What Does It Mean to Be Bald and a Liar? A New Option for a Unified Approach to Paradoxes

In his article, Vsevolod Ladov poses an important question – might paradoxes admit of a uniform solution? As an answer, I propose looking at an approach in which it is argued that we must recognize the truth predicate as merely analogous to a vague predicate. The proponents of this approach (V. McGee, J. Tap- penden, H. Field, G. Priest and D. Hyde) insist that there is a structural relation between sorites paradoxes and self-reference paradoxes and that they should have a unified solution

Sorites, curry and suitable models

In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of w-inconsistency.Fil: Da Re, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; ArgentinaFil: Teijeiro, Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentin

Inclosure and Intolerance

[eng] Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favoured dialetheic solution to the Inclosure paradoxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument purporting to show that that paradox is an Inclosure is unsound, and discuss some issues surrounding this fact

On assertion and denial in the logic for pragmatics

The aim of this paper is twofold: First, we present and develop a system of logic for pragmatics including the act of denial. Second, we analyse in our framework the so-called paradox of assertability. We show that it is possible to yield sentences that are not assertable. Moreover, under certain conditions, a symmetric result can be obtained: There is a specular paradox of deniability. However, this paradox is based on the problematic principle of classical denial equivalence

Система личных местоимений естественного языка: мереотопологический подход

The logical structure of the system of subjects in the natural language is examined. The subjects were limited to those expressed by either pronouns or other similar (from a linguistic viewpoint) phenomena, namely: personal pronouns (both explicit and implicit), subjects of indefinite sentences, subjects of impersonal sentences (pro), and subjects of non-finite clauses (PRO). The implicit propositions corresponding to different modes of choosing the subjects (agents) from the universe of agents are analysed. For this purpose, a mereotopological method has been developed which allows to deal with both consistent (classical) and inconsistent logics. It was demonstrated that, in the natural language, the subjects (agents) can be chosen using the procedures that are governed by either consistent or inconsistent logic. Namely, the subjects of impersonal sentences (pro) are to be chosen according to the paracomplete logic (allowing the contrary contradiction), and the subjects of non-finite clauses (PRO), according to the paraconsistent logic (allowing the subcontrary contradiction), whereas the subjects of both indefinite and self-referential sentences are to be chosen according to the non-alethic logic (allowing the contradictory contradiction).Проанализирована логическая структура системы подлежащих естественного языка, выраженных местоимениями или аналогичными с лингвистической точки зрения, объектами, а именно: личными местоимениями, как эксплицитными, так и имплицитными, подлежащими неопределенно-личных и безличных (pro) предложений, а также нефинитных клауз (PRO). В процессе анализа оценивалось содержание имплицитных пропозиций, соответствующих тому или иному выбору подлежащего (агента) из универсума агентов. Для процедуры логического анализа был разработан мереотопологический метод, позволяющий работать как с классической, так и неконсистентными логиками. Показано, что подлежащие (агенты) в естественном языке могут выбираться как по процедурам, соответствующим классической логике, так и по процедурам, соответствующим различным неконсистентным логикам. А именно, подлежащие безличных предложений (pro) выбираются соответственно паракомплектной логике (допускающей контрарное противоречие), подлежащие нефинитных клауз (PRO) выбираются соответственно параконсистентной логике (допускающей субконтрарное противоречие), а подлежащие как неопределенно-личных, так и автореферентных предложений выбираются соответственно неалетической логике (допускающей контрадикторные противоречия)

Inclosure and Intolerance

Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favored dialetheic solution to the Inclosure paradoxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument purporting to show that that paradox is an Inclosure is unsound, and discuss some issues surrounding this fact

Vagueness, Truth and Permissive Consequence

We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference

What If? The Exploration of an Idea

A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes