Termine

For the first definition we assume that naturality is an absolute notion in the sense that every property is either natural or not and we can not compare the degree of naturality of any two natural properties. In this case we establish a correspondence between a suitably axiomatized class of comparative similarity orders and a suitable defined class of property spaces. Our approach can be seen as an abstraction from the correspondence between the geometric notions of betweenness and
convexity. We compare this setting to Leitgeb's rendering of Carnap's quasi-analysis and to Williamson's axiomatization of the comparative similarities that arise from the notion of closeness in a metric.

In the second case naturality is a matter of degree, that is, properties are ordered according to their relative naturality. We provide a construction of a comparative similarity order in this setting and axiomatize the class of orders that arise from this construction. Moreover, we can show that our setting allows us to include the similarities that are determined by closeness in a metric as a special case.