The Renaissance architect, moral philosopher, cryptographer, mathematician, Papal adviser, painter, city planner and land surveyor Leon Battista Alberti provided the theoretical foundations of modern perspective geometry. Alberti’s work on perspective exerted a powerful influence on painters of the stature of Albrecht Dürer, Leonardo da Vinci and Piero della Francesca. But his Della pittura of 1435–36 contains also a hitherto unrecognized ontology of pictorial projection. We sketch this ontology, and show how it can be generalized to apply to representative devices in (...) general, including maps and spatial and non-spatial databases. (shrink)

A number of logicians and philosophers have turned their attention in recent years to the problem of developing a logic of interrogatives. Their work has thrown a great deal of light on the formal properties of questions and question-sentences and has led also to interesting innovations in our understanding of the structures of performatives in general and, for example, in the theory of presuppositions. When, however, we examine the attempts of logicians such as Belnap or Åqvist to specify what, precisely, (...) a question is, or what it is to ask or raise a question, then what we are offered is somewhat less illuminating. Two alternative reductionist accounts seem in particular to have gained most favor: questions are identified either as special sorts of statements, or as special sorts of requests. As we hope will become clear in what follows, neither of these accounts is even nearly adequate; and matters are not improved if questions are identified, by force majeure, as combinations of statements and requests. (shrink)

Holes are a good example of the sort of entity that down-to-earth philosophers would be inclined to expel from their ontological inventory. In this work we argue instead in favor of their existence and explore the consequences of this liberality—odd as they might appear. We examine the ontology of holes, their geometry, their part-whole relations, their identity and their causal role, the ways we perceive them. We distinguish three basic kinds of holes: blind hollows, perforating tunnels, and internal cavities, treating (...) these uniformly as immaterial bodies. We develop a morphology of holes, focusing on the way a hole can be filled, and then look at the main properties of the resulting conceptual framework: holes are parasitic upon the surfaces of their hosts; holes can move, fuse into each other, split; they can be born, develop, and die. Finally, we examine how some morphological features of holes are represented in perception, including the conditions whereby we have the impression that we see, feel, or even hear a hole. The book has over 150 pictures and is completed by a formal appendix, a section with puzzles and exercises, and a extensive annotated bibliography. (shrink)

Human cognitive acts are directed towards entities of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. A categorial scheme for the objects of human cognition should be (1) critical and realistic. Cognitive subjects are liable to error, even to systematic error of the sort that is manifested by believers in the Pantheon of Olympian gods. Thus not all putative object-directed acts should be recognized as having objects of their own. (...) Broadly, the objects towards which human cognition is directed should be parts of reality in a sense that is at least consistent with the truths of natural science. But such a scheme should also be (2) comprehensive: it should do justice to each sort of object on its own terms, and not attempt to eliminate objects of one sort in favour of objects of other, more favoured sorts. Linguistic and other forms of idealism, as well as Meinongian theories, which assign to each and every referring expression or intentional act an object tailored to fit, yield categorial schemes which fail to satisfy (1). Physicalistic and other forms of reductionism yield categorial schemes which fail to satisfy (2). What follows is a categorial scheme that is both critically realistic and comprehensive. Thus it enjoys some of the benefits of linguistic idealism and physicalism, without (or so it is hoped) the corresponding disadvantages of each. (shrink)

We take as our starting point a thesis to the effect that, at least for true judgments of many varieties, there are parts of reality which make such judgments are true. We argue that two distinct components are involved in this truthmaker relation. On the one hand is the relation of necessitation, which holds between an object x and a judgment p when the existence of x entails the truth of p. On the other hand is the dual notion of (...) projection, which holds between a judgment p and an object x when the truth of p entails the existence of x. A truthmaker for a judgment p is then a necessitator for p which satisfies the further constraint that it is part of p’s projection. We offer a formal theory of the truthmaker relation thus defined, exploiting ontological tools of basic mereology and the theory of dependence. We then apply the theory to a range of problems connected with generic expressions, ellipsis, vagueness, and indexical and perceptual judgments. (shrink)

Human cognitive acts are directed towards entities of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. A categorial scheme for the objects of human cognition should be (1) critical and realistic. Cognitive subjects are liable to error, even to systematic error of the sort that is manifested by believers in the Pantheon of Olympian gods. Thus not all putative object-directed acts should be recognized as having objects of their own. (...) What follows is a categorial scheme that is both critically realistic and comprehensive. Thus it enjoys some of the benefits of linguistic idealism and physicalism, without (or so it is hoped) the corresponding disadvantages of each.The starting point for our categorial scheme is the concept of extended entity. (shrink)

Relevance logic has become ontologically fertile. No longer is the idea of relevance restricted in its application to purely logical relations among propositions, for as Dunn has shown in his (1987), it is possible to extend the idea in such a way that we can distinguish also between relevant and irrelevant predications, as for example between “Reagan is tall” and “Reagan is such that Socrates is wise”. Dunn shows that we can exploit certain special properties of identity within the context (...) of standard relevance logic in a way which allows us to discriminate further between relevant and irrelevant properties, as also between relevant and irrelevant relations. The idea yields a family of ontologically interesting results concerning the different ways in which attributes and objects may hang together. Because of certain notorious peculiarities of relevance logic, however,1 Dunn’s idea breaks down where the attempt is made to have it bear fruit in application to relations among entities which are of homogeneous type. (shrink)

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical power and (...) great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations. (shrink)

The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...) In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis. (shrink)

In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We continue by classifying well-formed (...) partitions along three axes: (a) degree of correspondence between partition cells and objects in reality; (b) degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) degree of completeness and exhaustiveness with which a partition represents reality. This classification is used to characterize three types of partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain. (shrink)

Mereotopology faces problems when its methods are extended to deal with time and change. We offer a new solution to these problems, based on a theory of partitions of reality which allows us to simulate (and also to generalize) aspects of set theory within a mereotopological framework. This theory is extended to a theory of coarse- and fine-grained histories (or finite sequences of partitions evolving over time), drawing on machinery developed within the framework of the so-called ‘consistent histories’ interpretation of (...) quantum mechanics. (shrink)