A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda (...) ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Kim. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...) here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

With his theory of descriptions Russell wanted to solve two problems concerning denotation and reference, which are formulated here as Problem I and Problem II. After presenting each problem, we describe the main points of Russell’s solution. We deal with Russell’s concepts of existence and then elaborate his presuppositions concerning the relation of denoting and referring. Next we discuss the presuppositions or principles which underlie Russell’s understanding of the _objects_ of reference. These principles are such that if the objects of (...) reference are material objects, they are objects of classical mechanics, or very close to such an interpretation. Finally we show how these principles have to be relaxed if the objects of reference are objects of quantum mechanics or special or general relativity. (shrink)

In ‘On Denoting’ and to some extent in ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie’, published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous elimination (or contextual defi nition) of defi nite descriptions, but also a series of considerations against understanding defi nite descriptions as singular terms. At the end of ‘On Denoting’, Russell believes he has shown that all the theories that do treat defi nite descriptions as singular terms fall (...) logically short: Meinong’s, Mally’s, his own earlier (1903) theory, and Frege’s. (He also believes that at least some of them fall short on other grounds—epistemological and metaphysical—but we do not discuss these criticisms except in passing). Our aim in the present paper is to discuss whether his criticisms actually refute Frege’s theory. We fi rst attempt to specify just what Frege’s theory is and present the evidence that has moved scholars to attribute one of three different theories to Frege in this area. We think that each of these theories has some claim to be Fregean, even though they are logically quite different from each other. This raises the issue of determining Frege’s attitude towards these three theories. We consider whether he changed his mind and came to replace one theory with another, or whether he perhaps thought that the different theories applied to different realms, for example, to natural language versus a language for formal logic and arithmetic. We do not come to any hard and fast conclusion here, but instead just note that all these theories treat defi nite descriptions as singular terms, and that Russell proceeds as if he has refuted them all. After taking a brief look at the formal properties of the Fregean theories (particularly the logical status of various sentences containing nonproper defi - nite descriptions) and comparing them to Russell’s theory in this regard, we turn to Russell’s actual criticisms in the above-mentioned articles to examine the extent to which the criticisms hold.. (shrink)

We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase ‘incomplete symbols’ is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase ‘no meaning in isolation’ in a formal way.

Questions of definedness are ubiquitous in mathematics. Informally, these involve reasoning about expressions which may or may not have a value. This paper surveys work on logics in which such reasoning can be carried out directly, especially in computational contexts. It begins with a general logic of partial terms, continues with partial combinatory and lambda calculi, and concludes with an expressively rich theory of partial functions and polymorphic types, where termination of functional programs can be established in a natural way.