Theological Discourse and Logic

Theological Discourse and Logic Stanisław Krajewski and Marcin Trepczyński Abstract. The 2nd World Congress on Logic and Religion, held in Warsaw, Poland, in 2017, is summarized. Then the connective “and” is analyzed; we focus on its meaning in the title of the congress and the title of the present volume. Finally, all the eleven papers included here are briefly introduced; we indicate whether logic or theology is the primary topic in the given paper. Mathematics Subject Classification. Primary 03A05; Secondary 03-06. Keywords. Logic, religion, theology, discourse, the connective “and”, non-monotonic logic, paradox, mathematics, metatheory. 1. The 2nd World Congress on Logic and Religion The present volume of Logica Universalis constitutes the third, and final, outcome of the Second World Congress on Logic and Religion held in Warsaw, Poland, in June 2017. Two previous post-conference volumes have been published as issues of the Journal of Applied Logics, namely “Formal Approaches to the Ontological Argument” (ed. by Ricardo Silvestre and Jean-Yves Beziau), or [5], and “The Concept of God” (ed. by Stanisław Krajewski and Ricardo Silvestre), or [4]. One more volume, devoted to Indian thought, edited by Piotr Balcerowicz, will also be published soon. The Warsaw congress was initiated by Jean-Yves Beziau and Ricardo Silvestre who had organized the first congress in João Pessoa, Brazil, in April 2015. (See [1].) To organize the 2017 event they worked together with the two editors of the present volume and as well as other persons form the University of Warsaw, in particular Piotr Balcerowicz and Agata Łukomska. The organizers of the second congress proposed to discuss topics included in such fields as: impact of religious beliefs on logical structures, logic at the service of apologetics, rationalization of religious beliefs, justification in religious legal traditions (including Talmudic Logic), logics vis-a-vis illogicalities in religion, non-classical logics and religion, models of argumentation in religious discourse. The congress announcement met with positive response from a large number of scholars. Over 250 participants from more than a hundred institutions gathered at the University of Warsaw, including philosophers, logicians, mathematicians, orientalists, specialists in religious studies, and theologians. More than a hundred of them presented papers during the five days of this event, and the plenary lectures were delivered by: Johannes Bronkhorst, Jessica Frazier, Dov Gabbay, Michał Heller, Saul Kripke and Romina Padro, Laurent Lafforgue, Ricardo Strobino, Giuseppe Veltri, Yuhan Sohrab-Dinshaw Vevaina and Jan Woleński. Most of them participated in the panel discussion at the end of the congress. Full documentation of the congress, including the program, as well as pictures and recordings, can be found at the website: http://logicandreligion.uw.edu.pl. Further congresses “Logic and Religion” are planned, the next one in 2020, in Varanasi, India. 2. The “and” The term „Theological Discourse and Logic” is a bit more precise than the general phrase “Logic and Religion” that was the theme of the congresses. Indeed, when religion is considered in the context of logic most of its vital aspects – practice, faith, authority, holiness – are usually ignored and only the rational religious considerations, in the first place theological discourse, are taken into account. Sometimes, however, the arguments showing limitations of rationality and logic are presented, and then the ignored aspects are invoked in order to show that logic cannot grasp them in an accurate way. We are not attempting to define theology or theological discourse here. This domain has many aspects, only some of which are taken into account in the papers gathered in this volume. The authors refer to (at least) the following concepts: religious legal considerations, the filioque doctrine, theological account of scientific topics, the concept of infinity, the question of the existence of God and its (un)provability, religious antinomies, the issue of the adequacy of religious language. Logic is also understood quite broadly in this volume. It involves the following aspects: non-deductive inferences, classical and non-classical logical systems, including modal and nonmonotonic ones, logical diagrams, logical paradoxes, metalogical theorems established by Gödel, and also some essentially mathematical issues: infinity, game theory, mixed strategies, metamathematics. Rather than attempting an examination of the meanings of ‘logic’ and of ‘theology’ or ‘theological discourse’, which are vast topics treated in thousands of publications, it is of interest to consider the subtle meanings of the connective ‘and’. Logicians like to treat “and” as an indication of conjunction. Indeed, we may say that all the papers in the present volume deal with theological discourse and they also deal with logic. It is well known that “and” joining two sentences may indicate temporal sequence, causal relation and other relations. For example, compare “The driver lost consciousness and the car bumped into the wall.” with “The car bumped into the wall and the driver lost consciousness.” The phrase “theological discourse and logic” contains two names. When two names are linked with “and” many shades of meaning are possible. In its simplest meaning “and” indicates juxtaposition, or rather mere juxtaposition with no relevant connection between the terms. Cf. the statement that France is famous for its “wine and cheese.” Moreover, sometimes in the natural languages such interpretation of this connective involves additional information concerning the order of the elements, e.g. expressing their importance (for instance, often the order of the names of the authors of the text matters). This simplest meaning is undoubtedly not the sense of the “and” appearing in the title of this volume. It should be clear that in the phrase “theological discourse and logic” used in the present volume we assume that “and” indicates a relevant connection. Thus, it means that there are interesting relationships between the designates of these terms to be identified. Again, in some contexts the order of these designates may matter, for instance one can adopt the first of them as the starting point or the main subject which is to be examined in the context of the relationship with the latter. According to such interpretation of the connective “and” the relationship between two objects is not symmetric. Hence, “logic and theological discourse” would produce a different connotation than would “theological discourse and logic”. However, it often happens that the order is not so relevant. The two meanings presented below emphasize important relationships which, on a general level, are rather symmetric. Sometimes the “and” indicates opposition. Cf. “faith and reason.” And, indeed, the use of the “and” in “theological discourse and logic” to many critics of religion would suggest incompatibility: the two terms are opposite and no meaningful connection can be made. Yet the authors of the papers gathered here do not share this criticism, even if they see limitations of logic when applied to theology. Finally, participants in the Logic and Religion congress would rather treat the “and” as a term suggesting compatibility, or even more strongly, a possible union. Indeed, theology, or at least Western theology can be characterized by analyzing the term: it is as a synthesis of theos and logos, Θεός and λόγος. The synthesis was already made by Aristotle who described theology as science, a logical system of statements about the Divine. Later philosophers usually used the combination of these two words to indicate talking about God. Without more detailed considerations how to translate the two words taken together, we can say that they can be understood as “religion and logic,” or the classical logic applied to (Biblical) religion. The union of two very different elements can hardly be made in a smooth manner. If so, one could naturally ask which component dominates. In our case, the problem is whether logic or religious discourse is primary. In addition, one can ask what is the influence of one upon the other, and whether the influence, if any, is positive or negative. The papers in this volume vary in those respects. Various approaches are represented. There is no uniformity. However, this diversity can be seen as valuable: it reveals how many interesting problems appear at the interface of theological discourse and logic. 3. The papers The papers in the present volume have been arranged in a chronological order of sorts, namely 8 out of 11 have as their point of departure some non-contemporary authors and texts, so they can be naturally ordered. The last three papers have no substantial historical component, and are treated as entirely contemporary. The first paper, “The Talmudic Logic Project, ongoing since 2008” by Dov Gabbay, Ester David and Uri Schild, discusses the logical principles used in ancient religious reasonings contained in the Talmud. The project to analyze them using modern logical tools and, if necessary, introducing new constructions was initiated by Dov Gabbay and by now involves many researchers. In addition to an extension of our grasp of legal and other non-deductive logical inferences, like a fortiori or abduction, the project provides some new logical principles suggested by the Talmudic considerations. The ancient material, still diligently studied by traditional Jews, constitutes the background, logic is clearly the focus of the research described in the paper. We can see mutual influences of logic and theology. The second paper, “Counterpossibles and Normal Defaults in the Filioque Controversy” by Jacob Archambault, begins with the filioque controversy, or the early medieval Christian theological dispute whether the Spirit is only from God the Father or also from the Son. The defense of the filioque, or “and the Son,” by Anselm of Canterbury is analyzed as not so much as a dogmatic position, but as a logical position, anticipating “default logic”, which is a kind of non-monotonic logic. In the paper theological and logical aspects are described in similar detail. The third paper, “Non-monotonic Logic in Favour of Science and Religion Compatibility” by Marcin Trepczyński, provides an analysis of the views of the medieval thinker Boethius of Dacia who claimed that both the negation of the thesis that the world had a beginning, and Christian affirmation thereof can be retained. Their compatibility is possible only if a non-monotonic logic is assumed. In the paper the theological discourse is basic and logic is seen as a tool useful to clarify problems. The fourth paper, “Thomas Manlevelt: God in Logic” by Alfred van der Helm, describes the ideas of the fourteenth century nominalist Thomas Manlevelt, who claimed that substance does not exist. To argue for this thesis he was putting theological limitations to logic. For example, the nature of the Trinity defies our logic and shows that supreme knowledge belongs exclusively to God. In the paper theology is fundamental, and its influence on logic is studied. The fifth paper, „Mathematics and Theology in the Thought of Nicholas of Cusa” by Roman Murawski, deals with the mutual influences of mathematics and theology in the thought of the important fifteenth century philosopher. For Nicholas of Cusa mathematics provides tools assisting theology and enabling us to understand such difficult to grasp qualities as infinity. In the paper both theology and mathematics are starting points. Mathematics can be seen as the most advanced fruit of logical thinking; that is why the paper fits this collection. At the same time it is good to remember that the logicist identification of logic with mathematics is commonly rejected by modern philosophers of mathematics. An analysis of the fruitfulness of mathematical methods in theology can be found in [3]. Theological motives in mathematics, and especially in its “kitchen,” are considered, e.g., in [2]. The sixth paper, “Iterated Mixed Strategies and Pascal’s Wager” by Emil Badici, moves to more contemporary period and continues mathematical considerations. Here they are applied to the famous Pascal’s Wager that is allegedly justifying belief in God. The paper critically analyses the argument using mixed strategies that is invoked to show that the Wager fails. In the paper the focus is on mathematics, theology is only a starting point. The seventh paper, “Diagrammatic Reasoning with the Vesica Piscis and the St. Andrews Cross” by Jens Lemanski, deals with logic diagrams, especially those proposed as tools of syllogistic logic since the eighteenth century. The diagrams, like Venn’s circle diagrams, be presented in a way that resembles some religious symbols. Modern developments are also studied, for example the process of reduction of logic circle diagrams to the St. Andrew’s cross. The focus of the paper is on the history of logic, the theological aspect appears in a way that may be seen as inessential. However, if we consider religious symbols as an integral part of theological discourse, this paper offers another approach how to look at the relationship between such discourse and logic. The eighth paper, “The Antinomies of Religion: Recent Interpretations of Pavel Florensky’s Logical Ideas” by Paweł Rojek, presents the thought of an early twentieth century Russian thinker. He was among those who believed that theological discourse necessarily involves antinomies and contradictions. Several interpretations of his views are studied, using modern logical systems, including paraconsistent and other non-monotonic logics. The paper studies logical systems, and religious discourse, as interpreted by Florensky, serves as an inspiration and a source of problems. The ninth paper, and the first of the three remaining ones that do not involve a historical component, „Metalanguage and Revelation. Rethinking Theological Language” by Andrea Vestrucci, continues in some ways the theme of the previous paper. The inadequacy of language in any attempt to express revelation is discussed, and in conclusion the formal aspect of the inadequacy is stressed. Theology’s focus is seen as the formal interrelation between “meta” and “non-meta”. Religion is primary in the paper, logic is secondary. The tenth paper, “On Proving the Unprovability of God’s Existence” by Meir Buzaglo, relates the issue of the provability of unprovability of God’s existence – a stronger claim than the common thesis that God’s existence in unprovable – to Gödel’s Second Theorem. In this way an advanced mathematical result is taken into account and makes possible an investigation belonging to “meta-theology.” Gödel’s result implies limitations with regard to formal provability for a wide class of formal systems rather than for specifically religious discourse. While the general problem of the unprovability of the existence of God is explored, the paper focus is principally on metalogic. The last paper in this volume, „From Language to God. Knowability and Other Theological Semi-Paradoxes” by Franca d'Agostini, studies some paradoxes appearing in systems of modal logic containing the operator “p is known,” Fitch-Church proof that if everything is knowable, then everything is known, and also paradoxes related to classical logic, for example the Curry paradox that makes possible to “prove” any sentence. Sentences taken from theological discourse, notably “God exists,” provide particularly interesting examples. The focus of the paper is on logic, theology is invoked to have nice illustrations. References [1] Beziau, J.-Y., Silvestre, R.: Logic and Religion, Log. Univers. 1 (2017), 1-12. [2] Krajewski, S: Theological Metaphors in Mathematics. Studies in Logic, Grammar and Rhetoric 44 (57), 2016, the issue „Theology in Mathematics?” (ed. by Stanisław Krajewski and Kazimierz Trzęsicki), 13-30. [3] Krajewski, S.: Mathematical Models in Theology. A Buber-inspired Model of God and its Application to Shema Israel. Journal of Applied Logics 6(6), 2019, 1007–1020. [4] Krajewski, S., Silvestre, R. (eds.): “The Concept of God”, Journal of Applied Logics 6, No. 6, 2019. [5] Silvestre, R., Beziau, J.-Y. (eds.): “Formal Approaches to the Ontological Argument” Journal of Applied Logics 5, No. 6, 2018.