Bøger i Synthese Library serien

They look at how consciousness can help us with quantum mechanics as well as how quantum mechanics can contribute to our understanding of consciousness.

In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes ¿the mathesis [¿] shall deliver the method through which things that are conceivable can be exactly determined¿; in another fragment he takes the mathesis to be ¿the science of all things that are conceivable.¿ Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between ¿arbitrary objects¿ (¿objets quelconques¿). It is an abstract theory of combinations and relations among objects whatsoever.In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the ¿reasons¿ (¿Gründe¿) of others, and the latter are ¿consequences¿ (¿Folgen¿) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionisticlogic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations.

Chapters analyse the abstract model theory of institutions as a way of representing the structure of scientific theories, the semi-automatic generation of cognitive science theories, and computational process models in the social sciences.The volume offers a unique perspective on scientific discovery in the social sciences.

According to dispositional realism, or dispositionalism, the entities inhabiting our world possess irreducibly dispositional properties - often called 'powers' - by means of which they are sources of change.

This book highlights the existence of a diversity of methods in science, in general, in groups of sciences (natural, social or the artificial), and in individual sciences.

This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language ¿ and specifically, the ability to institute conventions for the truth conditions of sentences.This philosophical stance leads to an alternative way of practicing mathematics: instead of ¿building¿ objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory.Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis.Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell¿s paradox and the other mathematical paradoxes of self-reference.In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.

This volume examines the question ¿Do abstract objects exist?¿, presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word "exist¿ and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered.Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume provides a variety ofsamples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters.

A growing body of evidence from the sciences suggests that our moral beliefs have an evolutionary basis. The present literature has focused on the link between evolution and moral realism: if our moral beliefs enhance fitness, does this mean they track moral truths?

This book provides philosophers of science with new theoretical resources for making their own contributions to the scientific realism debate. Finally, they will see how scientific realism relates to scientific progress, scientific understanding, mathematical realism, and scientific practice.

This book presents a thoroughly empiricist account of physics. By providing an overview of the development of empiricism from Ockham to van Fraassen the book lays the foundation for its own version of empiricism. Empiricism for the author consists of three ideas: nominalism, i.e. dismissing second order quantification as unnecessary, epistemological naturalism, and viewing classification of things in natural kinds as a human habit not in need for any justification.The book offers views on the realism-antirealism debate as well as on the individuation of theories as a thoroughly neglected aspect of underdetermination. The book next discusses a broad range of topics, including the predicates body, spatial distance and time interval, the ontology of electromagnetism, propensities, the measurement problem and other philosophical issues in quantum theory. Discussions about the direction of time and about string theory make up the final part of thebook.

This book offers a defense against non-classical approaches to the paradoxes. In fact, he believes classical solutions fare better than non-classical ones with respect to key tests like Curry's Paradox, a Liar-like paradox that dialetheists are forced to solve in a way totally disjoint from their solution to the Liar.

Ever the outspoken firebrand, Hanson found many lessons and warnings from Galileo's trial that were relevant to Cold War America.This volume not only contains Hanson's best-known work in history and philosophy of science, but also highlights the breadth of his philosophical thought.

This volume handles in various perspectives the concept of function and the nature of functional explanations, topics much discussed since two major and conflicting accounts have been raised by Larry Wright and Robert Cummins' papers in the 1970s. Here, both Wright's 'etiological theory of functions' and Cummins' 'systemic' conception of functions are refined and elaborated in the light of current scientific practice, with papers showing how the 'etiological' theory faces several objections and may in reply be revisited, while its counterpart became ever more sophisticated, as researchers discovered fresh applications for it. Relying on a firm knowledge of the original positions and debates, this volume presents cutting-edge research evincing the complexities that today pertain in function theory in various sciences. Alongside original papers from authors central to the controversy, work by emerging researchers taking novel perspectives will add to the potential avenues to be followed in the future. Not only does the book adopt no a priori assumptions about the scope of functional explanations, it also incorporates material from several very different scientific domains, e.g. neurosciences, ecology, or technology. In general, functions are implemented in mechanisms; and functional explanations in biology have often an essential relation with natural selection. These two basic claims set the stage for this book's coverage of investigations concerning both 'functional' explanations, and the 'metaphysics' of functions. It casts new light on these claims, by testing them through their confrontation with scientific developments in biology, psychology, and recent developments concerning the metaphysics of realization. Rather than debating a single theory of functions, this book presents the richness of philosophical issues raised by functional discourse throughout the various sciences.

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s.The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics.The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

The main aim of this book is to discuss fundamental developments on the question of being in Western and African philosophy using analytic metaphysics as a framework. It starts with the two orthodox responses to the question of being, namely, the subject-verb-object language view and the rheomodic language view. In the first view, being is conceived through the analysis of language structure, where it is represented by subjects (particulars), objects, and relations (often universals). In the second view, there are different variations; however, the common idea is that the world's structure is revealed in the root verb of terms. This suggests a holistic and dynamic conception of being, where everything is in a continuous process of action. The book builds on analytic philosophy and explores metaphysical concepts such as space-time, modality, causation, indeterminism versus determinism, and mind and body. The book shows that in both Western and African thought, (i) similarities in different studies confirm that philosophy is a universal activity, (ii) differences within a context and beyond confirm the perspectival nature of human knowledge as individuals attempt to interpret reality, and (iii) language influences the conceptualization of being in a particular area. One of the novel aspects is the development of visual and mathematical African models of space and time.

This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn.Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions tocomputer science, such as knowledge representation and information processing.This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.

This book provides a detailed reassessment of the role and impact of analytic philosophy in the overall philosophical debate. It does so by focusing on several important turning points that have been particularly significant for analytic philosophy¿s overall history, such as Bertrand Russell's critique of Meinong, and the vindication of Heidegger's famous 'Nothing'- sentence. In particular, the book scrutinizes whether the theses written about such points have been convincingly argued for, or whether they have gained attraction as a type of rhetorical device. Due to its broad nature, this book is of interest to scholars interested in all aspects of philosophy, at both graduate level and above.

In this highly-interdisciplinary volume, we systematically study the role of metaphors and analogies in (mis)shaping our understanding of the world. Metaphors and Analogies occupy a prominent place in scientific discourses, as they do in literature, humanities and at the very level of our thinking itself. But when misused they can lead us astray, blinding our understanding inexorably. How can metaphors aid us in our understanding of the world? What role do they play in our scientific discourses and in humanities? How do they help us understand and skillfully deal with our complex socio-political scenarios? Where is the dividing line between their use and abuse? Join us as we explore some of these questions in this volume.

This book offers a new and externalist perspective in ignorance studies. Agnotology, the epistemology of ignorance, and, more generally, ignorance studies have grown to cover and explore different phenomena and subjects of research, from known events in history and sociology of science to the investigation of ordinary reasoning and cognitive processing. Nonetheless, although interested scholars have discussed ignorance phenomena and their impact on cognition, most of them have only adopted an internalist perspective to approach this theme. Meanwhile, even though externalist perspectives on cognition flourished in recent literature, authors have paid little attention to the emerging field of ignorance studies. Ignorance has been generally left out from the inquiries on the extension of cognitive states, cognitive processes, and predictive reasoning. Thus, in this volume, we seek to merge the two growing areas of research and to fill this research gap fruitfully. By addressing the uncomfortable themes that pertain to ignorance and related phenomena through an externalist perspective, this book aims to provide much food for thoughts to cognitive scientists and philosophers alike, enriching the current range and reach of both ignorance studies and externalist approaches to cognition.