Naturalness and Convex Class Nominalism

Synthese, 2016

The notion of conceptual space, proposed by Gärdenfors as a framework for the representation of concepts and knowledge, has been highly influential over the last decade or so. One of the main theses involved in this approach is that the conceptual regions associated with properties, concepts, verbs, etc. are convex. The aim of this paper is to show that such a constraint-that of the convexity of the geometry of conceptual regions-is problematic; both from a theoretical perspective and with regard to the inner workings of the theory itself. On the one hand, all the arguments provided in favor of the convexity of conceptual regions rest on controversial assumptions. Additionally, his argument in support of a Euclidean metric, based on the integral character of conceptual dimensions, is weak, and under non-Euclidean metrics the structure of regions may be non-convex. Furthermore, even if the metric were Euclidean, the convexity constraint could be not satisfied if concepts were differentially weighted. On the other hand, Gärdenfors' convexity constraint is brought into question by the own inner workings of conceptual spaces because: (i) some of the allegedly convex properties of concepts are not convex; (ii) the conceptual regions resulting from the combination of convex properties can be non-convex; (iii) convex regions may co-vary in non-convex ways; and (iv) his definition of verbs is incompatible with a definition of properties in terms of convex regions. Therefore, the mandatory character of the convexity requirement for regions in a conceptual space theory should be reconsidered.

Journal of Applied Logic, 2007

We invoke concepts from the theory of hypergraphs to give a measure of the closeness of family resemblance, and to make precise the idea of a composite likeness. It is shown that for any positive integer m, for any general term possessing any extent of family resemblance strictly greater than m, there is a taxonomical representation of the term whereby each subordinate taxon has an extent of family resemblance strictly greater than m.

Papers on Philosophy, Psychology, Sociology and Pedagogy, 2018

After stressing the importance of the notion of similarity for the theories of meaning, the author discusses the definition of similarity as 'feature matching' and proves it inadequate, offering another operational definition of similarity derived from late Wittgenstein’s idea of 'family resemblances'. Similarity is understood as a 'perceived' pattern of relation correspondences that precedes the abstraction of common features and cannot be reduced to it.

I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that anti-resemblism is true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch.

2015

Nominalism, which has its origins in the Middle Ages and continues into the Twenty-First Century, is the doctrine that there are no universals. This book is unique in bringing together essays on the history of nominalism and essays that present a systematic discussion of nominalism. It introduces the reader to the distinction between particulars and universals, to the difficulties posed by this distinction, and to the main motivations for the rejection of universals. It also describes the main varieties of nominalism about properties and provides tools to understand how they developed in the history of Western Philosophy. All essays are new and are written by experts on the topic, and they advance the discussion about nominalism to a new level.

Linguistics and Philosophy, 1989

English, and presumably any natural language, contains a small group of expressions referring to species of things found in nature. These species are defined by their internal structure, determined by genetics in the case of living things and by chemical or physical properties in the case of others. The reference of these terms is determined by these properties, but the properties are not semantically associated with the terms in question because the terms were introduced before science discovered the internal structure properties. Therefore, some of the terms are nondescriptional. Two theorists, Kripke and Putnam, have shown that in the case of this group of natural kind terms, humans let the natural essence or properties function as Locke's nominal essence, or sense. This is supported by evidence from a study of language use in ten-year-olds. However, this class of terms is smaller than was previously thought, and some questions about it remain, including the function of nondescriptional terms within the language, possible grammatical correlates of nondescriptionality, the relationship between descriptionality and decompositionality, and learnability.

Erkenntnis, 2018

Nominalism about attributes has serious difficulties in accounting for truths involving abstract nouns. Prominent among such truths are statements of comparative similarity among attributes (e.g., ‘Carmine resembles vermillion more than it resembles French blue’). This paper argues that one cannot account for the truth of such statements without invoking attributes.

2007

Resemblances obtain not only between objects but between properties. Resemblances of the latter sort-in particular, resemblances between quantitative properties-prove to be the downfall of David Armstrong's well-known theory of universals. This paper examines Armstrong's efforts to account for such resemblances, and explores several ways one might extend the theory in order to account for quantity. I argue that none succeed. 1 In this paper I am interested only in intrinsic resemblance, not extrinsic resemblance. For instance, I do not address cases where there is some sense in which two things resemble (perhaps each has the property of being five feet from a poodle), but where this resemblance does not arise from the intrinsic properties of each object alone. 2 See Armstrong (1978) and (1989a). 3 See Armstrong (1988) and (1989a, pg. 101-105). 4 See Armstrong (1989a, pg. 101).

Philosophical Papers, 2019

This paper considers whether an analogy between distance and dissimilarlity supports the thesis that degree of dissimilarity is distance in a metric space. A straightforward way to justify the thesis would be to define degree of dissimilarity as a function of number of properties in common and not in common. But, infamously, this approach has problems with infinity. An alternative approach would be to prove representation and uniqueness theorems, according to which if comparative dissimilarity meets certain qualitative conditions, then it is representable by distance in a metric space. I will argue that this approach faces equally severe problems with infinity.

Metascience, 2009

This is a collection of twelve previously published and two new articles on topics in the philosophy of mathematics, ontology, modality, and the theory of reference, accompanied by a useful introduction. Written by a respected logician and philosopher, the articles are technically and historically well informed, philosophically interesting, and at times provocative. Readers acquainted with Burgess's work will recognise some familiar themes, such as his radical naturalism, anti-revisionism vis-a`-vis scientific practice, and careful logical analyses. Anyone working in the relevant areas will find much to learn in this book. Good philosophy should according to Burgess be Ônaturalistic'in Quine's sense that it ''abstains from imposing philosophical constraints on science'' (p. 48). Thus one central theme in the book is naturalism in the philosophy of mathematics. Burgess's naturalistic approach was first laid out in his influential ÔWhy I am not a Nominalist' (1983), which developed an early version of an important argument later refined in his 1997 book with Gideon Rosen: A Subject Without an Object. Although science makes extensive use of mathematical objects, nominalists deny that there are any such objects. Burgess distinguishes two forms of nominalism. Hermeneutic nominalists claim that, properly interpreted, science isn't committed to mathematical objects. Revolutionary nominalists claim there are scientific reasons to Ônominalise' physics. The former claim belongs to linguistics and should be evaluated as such. The latter belongs to physics and should be