Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised. What has been missing until now is an attempt to unite the motives underlying both approaches. Paul Hoyningen-Huene’s Formal Logic seeks to find a balance between the (...) necessity of formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine’s artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom. (shrink)

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint . Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Perfect for students with no background in logic or philosophy, Simple Formal Logic provides a full system of logic adequate to handle everyday and philosophical reasoning. By keeping out artificial techniques that aren’t natural to our everyday thinking process, Simple Formal Logic trains students to think through formal logical arguments for themselves, ingraining in them the habits of sound reasoning. Simple Formal Logic features: a companion website with abundant exercise worksheets, study (...) supplements (including flashcards for symbolizations and for deduction rules), and instructor’s manual two levels of exercises for beginning and more advanced students a glossary of terms, abbreviations and symbols. This book arose out of a popular course that the author has taught to all types of undergraduate students at Loyola University Chicago. He teaches formal logic without the artificial methods–methods that often seek to solve farfetched logical problems without any connection to everyday and philosophical argumentation. The result is a book that teaches easy and more intuitive ways of grappling with formal logic–and is intended as a rigorous yet easy-to-follow first course in logical thinking for philosophy majors and non-philosophy majors alike. (shrink)

The wider topic to which the content of this paper belongs is that of the relationship between formal logic and real argumentation. Of particular potential interest in this connection are held to be substantive arguments constructed by philosophers reputed equally as authorities in logical theory. A number of characteristics are tentatively indicated by the author as likely to be encountered in such arguments. The discussion centers afterwards, by way of specification, on a remarkable piece of argument quoted in (...) Cicero’s dialog On Divination and ascribed to Stoic thinkers. The Stoics’ formal theory of inference is summarily referred to in this context, with special emphasis on their basic deductive schemata (‘indemonstrables’), some of them recognizable as links in the overall structure of the quoted argument. The main lines of Cicero’s criticism of the Stoic argument are next commented upon, with emphasis on his implied view as to the requirements of a good argument. Towards the end of the paper, a few considerations are added on the changes in the prevailing style of argumentation conspicuous in the three famous Roman Stoics. (shrink)

... and a reading knowledge of formal logical symbolism is essential too. (Philosophers often use bits of logical symbolism to clarify their arguments.) Because the artificial and simply formal languages of logic give us highly illuminating objects of comparison when we come thinking about how natural languages work. (Relevant to topics in ‘philosophical logic’ and the philosophy of language.) But mainly because it us the point of entry into the study of one of the major intellectual (...) achievements by philosophers of the 20th – i.e. the development of mathematical logic. (Not least in Cambridge: Russell and Whitehead, Ramsey, Turing.). (shrink)

Central topics in medieval logic are here treated in a way that is congenial to the modern reader, without compromising historical reliability. The achievements of medieval logic are made available to a wider philosophical public then the medievalists themselves. The three genres of logica moderna arising in a later Middle Ages are covered: obligations, insolubles and consequences - the first time these have been treated in such a unified way. The articles on obligations look at the role of (...) logical consistence in medieval disputation techniques. Those on insolubles concentrate on medieval solutions to the Liar Paradox. There is also a systematic account of how medieval authors described the logical content of an inference, and how they thought that the validity of an inference could be guaranteed. (shrink)

This work brings together three themes whose relationship has gone unexplored in the recent literature of philosophy: the transcendental phenomenology of Edmund Husserl, the phenomenological ontology of Martin Heidegger and the discipline of logic, especially formal logic. Part One and Two of the work present a detailed explication of Husserl's and Heidegger's philosophy of logic which are respectively characterized as an archeology of logic based upon transcendental phenomenological criticism and a radical phenomenology of logic (...) based upon phenomenological criticism which issues from a concern with the question of the meaning of Being. Part Three, then, offers a comparative analysis combined with a critical appraisal of these two philosophies of logic in order to achieve a more penetrating understanding of the relationship between Husserl and Heidegger. Thus, in one sense, this work takes the domain of logic and the varying approaches to it by Husserl and Heidegger as a clue to the similarities and dissimilarities within the thinking of these two phenomenologists, especially with regard to the understanding each has of the goal and method of phenomenology, and the results proper to phenomenological reflection. (shrink)

This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect (...) it with human reasoning, thus providing a uniform argumentation-based view of both informal and formal logic. (shrink)

In addition to a somewhat detailed exposition of certain portions of what may be called the book-work of formal logic, the following pages contain a number of problems worked out in detail and unsolved problems, by means of which the student may test his command over logical processes. In the expository portions of Parts I, II, and III, dealing respectively with terms, propositions, and syllogisms, the traditional lines are in the main followed, though with certain modifications; e.g., in (...) the systematisation of immediate inferences, and in several points of detail in connexion with the syllogism. For purposes of illustration Euler's diagrams are employed to a greater extent than is usual in English manuals. In Part IV, which contains a generalisation of logical processes in their application to complex inferences, a somewhat new departure is taken. So far as I am aware this part constitutes the first systematic attempt that has been made to deal with formal reasonings of the most complicated character without the aid of mathematical or other symbols of operation, and without abandoning the ordinary non-equational or predicative form of proposition. This attempt has on the whole met with greater success than I had anticipated; and I believe that the methods formulated will be found to be both as easy and as effective as the symbolical methods of Boole and his followers. The book concludes with a general and sure method of solution of what Professor Jevons called the inverse problem, and which he himself seemed to regard as soluble only by a series of guesses. (shrink)

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and (...) computational. (shrink)

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each (...) step, and the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic’s coming of age in the 20th century: Godel’s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing (...) logical formalism. I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

After critiquing the arguments against using formal logic to teach critical thinking, this paper argues that for theoretical, practical, and empirical reasons, instruction in the fundamentals of formal logic is essential for critical thinking, and so should be included in every class that purports to teach critical thinking.

The problem of the relationship between formal logic and philosophy, which arose when formal logic arose, continues to concern both Soviet and foreign philosophers and logicians. Interest in this problem is traceable to a number of factors, among which, it should be noted at the outset, is the appearance of dialectical, logic. With the emergence of dialectical logic, the question of the relationship of formal logic to philosophy is posed anew. No matter (...) how we approach the question of the subject matter of dialectical logic, there is no doubt of the fact that, being logic, it is concerned with the investigation of philosophical problems. It follows that logic is at the same time philosophy or, at least, a portion of philosophy. (shrink)

_Formal Logic_ is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are (...) taught through over 400 exercises. A companion website offers supplemental practice software and tutorial videos. (shrink)

I critically review Raymond Turner’s Computational Artifacts – Towards a Philosophy of Computer Science by placing beside his position a rather different one, according to which computer science is a branch of, and is therefore subsumed by, immaterial formal logic.

In everyday speech, expressions of the type "that thing exists" are frequently employed. What do they mean? They must be dealt with at the logical level where we seek greater precision. Also at the philosophical level, the predicate "exists" stands in need of analysis, inasmuch as its meanings are associated in one way or another with the meanings of the term "reality." It might also be stated that every entity, to the degree that it is "real" in one sense or (...) another, exists in a manner distinctive to it. In this sense, one might say that this is a problem of cognition of the history of an object, and its results are set forth in various existential judgments. Nevertheless, analysis of "existence" precisely as a predicate is necessary. It bears a specifically logical character and, moreover, is related in a lesser degree to the purely linguistic side of things than in the case of analysis of the meanings of the predicate "to be.". (shrink)

Science studies not only material entities and phenomena, but their reflections in the minds of men, in the form of sensations, perceptions, concepts, and the like. The study of a phenomenon like language involves simultaneous examinations of material entities and the aspect of language which pertains to meaning, which takes shape as a result of man's reflection in cognition of the world around him.

Originally published in 1937. A short account of the traditional logic, intended to provide the student with the fundamentals necessary for the specialized study. Suitable for working through individualy, it will provide sufficient knowledge of the elements of the subject to understand materials on more advanced and specialized topics. This is an interesting historic perspective on this area of philosophy and mathematics.

Aristotle's logical and metaphysical works contain elements of three distinct types of formal theory: an ontology, a theory of consequences, and a theory of reasoning. His formal ontology (unlike that of certain later thinkers) does not require all propositions of a given logical form to be true. His formal syllogistic (unlike medieval theories of consequences) was guided primarily by a conception of logic as a theory of reasoning; and his fragmentary theory of consequences exists merely as (...) an adjunct to the syllogistic. When theories of consequences took centre stage in the Middle Ages, the original motivation for the theory of the syllogism was forgotten. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

_A Pocket Guide to Formal Logic_ is a succinct primer meant especially for those without any prior background in logic. Its brevity makes it well-suited to introductory courses in critical thinking or introductory philosophy with a formal logic component, and its friendly tone offers a welcoming introduction to this often-intimidating subject. The book provides a focused presentation of common methods used in statement logic, including translations, truth tables, and proofs. Supplemental materials—including more detailed treatments of (...) select methods and concepts as well as additional sample questions and answers—are available on a companion website. (shrink)

In his article “On Teaching Logic,” Peter Geach reminds us of a distinction that will prove convenient in the present context, despite the ambiguity on both sides of the distinction.

Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties (...) without sacrificing insight into argument. (shrink)

In the paper I ask the question about the relation between formal logic and the natural logic of human mind. By a natural logic I mean the ways of thinking of a person that is intelligent but untrained in formal logic. As it turns out that the laws, rules or properties of formal logic in some cases diverge from the natural ways of reasoning, I explain the causes of this divergence. Since the (...) majority of research in this area has been carried out from the standpoint of psychology, as a logician I suggest a slight change of the angle from which we look at the problem. I argue that certain narrowing of an interdisciplinary research would be helpful in getting a better picture of natural logic, and might provide a new stimulus for formal investigations. (shrink)