Introduction: At the Limit of Comprehension

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true.

The Enigma of Divine Revelation: Between Phenomenology and Comparative Theology, eds. Jean-Luc Marion and Christiaan Jacobs-Vandegeer, , 2020

No longer trusting the once-dominant disciplines of reasoning in the modern academy, contemporary discussions of theology often turn to tradition-or experience-based sources of religious knowledge. While applauding the turn, for example to scripturally grounded theology, I argue that this should not entail a turn away from all logic-based disciplines of reasoning. The genres of modern reasoning that merit postmodern criticism-foundationalist and other types of reductive reasoningare all informed by two-valued, disjunctive logics. Many classic and medieval scriptural commentaries are informed, however, by non-disjunctive disciplines of reasoning that may be formalized, today, in any of a range of multi-valued logics. There is therefore no justification for extending postmodern suspicions of disjunctive disciplines of reasoning to non-disjunctive disciplines. By way of illustration, I introduce a semiotic method (the "Logic of Revelation," LR) for diagramming patterns of non-disjunctive reasoning in practices of tradition-based, scriptural theology. An analyst may, of course, lack reasonable evidence for attributing such patterns to a given project of theological writing. The detailed work of this chapter is to illustrate the kind of reading and modeling that provides reasonable evidence. According to LR, patterns of non-disjunctive reasoning are specific to a given sub-tradition of practice. I therefore illustrate LR through the case of classic rabbinic reasoning about scripture (midrash) as examined by a set of contemporary rabbinic scholars. Rabbinic reasoning adopts revealed words as its first premises and prototypically attends to catastrophic loss as context for its innovative, midrashic interpretations.

2002

We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism.

Dialegesthai, 2022

There is a lively debate in contemporary Analytic Philosophy of Religion about the consistency of the Trinitarian doctrine. In this context, the notion of ‘mystery’ has become crucial. However, although it is currently considered the main challenge of Trinitarian theology, its definition remains rather partial and superficial. After a brief description of today’s Mysterianism, I analyse three ‘emblematic’ positions in light of the current debate: Aquinas, Leibniz and Hegel present three ways to believe in a mysterious Trinity. I will point out a few possible weaknesses in the positions of the first two authors in order to better highlight the usefulness of the Hegelian position, often underestimated in the contemporary analytic debate. I will also analyse the connection between the three positions and their respective metaphysics, showing the epistemological premises (e.g., analogy and univocity) that need to be better investigated in the future.

maimonides-guide.com, 2017

This is my second interpretive essay on Maimonides's Introduction to his Guide of the Perplexed. Its purpose is to come to a clear understanding of Maimonides' use of his famous seven contradictions introduced at the end of that Introduction. In it I mostly follow Marvin Fox' approach, although I explain the relationship between that approach and the necessity, pursuant to the second Mishnah in Hagiga, to prevent certain kinds of material from entering public discussion.

introductory chapter of the dissertation.

Ancient Philosophy, 2006

In examining what Aristotle says about the principle of non-contradiction (PNC), two sets of claims seem to be at odds. On the one hand, the PNC is an axiom. Axioms are one of three types of scientific principles identified in the Posterior Analytics, and principles are said to be more intelligible by nature or without qualification in contrast to those things initially more intelligible to us. On the other hand, certain passages imply that axioms are known to everyone, expert and non-expert alike; other passages go so far as to claim that unless one has the PNC in particular no learning of any sort can take place. But if the PNC is and must be ‘better known to us’ from the beginning, the priority of things better known by nature is confused. We are faced with a seeming paradox: we begin with things better known to us and proceed to things intelligible by nature; but the most intelligible principle of all is somehow already known to us at the start of inquiry. But how can a principle be better known to us from the beginning? In this paper, I resolve the paradox by considering the special knowledge had by the philosopher of an axiom known in a way to everyone.

Logica universalis, 2019

This is a draft of the paper that will introduce the volume "Theological Discourse and Logic" (ed. by Marcin Trepczynski and Stanislaw Krajewski), an issue of Logica Universalis. 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. See https://link.springer.com/article/10.1007/s11787-019-00238-w (Unfortunately, it was not released by the publisher as an open access paper.)

Philosophia

Dialetheism is the view that some contradictions are true. One common motivation to the view concerns cases of contradictory concepts obtaining together. Allegedly, in these cases such concepts lead to a true contradiction. In this paper, we argue that this path is closed as a motivation for dialetheism. There are two basic difficulties to articulate the view: i) once contradictory or incompatible concepts are granted to obtain together, there is no longer any reason to claim that they were incompatible to begin with, and ii) it is not easy to go from such concepts to clear cases of negation-involving contradictions without already assuming the truth of dialetheism. Further difficulties discussed here concern the maintenance of the meaning of important concepts such as "contradiction" in a dialetheist setting. Those difficulties make the case for dialetheism hard to motivate via contradictory concepts.

Faith and Philosophy, 1994

The paper gives a model of the sentences that express the core of the doctrine of the Trinity. The new elements in the model are: (1) an underlying map between DIVINE PERSON and GOD-in place of set-theoretic inclusion, and (2) the notion of a predicable keeping or not keeping phase in a system of kinds. These elements, which are explained in the text, are common in everyday language. The model requires no tampering with the fundamental laws of logic, nor does it require the use of any such difficult metaphysical notions as substance and essence as distinct from person. "Licet enim Trinitas Personarum demonstratione probari non possit. .. convenit tamen, ut per aJiqua magis manifesta declaretur."-St. Thomas Aquinas, S.Th., q. 39, art. 6.

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction? The notion of contradiction is far from simple, it turns out, and the search for clarification points up a menagerie of different forms of the Law of Non-Contradiction and Dialetheism as well. Might some of these at least be eliminated as trivially true or false—true or false by definition, perhaps—allowing us to concentrate on the more interesting forms? Even the attempt to settle the easy cases raises a potential impasse in the dynamics of the debate—an impasse that can be expected to characterize the debate quite generally. The remainder of the paper is devoted to the question of whether that impasse might be broken.

Review of Symbolic Logic

Is there a notion of contradiction – let us call it, for dramatic effect, “absolute” – making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First, it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crip-pling expressive limitations and from revenge paradoxes – pending a rigorous non-triviality proof for a formal dialetheic theory including it.

he Betrayal of Tradition: Essays on the Spiritual Crisis of Modernity, ed. Harry Oldmeadow, 2005

For the person of simple religious faith the sense of being irrational in the light of modern science can be a difficulty if not an embarrassment. Such people often find themselves believing in a science based on the seen and the knowable, yet having faith in the unseen and the unknowable. Inevitably they feel themselves caught in a contradiction. The scientism of the modern era claims a rational view of reality. Up against this rationality it places what it takes to be the often incongruous demands of religious faith. However, it is a gross error to suggest that rationality and faith-based perspectives are irreconcilable. Faith, fully understood, is conformity to Truth.

Modern Theology, 2014

A polydox theology starts from the insight, as Catherine Keller and Laurel Schneider state in the introduction to Polydoxy: Theology of Multiplicity and Relation, that "multiplicity itself has become theology's resource," unexpectedly and "miraculously" transformed from "liability" to "friend." 1 Polydoxy values "multiplicity, the evolutionary uncertainty it unfolds, and the relationality that it implies" in its understanding of divinity as well as in the resources it uses to interpret that divinity (Keller and Schneider, "Introduction," 1). A response to Polydoxy, like the practice of polydox theology itself, must then operate in variegated registers. A Christian theology that recognizes the differences among its own sources while remaining faithful in its commitments to, in Marcella Althaus-Reid's terms, the God whose back is made of difference, 2 will necessarily be an open-ended theology. After all, the most firmly established canon of Christian interpretation is that Christians do not agree on it. Christianity is always polydox, as the authors of Polydoxy remind us (Schneider, "Crib notes from Bethlehem," 21). As a theological method, polydoxy does not then transplant the practice of Christian theology into strange territory, despite its recommendation of "[a] responsible pluralism of interdependence and uncertainty" against Christian theology's apparent insistence on singularity in its approach to the uniqueness of its divinity (Keller and Schneider, "Introduction," 1). Valuing polydoxy rather than

Faith and Philosophy, 1989