Two Conceptions of Similarity

Abstract

Abstract. There are at least two traditional conceptions of numerical degree of similarity. According to the first, the degree of dissimilarity between two particulars is their distance apart in a metric space. According to the second, the degree of similarity between two particulars is a function of the number of (sparse) properties they have in common and not in common. This paper argues that these two conceptions are logically independent, but philosophically inconsonant.Keywords: similarity, resemblance, properties, distance, metric spaces. 1.There are at least two traditional conceptions of numerical degree of similarity. According to the first conception, the degree of similarity between particulars is a function of their number of (sparse) properties in common and not in common. This conception has its home in debates over the metaphysics of properties (see especially Armstrong, 1978b, 97-98, Oliver, 1996, 52 and Rodriguez-Pereyra, 2002, but is also found in the debate over the resemblance theory of pictorial representation (Blumson, 2014, 179-198).According to the second, the degree of dissimilarity between particulars is their distance apart in a metric space. This conception has its home in

Measures of Similarity

“…2 For discussions of single aspect similarity measures supported by intuitions, see Carmichael et al (1965); for multiple aspect similarity measures supported by intuitions, see Gower (1971), Williamson (1988) and Blumson (2018a); for single aspect similarity measures supported by experiences, see Eisler and Ekman (1959) and Künnapas and Künnapas (1974); for multiple aspect similarity measures supported by experiences, see Attneave (1950), Shepard (1962) and Tversky (1977). Let us thus continue by considering the concepts of (single aspect) similarity and dissimilarity.…”

“…See Blumson (, p. 34) for an analysis of dissimilarity that requires a maximum and Blumson (, p. 34; , p. 19) for an analysis that does not.…”

Naturalness and Convex Class Nominalism

“…A simple answer would be a definition of degree of dissimilarity as a function of number of natural properties in common and not in common. The degree of dissimilarity between two particulars could be defined, for example, as their total number of natural properties not in common or, more plausibly, as their proportion of natural properties not in common (Blumson, , 11–14).…”

“…What justifies the presupposition that degree of dissimilarity is distance in a metric space in the first place? A simple answer would be to define the degree of dissimilarity between two individuals as their total number of natural properties not in common or, in other words, the number of natural properties the first has not in common with the second, plus the number of natural properties the second has not in common with the first (Blumson, , 11–12). In this section, I explain how this definition meets the four conditions of definition (1).…”

“…Assuming that every particular has at least one natural property, and so the denominator of the proportion of properties not in common is always positive (and continuing to focus on the finite case, so both the numerator and denominator are finite), then this definition satisfies the first three conditions of the definition of a metric space for the same reason as its predecessor (Blumson, , 12–14).…”