Citations of:
If It's Clear, Then It's Clear That It's Clear, or is It? HigherOrder Vagueness and the S4 Axiom
In B. Morison K. Ierodiakonou (ed.), Episteme, etc.: Essays in honour of Jonathan Barnes. OUP UK (2012)
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ABSTRACT: Stewart Shapiro recently argued that there is no higherorder vagueness. More specifically, his thesis is: (ST) ‘Socalled secondorder vagueness in ‘F’ is nothing but firstorder vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higherorder vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) 

The aim of this paper is to present a topological method for constructing discretizations of topological conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. The aim of this paper is to show that Alexandroff spaces, as they are called today, have many interesting properties that can be used to explicate and clarify a variety of problems in philosophy, cognitive science, and related disciplines. For instance, recently, (...) 

ABSTRACT: This paper argues that the socalled paradoxes of higherorder vagueness are the result of a confusion between higherorder vagueness and the distribution of the objects of a Sorites series into extensionally nonoverlapping nonempty classes. 

On the one hand, philosophers have presented numerous apparent examples of indeterminate individuation, i.e., examples in which two things are neither determinately identical nor determinately distinct. On the other hand, some have argued against even the coherence of the very idea of indeterminate individuation. This paper defends the possibility of indeterminate individuation against Evans’s argument and some other arguments. The Determinacy of Identity—the thesis that identical things are determinately identical—is distinguished from the Determinacy of Distinctness—the thesis that distinct things are (...) 

Most descriptions of higherorder vagueness in terms of traditional modal logic generate socalled higherorder vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, nonstandard theories. However, there is no need for this.In this paper I introduce a theory of higherorder vagueness that is paradoxfree and can be expressed in the firstorder extension of a normal modal system that is complete with respect to singledomain Kripkeframe semantics. This is the system QS4M+BF+FIN. It corresponds (...) 

This paper is a tribute to Delia Graff Fara. It extends her work on failures of metarules for validity as truthpreservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vaguenessrelated operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a contextdependent background. This paper extends her argument to: quantifier metarules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the (...) 

There are some properties, like being bald, for which it is vague where the boundary between the things that have it and the things that do not lies. A number of arguments threaten to show that such properties can still be associated with determinate and knowable boundaries: not between the things that have it and those that don’t, but between the things such that it is borderline at some order whether they have it and the things for which it is (...) 

This paper examines the Stoic account of apprehension (κατάληψις) (a cognitive achievement similar to how we typically view knowledge). Following a seminal article by Michael Frede (1983), it is widely thought that the Stoics maintained a purely externalist causal account of apprehension wherein one may apprehend only if one stands in an appropriate causal relation to the object apprehended. An important but unanswered challenge to this view has been offered by David Sedley (2002) who offers reasons to suppose that the (...) 

This paper shows that the following common assumption is false: that in modallogical representations of higherorder vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal). 

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 (...) 

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. 