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Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 11 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) 

This paper intends to further the understanding of the formal properties of (higherorder) vagueness by connecting theories of (higherorder) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higherorder vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction (...) 

It is notoriously difficult to model the range of application of vague predicates relative to a suitable sorites series. In this paper I offer some critical remarks against an interesting view that has received little attention in the literature. According to it, the sharp cutoffs we find in our semantic models are just artifacts of the theory, and, as such, they are harmless. At the end I discuss a contextualist view that, at a cost, may be able to get around (...) 

According to columnar higherorder vagueness, all orders of vagueness coincide: any borderline case is a borderline borderline case, and a thirdorder borderline case, etc. Bobzien has worked out many details of such a theory and models it with a modal logic closely related to S4. I take up a range of questions about the framework and argue that it is not suitable for modelling the structure of vagueness and higherorder vagueness. 

ABSTRACT: This chapter offers a revengefree solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why  and how  truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of (...) 

This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...) 

This paper deals with higherorder vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higherorder vagueness collapses to secondorder vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...) 

This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higherorder vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higherorder vagueness, or Vagueness is higherorder vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in response to Keefe’s (...) 