Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.

In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

Las reflexiones recogidas en este volumen constituyeron, en su mayor parte, el contenido del Seminario de Semántica celebrado en la Universidad de Oviedo, y uno de los textos ("Léxico y cognición: ¿hay términos de base?") formó parte del programa de conferencias de Año Europeo de las Lenguas. Conforme al espíritu de esas jornadas centradas en la pluralidad lingüística, esta publicación se hace simultáneamente en dos lenguas: español y francés. Aunque se tomen como referencia aspectos concretos de dos lenguas concretas, la (...) española y la francesa, los problemas que aquí se suscitan son de índole general, ya que afectan, y de manera crucial, a todas las lenguas. (shrink)

The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it (...) says (only) that it is false. -/- How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. -/- JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. (shrink)

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

In his book The Austrian Mind (1972) W. M. Johnston observes that between 1861 and 1938 a striking number of Austrian intellectuals committed uicide. He also remarks that prior to 1920 suicide was relatively rare among Hungarian intellectuals, and as a possible explanation he refers to their more intensive political activity. The present paper investigates relations between a society's intellectual life and its general suicidal tendencies. In so doing it takes up a central theme of T. G. Masaryk's Suicide as (...) a Social Mass Phenomenon of Modern Civilization, published in Vienna in 1881. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.

The dominating theologian in Europe between Thomas Aquinas and John Duns Scotus, Henry of Ghent produced a massive Summa of Ordinary Questions as well as fifteen quodlibets during his long tenure at the University of Paris. His work constituted a new synthesis of faith and reason which competed with that of Thomas Aquinas and influenced the history of both philosophy and theology. The first five articles of the Summa, dealing with various issues associated with human knowledge, constitute an adequate introduction (...) to Henry's thought. In them we find his approach to fundamental principles and themes developed in detail in the rest of his corpus. Of the five, only article one has appeared as a whole in English translation. The next four articles reinforce and develop the findings of the first article, providing additional treatments that indicate Henry's principles and orientation. In fact, these four articles alone provide a condensed but remarkably rich portrait of Henry's basic thought, and so are an invaluable resource for beginning and advanced students alike. Articles 2-5 include important positions on knowledge and reality, a conception of humanity's ultimate purpose and the pursuits most conducive to it, and an approach to faith and reason. These four articles are presented here for the first time in English translation with an introduction and notes. Along with the translation, the volume includes the Latin text of the modern critical edition. --Book cover. (shrink)

The Liar paradox raises foundational questions about logic, language, and truth. A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says that it is false.How, (...) then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another.JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. (shrink)

I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection on (...) the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)

This chapter first surveys general issues in the epistemic internalism / externalism debate: what is the distinction, what motivates it, and what arguments can be given on both sides. -/- The second part of the chapter will examine the internalism / externalism debate as regards to the specific case of the epistemology of memory belief.

On the face of it, Maurice Merleau-Ponty’s views bear a strong resemblance to contemporary disjunctivist theories of perception, especially John McDowell’s epistemological disjunctivism. Like McDowell (and other disjunctivists), Merleau-Ponty seems to be a direct realist about perception and holds that veridical and illusory perceptions are distinct. This paper furthers this comparison. Furthermore, it is argued that elements of Merleau-Ponty’s thought provide a stronger case for McDowell’s kind of epistemological view than McDowell himself provides. Merleau-Ponty’s early thought can be used to (...) develop a unique version of epistemological disjunctivism that is worth consideration alongside contemporary views on perceptual knowledge. (shrink)

In this volume of fourteen original essays, a distinguished team of contributors explore the extent to which, if at all, deflationism can accommodate paradox.