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Syllogisms are the oldest and most carefully studied logical forms. This book attempts to convey some sense of the tradition in which syllogistic logic has developed; but the book also goes well beyond the classical theory. Rather than limiting syllogistic logic to the quantifiers 'all' and 'some', this book begins with an expanded group of ordinary language quantifiers, including 'few', 'most', and 'many', and ends with a full range of proportional quantifiers, such as '23% of' and 'more than 98% of'. The book gives a point by point explanation of syllogistic logic, directed primarily at beginners, but offering material that will be new and interesting even to advanced scholars.
The book begins with an extensive survey of the history of logic diagrams, including looking at possible diagrams from Aristotle, the development of both linear and closed figure diagrams by Leibniz, Lambert, Euler, Venn’s new system, Peirce’s Existential Graphs, and Frege’s two-dimensional notation as a kind of logic diagram system. During most of the 20th century, there was little regard for efforts to construct logic diagrams. However, since the 1980s there has been an increasing interest in such diagrams. Ever larger numbers of philosophers, logicians, mathematicians, computational scientists, and cognitive scientists have turned their attention to building, analyzing, using, or exploring in other ways systems of logic diagrams. The system offered here makes use of line segments and points and it enjoys a number of important advantages: it is simple, natural, and both expressively and inferentially powerful. It can be used to analyze syllogisms (including those involving relational terms) and arguments involving unanalyzed statements. Understanding such a system can shed valuable light on how ordinary people naturally reason.
By delving into the history and envelopment of logic from its beginnings to the modern era, George Englebretsen rehabilitates term logic and demonstrates that an enhanced traditional logic remains a viable possibility. Taking inspiration from Fred Sommers' work, he creates an updated and fascinating version of term logic; one he believes to be just as legitimate as, and in ways superior to, the currently predominant mathematical logic.
If you love words, you’ll love -iSMs! There are words—and then there are -ISMs. More than just expressions with a wacky suffix, -ISMs are the eccentric geniuses of the English language. From esoteric philosophies and arcane religions to avant-garde artistic movements and kinky sexual practices, -ISMs describe our highest forms of human thought and endeavor—and our very lowest. In this engaging and enlightening book, you’ll explore more than 200 of the most interesting, mysterious, and obscure -ISMs, discovering the true meaning of these intriguing words as well as the often bizarre etymologies, mythologies, and the common and not-so-common usage behind them. With -ISMs as your guide, you’ll be the most sophisticated wordsmith since Yogi Berra.
This book constitutes the refereed proceedings of the 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, held in Tallinn, Estonia, in August 2020.* The 20 full papers and 16 short papers presented together with 18 posters were carefully reviewed and selected from 82 submissions. The papers are organized in the following topical sections: diagrams in mathematics; diagram design, principles, and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; logic and diagrams; and posters. *The conference was held virtually due to the COVID-19 pandemic. The chapters ‘Modality and Uncertainty in Data Visualization: A Corpus Approach to the Use of Connecting Lines,’ ‘On Effects of Changing Multi-Attribute Table Design on Decision Making: An Eye Tracking Study,’ ‘Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs,’ ‘The DNA Framework of Visualization’ and ‘Visualizing Curricula’ are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
This title was first published in 2000: Intermediate quantifiers express logical quantities which fall between Aristotle's two quantities of categorical propositions - universal and particular. "Few", "many" and "most" express the most commonly referred to intermediate quantifiers, but this book argues that an infinite number can be understood through a deeper examination of the logical nature of all intermediate quantifiers. Presenting and analyzing the logical and linguistic features of intermediate quantifiers, in a fashion typical of traditional logic, Philip L. Peterson presents an account integrating the logic and semantics of intermediate quantifiers with the two traditional quantities by traditional methods. Having introduced the basic idea of how to approach the task in the first chapter, with heavy emphasis on the linguistic meanings and ordinary uses of English intermediate quantifier expressions, Peterson then undertakes the task of completely integrating the three basic intermediate quantities into traditional logic in the following chapter.
This book constitutes the refereed proceedings of the 9th InternationalConference on the Theory and Application of Diagrams, Diagrams 2016,held in Philadelphia, PA, USA, in August 2016. The 12 revised full papers and 11 short papers presented together with 5 posters were carefully reviewed and selected from 48 submissions. The papers are organized in the following topical sections: cognitive aspects of diagrams; logic and diagrams; Euler and Venn diagrams; diagrams and education; design principles for diagrams; diagrams layout.
This title was first published in 2000: Intermediate quantifiers express logical quantities which fall between Aristotle's two quantities of categorical propositions - universal and particular. "Few", "many" and "most" express the most commonly referred to intermediate quantifiers, but this book argues that an infinite number can be understood through a deeper examination of the logical nature of all intermediate quantifiers. Presenting and analyzing the logical and linguistic features of intermediate quantifiers, in a fashion typical of traditional logic, Philip L. Peterson presents an account integrating the logic and semantics of intermediate quantifiers with the two traditional quantities by traditional methods. Having introduced the basic idea of how to approach the task in the first chapter, with heavy emphasis on the linguistic meanings and ordinary uses of English intermediate quantifier expressions, Peterson then undertakes the task of completely integrating the three basic intermediate quantities into traditional logic in the following chapter.
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