Giuseppe Primiero - Böcker

Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, combining both historical and systematic analyses. The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues. For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future.

Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, combining both historical and systematic analyses.The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues.For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future.

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.

This book constitutes the refereed proceedings of the 15th Conference on Computability in Europe, CiE 2019, held in Durham, UK, in July 2019.The 20 revised full papers presented were carefully reviewed and selected from 35 submissions. In addition, this volume includes 7 invited papers. The conference CiE 2018 had the following six special sessions: computational neuroscience, history and philosophy of computing, lowness notions in computability, probabilistic programming and higher-order computation, smoothed and probabilistic analysis of algorithms, and transnite computations.

This book presents a historical and philosophical analysis of programming systems, intended as large computational systems like, for instance, operating systems, programmed to control processes.

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.

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference.The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.