Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic logicians, (...) Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

By delving into the history and development 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.

"This accessibly written book surveys all of the major competing theories of truth before formulating the new defence of the correspondence theory and then exploring the consequences of the theory for issues in epistemology and ontology. The book concludes by showing how the idea of 'propositional depth' can be used to dissolve the Liar paradoxes."--BOOK JACKET.

This essay argues that propositions are made true by facts. A proposition is the sense expressed by a statement (sentence token used to make a truth claim). Facts are positive or negative constitutive properties of the domain of discourse (usually the actual world). The presence of horses is a positive constitutive property of the world; the absence of unicorns is a negative one. This notion of constitutive properties accords well with the Hume-Kant claim that existence is not a property of (...) any individual said to exist. While Frege held existence to be a property of concepts and Russell held it to be a property of propositional functions, our view sees existence as a property of a domain of discourse. To say that Native Dancer exists is simply to say that the world is characterized by the presence of Native Dancer; to say that Pegasus does not exist is to say the world is characterized by the absence of Pegasus. Such properties of presence and absence are facts. Facts make true propositions true; nothing makes false propositions false (they simply fail to be made true). Facts are not items in the world; they are (constitutive) properties of the world. (shrink)

Post-Fregean logicians tend to ignore the traditional logic of Aristotle and the Scholastics, while in recent years, following the lead of Fred Sommers, the viability of a renewed logic of terms has been shown. This new term logic surpasses today s standard logic in simplicity and naturalness. The book exhibits how such a logic can shed light on a variety of challenges that face any system of formal logic.".

This text presents a number of reasons for the reinstatement of a traditional terminist logic, contributing to the ongoing debate concerning the proper connections between formal logic, natural language, artificial reasoning, and mathematics.

Quine has often expressed his impatience with the fact that "Identity evidently invites confusion between sign and object" He finds the confusion in the works of a great many philosophers. What is most interesting, however, is that he excludes Aristotle from his disapprobation. "On the other hand Aristotle had the matter straight: things are identical when 'whatever is predicated of the one should be predicated of the other'. I believe a closer inspection of Aristotle's views would lead Quine to abandon (...) this small truce with the Philosopher--unfortunately for Quine. (shrink)

Contemporary analytic philosophy can generally be characterized by the following tendencies: commitment to first-order predicate logic as the only viable formal logic; rejection of correspondence theories of truth; a view of existence as something expressed by the existential quantifier; a metaphysics that doesnOCOt give the world as a whole its due. This book seeks to offer an alternative analytic theory, one that provides a unified account of what there is, how we speak about it, the underlying logic of our language, (...) how the truth of what we say is determined, and the central role of the real world in all of this. The result is a robust account of reality. The inspiration for many of the ideas that constitute this overall theory comes from such sources as Aristotle, Leibniz, Ryle, and Sommers.". (shrink)

I argue here that recent discussions of f. sommers' "rule for enforcing ambiguity" have been mistaken on one of two grounds. either they misrepresent the sense of the rule or they misunderstand its intent. the rule is neither a sense rule nor a categorial rule, but a 'translation' rule relating senses of terms to categories of individuals. rather than a test for term ambiguity the rule is a test for theory coherence. finally, i show that there are many possible ways (...) of applying the rule. (shrink)

Es läßt sich zeigen‚ daß Leibniz' These, singuläre Subjekte könnten in gleicher Weise entweder als partikulär oder universell verstanden werden ‚ eine Folgerung aus zwei anderen Leibnizschen Thesen ist: 1. daß die Wahrheit eines Satzes eine Sache der Enthaltensbeziehung zwischen der Denotation oder Bedeutung seines Subjekt-und Prädikatbegriffs ist, und 2. daß der Begriff des Individuums vollständig ist. Hieraus ergibt sich u. a.‚ daß die These der wilden Quantität verstanden werden kann als integraler Teil von Leibniz' allgemeinem logisch-metaphysischen Programm.

A volume integrating various parts of Fred Sommer's theory on logic and the philosophy of language and also extending it in a variety of ways, such as semantics and modal logic.

Der Aufsatz wendet sich gegen die verbreitete Auffassung, Frege sei der Vater der modernen mathematischen Logik und Leibniz sei sein berühmtester Vorlaufer. Leibniz kann nur in einem sehr allgemeinen Sinne als Vorlaufer der mathematischen Logik in Anspruch genommen werden. Er mufß vielmehr als größter Vertreter der traditionellen Syllogistik bezeichnet werden. Denn Leibniz geht mit der Tradition aus vom kategorischen Satz, in welchem ein Prädikat von einem Subjekt ausgesagt wird. Im Gegensattz dazu legt Frege seiner Logik die Korrelation zwischen Fünktion und (...) Argument zugrunde. Fur Leibniz und die Tradition sind daher die Quantoren, die in der mathematischen Logik eine zentrale Rolle spielen, von untergeordneter Bedeutung. Für die Syllogistik bereiten Relationssätze besondere Probleme. Daß Leibniz versucht hat, diese Satze in die Syllogistik einzubeziehen, zeigt, daft er die Leistungsfahigkeit der formalen Logik besser erkannt hat als alle anderen. Fred Sommers und seine Schule haben Leibniz' Pläne zur Vollendung geführt. (shrink)

This title introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols. Taking students beyond classical mathematical logic, "Philosophical Logic" is a wide-ranging introduction to more advanced topics in the study of philosophical logic. Starting by contrasting familiar classical logic with constructivist or intuitionist logic, the book goes on to offer concise but easy-to-read introductions to such subjects as quantificational and syllogistic logic, modal logic and set theory. (...) Chapters of this title include: Sentential Logic; Quantificational Logic; Sentential Modal Logic; Quantification and Modality; Set Theory; Incompleteness; An Introduction to Term Logic; and, Modal Term Logic. In addition, the book includes a list of symbols and a glossary of terms for ease of reference and exercises throughout help students master the topics covered in the book. (shrink)

Les arguments contemporains en faveur de l'asymétrie des sujets et des prédicats prétendent que l'on ne peut nier, conjoindre, et disjoindre que des prédicats. Ces arguments se basent sur une assomption de Frege, à savoir, que des sujets doivent toujours être termes singuliers avec une référence à un objet individuel. Par contraste avec cette position, il y a un plus ancien point de vue qui n'accepte pas une telle assomption. Selon Leibniz, n'importe quels termes, y compris des singuliers, peuvent être (...) construits par combinaison. Une conséquence d'une telle combinaison est qu'un terme singulier et nié n'est pas singulier. De plus, des singuliers conjoints et disjoints, lorsque l'on les quantifie, font simplement référence distribuée/non-distribuée aux individus dont il est question. (shrink)

Fred Sommers passed away in October of 2014 in his 92nd year. Having begun his teaching at Columbia University, he eventually became the Harry A. Wolfson Chair in Philosophy at Brandeis University, where he taught from 1963 to 1993. During his long and productive career, Sommers authored or co-authored over 50 books, articles, reviews, etc., presenting his ideas on numerous occasions throughout North America and Europe. His work was characterized by a commitment to the preservation and application of historical insights (...) and to the value of a well-articulated, coherent logical system. He was recognized for his independence and refusal to accept any view on the basis of authority alone. This made him a formidable critic but accounted in part for his many innovative and original ideas. In spite of his general contrariness in logic, Sommers earned the respect of the majority of his contemporaries, including Russell, Quine, van Benthem, Hacking, Suppes, and Strawson. In 2005, he was the subjec... (shrink)

W.V. Quine has led many logicians in thinking that mathematical logic can offer insights into the syntax of natural language. One example of such an insight is the use of quantifier scope difference to resolve the ambiguity of sentences like ' I don't know every poem'. Such differences also are claimed to be useful in analyzing phrases such as 'the lady I saw you with'. But an older, Aristotelian theory of logical syntax can equally well resolve the ambiguity problem in (...) terms of term distribution. And it provides a better analysis of 'the lady' phrase by treating quantifiers as subject formatives rather than pronoun binders. (shrink)

Peter Geach has charged Aristotle with the sin of corrupting logic by initiating a process which led to the view that a sentence consists logically of just two names. This charge can only result from a clearly mistaken view of Aristotle's theory of logical syntax. Aristotle, unlike Geach, was careful to distinguish subjects from subject-terms and predicates from predicate-terms. He took both subjects and predicates as syntactical complexes. Geach, following Frege, holds a very different theory of logical syntax which takes (...) predicates, but not subjects, as syntactically complex. (shrink)

Les travaux de Fred Sommers dans le domaine de l'ontologie ont été l'objet, jusqu'à présent, de beaucoup moins d'attention critique qu'ils ne sont aptes à en susciter. C'est au cours des années soixante que Sommers a élaboré sa théorie et qu'il l'a rendue publique par le moyen d'une série d'articles et de conférences. Bien que ses travaux aient alors fait l'objet de quelques critiques ou commentaires, ils ont, depuis, généralement été passés sous silence. Récemment, la revue Monist a fait paraître (...) un numéro spécial entièrement consacré au thème des catégories. Considérant le thème, l'importance et la qualité des articles regroupés dans ce numéro, il est surprenant de constater que les idées hautement originales et suggestives de Sommers ne soient mentionnées par aucun des auteurs. Evidemment, une des raisons pour lesquelles les idées de Sommers suscitent présentement si peu d'intérêt est le fait que, depuis la fin des années soixante, il a lui-même laissé de côté l'ontologie pour se tourner vers la logique—un domaine où il a fait et fait toujours couler beaucoup d'encre. (shrink)