Introduction -- The concept of logical consequence -- Tarski's characterization of the common concept of logical consequence -- The logical consequence relation has a modal element -- The logical consequence relation is formal -- The logical consequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in terms of their inferential properties -- Model-theoretic and deductive-theoretic conceptions of logic -- Linguistic (...) preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logical consequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logical consequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logical consequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system? (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

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.

La lógica de la Edad Media se presenta a los lógicos contemporáneos, filósofos medievalistas, historiadores y filósofos de la lógica, como un campo tan fascinante como de difícil acceso. Parece demasiado intrincado para casi cualquier investigador de estas áreas encontrar la punta del ovillo que lo conduzca a transitar una presentación ordenada e inteligible de la lógica medieval. Este libro pretende solucionar este problema. Para ello, presenta de manera ordenada y autocontenida los desarrollos lógicos de la parte técnicamente más evolucionada (...) de la lógica de la Edad Media: el siglo XIV. A diferencia de otras presentaciones no evade los hechos históricos y culturales que conforman el panorama de la época ni las cuestiones filosóficas detrás de los desarrollos lógicos, a fin de entender cabalmente las cuestiones técnicas y no desnaturalizar la propuesta medieval. Los primeros tres capítulos se abocan a cuestiones introductorias, históricas y a la genealogía de los tópicos más importantes. El cuarto capítulo está dedicado a la presentación sintáctica del lenguaje de la lógica medieval. El quinto y el sexto a la metateoría de esta lógica. El séptimo explora y presenta la semántica. Los dos últimos nos brindan una reconstrucción racional, en términos del lenguaje simbólico contemporáneo, de la lógica de finales del siglo XIV. (shrink)

Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-order logic which is invariant for generated (...) submodels. We then show that $\mathscr{H}$ enjoys interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage $\mathscr{H}$. Finally, we provide complexity results for $\mathscr{H}$ and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}$. (shrink)

_ Source: _Volume 54, Issue 4, pp 335 - 355 Ian Rumfitt has recently drawn our attention to a couple of paradoxes of signification, claiming that although Thomas Bradwardine’s “multiple-meanings” account of truth and signification can solve the first of them, it cannot solve the second. The paradoxes of signification were in fact much discussed by Bradwardine’s successors in the fourteenth century. Bradwardine’s solution appears to turn on a distinction between the principal and the consequential signification of an utterance. However, (...) although such a distinction played an important role in his successors’ theories, it is shown that Bradwardine’s account of signification does not admit any such distinction, no part being prior to the others. Accordingly his solution, unlike those of his successors, does not fall prey to Rumfitt’s paradoxes. (shrink)

_ Source: _Page Count 21 Ian Rumfitt has recently drawn our attention to a couple of paradoxes of signification, claiming that although Thomas Bradwardine’s “multiple-meanings” account of truth and signification can solve the first of them, it cannot solve the second. The paradoxes of signification were in fact much discussed by Bradwardine’s successors in the fourteenth century. Bradwardine’s solution appears to turn on a distinction between the principal and the consequential signification of an utterance. However, although such a distinction played (...) an important role in his successors’ theories, it is shown that Bradwardine’s account of signification does not admit any such distinction, no part being prior to the others. Accordingly his solution, unlike those of his successors, does not fall prey to Rumfitt’s paradoxes. (shrink)

This book traces the development of formal logic from its origins inancient Greece to the present day. The authors first discuss the work oflogicians from Aristotle to Frege, showing how they were influenced by thephilosophical or mathematical ideas of their time. They then examinedevelopments in the present century.

Indexical reference is personal, ephemeral, confrontational, and executive. Hence it is not reducible to nonindexical reference to what is not confronted. Conversely, nonindexical reference is not reducible to indexical reference. (Castañeda 1989, p. 70).

Terence Parsons presents a new study of the development and continuing value of medieval logic, which expanded Aristotle's basic principles of logic in important ways. Parsons argues that the resulting system is as rich as contemporary first-order symbolic logic.

The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence (...) was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

Indexicals are linguistic expressions whose reference shifts from context to context: some paradigm examples are ‘I’, ‘here’, ‘now’, ‘today’,‘he’, ‘she’, and ‘that’. Two speakers who utter a single sentence that contains an indexical may say different things. For instance, Fred and Wilma say different things when they utter the sentence ‘I am female’. Many philosophers (following David Kaplan 1989a) hold that indexicals have two sorts of meaning. The first sort of meaning is often called ‘character’ or ‘linguistic meaning’; the second (...) sort is often called ‘content’. Using this terminology, we can say that the word ‘I’ has a single character (or linguistic meaning), but has different contents in different contexts. (shrink)

This is the first full-length translation of a work by the influential medieval logician Walter Burley. As such, it is an important addition to our knowledge of medieval logic, and will undoubtedly spur further research.

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional matrices and (...) the distinction between the context of formation and the context of evaluation of utterances. (shrink)

This paper argues for two principal conclusions about natural language semantics based on John Buridan's considerations concerning the notion of formal consequence, that is, formally valid inference. (1) Natural languages are essentially semantically closed, yet they do not have to be on that account inconsistent. (2) Natural language semantics has to be token based, as a matter of principle. The paper investigates the Buridanian considerations leading to these conclusions, and considers some obviously emerging objections to the Buridanian approach.

The expressions “now,” “today,” “tomorrow,” “yesterday,” “last month,” “a year ago,” “past,” “future,” “present,” and others like them are temporal indexicals. Temporal indexicals and dates are both quite different from names. Temporal indexicals often play an important part in philosophical arguments about time. An example is this claim of McTaggart's in his famous essay about the unreality of time. Role‐linking is the key to understanding why temporal indexicals are useful. The system of temporal indexicals and system of dates correspond to (...) two different but interconnecting ways people think about things – role‐based and descriptive. Both contrast with a third way, via detached notions. McTaggart's argument for the unreality of time has two sides. According to McTaggart, these two essential properties of time cannot be combined; people's concept of time is incoherent; there is not and could not be anything that fits the conception; time is unreal. (shrink)

Inference versus consequence , an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997 , Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is (...) republished here with only bibliographical changes and an afterword. (shrink)

Common representational content allows the Buridanian classification of human concepts discussed in the fourth chapter, which provides the first thoroughgoing, systematic survey of Buridan’s conception of a mental language. The chapter discusses the divisions of concepts into syncategorematic and categorematic, simple and complex, absolute and connotative, and singular and common concepts. Besides presenting these classifications, the chapter provides a detailed discussion of the idea of conceptual complexity as semantic compositionality, its role in Buridan’s nominalist program of “ontological reduction,” and his (...) precarious positioning of his account of the distinction between the representational contents of universal and singular concepts “somewhere between” those of Ockham and Aquinas. The discussion relates the emerging issues to contemporary concerns in the philosophy of mind and language, such as the possibility of forming genuinely singular concepts and simple substantial concepts that would allow some terms of our language to function as rigid designators; the differences between consciousness and mental content; and the problem of universal representation without real universals. (shrink)

This is a brief, accessible introduction to the thought of the philosopher John Buridan (ca. 1295-1361). Little is known about Buridan's life, most of which was spent studying and then teaching at the University of Paris. Buridan's works are mostly by-products of his teaching. They consist mainly of commentaries on Aristotle, covering the whole extent of Aristotelian philosophy, ranging from logic to metaphysics, to natural science, to ethics and politics. Gyula Klima argues that many of Buridan's academic concerns are strikingly (...) similar to those of modern philosophy and his work sometimes quite directly addresses modern philosophical questions. (shrink)

Buridan's life, works, and influence -- Buridan's logic and the medieval logical tradition -- The primacy of mental language -- The various kinds of concepts and the idea of a mental language -- Natural language and the idea of a formal syntax in Buridan -- Existential import and the square of opposition -- Ontological commitment -- The properties of terms (proprietates terminorum) -- The semantics of propositions -- Logical validity in a token-based, semantically closed logic -- The possibility of scientific (...) knowledge -- Buridan's anti-skepticism -- Buridan's essentialist nominalism. (shrink)

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be (...) familiar with the medieval logicians and their work. In this article we give an overview of Prior's work in ancient and medieval logic. (shrink)

We present Prior's discussion of a puzzle about valditity found in the writings of the fourteenth-century French logician Jean Buridan and show how Prior's study of this puzzle may have provided the conceptual inspiration for his development of hybrid logic.