Explains Aristotle's views on the possibility of continuous variation between biological species. While the Porphyrean/Linnean classification of species by a tree suggests species are distributed discretely, Aristotle admitted continuous variation between species among lower life forms.

This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)

The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...) in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

In Studies on Early Modern Aristotelianism Paul Richard Blum shows that Aristotle’s thought remained the touchstone of modern philosophy; for it was the philosophy taught at universities. The concept of philosophy at Jesuit schools forms the first part of this book. Their impact on the sciences and mathematics in combination with Renaissance ideas of nature is the topic of the second part. The transformation of Aristotelian metaphysics and theology under the influence of the Renaissance is the third area of this (...) book. Surprising continuity from the late Middle Ages into modernity and the radical difference of subject centered modern philosophy from ‘teachable’ school philosophy are innovative in these studies. (shrink)

This paper contains a discussion of striking similarities between influential philosophical concepts of the past and the approaches currently employed in selected areas of computer science. In particular, works of the Pythagoreans, Plato, Abelard, Ash’arites, Malebranche and Berkeley are presented and contrasted with such computer science ideas as digital computers, object-oriented programming, the modelling of an object’s actions and causality in virtual environments, and 3D graphics rendering. The intention of this paper is to provoke the computer science community to go (...) off the beaten path in order to find inspiration for the development of new approaches in software engineering. (shrink)

Programming languages have developed significantly over the past century to provide complex models to think about and describe the world and processes of computation. Out of Alan Kay’s Smalltalk and a number of earlier languages, object-oriented programming has emerged as a preeminent mode of writing and organizing programs. Tracing the history of object-oriented programming from its origins in Simula and Sketchpad through Smalltalk, particularly its philosophical and technical developments, offers unique insights into philosophical questions about objects, language, and our digital (...) technologies. These early attempts to understand objects as basic elements of computation demonstrate the ways in which language, while firmly planted in the material reality of computation, must delimit objects from each other. This essay critically explores this history and explicates a theory of objects suggested by the development of object-oriented programming languages, which insists on the importance of language for representing and delimiting objects. It argues that the philosophies behind object-oriented programming are ultimately opposed to the claims of object-oriented ontology and find themselves more closely allied with philosophies that insist on the mediation of what exists through language. (shrink)

For nearly four centuries Peter of Spain's influential Summaries of Logic was the basis for teaching logic; few university texts were read by more people. This new translation presents the Latin and English on facing pages, and comes with an extensive introduction, chapter-by-chapter analysis, notes, and a full bibliography.

The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...) two new logical geometries, and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams. (shrink)

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

Chisholm, in these 18 essays, combines an internal approach to knowledge with an international approach to metaphysics, presupposing that the self is best known, and that knowledge of the self can serve as a key for further understanding. Among his topics are the whole and parts, freedom and the self, and substance and attribution. Annotation copyrighted by Book News, Inc., Portland, OR.

Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...) to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before. (shrink)