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Relational Syllogisms and the History of Arabic Logic, 900-1900
Relational inferences are a well-known problem for Aristotelian logic. This book charts the development of thinking about this problem by logicians writing in Arabic from the ninth to the nineteenth century. It shows that that the development of Arabic logic did not - as is often supposed - come to an end in the fourteenth century.
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Fuzzy logic and mathematics : a historical perspective
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.
eBook
Non-Boolean classical relevant logics I
Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing.
Journal Article
Made with words
Hobbes's extreme political views have commanded so much attention that they have eclipsed his work on language and mind, and on reasoning, personhood, and group formation. But this work is of immense interest in itself, as Philip Pettit shows inMade with Words, and it critically shapes Hobbes's political philosophy.
Pettit argues that it was Hobbes, not later thinkers like Rousseau, who invented the invention of language thesis--the idea that language is a cultural innovation that transformed the human mind. The invention, in Hobbes's story, is a double-edged sword. It enables human beings to reason, commit themselves as persons, and incorporate in groups. But it also allows them to agonize about the future and about their standing relative to one another; it takes them out of the Eden of animal silence and into a life of inescapable conflict--the state of nature. Still, if language leads into this wasteland, according to Hobbes, it can also lead out. It can enable people to establish a commonwealth where the words of law and morality have a common, enforceable sense, and where people can invoke the sanctions of an absolute sovereign to give their words to one another in credible commitment and contract.
Written by one of today's leading philosophers,Made with Wordsis both an original reinterpretation and a clear and lively introduction to Hobbes's thought.
eBook
Locke and “ad”
In IV, xvii, 19–22 of his Essay, Locke employs Latin labels for four kinds of argument, of which one (ad hominem) was already in circulation and one (ad judicium) has never had much currency. The present proposal seeks to locate and clarify what Locke was aiming to describe, and to contrast what he says with some subsequent uses that have been made of these labels as if they named fallacies. Though three of the four kinds of argument that Locke picks out are often less than decisive, he casts no aspersion on the legitimacy of their use in debate.
Journal Article
The medieval theory of consequence
The recovery of Aristotle's logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle's theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as 'If it's a man, then it's an animal'. Aristotle's notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation.
Journal Article
Fallacies and Their Place in the Foundations of Science
It has been said that there is no scholarly consensus as to why Aristotle’s logics of proof and refutation would have borne the title Analytics. But if we consulted Tarski’s (Introduction to logic and the methodology of deductive sciences, Oxford University Press, New York, 1941) graduate-level primer, we would have the perfect title for them: Introduction to logic and to the methodology of deductive sciences. There are two strings to Aristotle’s bow. The methodological string is the founding work on the epistemology of science, and the logical string sets down conditions on the proofs that bring this knowledge about. The logic of proof presents a difficulty whose solution exceeds its theoretical reach. The logic of refutation takes the problem on board, and advances a solution whose execution is framed by fallacy-avoidance at the beginning and fallacy-adoption at the end. But with a difference: the avoidance-fallacies are of Aristotle’s own conception, whereas the adoption-fallacies, so judged in the modern tradition, aren’t fallacies at all for Aristotle. The avoidance-fallacies are begging the question and ignoratio elenchi, and the adoption-fallacies, fallacies in name only, are the ad hominem and ad ignorantiam, an inductive turning in the first instance, and an abductive finish in the second.
Journal Article
Defeasible normative reasoning
The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations (in analogy to intrinsic and extrinsic utilities). It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function (as suggested in qualitative decision theory). The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism.
Journal Article
Alan Turing : his work and impact
In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences Mathematics, also from the AAPNamed a 2013 Notable Computer Book in Computing Milieux by Computing ReviewsAffordable, key collection of the most significant papers by A.M. TuringCommentary explaining the significance of each seminal paper by preeminent leaders in the fieldAdditional resources available online
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