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.

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)

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)

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)

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)

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.