*Radim Belohlavek, Joseph W. Dauben, and George J. Klir*

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780190200015
- eISBN:
- 9780190200039
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190200015.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, General

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the ...
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The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.Less

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.

*Penelope Maddy*

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199391752
- eISBN:
- 9780199391776
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199391752.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, General

This book is an examination of Wittgenstein’s philosophy of logic, early and late, undertaken from an austere naturalistic perspective called ‘‘Second Philosophy’’. On a generally metaphysical ...
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This book is an examination of Wittgenstein’s philosophy of logic, early and late, undertaken from an austere naturalistic perspective called ‘‘Second Philosophy’’. On a generally metaphysical account of the Tractatus, a key unnaturalistic assumption can be isolated. When it’s removed, the general outlines of the resulting position on the ground of logic come surprisingly close to the Second Philosopher’s roughly empirical account. In his later discussions of logic in Philosophical Investigations and Remarks on the Foundations of Mathematics, Wittgenstein also rejects this earlier assumption in favor of a picture rooted in the famous rule-following considerations. Here Wittgenstein and the Second Philosopher operate in even more thorough harmony. The parting comes when the Second Philosopher elaborates and confirms the account with empirical investigations into logical structure and cognition. At this point, Wittgenstein balks, but as a matter of personal animosity rather than philosophical principle.Less

This book is an examination of Wittgenstein’s philosophy of logic, early and late, undertaken from an austere naturalistic perspective called ‘‘Second Philosophy’’. On a generally metaphysical account of the *Tractatus*, a key unnaturalistic assumption can be isolated. When it’s removed, the general outlines of the resulting position on the ground of logic come surprisingly close to the Second Philosopher’s roughly empirical account. In his later discussions of logic in *Philosophical Investigations* and *Remarks on the Foundations of Mathematics*, Wittgenstein also rejects this earlier assumption in favor of a picture rooted in the famous rule-following considerations. Here Wittgenstein and the Second Philosopher operate in even more thorough harmony. The parting comes when the Second Philosopher elaborates and confirms the account with empirical investigations into logical structure and cognition. At this point, Wittgenstein balks, but as a matter of personal animosity rather than philosophical principle.

*Luciano Floridi*

- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199232383
- eISBN:
- 9780191594809
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232383.001.0001
- Subject:
- Philosophy, General, Logic/Philosophy of Mathematics

This book brings together the outcome of ten years of research. It is based on a simple project, which was begun towards the end of the 1990s: information is a crucial concept, which deserves a ...
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This book brings together the outcome of ten years of research. It is based on a simple project, which was begun towards the end of the 1990s: information is a crucial concept, which deserves a thorough philosophical investigation. So the book lays down the conceptual foundations of a new area of research: the philosophy of information. It does so systematically, by pursuing three goals. The first is metatheoretical. The book describes what the philosophy of information is, its problems, and its method of levels of abstraction. These are the topics of the first part, which comprises chapters one, two and three. The second goal is introductory. In chapters four and five, the book explores the complex and diverse nature of several informational concepts and phenomena. The third goal is constructive. In the remaining ten chapters, the book answers some classic philosophical questions in information-theoretical terms. As a result, the book provides the first, unified and coherent research programme for the philosophy of information, understood as a new, independent area of research, concerned with (1) the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilization, and sciences; and (2) the elaboration and application of information-theoretic and computational methodologies to philosophical problems.Less

This book brings together the outcome of ten years of research. It is based on a simple project, which was begun towards the end of the 1990s: information is a crucial concept, which deserves a thorough philosophical investigation. So the book lays down the conceptual foundations of a new area of research: the philosophy of information. It does so systematically, by pursuing three goals. The first is metatheoretical. The book describes what the philosophy of information is, its problems, and its method of levels of abstraction. These are the topics of the first part, which comprises chapters one, two and three. The second goal is introductory. In chapters four and five, the book explores the complex and diverse nature of several informational concepts and phenomena. The third goal is constructive. In the remaining ten chapters, the book answers some classic philosophical questions in information-theoretical terms. As a result, the book provides the first, unified and coherent research programme for the philosophy of information, understood as a new, independent area of research, concerned with (1) the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilization, and sciences; and (2) the elaboration and application of information-theoretic and computational methodologies to philosophical problems.