This paper proposes a novel truth-functional semantics for modal logic by replacing Kripke-style possible worlds with many-valued matrix systems. Each finite model with n worlds is represented by a many-valued logic with 2^n truth-values, encoded as binary strings corresponding to world-indexed truth assignments. Accessibility relations are captured through truth-functional operations, yielding a unique modal matrix for each frame. This framework enables a fully algebraic treatment of modal operators, handling frame-dependent validity in a purely truth-functional way. While Dugundji’s theorem is standardly seen as precluding matrix semantics of this kind, we demonstrate how the approach here sidesteps those results by indexing semantics to individual frames. We establish several technical results: a general procedure for generating matrices from Kripke frames, injectivity of the frame-to-matrix mapping, and frame recoverability given a modal matrix. We outline matrix-theoretic completeness results for the modal logic , and define bisimulation in the matrix setting. Expressivity is examined and infinite extensions are explored. Finally, we introduce the concept of structural bivalence, which underwrites the constructions developed here, alongside broader technical and philosophical implications.
This paper applies eleven complementary methodological procedures to the question “What is God?”, following the Socratic-Platonic ti esti tradition — asking what something is before denying it, glorifying it, or confining it within a closed theory or dogma. The inquiry steers between the north pole of mere enumeration and the south pole of dogmatic definition, seeking an equatorial equilibrium or a southern tropical paradise. Drawing on definitions, quotations, proverbs, jokes, word clouds, Venn diagrams, opposition theory, the pyramid of meaning, categorization, typification, and symbolization, the paper maps the concept of God across its philosophical, religious, and cultural dimensions. Quotations from Einstein, Oscar Wilde, and Baron de Chambourcy illuminate ontological, ironic, and psychological aspects of the divine. Proverbs and jokes from Jewish, Sufi, and Buddhist traditions reveal how humor and folk wisdom encode deep theological insights. A semantic word cloud exposes the heterogeneous neighborhood of the concept, while a Venn diagram situates God among the notions of the Sacred and the Absolute, yielding seven distinct conceptual regions. Opposition theory breaks classical dichotomies — God/Devil, Reason/Faith — through trichotomies and hexagons. The pyramid of meaning distinguishes God as word, idea, and reality, placing the notion at its apex. Five categories organize the main conceptions of the divine: monotheism, polytheism, the non-personal absolute, pantheism/panentheism, and critical postures. Typification illustrates each category through representative images. Finally, symbolization identifies strong symbols — the Christian cross, Bastet, and Inti — as condensed expressions of the divine. The paper concludes not with closure but with clarification, keeping the door of philosophical wonder open.
This preface introduces a special issue of Logica Universalis documenting the 3rd and 4th World Congresses on Logic and Religion (WoCoLoR), held respectively in Varanasi (2022) and Sinaia (2023). It situates the Logic and Religion project within a broader philosophical argument: that rationality, as formally represented by logic, and religion are two foundational and historically intertwined dimensions of human nature. The authors — Agnieszka Rostalska and Jean-Yves Beziau — reflect on the personal and intellectual journeys that shaped their involvement, tracing connections to Krishnamurti, Buddhist thought, Jain studies, and Hindu philosophy. The preface also outlines the structure and mission of the Logic and Religion Association (LARA), based in Warsaw, which serves as the institutional framework for fostering dialogue between logicians and theologians across traditions. Both congresses are described in terms of their thematic scope, keynote commitments to gender balance, and the notable Schopenhauer workshops held in Varanasi and Sinaia. The 16 papers gathered in this special issue span topics ranging from Indian religious philosophy and Christian theology to foundational logical questions. Looking ahead, the authors announce the 5th WoCoLoR, to be held in Vancouver in 2026, chosen for its accessibility, political neutrality, and cosmopolitan religious diversity. The issue as a whole reflects the project’s core commitment to inclusive, rigorous, and genuinely interreligious academic inquiry.
This paper takes as its starting point an ordinary encounter with a conversational artificial intelligence system in order to interrogate, from a philosophical standpoint, what is actually meant by the expression "Artificial Intelligence". Bringing together the etymological roots of "intelligence" - understood, following Robert Brandom, as the capacity to respond to reasons - and the classical discussions of Turing, Searle, Descartes and Wittgenstein on machine cognition, the paper argues that contemporary AI, however linguistically fluent, occupies only the domain of formal-syntactic calculation, without ever entering what John McDowell calls the "space of reasons". Two philosophical diagrams - a Venn diagram and a square of oppositions - are used to map the ontological position of AI relative to biological life and consciousness. The paper concludes that Artificial Intelligence is best understood not as a rival mind but as a normative mirror: a device that reflects the structure of human reasoning back to us without ever inhabiting it, exposing, in this reflection, what is most mechanical and least human in ourselves.
The words of institution of the Eucharist, “This is my body” and “This is my blood,” appear to generate a contradiction concerning identity, since they seem to affirm that two non-identical things are nevertheless identical. I refer to this tension as the logical problem of the Eucharist. In this paper, I propose a solution based on Peter Geach’s version of Relative Identity Theory. First, I reconstruct the logical problem of the Eucharist and its underlying assumptions. I then introduce Geach’s Relative Identity Theory and examine its application to the logical problem of the Trinity. Building upon this framework, I apply Relative Identity Theory to the Eucharistic case and address several metaphysical objections inspired by David Wiggins’s critique of Geach. Finally, I analyze the implications of this debate for my Geachian solution to the logical problem of the Eucharist. I conclude that, although a Geachian framework may successfully preserve the logical coherence of Jesus’s words at the institution of the Eucharist, it encounters significant difficulties in maintaining a robust realist account of the bread and Christ’s body.
