W artykule przedstawiam i wyjaśniam graficzną metodę przeprowadzania logicznych dowodów - prawdokrzew. Swoją prezentację ograniczyłem do klasycznego rachunku zdań. Artykuł jest również propozycją polskiego tłumaczenia pojęć występujących w tej metodzie. Tak dobrałem polską terminologię, aby przez wywoływanie emocjonalnych obrazów omawiana metoda stała się bardziej zrozumiała i łatwiejsza do zapamiętania.

Our goal is to articulate a clear rationale for relevance-sensitive propositional logic. The method: truth-trees. Familiar decomposition rules for truth-functional connectives, accompanied by novel ones for the for the arrow, together with a recursive rule, generate a set of ‘acceptable’ formulae that properly contains all theorems of the well-known system R and is closed under substitution, conjunction, and detachment. We conjecture that it satisfies the crucial letter-sharing condition.

We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely (...) specifies thatgrammatical object. More common is the situation, corresponding tounderspecification, in which there is more than one model. A situation inwhich there are no models corresponds to an ungrammatical input. (shrink)

This papers aims to analyse sentences of a self-referential language containing a truth-predicate by means of a Smullyan-style tableau system. Our analysis covers three variants of Kripke's partial-model semantics (strong and weak Kleene's and supervaluational) and three variants of the revision theory of truth (Belnap's, Gupta's and Herzberger's).

The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite tree (...) property. (shrink)

A method of supervaluation for Kripke’s theory of truth is presented. It differs from Kripke’s own method in that it employs trees; results in a compositional semantics; assigns the intuitively correct truth values to the sentences of a particularly tricky example of Gupta’s; and – it is argued – is acceptable as an explication of the correspondence theory of truth.

Recent experimental work has shown that the truth-value judgments of color predications, i.e. utterances of the form “the leaves on my tree are green” or “these walls are brown,” are influenced by slight changes in the context of utterance (Hansen and Chemla 2013, Ziółkowski, 2021). Most explanations of this phenomenon focus on the semantics of color adjectives. However, it is not clear if these explanations do justice to the nuances of the empirical data on context-sensitivity of color predications (...) (Ziółkowski, 2021). In contrast to the adjectival explanations, Agustin Vicente (2015) has recently proposed that the context-sensitivity of color predications can be explained by invoking the polysemy of the noun. In this paper, we present the results of three studies designed to empirically test this hypothesis: a traditional survey experiment (Study 1), an exploratory correlational study inspired by the semantic integration paradigm (Study 2a), and a follow-up experiment (Study 2b) that was designed to mitigate possible shortcomings of Study 2a. The results of our studies present preliminary evidence against Vicente’s theory. (shrink)

This study contrasts the evidence exclusion principles within the adversarial legal system of the United States, particularly the “fruit of the poisonous tree” doctrine, with the inquisitorial system of Vietnam. The U.S. model, emphasizing the exclusion of unlawfully obtained evidence to protect the presumption of innocence and ensure fair trials, relies on the Fourth Amendment to prevent police misconduct. Conversely, Vietnam, with its focus on uncovering the truth, has started to adopt adversarial elements, including evidence exclusion, to align (...) with international standards and enhance human rights protections within its criminal justice system. The research examines the application of the “fruit of the poisonous tree” doctrine in the U.S. and its implications for Vietnamese legal reforms, especially the proposed amendments to Article 87 of Vietnam's Criminal Procedure Code. These reforms aim to exclude unlawfully obtained evidence while allowing for the use of evidence collected independently from illegal actions. Highlighting the need for a balanced approach that respects procedural rights and promotes justice, the study advocates for comprehensive legal reforms in Vietnam. It suggests amendments to refine evidence exclusion principles, ensuring they reflect both the Vietnamese context and the progressive features of U.S. criminal justice practices, thereby enhancing the fairness and integrity of criminal proceedings. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups (...) of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

Public reason is central to John Rawls’s political liberalism, as a mechanism for citizens to discuss about matters of common interest. Although free and equal, reasonable and rational, citizens of a democratic society disagree on their understanding of truth and right, giving rise to the fact of reasonable pluralism. Thus, Rawls works out an idea of public reason which allows citizens to argue about political matters and yet remaining divided in their comprehensive doctrines. On the other hand, African culture (...) has developed the practice of palaver as way of dealing with social and political questions of the community. Usually held under a tree, scholars believe that the palaver is the African version of deliberative democracy. In this article, I elaborate the two ideas and compare them in order to see whether they are completely opposite or whether they can enrich each other. Thus, the first section focuses on Rawls’s idea of public reason, the second explores the palaver practice and the last section compares them. (shrink)

Common ancestry is a central feature of the theory of evolution, yet it is not clear what “common ancestry” actually means; nor is it clear how it is related to other terms such as “the Tree of Life” and “the last universal common ancestor”. I argue these terms describe three distinct hypotheses ordered in a logical way: that there is a Tree of Life is a claim about the pattern of evolutionary history, that there is a last universal (...) common ancestor is an ontological claim about the existence of an entity of a specific kind, and that there is universal common ancestry is a claim about a causal pattern in the history of life. With these generalizations in mind, I argue that the existence of a Tree of Life entails a last universal common ancestor, which would entail universal common ancestry, but neither of the converse entailments hold. This allows us to make sense of the debates surrounding the Tree, as well as our lack of knowledge about the last universal common ancestor, while still maintaining the uncontroversial truth of universal common ancestry. (shrink)

This chapter focuses on the different styles of moral relativism. The history of moral relativist thinking features different branches to the family tree, each representing a different impetus to relativism, and so producing a different style of moral relativist thought. At the root, however, is a broadly subjectivist parent idea that morality is at least in part the upshot of a shared way of life, and shared ways of life tend to vary markedly from culture to culture. The discussions (...) cover the branches of moral historicism, moral reasons, moral truth, and moral plurality. (shrink)

THE WEST AFRICAN NOTION OF THE "PALAVER," AS DESCRIBED BY CONgolese theologian Bénézet Bujo, is an excellent resource for postconflict reconciliation. The palaver creates physical, social, and psychological space for open communication so that persons can be integrated into the life and expectations of their communities. Through the palaver African communities heal sickness, educate their members about moral standards, and reconcile enemies. Three palaver-based commitments intersect with goals of postconflict reconciliation: a commitment to open communication, especially truth-telling; a commitment (...) to memory or developing a shared sense of the past; and a commitment to reconciliation at the communal level. Given the violent conflict still roiling parts of Africa today, it is critical to make explicit those African traditions that can encourage postconflict reconciliation and promote a just peace. (shrink)

Although the truth value (falsity) of "Henry knows that (dogs live in trees and beavers chew wood)" remains unchanged no matter what sentence is substituted in it for "beavers chew wood", we want not to regard the second as a truth functional component (tfc) of the first. Many definitions of "tfc" (e.g., Quine's) fail to insure satisfaction of the following principle: if p is a component of r which is in turn a component of q, then p is (...) a tfc of q if and only if 1) p is also a tfc of r, and 2) r is also a tfc of q. (shrink)

The title of the film Avatar specifically refers to the extension of the consciousness or spirit of a human individual into the body of an artificially created human–Na'vi hybrid. In his Philosophy of Nature, Wilhelm Friedrich Hegel argues that Nature is the embodiment – or, as we might say, the “avatar” – of what he calls the Absolute Spirit or God. Scientists, with their mechanistic models of nature, are essentially in league with the practical exploitation of the Earth. Their arid (...) abstractions abet the arrogant approach of commercial interests, whose dismissive attitude toward nature is captured well in Selfridge's remark: “They're just goddamn trees.” When Jake passes through “the eye of Eywa” at the conclusion of Avatar, leaving his former body and his former life behind and becoming fully embodied as part of “the people,” he implicitly recognizes the truth of Hegel's definition of Spirit. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 151-165 [Access article in PDF] Santayana and Buddhism: The Choice between the Cross and the Bo Tree Paul Grimley KuntzEmory UniversitySantayana honors Gotama Buddha as a profound religious genius as well as an original philosopher. Gotama's way is genuine spiritual wisdom, and constantly compared with Christian mysticism as a way of enlightenment. It is therefore understandable that a Spaniard, who learned his catechism in (...) Ávila, and who was educated in the New England of Emerson and other Transcendentalists who honored Oriental wisdom, should have so much to say about the Buddha and Buddhism.The effort of this paper is to gather many of the isolated passages to give a coherent picture of Santayana and Buddhism. One difficulty to be overcome is that the philosopher rarely quotes his sources (the exception is a single quotation from Dasgupta). Although Santayana has numerous opinions, he does not reveal on which translations he has relied. Nor does he contrast different traditions of Buddhists. To overcome the vagueness of scholarship, I have used the volumes found in Widener Library: the sorts of books known to Santayana's dissertation director, Josiah Royce, and those of a sympathetic sort that had led Santayana as early as the writing of his dissertation on Rudolf Hermann Lotze to reject the latter's defiantly Christian and Western contempt for oriental "superstition." The sympathy can be expressed as similar to that of Schopenhauer in reading the Upanishads or Wilhelm von Humboldt in studying the Bhagavadgita. Santayana's study makes him aware of his Catholicism but he is unlike the Jesuit Dahlmann who attacks Buddhism as Nihilism. Santayana is more like his contemporaries who worked in psychology and philosophy of religion. Although Friedrich Heiler's work 1 and writings of James Bissett Pratt 2 were a bit too late to have influenced Santayana, comparison serves to illuminate and strengthen Santayana's conclusions. Perhaps Heiler is even more appropriate because Buddhistic insights remind him of those of St. Theresa. Santayana would support Pratt's view that Nirvana is not the annihilation of all desire but the extinguishing of evil passions. What Santayana finds congenial in Christian Neo-Platonism and in Spinoza, as well as in Buddhism, is the achievement of freedom of the spirit. 3 It has become a commonplace of world history that the two greatest founders of religion whose ways of salvation triumphed in Europe and in Asia respectively are the Christ and the Buddha. Philosophers of religion like Heiler accept both as saviors with a universal message, one, Jesus "the master of prayer" ("der Meister des Gebets"), the [End Page 151] other, Gotama "the master of contemplation" ("der Meister der Versenking"). Santayana is not concerned with the fact of the success of their missions, for there are indeed other triumphs such as Mohammed's Islam, and if it be classified as a religion, Marx's Communism. Santayana is hardly offering his services as a philosophic mediator, as Whitehead tries to do in Religion in the Making, to bring the two communities of faith to a closer approximation of a truly universal religion. 4Santayana reveals great personal depth as he ponders the contrast between the Gospel and the Fourfold Noble Truth. What is the appeal of Christ on the Cross dying "to save us?" What is the appeal of "the serene Buddha, lifting the finger of meditation and profound counsel?" 5 These questions are asked in a meditation in Soliloquies in England in the sympathetic way of those American philosophers who like Pratt have the option of remaining Christian or converting to Buddhism. William James might well have patted Santayana on the back for struggling with the alternatives, for wrestling with a live option. Probably because of Buddha's message of truth, Santayana has shifted from religion as poetry, which James considered "rotten," to how "a general truth about existence and experience" is symbolized poetically, which James would consider healthy.In answering the question "What does the cross signify?" Santayana strips away the "various analogies, legal, sentimental, or chivalrous," and he... (shrink)

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus (...) for the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof. (shrink)

A fairly simple theory of the semantics of tense is obtained by combining three claims: (i) for any time t, a present-tense sentence `p' is either true or false at t; (ii) for any time t0 earlier than t, the future-tense sentence `It will be the case that p at t' is true at t0 if `p' is true at t, false otherwise; (iii) for any time t0 later than t, the past-tense sentence `It was the case that p at (...) t' is true at t0 if `p' is true at t, false otherwise. This theory, which has been called the theory of timeless truth, is often dismissed on the basis of its alleged incapacity to comply with indeterminism. Here, instead, it will be suggested that there is no reason to be dismissive. Section 1 provides some elucidations about the theory. Sections 2 and 3 explain how a foregone objection to it can be resisted. Sections 4 and 5 show that there is a plausible sense in which (i)-(iii) are compatible with indeterminism. Sections 6 and 7 dispel some misunderstandings that may lead to think that indeterminism is not vindicated in some important sense other than that outlined. (shrink)

Art is the one corner of human life in which we may take our ease. To justify our presence there the only thing that is demanded of us is a passion for representation. In other places our passions are conditional and embarrassed; we are allowed to have only so many as are consistent with those of our neighbours; with their convenience and well-being, with their convictions and prejudices, rules and regulations. Art means an escape from all this. Wherever her brilliant (...) standard floats the need for apologies and exonerations is over; there it is enough simply that we please or that we are pleased. There, the tree is judged only by its fruits. If these are sweet, one is welcome to pluck them.1. (shrink)

The subjective impression that statements are true increases when statements are presented repeatedly. There are two sources for this truth effect: An increase in validity based on recollection and increase in processing fluency due to repeated exposure . Using multinomial processing trees , we present a comprehensive model of the truth effect. Furthermore, we show that whilst the increase in processing fluency is indeed automatic, the interpretation and use of that experience is not. Experiment 1 demonstrates the standard (...) use of the fluency experience and Experiment 2 demonstrates that people can change the interpretation of the experience according to its ecological validity. By implication, the truth effect represents the adaptive usage of feedback received from internal processes. (shrink)

The book contains an introduction to basic logical concepts and methods. It covers traditional logic of categorical judgment and syllogism, modern propositional logic, and introductory elements of predicate logic with corresponding methods (truth tables, natural deduction, truth trees).

As I'm a writer, I'll begin with a story. It's not, I'm sorry to say, one of my own – I wish it were – but it is very philosophical. It's by the great blind Argentinian, Jorge Luis Borges, and it's called ‘Funes the Memorious’. Somewhere in a marshy province of Uruguay, Borges comes across a young man called Funes who has gone into an extraordinary mental state after a crippling fall from a horse. He is quite unable to forget (...) anything that has ever happened to him in his physical or mental life. He ‘not only remembered every leaf on every tree of every wood, but even every one of the times he had perceived or imagined it’ – and with exceptional vividness. In an attempt to manage this colossal burden, Funes thinks about classifying and reducing his memories to some practical order. But ‘two considerations dissuaded him: the thought that the task was interminable, and the thought that it was useless. He knew that at the hour of his death he would scarcely have finished classifying even all the memories of his childhood.’. (shrink)

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents (...) all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website. -/- Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject. -/- Provides an essential introduction to classical logic Emphasizes the how and why of logic Covers both formal and philosophical issues Presents all the major forms of proof--from trees to sequent calculus Features numerous exercises, with solutions available online The ideal textbook for undergraduates and graduate students . (shrink)

_The Logic of Our Language_ teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal symbols. Other logical (...) tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website. (shrink)

This paper is about The Truthmaker Problem for Presentism. I spell out a solution to the problem that involves appealing to indeterministic laws of nature and branching semantics for past- and future-tensed sentences. Then I discuss a potential glitch for this solution, and propose a way to get around that glitch. Finally, I consider some likely objections to the view offered here, as well as replies to those objections.

This book is highly recommended for those who want to break into the current realism/anti-realism debate, as it ranges over the fields of Philosophy of Science, Linguistic Analysis, Cognitive Science, etc. It would make an ideal text for those teachers who want to give their students a "map of the territory," indicating the various positions and implications of positions, and stances of the major "players"--Kuhn, Feyerabend, Van Fraasen, Davidson, Dummett, Putnam, Quine. In Devitt's view, two errors plague much of the (...) contemporary discussion: There is a confusion between what constitutes realism and what should be evidence for realism. The issue of truth is attacked first, and only subsequently the issue of realism. The order should properly be reversed. The more encompassing theory of the world takes up the realism/anti-realism debate; this should be settled first, on the usual grounds for accepting any theory-usefulness, plausibility, etc. The semantic issue of truth arises only in the relatively parochial and circumscribed sub-set of our general theory, the theory of people and their behavior, especially, for Devitt, their teaching, learning, and general communication. Our answer to the latter should not reflect back upon and control our answer to the former, as it has often done in the modern period, where the issue of certainty confused the issue of truth and made anti-realism more attractive than realism. Devitt gives the best description of his own position as follows: "he theory of understanding is the wrong place to start. The task is to put together the most plausible comprehensive theory of the phenomena that confront us. Theories of language and understanding are only two among many scientific theories that must be fitted into the comprehensive picture. Realism is an overarching empirical theory or principle. It is initially plausible. It is supported by arguments that make no appeal to theories of language or understanding. Its rivals all fail. What firmer place could there be to stand than Realism, as we theorize in such undeveloped areas as those of language and understanding? In contrast, the poor state of theories in those areas, whether verificationist or not, makes them a bad place from which to start theorizing, particularly in determining overarching principles about the nature of reality. To think otherwise is to put the cart before the horse". The arguments for the above claims are tight and reward the effort needed to work through them. Frequent cross-references keep the reader from losing the forest for the trees. The realist has felt naked and defenseless before the recent onslaughts of the above-mentioned anti-realists. Devitt, following the lead of Hartry Field, gives him a suit of clothes, indeed, in this reader's opinion, a suit of armor. Devitt chases down the enemies of realism into their rabbit holes; not the least impressive aspect of this work occurs when Devitt indicates the valid criteria of what should count as an "adequate explanation"--what should rationally be demanded--and how these can be abused. Devitt unmasks the "coyness" of certain well-known anti-realists for what it is--an inability to provide an explanation when one is truly needed, an inability camouflaged by demanding of the realist an "explanation" where none in fact is needed. This is an unusually comprehensive work, and a powerful, first-rate performance.--Patrick Madigan, Loyola University, New Orleans. (shrink)

A fairly simple theory of the semantics of tense is obtained by combining three claims: (i) for any time t, a present-tense sentence `p' is either true or false at t; (ii) for any time t0 earlier than t, the future-tense sentence `It will be the case that p at t' is true at t0 if `p' is true at t, false otherwise; (iii) for any time t0 later than t, the past-tense sentence `It was the case that p at (...) t' is true at t0 if `p' is true at t, false otherwise. This theory, which has been called the theory of timeless truth, is often dismissed on the basis of its alleged incapacity to comply with indeterminism. Here, instead, it will be suggested that there is no reason to be dismissive. Section 1 provides some elucidations about the theory. Sections 2 and 3 explain how a foregone objection to it can be resisted. Sections 4 and 5 show that there is a plausible sense in which (i)-(iii) are compatible with indeterminism. Sections 6 and 7 dispel some misunderstandings that may lead to think that indeterminism is not vindicated in some important sense other than that outlined. (shrink)

Hilary Putnam observes that a typical competent English speaker who cannot tell an elm tree from a beech tree may nevertheless use the word “elm” to make assertions and ask questions about elm trees. Putnam also observes that scientists may be wrong about the phenomena they investigate, while still being able to use their words to identify and raise research questions about it. This prompts him to ask what “language use” means in these contexts. He proposes two closely (...) related methods for answering this question. The first method is to investigate and clarify the uses of sentences and words in a given linguistic practice from the point of view of a participant in the practice. The second is to explain our applications of ‘is true’ and ‘refers’ to sentences and words whose uses are described in accord with the first method. In this paper I raise several problems for Putnam’s applications of these methods and sketch a different way of applying the methods that avoids the problems. (shrink)

Not only does Hoffman claim that we do not see reality as it is, but that unperceived brains, trees and moons do not exist. His “interface theory of perception” is a peculiar blend of metaphorical ontology (objects are icons, space-time is a desktop) and mathematical modelling (the game-theoretical argument that fitness trumps truth. Conflating abstractions with concrete experience, evolution is used to refute everything (including evolution itself. Hoffman’s sweeping iconoclasm then lands where it took off: addressing the problem of (...) consciousness. After arguing against reality, he will tell us what it is. (shrink)

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting (...) set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition. (shrink)

Designed for use by philosophy students, this 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues (...) concerning the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" (...) places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

A new theoretical approach to Aristotelian Logic based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof method for PL (...) inspired by the AL axioms is presented. This method mimics the underlying mechanics of the proof method from AL, and offers a complementary alternative to proof methods such as truth trees. (shrink)

The new edition of this widely used and respected textbook includes three new chapters on conditional logic. Other chapters have been revised and updated, making the second edition a fully comprehensive introduction to modal logics and their application. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, Modal Logics and Philosophy focuses on showing how useful modal logic can be as a tool for formal philosophical analysis. In Part 1, the reader is introduced to (...) some standard systems of modal logic and provided with a series of exercises that encourage proficiency in manipulating these logics. Girle emphasizes possible world semantics for modal logics and its formal method, Jeffrey-style truth-trees, in which standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, and obligation and permission. (shrink)

This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.

Table of Contents Volume I Preface to Volumes I and II: A Guide to the Primer Chapter 1, Basic Ideas and Tools Chapter 2, Transcription between English and Sentence Logic Chapter 3, Logical Equivalence, Logical Truths, and Contradictions Chapter 4, Validity and Conditionals Chapter 5, Natural Deduction for Sentence Logic: Fundamentals Chapter 6, Natural Deduction for Sentence Logic: Strategies Chapter 7, Natural Deduction for Sentence Logic: Derived Rules and Derivations without Premises Chapter 8, Truth Tree for Sentence Logic: (...) Fundamentals Chapter 9, Truth Trees for Sentence Logic: Applications Index for Volume 1 Solutions Manual for Volume 1 Table of Contents to Volume II Introduction to Predicate Logic Notes Chapter 1, Predicate Logic: Syntax Chapter 2, Predicate Logic: Semantics and Validity Chapter 3, More about Quantifiers Chapter 4, Transcription Chapter 5, Natural Deduction for Predicate Logic: Fundamentals Chapter 6, More on Natural Deduction for Predicate Logic Chapter 7, Truth Tress for Predicate Logic: Fundamentals Chapter 8, More on Truth Tress for Predicate Logic Chapter 9, Identity, Functions, and Definite Descriptions Chapter 10, Metatheory: The Basic Concepts Chapter 11, Mathematical Induction Chapter 12, Soundness and Completeness for Sentence Logic Trees Chapter 13, Soundness and Completeness for Sentence Logic Derivations Chapter 14, Koenig’s Lemma, Compactness, and Generalization to Infinite Sets of Premises Chapter 15, Interpretations, Soundness, and Completeness for Predicate Logic Index for Volume II Solutions Manual for Volume II Diagrammatic Summary of Rules Corrections to the Text. (shrink)

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

A comprehensive introduction to formal logic, Logic and Philosophy: A Modern Introduction is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Abundant, carefully crafted exercise sets accompanied by a clear, engaging exposition build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, identity, relations, set theory, modal logic, and Aristotelian logic. And as its title suggests, Logic and Philosophy is devoted not only to logic but also to the philosophical (...) debates that led to the development of the field. Much new material has been added for the 13th edition. An introduction to set theory and its relationship to logic and mathematics, including philosophical issues, is now part of Chapter 13. Chapter 15 is an introduction to modal logic and Kripke semantics, concluding with a discussion of philosophical problems with any logical accommodation of modalities. Instructors who do not wish to present proof methods will find chapters on truth trees for both sentential and first-order logic, and a presentation of trees for modal logic. Special features of this text include presentations of the history of logic, alternatives to traditional methods of conditional and indirect proof, and a discussion of semantic problems with universal and existential instantiations. Throughout, the authors are sensitive to philosophical issues that arise from the relationship between ordinary language, symbolic logic, and justifications for the syntax and semantics of the various symbolic languages. Discussions range from the justification of the truth table for the sentential rendering of if... then statements to semantic and syntactic paradoxes, including some troubling paradoxes that arise in ordinary language (e.g., the so-called hangman or surprise quiz paradox). Logic and Philosophy includes ample material for a one-semester or two-semester course and provides a thorough preparation for more advanced logic courses. (shrink)

INTRODUCTION TO LOGIC is a combined text and workbook for students beginning their study of logic. The workbook style allows students to proceed at their own pace, checking their progress in the end-of-chapter exercises. The text covers propositional logic and predicate logic with identity, the focus being on arguments. The methods of proof are truth-tables and truth-trees in the style of Jeffrey. This text is suitable for students of philosophy, computer science, mathematics and science in general.

REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Logic covers the basic concepts of logic, including sentences, arguments, and the evaluation of arguments. This book will give (...) the reader a clear understanding of sentence logic such as symbolization, semantics, and truth trees by giving concise definitions and examples of each. (shrink)

This clearly written book makes logic interesting and easier to learn without sacrificing content or rigor. KEY TOPICS: It covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. Logic is applied to materials with which readers will be familiar; both examples and exercises are drawn from newspapers, television, and other popular sources. MARKET: For individuals intrigued by the formal study of (...) logic. (shrink)

This clearly written book makes logic interesting and easier to learn without sacrificing content or rigor. It covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. Logic is applied to materials with which readers will be familiar; both examples and exercises are drawn from newspapers, television, and other popular sources. For individuals intrigued by the formal study of logic.

Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, _Logic_ introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic (...) including the Theory of Descriptions. _Logic _is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com. (shrink)

How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using “truth trees,” (...) as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. A concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics. (shrink)

First Logic is an introduction to the study of logic. Understanding the concepts of validity, invalidity, and acceptability, unacceptability of arguments is the primary focus of this book. The first chapter introduces the reader to some of the basic concepts, such as validity, soundness, and acceptability. Chapters two and three are devoted to Aristotelian logic, including the traditional square of opposition and Venn diagrams for sentences and arguments. Chapter four is a treatment of a number of important informal fallacies of (...) reasoning . Chapters five through eight are on various aspects of formal/symbolic logic: translating from natural language to the artificial language of logic; truth tables and truth trees; the method of natural deduction; predicate logic, including the logic of relations; and the concept and use of identity and its symbolization. (shrink)

The truth table method, natural deduction, and the truth tree method, the three validity proving methods standardly taught in an introductory logic course, are too clumsy for the battlefield of real-life. The “short truth table” test is handy at times, but it stumbles at many other times. In this paper, we set up a general method that can beat all the methods mentioned above in a contest of speed. Furthermore, the procedure can be step-by-step paraphrased in (...) a natural language, so that, unlike the other methods, a real-life logical problem can be analyzed and explained in a real-life language too. (shrink)

New features in this edition, in addition to truth tree systems for classical and nonclassical logics, include new and simpler rules for modal logic, deontic ...

Designed to make logic interesting and accessible -- without sacrificing content or rigor -- this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. Organizes content around natural-deduction formal-proof procedures, truth tables, and truth trees. Also presents logical statement connectives gradually, one per chapter, and finally, increases readers' awareness of the arguments they read and hear every day by providing examples of actual (...) arguments to which they can readily relate. (shrink)

Readers will learn what logic is, use truth tables and truth trees, make sense of complex arguments, and use logic every day.