The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated (...) pair), that were classically reducible to the first, gain independency in fuzzy setting. (shrink)

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like “antitone” or “isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering (...) thus the case of a possibly non-commutative conjunction too. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

The objects we encounter in ordinary life and scientific practice - cars, trees, people, houses, molecules, galaxies, and the like - have long been a fruitful source of perplexity for metaphysicians. The Structure of Objects gives an original analysis of those material objects to which we take ourselves to be committed in our ordinary, scientifically informed discourse. Koslicki focuses on material objects in particular, or, as metaphysicians like to call them "concrete particulars", i.e., objects which occupy a single region (...) of space-time at each time at which they exist and which have a certain range of properties that go along with space-occupancy, such as weight, shape, color, texture, and temperature. The Structure of Objects focuses in particular on the question of how the parts of such objects, assuming that they have parts, are related to the wholes which they compose. (shrink)

A highly condensed account of the author's present view of some philosophical problems unresolved in The Structure of Scientific Revolutions. The concept of incommensurability, now considerably developed, remains at center stage, but the evolutionary metaphor, introduced in the final pages of the book, now also plays a principal role.

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman (...) also suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do. (shrink)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Divided into three parts, this work is a record of the direction Kuhn was taking during the last two decades of his life. It consists of essays in which he refines the basic concepts set forth in "Structure"--Paradigm shifts, incommensurability, and the nature of scientific progress.

Berkeley's philosophy is meant to be a defense of commonsense. However, Berkeley's claim that the ultimate constituents of physical reality are fleeting, causally passive ideas appears to be radically at odds with commonsense. In particular, such a theory seems unable to account for the robust structure which commonsense (and Newtonian physics) takes the world to exhibit. The problem of structure, as I understand it, includes the problem of how qualities can be grouped by their co-occurrence in a single (...) enduring object and how these enduring objects can bear spatiotemporal, causal, and other relations to one another. I argue that Berkeley's solution to these problems lies in his views about language. At one level, human language allows us to exploit patterns in our perceptions to construct a highly structured representation of the physical world which allows us to make accurate predictions at minimal cognitive expense. At a deeper level, these patterns occur in perception because our perceptions themselves form a language in which God speaks to us. (shrink)

A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be (...) distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)

Clark Glymour, Richard Scheines, Peter Spirtes and Kevin Kelly. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling.

Recent arguments concerning the nature of causation in evolutionary theory, now often known as the debate between the 'causalist' and 'statisticalist' positions, have involved answers to a variety of independent questions – definitions of key evolutionary concepts like natural selection, fitness, and genetic drift; causation in multi-level systems; or the nature of evolutionary explanations, among others. This Element offers a way to disentangle one set of these questions surrounding the causal structure of natural selection. Doing so allows us to (...) clearly reconstruct the approach that some of these major competing interpretations of evolutionary theory have to this causal structure, highlighting particular features of philosophical interest within each. Further, those features concern problems not exclusive to the philosophy of biology. Connections between them and, in two case studies, contemporary metaphysics and philosophy of physics demonstrate the potential value of broader collaboration in the understanding of evolution. (shrink)

Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

This article takes stock of the basic notions of Information Structure (IS). It first provides a general characterization of IS following Chafe (1976) within a communicative model of Common Ground (CG), which distinguishes between CG content and CG management. IS is concerned with those features of language that concern the local CG. It then defines and discusses the notions of Focus (as indicating alternatives) and its various uses, Givenness (as indicating that a denotation is already present in the CG), (...) and Topic (as specifying what an statement is about). It also proposes a new notion, Delimitation, which comprises contrastive topics and frame setters, and indicates that the current conversational move does not satisfy the local communicative needs totally. It also points out that the rhetorical structuring partly belongs to IS. (shrink)

Why do speakers of all languages use different grammatical structures under different communicative circumstances to express the same idea? In this comprehensive study, Professor Lambrecht explores the relationship between the structure of sentences and the linguistic and extra-linguistic contexts in which they are used. His analysis is based on the observation that the structure of a sentence reflects a speaker's assumptions about the hearer's state of knowledge and consciousness at the time of the utterance. This relationship between speaker (...) assumptions and formal sentence structure is governed by rules and conventions of grammar, in a component called 'information structure'. Four independent but interrelated categories are analysed: presupposition and assertion, identifiability and activation, topic, and focus. (shrink)

This book develops a philosophical structure for historical explanation that resolves disputes about the scientific status of history that have persisted since the nineteenth century. It does this by showing why historical explanations must take the form of a narrative and by making their logic explicit. The books formulates a unique positive account of the logic of narrative explanations. This logic reveals how the rational evaluation of narrative explanation becomes possible. The book also develops a nonrealist (irrealist) metaphysics and (...) epistemology of history--that is, it argues that there exists no one fixed past but many pasts. It includes a novel reading of Kuhn's The Structure of Scientific Revolutions, displaying how Kuhn offers a narrative explanation of theory change in science. The book situates narrative explanations within a naturalistic framework. Naturalism regards all canons of rational inquiry as evolving and contingent. The book also argues for the general philosophical significance of historical explanation. The first four chapters defuse methodological and the metaphysical objections to narrative explanations. The final three chapters explore how narrative explanations relate to other sciences. It will be of interest to researchers in historiography, theory of history, philosophy of history, philosophy of science, philosophy of social science, and epistemology"--Provided by publisher. (shrink)

Although much of its history has been neglected or misunderstood, a structuralist 'tendency' has re-emerged within the philosophy of science. Broadly speaking, it consists of two fundamental strands: on the one hand, there is the identification of structural commonalities between theories; on the other, there is the metaphysical decomposition of objects in structural terms. Both have been pressed into service for the realist cause: the former has been identified primarily with Worrall's 'epistemic' structural realism; the latter with Ladyman's 'ontic' form. (...) And both raise important issues of general interest within the philosophy of science and metaphysics, respectively. The former invites questions regarding the identification and appropriate representation of these commonalities; the latter touches on different views regarding the nature of objects, the constitutive role of properties and the seat of causal powers. Both strands have recently come under critical fire. It is my intention to present a unified account of the 'structuralist tendency' which emphasizes the dual roles of structure as representational and constitutive, and to indicate how the more acute critical remarks can be dealt with. (shrink)

in Charles Travis (ed.), Meaning and Interpretation (Oxford and New York: Blackwell 1986), 159-174.

TWO OPPOSING VIEWS ABOUT THE RELATIONSHIP between concepts and the world can be found in the history of philosophy. One view—deriving from Immanuel Kant and endorsed by Karl Popper, among many others—claims that in forming and using concepts we structure the world. Concepts produce or increase order. Hence, the world, insofar as it is knowable by human beings, is necessarily a conceptually structured world. The second, still older view—represented by the Aristotelian tradition and by John Locke, for example—holds that (...) concepts are formed by abstracting from the particularities of the world. By leaving out the accidental or irrelevant features of particular entities, we abstract a concept as a general representative of a kind. (shrink)

In this paper I shall be concerned with the relation between a particular account of linguistic meaning and the property of compositionality in natural language.1 The account, proposed by Donald Davidson, is that based on considerations about radical interpretation. I shall argue that there is a fundamental conflict between, on the one hand, the view that the meaning of expressions of natural languages is determined purely according to canons of radical interpretation, and, on the other hand, the view that natural (...) languages exhibit compositional structure. I shall also argue that if there is such a conflict, this speaks against the proposed account. (shrink)

In 1974, John Maynard Smith wrote in his little book Models in Ecology, A theory of ecology must make statements about ecosystems as a whole, as well as about particular species at particular times, and it must make statements that are true for many species and not just for one… For the discovery of general ideas in ecology, therefore, different kinds of mathematical description, which may be called models, are called for. Whereas a good simulation should include as much detail (...) as possible, a good model should include as little as possible. (1974. (shrink)

FOUNDATIONALISM IN PHILOSOPHY n his autobiographical work, The Education of Henry Adams, this I brooding and disillusioned offspring of American presidents confronted, at age sixty, his own perplexity concerning the new scientific world-view that was emerging at the end of the century. He noted that the unity of things, long guaranteed morally by the teachings of Christianity and scientifically by the Newtonian world-view, was being challenged by a newer vision of things that found only incomprehensible multiplicity at the root of (...) the world: What happened if one dropped the sounder into the ab yss-let it go-frankly gave up Unity altogether? What was Unity? Why was one to be forced to affirm it? Here every body flatly refused help.... [Adams] got out his Descartes again; dipped into his Hume and Berkeley; wrestled anew with his Kant; pondered solemnly over his Hegel and Scho penhauer and Hartmann; strayed gaily away with his Greeks-all merely to ask what Unity meant, and what happened when one denied it. Apparently one never denied it. Every philosopher, whether sane or insane, naturally af firmed it. I Adams, then approaching with heavy pessimism a new century, felt instinc tively that, were one to attack the notion of unity, the entire edifice of human knowledge would quickly collapse. For understanding requires the unification of apparently different phenomena. (shrink)