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Author: Carlo Cellucci
Publisher: Springer Science & Business Media
ISBN: 9400760914
Category : Philosophy
Languages : en
Pages : 391
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Book Description
This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
Author: Carlo Cellucci
Publisher: Springer Science & Business Media
ISBN: 9400760914
Category : Philosophy
Languages : en
Pages : 391
Get Book Here
Book Description
This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
Author: David Danks
Publisher: Springer
ISBN: 3319727877
Category : Philosophy
Languages : en
Pages : 282
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Book Description
This book explores new findings on the long-neglected topic of theory construction and discovery, and challenges the orthodox, current division of scientific development into discrete stages: the stage of generation of new hypotheses; the stage of collection of relevant data; the stage of justification of possible theories; and the final stage of selection from among equally confirmed theories. The chapters, written by leading researchers, offer an interdisciplinary perspective on various aspects of the processes by which theories rationally should, and descriptively are, built. They address issues such as the role of problem-solving and heuristic reasoning in theory-building; how inferences and models shape the pursuit of scientific knowledge; the relation between problem-solving and scientific discovery; the relative values of the syntactic, semantic, and pragmatic view of theories in understanding theory construction; and the relation between ampliative inferences, heuristic reasoning, and models as a means for building new theories and knowledge. Through detailed arguments and examinations, the volume collectively challenges the orthodox view’s main tenets by characterizing the ways in which the different “stages” are logically, temporally, and psychologically intertwined. As a group, the chapters provide several attempts to answer long-standing questions about the possibility of a unified conceptual framework for building theories and formulating hypotheses.
Author: Emiliano Ippoliti
Publisher: Springer
ISBN: 331909159X
Category : Technology & Engineering
Languages : en
Pages : 194
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Book Description
How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.
Author: Carlo Cellucci
Publisher: Springer Nature
ISBN: 3030897311
Category : Mathematics
Languages : en
Pages : 457
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Book Description
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Author: Sorin Bangu
Publisher: Routledge
ISBN: 1351998447
Category : Mathematics
Languages : en
Pages : 319
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Book Description
This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.
Author: Carlo Cellucci
Publisher: Springer
ISBN: 3319532375
Category : Philosophy
Languages : en
Pages : 432
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Book Description
This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality.
Author: Anna Esposito
Publisher: Springer
ISBN: 331956904X
Category : Technology & Engineering
Languages : en
Pages : 380
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Book Description
This book presents a collection of contributions in the field of Artificial Neural Networks (ANNs). The themes addressed are multidisciplinary in nature, and closely connected in their ultimate aim to identify features from dynamic realistic signal exchanges and invariant machine representations that can be exploited to improve the quality of life of their end users. Mathematical tools like ANNs are currently exploited in many scientific domains because of their solid theoretical background and effectiveness in providing solutions to many demanding tasks such as appropriately processing (both for extracting features and recognizing) mono- and bi-dimensional dynamic signals, solving strong nonlinearities in the data and providing general solutions for deep and fully connected architectures. Given the multidisciplinary nature of their use and the interdisciplinary characterization of the problems they are applied to – which range from medicine to psychology, industrial and social robotics, computer vision, and signal processing (among many others) – ANNs may provide a basis for redefining the concept of information processing. These reflections are supported by theoretical models and applications presented in the chapters of this book. This book is of primary importance for: (a) the academic research community, (b) the ICT market, (c) PhD students and early-stage researchers, (d) schools, hospitals, rehabilitation and assisted-living centers, and (e) representatives of multimedia industries and standardization bodies.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
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Book Description
Author: Shahid Rahman
Publisher: Springer Nature
ISBN: 3030223825
Category : Philosophy
Languages : en
Pages : 285
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Book Description
This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor (qiyās al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyās al-dalāla, qiyās al-shabah). The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.
Author: Emiliano Ippoliti
Publisher: Springer
ISBN: 3319281631
Category : Science
Languages : en
Pages : 256
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Book Description
The book answers long-standing questions on scientific modeling and inference across multiple perspectives and disciplines, including logic, mathematics, physics and medicine. The different chapters cover a variety of issues, such as the role models play in scientific practice; the way science shapes our concept of models; ways of modeling the pursuit of scientific knowledge; the relationship between our concept of models and our concept of science. The book also discusses models and scientific explanations; models in the semantic view of theories; the applicability of mathematical models to the real world and their effectiveness; the links between models and inferences; and models as a means for acquiring new knowledge. It analyzes different examples of models in physics, biology, mathematics and engineering. Written for researchers and graduate students, it provides a cross-disciplinary reference guide to the notion and the use of models and inferences in science.
