EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes

The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes

Two modal paradoxes and their solutions.

Chisholm\u27s Paradox and the Four Worlds Paradox are paradoxes about the cross-world identity of artifacts that are made of parts. The paradoxes are described as derivable in S5 modal logic from principles concerning the essentiality of the original matter of an artifact and the Tolerance Principle concerning possible changes in the original matter. On one hand, the original matter is essential to the artifact; on the other hand, bare identity or distinctness with respect to the original matter can be inferred by applying the Tolerance Principle in S5. This dissertation analyzes two solutions that have been proposed. Nathan Salmon developed an Intransitive Accessibility Solution that rejects S5 as the logic for metaphysical modality. We show that Salmon\u27s argument for the intransitivity of metaphysical possibility is unsound. The fundamental problem in Salmon\u27s account is his attempt to derive the mode of metaphysical possibility from the accessibility relation between the possible worlds, which, by the theory of possible worlds that Salmon advocates, has to be determined by metaphysical possibilities with a pre-determined mode. The conclusion of Salmon\u27s argument only reiterates a premise of the argument. We also discuss Salmon\u27s other defenses, and show that these defenses are unsuccessful. Graeme Forbes proposes a Counterpart Solution. His solution replaces the standard two-valued semantics by a counterpart semantics with infinitely many degrees of truth-value. Our view is that Forbes\u27 solution is unsatisfactory. Forbes avoids the identity problem by formulating the problem in terms of similarity relation. We argue that the similarity relation must not be a semantic device for representing identity. Our analysis reveals two versions of tolerance principle that have not been distinguished in literature. The paradoxes are associated with the Strong Tolerance Principle. We argue that the Strong Tolerance Principle is false. The intuition of tolerance is sufficiently described by the Weak Tolerance Principle. Moreover, we argue that the knowing of the possibilities about the origination of an artifact is empirical. The knowledge of the historical background and the origination of the artifact is needed for knowing the possibilities. With this view, S5 as the logic of metaphysical modality can be defended

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics

The Knowability Argument and the syntactic type-theoretic approach

Recently, there have been some attempts to block the Knowability Paradox and other modal paradoxes by adopting a type-theoretic framework in which knowledge and necessity are regarded as typed predicates. The main problem with this approach is that when these notions are simultaneously treated as predicates, a new kind of paradox appears. I claim that avoiding this paradox either by weakening the Knowability Principle or by introducing types for both predicates is rather messy and unattractive. I also consider the prospect of using the truth predicate to emulate necessity, knowledge and other modal notions. It turns out that this idea works much better.Recientemente, ha habido intentos por resolver la Paradoja de la Cognoscibilidad y otras paradojas modales por medio de la adopción de un enfoque de tipos en el cual las nociones de conocimiento y necesidad se representan utilizando predicados tipeados. El principal problema con esta propuesta es que cuando estas nociones son tratadas simultáneamente como predicados, una nueva clase de paradoja aparece. En este artículo sostengo que evitar esta paradoja debilitando el Principio de Cognoscibilidad o introduciendo tipos para ambos predicados no es una solución atractiva. También considero una propuesta alternativa, la de utilizar el predicado veritativo para emular las nociones de necesidad, conocimiento y otras nociones modales. Resulta que esta última idea funciona mucho mejor.Fil: Rosenblatt, Lucas Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics

The Knowability Argument and the Syntactic Type-Theoretic Approach

Recientemente, ha habido intentos por resolver la Paradoja de la Cognoscibilidad y otras paradojas modales por medio de la adopción de un enfoque de tipos en el cual las nociones de conocimiento y necesidad se representan utilizando predicados tipeados. El principal problema con esta propuesta es que cuando estas nociones son tratadas simultáneamente como predicados, una nueva clase de paradoja aparece. En este artículo sostengo que evitar esta paradoja debilitando el Principio de Cognoscibilidad o introduciendo tipos para ambos predicados no es una solución atractiva. También considero una propuesta alternativa, la de utilizar el predicado veritativo para emular las nociones de necesidad, conocimiento y otras nociones modales. Resulta que esta última idea funciona mucho mejor

All Properties are Divine or God exists

A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D, and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are D we in Section 2 derive the thesis (40) that all properties are D or some individual is G. In Section 3 theorems 1 to 3 suggest a sufficient kinship to Gödelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Gödel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a fixed point analysis is used as diagnosis so that atheists may settle for the minimal fixed point. Theorem 3 shows it consistent to postulate theistic fixed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g, then necessarily all objects which are G are identical with g. The impredicative origin of D suggests weakened Gaunilo-like objections that offer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we finesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts `God’ allow thorough indifference as to whether God exists or not

Is Time Travel Too Strange to Be Possible? Determinism and Indeterminism on Closed Timelike Curves

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves (CTCs) occur. On these curves time loops back onto itself, which has exotic consequences. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by conjecturing a chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region (such hypersurfaces fail to be Cauchy surfaces). By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC-indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC-determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible

Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4

The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases