely understudied comparison between these two contemporary philosophers, the authors highlight the significant similarities in some of their fundamental ideas.  This volume consists of eleven chapters under four parts. The first part concerns methodologies and main principles of the two philosophers. An introductory chapter outlines central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic. The third part includes contributions on philosophy of mathematics. Chapters in the final part deal with  the theory of cognition, consciousness and intentionality. The closing chapter provides an extended glossary of central terms of Peirce’s theory of phaneroscopy, explaining them from the viewpoint of the theory of cognition.

The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic.

This book offers insights relevant to modern history and epistemology of physics,mathematics and, indeed, to all the sciences and engineering disciplines emergingof 19th century. This research volume is the first of a set of three Springer books onLazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines inGeneral (Essai sur les machines en général [1783] 1786). The other two forthcomingvolumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) andGéométrie de position (1803).Lazare Carnot – l'organisateur de la victoire – in Essai sur le machine en général (1786)assumed that the generalization of machines was a necessity for society and its economicdevelopment. Subsequently, his new coming science applied to machines attractedconsiderable interest for technician, as well, already in the 1780’s. With no lack inrigour, Carnot used geometric and trigonometric rather than algebraic arguments, andusually went on to explain in words what the formulae contained. His main physical–mathematical concepts were the Geometric motion and Moment of activity–concept ofWork . In particular, he found the invariants of the transmission of motion (by statingthe principle of the moment of the quantity of motion) and theorized the condition ofthe maximum efficiency of mechanical machines (i.e., principle of continuity in thetransmission of power).While the core theme remains the theories and historical studies of the text, the bookcontains an extensive Introduction and an accurate critical English Translation –including the parallel text edition and substantive critical/explicative notes – of Essaisur les machines en général (1786). The authors offer much-needed insight into therelation between mechanics, mathematics and engineering from a conceptual, empiricaland methodological, and universalis point of view. As a cutting–edge writing byleading authorities on the history of physics and mathematics, and epistemologicalaspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology).

This book offers insights relevant to modern history and epistemology of physics,mathematics and, indeed, to all the sciences and engineering disciplines emergingof 19th century. This research volume is the first of a set of three Springer books onLazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines inGeneral (Essai sur les machines en général [1783] 1786). The other two forthcomingvolumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) andGéométrie de position (1803).Lazare Carnot – l'organisateur de la victoire – in Essai sur le machine en général (1786)assumed that the generalization of machines was a necessity for society and its economicdevelopment. Subsequently, his new coming science applied to machines attractedconsiderable interest for technician, as well, already in the 1780’s. With no lack inrigour, Carnot used geometric and trigonometric rather than algebraic arguments, andusually went on to explain in words what the formulae contained. His main physical–mathematical concepts were the Geometric motion and Moment of activity–concept ofWork . In particular, he found the invariants of the transmission of motion (by statingthe principle of the moment of the quantity of motion) and theorized the condition ofthe maximum efficiency of mechanical machines (i.e., principle of continuity in thetransmission of power).While the core theme remains the theories and historical studies of the text, the bookcontains an extensive Introduction and an accurate critical English Translation –including the parallel text edition and substantive critical/explicative notes – of Essaisur les machines en général (1786). The authors offer much-needed insight into therelation between mechanics, mathematics and engineering from a conceptual, empiricaland methodological, and universalis point of view. As a cutting–edge writing byleading authorities on the history of physics and mathematics, and epistemologicalaspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology).

The book offers a reflection on the nature, scope, and limits of knowledge that have been at the focus of the author's work over decades. They join in exploring the lay of the land at the boundaries of knowledge. The first chapters address basic facts regarding the conceptualization of knowledge.

The book offers a reflection on the nature, scope, and limits of knowledge that have been at the focus of the author's work over decades. They join in exploring the lay of the land at the boundaries of knowledge. The first chapters address basic facts regarding the conceptualization of knowledge.

The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic.

The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic.