Intuitionism and the Modal Logic of Vagueness

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness

Fronteiras contingentes e conhecimento limitado

Este artigo mostra que combinando as noções lógicas de 'contingência' e 'conhecimento' nós podemos formular uma tese cética de acordo com a qual 'o mundo não pode ser conhecido'. Além disso, ele mostra que tal tese é plausível do ponto de vista epistemológico

A Non-standard kripke semantics for the minimal deontic logic

In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operatorCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPESFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP001403272/2019-02016/25891-

Interplays of knowledge and non-contingency

This paper combines a non-contingency logic with an epistemic logic by means of fusions and products of modal systems. Some consequences of these interplays are pointed out

Two Temporal Logics of Contingency

This work concerns the use of operators for past and future con-tingency in Priorean temporal logic. We will develop a system namedCt, whose language includes a propositional constant and prove that(i) Ct is complete with respect to a certain class of general frames and(ii) the usual operators for past and future necessity are denable insuch system. Furthermore, we will introduce the extension Ctlin thatcan be interpreted on linear and transitive general frames. The theo-retical result of the current work is that contingency can be treatedas a primitive notion in reasoning about temporal modalities

The Boxdot Conjecture and the Language of Essence and Accident

We show the Boxdot Conjecture holds for a limited but familiar range of Lemmon-Scott axioms. We re-introduce the language of essence and accident, first introduced by J. Marcos, and show how it aids our strategy