1 The issue The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of 'rich', then 'Jackie is rich and Jackie isn't r...

In this paper, the concept of v-filters on lattice implication algebras is introduced by linking the Vague set and filter theory of lattice implication algebras; The properties and equivalent characterizations of v-filters are investigated; The relations between v-filters and filters are studied.

Conscious and unconscious brain mechanisms, including cognition, emotions and language are considered in this review. The fundamental mechanisms of cognition include interactions between bottom-up and top-down signals. The modeling of these interactions since the 1960s is briefly reviewed, analyzing the ubiquitous difficulty: incomputable combinatorial complexity (CC). Fundamental reasons for C...

Different languages that are offered to model vague preferences are reviewed and an interval-valued language is proposed to resolve a particular difficulty encountered with other languages. It is shown that interval-valued languagesare well definedfor De Morgan triples constructedby continuoustriangular norms, conorms and a strong negation function. A new transitivity condition for vague prefer...

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

We propose that not all such arguments are on a par. The first section of the paper distinguishes dialectically effective from dialectically ineffective arguments against metaphysical vagueness. The second section constructs an argument against metaphysical vagueness – specifically, an argument against objects that are indeterminate in what parts they have – which promises to be dialectically e...