Comparative concepts such as greener than or higher than are ways of ordering objects. They are fundamental to our grasp of gradable concepts, that is, the type of meanings expressed by gradable general terms, such as "is green" or "is high", which are embeddable in comparative constructions in natural language. Some comparative concepts seem natural, whereas others seem gerrymandered. The aim of this paper is to outline a theoretical approach to comparative concepts that bears both on the account of naturalness (...) for comparative concepts and on the theory of gradable concepts. The approach is novel in that it carries some basic assumptions from Peter Gärdenfors' conceptual spaces account of categorical concepts over to comparative concepts. The offered approach is more general than Gärdenfors' account in that it supplies a framework of graded categorisation that includes his categorisation rule as a limiting case. Importantly, it provides also a new argument for adopting Gärdenfors' particular model of categorisation. (shrink)

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic. (shrink)