We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. To be more (...) precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. (shrink)

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...) and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK. (shrink)

In a rather general setting, we prove a number of basic theorems concerning computational complexity of derivability in adaptive logics. For that setting, the so-called standard format of adaptive logics is suitably adopted, and the corresponding completeness results are established in a very uniform way.

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump (...) semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas. (shrink)

The article is devoted to the analysis of the legal theories of P.I. Novgorodtsev and B.A. Kistyakovsky, based on the moral philosophy of I. Kant in comparison with the psychological theory of law of L.I. Petrazhitsky. The unity of the positions of Novgorodtsev and Kistyakovsky in focusing on the ethical aspects of law, as well as highlighting morality as the highest principle, is revealed. Attention is paid to the disclosure of neo-Kantian motives in the philosophy of law and in the (...) context of the development of the theory of natural law in Russia. The main content of the article is a consistent analysis of Novgorodtsevʼs ideas in their dynamics, compared with the neo-Kantian philosophy of law of Kistyakovsky. It is emphasized that the psychological theory of the source of Petrazhitskyʼs legal relations is in the same intention of thought with the motives of the Russian neo-Kantians, which allows them to be compared in the history of the development of the Russian theory of law. The modern scientific literature is analyzed in order to identify the problem of comparing different approaches in the history of Russian philosophy of law, in which German transcendental philosophy is one of the key foundations. The question of the independence of Russian scientists in the construction of ethical and legal doctrines is actualized, but, at the same time, a single motive is emphasized with the Kantian provision on the need to establish a general civil society on the principles of a developed system of rules and norms. (shrink)

This article examines some of S. Lem’s statements about his philosophical and worldview positions regarding the mysterious nature of language and the linguistic sign, the connection between language, mind and reality. The main goal of the paper is to understand what texts on the philosophy of language the Polish thinker read and what attitude he has formed towards them. Lem is the follower of an analytical intellectual culture that focuses on the naturalistic worldview and the consequences of the “linguistic turn” (...) in Western philosophy. For Lem, language is not only an interesting philosophical object, but also a complex precise instrument of his own creative thinking. In this regard, the philosophy of language for a writer cannot be based only on logical-linguistic atomistic methodology. Lem seeks in his contemporary interdisciplinary methods ways to combine realistic and anti-realist positions. Many concepts, such as “the effect of semantic transparency”, “polymorphic language model”, “variation model” are quite correlated with modern theories of language and require additional philosophical comments. (shrink)

We prove that all algebras P/IR, where the IR-'s are ideals generated by partitions of W into finite and arbitrary large elements, are isomorphic and homogeneous. Moreover, we show that the smallest size of a tower of such partitions with respect to the eventually-refining preordering is equal to the smallest size of a tower on ω.

This paper is a book review of 'A Treatise of Master Hervaeus Natalis († 1323), The Doctor Perspicacissimus, On second Intentions' by John P. Doyle.

Advocates have sought to prove that underdetermination obtains because all theories have empirical equivalents. But algorithms for generating empirical equivalents simply exchange underdetermination for familiar philosophical chestnuts, while the few convincing examples of empirical equivalents will not support the desired sweeping conclusions. Nonetheless, underdetermination does not depend on empirical equivalents: our warrant for current theories is equally undermined by presently unconceived alternatives as well-confirmed merely by the existing evidence, so long as this transient predicament recurs for each theory and body (...) of evidence we consider. The historical record supports the claim that this recurrent, transient underdetermination predicament is our own. (shrink)

The purpose of this study is to examine the relationship between the corporate social performance of an organization and three variables: the size of the organization, the financial performance of the organization, and the environmental performance of the organization. By empirically testing data from 1987 to 1992, the results of the study show that a firm's corporate social performance is indeed impacted by the size of the firm, the level of profitability of the firm, and the amount of pollution emissions (...) released by the firm. (shrink)

It is fortunate for my purposes that English has the two words ‘almighty’ and ‘omnipotent’, and that apart from any stipulation by me the words have rather different associations and suggestions. ‘Almighty’ is the familiar word that comes in the creeds of the Church; ‘omnipotent’ is at home rather in formal theological discussions and controversies, e.g. about miracles and about the problem of evil. ‘Almighty’ derives by way of Latin ‘omnipotens’ from the Greek word ‘pantokratōr’; and both this Greek word, (...) like the more classical ‘pankratēs’, and ‘almighty’ itself suggest God's having power over all things. On the other hand the English word ‘omnipotent’ would ordinarily be taken to imply ability to do everything; the Latin word ‘omnipotens’ also predominantly has this meaning in Scholastic writers, even though in origin it is a Latinization of ‘pantocratōr’. So there already is a tendency to distinguish the two words; and in this paper I shall make the distinction a strict one. I shall use the word ‘almighty’ to express God's power over all things, and I shall take ‘omnipotence’ to mean ability to do everything. (shrink)

By the time of his death in 2006, Sir Peter Strawson was regarded as one of the world's most distinguished philosophers. Unavailable for many years,_ Scepticism and Naturalism_ is a profound reflection on two classic philosophical problems by a philosopher at the pinnacle of his career. Based on his acclaimed Woodbridge lectures delivered at Columbia University in 1983, Strawson begins with a discussion of scepticism, which he defines as questioning the adequacy of our grounds for holding various beliefs. He then (...) draws deftly on Hume and Wittgenstein to argue that we must distinguish between 'hard', scientific naturalism; or 'soft', humanistic naturalism. In the remaining chapters the author takes up several issues in which sceptical doubts play an important role, in particular the nature of transcendental arguments and including the objectivity of moral philosophy, the mental and the physical, and the existence of abstract entities. _Scepticism and Naturalism_ is essential reading for those seeking an introduction to the work of one of the twentieth century’s most important and original philosophers. This reissue includes a substantial new foreword by Quassim Cassam and a fascinating intellectual autobiography by Strawson, which together form an excellent introduction to his life and work. (shrink)

This fourth and final volume of the monumental commentary on Wittgenstein's _Philosophical Investigations_ covers pp 428-693 of the book. Like the previous volumes, it consists of philosophical essays and exegesis.

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

Knowing Persons is an original study of Plato's account of personhood. For Plato, embodied persons are images of a disembodied ideal. The ideal person is a knower. Hence, the lives of embodied persons need to be understood according to Plato's metaphysics of imagery.For Gerson, Plato's account of embodied personhood is not accurately conflated with Cartesian dualism. Plato's dualism is more appropriately seen in the contrast between the ideal disembodied person and the embodied one than in the contrast between mind or (...) soul and body.This study argues that Plato's analysis of personhood is intended to cohere with his two-world metaphysics as well as a radical separation of knowledge and belief. Gerson demonstrates that Plato's account of persons plays a key role not just in his theory of mind, but in his theory of knowledge, his metaphysics, and his ethics. A proper understanding of Plato's account of persons must therefore place it in the context of his doctrines in these areas. Knowing Persons fills a significant gap by showing the way to such an understanding. (shrink)

By the time of his death in 2006, Sir Peter Strawson was regarded as one of the world's most distinguished philosophers. Unavailable for many years,_ Scepticism and Naturalism_ is a profound reflection on two classic philosophical problems by a philosopher at the pinnacle of his career. Based on his acclaimed Woodbridge lectures delivered at Columbia University in 1983, Strawson begins with a discussion of scepticism, which he defines as questioning the adequacy of our grounds for holding various beliefs. He then (...) draws deftly on Hume and Wittgenstein to argue that we must distinguish between 'hard', scientific naturalism; or 'soft', humanistic naturalism. In the remaining chapters the author takes up several issues in which sceptical doubts play an important role, in particular the nature of transcendental arguments and including the objectivity of moral philosophy, the mental and the physical, and the existence of abstract entities. _Scepticism and Naturalism_ is essential reading for those seeking an introduction to the work of one of the twentieth century’s most important and original philosophers. This reissue includes a substantial new foreword by Quassim Cassam and a fascinating intellectual autobiography by Strawson, which together form an excellent introduction to his life and work. (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

We develop and apply a multi-dimensional conception of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial condition fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.