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.
Jaina concern with epistemological issues has two main functions: (i) provide basis for an intelligible discourse on matters of common, everyday experience; (ii) demarcate this area from what constitutes the knowledge of the ‘ultimates’ of reality. In other words, what is it that we know, and how do we know what we believe we have come to know? These are, of course, standard epistemological questions in pramāṇavāda, theories of knowledge, which most schools in Indian philosophy subscribe to in one form or another, even if they end up demolishing the same. The Jainas also subscribed to pramāṇavāda; but at some point, their theories seek to transcend the bounds of ordinary sensory and for that matter even rational knowledge (considered as parokṣajñāna). They believed in the possibility of direct intuition (pratyakṣa), where consciousness “touches” the objects and their forms (universals). Pratyakṣa is curiously used for direct knowing, in a sense stronger than in Nyāya (via Matilal)’s direct realism. Thus, it is possible for beings to develop deeper insights (dṛṣṭi) by means of perfecting the instruments of knowing, working through universals (sāmānya, jāti,) and broader patterns (gestalts, adṛṣṭa) in the minds encounter with that which is real, in order to attain kevala sarvajña (the solitary all-knowing state or omniscience). This is not unlike Descartes’ view that in the ‘clear light of mind’, the pure ideas are none other than Ideas in God’s Mind (i.e. their identity is absolute; though God is absent in Jainism). Or that the “I-am” (ahaṃartha) is ultimately the knowing consciousness of the jīvātman (‘soul-self’), which makes the subject aware of the object grasped in the act of cognition, and thus makes it the act of acquiring become knowledge; this knowing is independent from the act of knowing, and is non-negotiable.
Hegel’s dialectical syllogism links his logic to his theology. For the middle term of the syllogism in logic is essentially mediated by the absolute Idea of Logic, as ultimately by the self-return of Logic in Spirit, and the Holy Trinity of the Christian Religion in a trinitarian ontology of logic, that is, a trinitarian logic. This link of logic to theology signals the clearest contribution to what I designate as ‘theology of logic’. Theology of logic is a theological interpretation of logic: in contrast to philosophy of logic, it asks the prior question of the contingent grounds for our very belief in logic. Hegel has, in the Syllogism chapter of his Logic, developed a post-Aristotelian dialectical syllogism, in which the Concept dynamically differentiates even as it sublates its extremes to produce new knowledge. This dialectical syllogism is distinguished as a dynamic self-mediating cycle of judgments, where indifferently connected judgments are circuitously united through the reciprocal intermediation of a shared middle term. Since mediation and extremity mutually coincide, each syllogism may be intermediated by each other. This exchange of judgments further implies an interchangeability of concepts, where each subordinate concept interchangeably cycles within every superordinate concept, in dialectical triads consisting of a self-dirempting universal, a coincident opposition of mutually related particulars, and a reconciling concrete singular. Every such dialectical triad of concepts can then cycle around one another, through such interchangeable relations of mediation and extremity, like a ‘circle of circles’, in which the intermediating centre and the furthermost periphery forever coincide. Hegel presents the Holy Trinity in the Lectures on the Philosophy of Religion as the absolute triad of all triads in each syllogism, which comprises this ‘absolute syllogism’ of the entire system of philosophy. Since, finally, the system itself is an absolute syllogism, and this absolute syllogism is the economic procession of the Trinity, every conceptual category of the system can ultimately be sublated and re-posited in and through the logic, dialectic, and syllogisticity of the Holy Trinity. The Christian Trinity thus not only figuratively corresponds to but truly coincides with the logical moments of every concept, and any thought. In answer to this absolute theological questioning of logic, Hegel shows logic to be ontology, ontology to be theology, and theology to be trinitarian, in a trinitarian ontology of logic, that is, a trinitarian logic.
This article examines Udayana’s defense of the existence and persistence of the self in the Ātmatattvaviveka. It argues that Udayana’s contribution should be understood as a logical defense in a broad Nyāya sense: an argumentative strategy that combines inference (anumāna), analysis of perception (pratyakṣa), dialectical refutation of rival views, and attention to the conditions of memory, karma, and liberation. The paper first clarifies the Nyāya background and then reconstructs Udayana’s polemical targets, especially Buddhist momentariness, Yogācāra idealism, materialist reductionism, and the objection from non-apprehension. It distinguishes Udayana’s own appeal to indeterminate perception from both earlier inferential accounts of the self and later Naiyāyika theories of internal mental perception. Two central arguments, from memory and from karmic continuity, are reconstructed in formal terms and in a Nyāya five-member format. The article concludes that Udayana’s treatment of the self is not merely a doctrinal defense of ātman, but a sophisticated contribution to global philosophy of religion and to the Logic and Religion project, because it shows how religiously significant metaphysical claims can be assessed through rigorous methods of reasoning.
This paper examines the ultrafilter interpretation of Kurt Gödel’s ontological argument and explores its philosophical and mathematical consequences. After reviewing the formulations of Anselm of Canterbury, Gottfried Wilhelm Leibniz, and Gödel, we show how Gödel’s positivity axioms can be understood extensionally as defining an ultrafilter over the domain of individuals. We argue that this perspective sheds new light on the modal collapse, suggesting that it reflects not merely features of the modal framework, but deeper structural properties of the underlying ultrafilter. We then relate this interpretation to the work of Harvey Friedman, where non-principal ultrafilters and divine objects are used to obtain relative consistency results in set theory.
This brief paper deals with aspects of Schopenhauer’s philosophy regarding different facets of his concept of knowledge, in light of the contemporary distinction between mythos and logos. Schopenhauer’s philosophy of knowledge is here understood as plural, given that he admits the epistemically valid coexistence of different accounts of the world, such as philosophy and religion. The paper revisits selected passages of Schopenhauer’s texts with a view to arguing that this acceptance by the philosopher points to an epistemic pluralism on his part, which in turn suggests that the modern clear-cut distinction between the two Greek terms may not be found in Schopenhauer’s philosophy.
Apophatic philosophers and mystics appear to accept contradictory reasoning: when they deem the divine ineffable, they render it not ineffable. That is, the claim “the divine is ineffable” entails that we can say something about the divine (i.e., that it is ineffable). This paper undermines the so-called ineffability paradox (if X is unspeakable, then it is speakable) through a Neo-Aristotelian/Neo-Pāṇinian analysis of Maimonides’ and Pseudo-Dionysus’ apophatic negations. In so doing, I show that both only endorse a limited conception of ineffability.
This paper examines the early modern history of Eulerian diagrams and argues that their development was shaped by confessional contexts. While logic is often viewed as a neutral and purely rational discipline, we show that logic diagrams in the 16^th and 17^th centuries were embedded in broader religious, philosophical, and institutional traditions. After clarifying the concept of logic diagrams and the specific characteristics of Eulerian representations, we identify methodological challenges in reconstructing their history and outline several external factors that influenced their use. Using two case studies—Nicolaus Reimers Ursus in the 16^th century and Erhard Weigel in the 17^th century—we demonstrate that Eulerian diagrams were predominantly cultivated in Protestant circles, in contrast to Byzantine and Roman Catholic diagrammatic traditions such as crescent diagrams, the square of opposition, and phoebifer axis diagrams. These competing traditions differed not only in form but also in their underlying representations of proof, particularly regarding direct versus indirect methods. The paper argues that confessional affiliation, together with philosophical convictions such as empiricism and rationalism, contributed to the selection and evaluation of diagrammatic techniques. By situating early modern logic within its cultural context, the study highlights the role of external factors in shaping representational practices in logic.
This paper aims to trace the emergence and articulation of the concept of ‘superstition’ (andh-vishwas; andh-shraddha in vernaculars) in 19 ^th century colonial India and its role in the construction of modern Hinduism. It begins by tracing the evolutionary history of this concept in Europe where it first functioned as a relational concept to differentiate between true-and false religion, and later been religion and science. Drawing upon recent scholarship that conceptualizes religion, superstition, and the secular as constituting a triadic relationship and examines its role in the boundary-making processes through which religion was historically defined in Europe and East Asia, this paper explores a similar process in colonial India, though under different historical conditions. Through an analysis of the writings of Rammohan Roy, Dayananda Saraswati, and Swami Vivekananda, it explores how ‘superstition’ (idolatry, miracles, astrology, etc.) served as a central concept through which these reformers defined true religion and, by extension, delineated the boundaries of ‘true Hinduism’ in the context of colonial modernity.
This paper examines the religious and mythological foundations of some central principles of Western logic, especially the laws of non-contradiction and excluded middle. It traces those logical laws to the very beginning of the Greek creation myth. The foundation of Greek metaphysics and logic was the principle of exclusion, first expressed in Greek myth, then conceptualized in early Greek philosophy, and finally formalized in Aristotelian logic. The paper traces this exclusionary framework through Anaximander, Parmenides, Aristotle, Hume, Leibniz, Hegel, Carnap, and contemporary non-classical logics. It also asks whether paraconsistent, paracomplete, and many-valued logics genuinely surpass exclusion, or merely relocate exclusion at a higher metalinguistic level. Finally, the paper contrasts this Western framework with Buddhist catuskoti and the metaphysics of no-self, arguing that non-Western traditions may offer alternative forms of rationality that should not be reduced to Western logical categories.
In this paper we address the astonishing hypothesis that one of the roots of institution theory (a very abstract mathematical theory on the semantics of logic) lies in the Buddhist approach to reality. I dedicate this work to the memories of my dear mentor, Joseph Goguen, and of his friend, Rod Burstall, the two great scientists and Buddhist practitioners who invented institution theory.
We construct a class K of infinite convex geometries by taking unions of chains of finite convex geometries, and prove that every member of K is both lower semi-modular and join semi-distributive. These properties, while automatic in the finite case, can fail for infinite convex geometries in general. We also show that not all infinite convex geometries arise via this construction, so that K is a proper subclass of the class of all infinite convex geometries.
Deontic logic aims to formulate moral concepts consisting of obligation, permission, and prohibition. Although the standard system of deontic logic (SDL) has long provided a fundamental framework for this kind of formalization, its application to non-ideal normative contexts continues to provide challenges. This paper provides a conceptual examination of SDL by analyzing its fundamental principles, semantic assumptions, and well-known paradoxes. The analysis emphasizes how moral conflicts and contrary-to-duty imperatives reveal structural tensions within conventional deontic frameworks, with a focus on classic paradoxes like the Chisholm and Ross paradoxes. The paper seeks to explain these challenges and demonstrate how they represent deeper conceptual constraints in modeling normative reasoning using idealized modal logics, rather than suggesting a new logical system. The main contribution of the paper is therefore clarificatory: it situates the limits of SDL in the context of larger philosophical discussions on moral conflict and normative consistency.
A variety of modal logics were developed in Helsinki during the 50s. Alethic, epistemic, and deontic systems with quantified extensions were studied both from syntactic and semantic viewpoints in a series of publications by Georg Henrik von Wright and his student Jaakko Hintikka. This paper surveys and critically assesses these contributions.
After telling the story of the world logic prizes contest and its origin, we explain the value of such a contest by examining what is a prize. We compare the idea of a World Logic Prize with other prizes, awards, medals, highlighting the importance of logic, as the characteristic feature of human beings. We then explain how the contest is organized, pointing out the similar perspective to that of the World Logic Day, launched on January 14, 2019, about six months after the first edition of the World Logic Prizes Contest, June 24, 2018.
This paper examines Ibn Taymiyya’s (1263–1328) critique of the Aristotelian logical tradition, with a particular focus on his theory of definition (ḥadd). Ibn Taymiyya argues that Aristotelian logic, premised upon fixed metaphysical categories, fails to serve as a practical instrument for epistemic inquiry and knowledge production, as it claims. Ibn Taymiyya’s critique can be divided into two main classes: general and metaphysical. His general criticisms undermine the validity of Aristotelian definitions through multiple dialectical arguments such as regress, disagreement, and redundancy, showing that definitions are not epistemically useful. His metaphysical criticisms, on the other hand, strike at the foundations of Peripatetic metaphysics by rejecting the distinctions between a) quiddity and its existence, and between b) essential and concomitant predicates. I have also argued that Ibn Taymiyya’s position cannot be reduced to nominalism, empiricism, or conventionalism. Rather, his theory of meaning aligns more closely with modern pragmatics, wherein speech acts derive their meaning from their communicative, intentional, and contextual functions.
Around 300 BCE, a debate emerged concerning the truth conditions of conditional propositions–a debate that, to this day, has not culminated in a formulation genuinely satisfying to philosophers. Nevertheless, the material implication proposed by Philo the Dialectician achieved considerable prominence, despite its evident divergence from the patterns of ordinary human reasoning. Its success may be attributed, at least in part, to its formal simplicity. It is now widely acknowledged, however, that Philo’s implication is not the long-sought representation of implication that would faithfully capture intuitive reasoning. This recognition is underscored by the vigorous development of formal logic, much of which has been driven by the search for a notion of implication that aligns more closely with our cognitive intuitions. As Susan Haack once remarked, a true solution to a philosophical problem is recognizable by the deep internal conviction it evokes regarding its adequacy. Arguably, none of the proposed definitions of implication to date have elicited such conviction, not even among their originators–hence, the search continues. The present study introduces a principle that appears to underlie human reasoning regardless of its subject matter–whether one is engaged in mathematical theorizing or reflecting on matters of everyday life, the same logical structure, the same inferential tool, seems to be consistently employed. We propose that this tool is the Universal Principle of Consistency (UPC), or, in its strengthened form, the Strong Universal Principle of Consistency (SUPC). This universal principle is derived from the definitions of two content-based implications: the hyperintensional content inclusion implication and the intensional content relationship implication. Both appear to align closely with the structure of ordinary reasoning, both resonate with the logical intuitions of the Ancients–particularly Chrysippus and Diodorus–and both prove effective in domains such as legal and mathematical reasoning. Moreover, they offer a precise account of key pragmatic phenomena, including presupposition and implicatures. If the proposal put forward here is accurate, it may be argued that it brings to a close the debate that began in antiquity.
