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)

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)

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.

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.

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.

P.M.S. Hacker 1. _The problems of Intentionality_ The problems of intentionality have exercised philosophers since the dawn of their subject. In the last century they were brought afresh into the limelight by Brentano. Famously he remarked that.

‘To Gödel via Babel’, MIND, July 1966.In (1), the last clause should read: ‘then the GN of the resulting P-sentence is x100.y’ In (21), the expression in Roman numerals should read: ‘$$Y.\frac{\hbox{ L }Y}{\hbox{ XIX }}$$’ In (25) and (27), the expression in Roman numerals should read: ‘$${(\hbox{ C }}^{\hbox{ XVII }}.\hbox{ D })\hbox{ . }\frac{\hbox{ L }\left({\hbox{ C }}^{\hbox{ XVII }}.\hbox{ D }\right)}{\hbox{ XIX }}$$’.

The desire to see a sign phenomenon in different ways always has a reason to interpret it in an unbiased, panoramic way, and in some places - even allowing for contradictions in its understanding by different participants in the interpretative process. For modern humanities, this disposition is quite understandable, since it follows from its very postmodern nature, thereby defining the semantic semantic fields of the leading humanities. True, it is not so wide-spread, but instead, it is evident that Ukrainian religious (...) thinkers of the Middle Ages and Baroque have interpreted the iconic phenomena more deeply. In the story of Petro Mohyla "On the Wonderful Elder Grigory Mezhyhirsky" the metropolitan Mohyla clearly expresses the need to build before the thinking gaze of the reader his own, immanently religious-philosophical conception of the Divine, which every time would present him not just as an act of manifestation, otherwise he appears before the person, while remaining alone. The contemporary study of this issue in order to integrate its leading concepts in the religious-philosophical and general cultural discourse of the postmodern era has largely determined the relevance of the proposed article. The study of the phenomenon of "leaving" by itself in changing forms of the phenomenon of the Divine is also one of the key ones in the proposed studio, because it expresses the very meaning of the Divine as a religious, and therefore a cultural phenomenon. (shrink)

Richard Taylor was born in Charlotte, Michigan on 5 November 1919. He received his A. B. from the University of illinois in 1941, his M. A. from Oberlin College in 1947, and his Ph. D. from Brown University in 1951. He has been William H. P. Faunce Professor of Philosophy at Brown University, Professor of Philosophy (Graduate Faculties) at Columbia University, and Professor of Philosophy at the University of Rochester. He is the author of about fifty articles and of five (...) philosophical books. This volume consists of essays presented to Richard Taylor on the occa sion of his sixtieth birthday. Some of the contributors have been Taylor'S students; some have been his colleagues; and all have been, and continue to be, his admirers. I have made several attempts to articulate what it is I (I would not presume to speak for anyone else) admire about Richard Taylor: (1) There is a particular 'flavor' to Taylor's philosophical writing and con versation that is wholly delightful. Like any other flavor, it can be tasted and enjoyed and remembered but never adequately described. (If there should be someone who has picked up this book who does not know what I mean, I recommend that he read the chapter on 'God' in Taylor's Metaphysics. ) (2) Taylor is a masterful dialectician. (shrink)

Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means of well-motivated assumptions expressed in terms of a transition probability function defined on the set of all pure states of the system, we construct a system of elementary propositions, i.e., a complete orthomodular atomic lattice satisfying the covering law. We also study in this (...) framework the important notion of compatibility of propositions, and we define the superpositions and the mixtures of the states of the physical system. (shrink)

This essay engages Mary Shelley’s Frankenstein or The Modern Prometheus as a salient intervention into modern political theory. I analyze the work as a cipher for the tensions inhabiting Euro-modernity’s stitched together fictions of racial determinism and racial dynamism legible in slavery, assimilationist projects and White fears reverberating throughout. Adapting the mythical ancient Prometheus as one who steals fire from the gods to create humans and civilization, Frankenstein dramatizes the risks and monstrous results of White imperial masculinity as a Euro-colonial (...) Promethean project of subject formation and race-making. Viewed through the prism of the Modern Prometheus, modernity in general and liberal humanism in particular are recast as monster-making projects. The European “discovery” of Indigenous peoples amplified Promethean aspirations to create subjects through civilizational processes of religious conversion, the infusion of Enlightenment rationality, and assimilation into whiteness. Politically, the Promethean capacity to engineer humans and proto-humans using Native peoples as raw material allowed progressives to argue against outright extermination in favor of cultural genocide. Seeking to create a subserviant species, Victor Frankenstein confronts a revolting insurrection of his own making—a Creature who refuses slavery, claims mastery over his creator and demands a female companion. Yet Frankenstein’s fear of creating “a race of devils” betrays a terror of what Whites know, but refuse to acknowledge, about themselves and racial others. (shrink)