The prevalent interpretation of Gödel’s Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of the underlying mathematical theorem depends on several arbitrary formalisation choices. In this paper I examine the theorem’s dependency regarding Gödel numberings. I introducedeviantnumberings, yielding provability predicates satisfying Löb’s conditions, which result in provable consistency sentences. According to the main result of this paper however, these (...) “counterexamples” do not refute the theorem’s prevalent interpretation, since once a natural class ofadmissiblenumberings is singled out, invariance is maintained. (shrink)

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study (...) of certain principles of self-referential truth. (shrink)

On business ethics of Papuan peoples in Indonesia.

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

There is a well-known gap between metamathematical theorems and their philosophical interpretations. Take Tarski’s Theorem. According to its prevalent interpretation, the collection of all arithmetical truths is not arithmetically definable. However, the underlying metamathematical theorem merely establishes the arithmetical undefinability of a set of specific Gödel codes of certain artefactual entities, such as infix strings, which are true in the standard model. That is, as opposed to its philosophical reading, the metamathematical theorem is formulated (and proved) relative to a specific (...) choice of the Gödel numbering and the notation system. A similar observation applies to Gödel’s and Church’s theorems, which are commonly taken to impose severe limitations on what can be proved and computed using the resources of certain formalisms. The philosophical force of these limitative results heavily relies on the belief that these theorems do not depend on contingencies regarding the underlying formalisation choices. The main aim of this paper is to provide metamathematical facts which support this belief. While employing a fixed notation system, I showed in previous work (_Review of Symbolic Logic_, 2021, 14(1):51–84) how to abstract away from the choice of the Gödel numbering. In the present paper, I extend this work by establishing versions of Tarski’s, Gödel’s and Church’s theorems which are invariant regarding _both_ the notation system and the numbering. This paper thus provides a further step towards absolute versions of metamathematical results which do not rely on contingent formalisation choices. (shrink)

Ce livre est la brillante synthèse d'une œuvre qui figure au premier plan de la pensée catholique au XXe siècle. L'élan qui anime tous les écrits de Hans Urs von Balthasar ne s'affirme dans aucun livre mieux que dans cette Théologie de l'histoire. Celle-ci est parfaitement centrée sur le temps du Christ : Dieu toujours présent parmi les hommes. Depuis l'incarnation, l'histoire se déroule dans ce temps nouveau ; il est la norme de l'évolution humaine ; c'est lui qui (...) mesure le cours de l'existence, le progrès vertical et horizontal de l'humanité. Une fresque extraordinaire se déploie sous les yeux du lecteur l'histoire s'intériorise en un destin personnel, la vocation de chacun se situe dans un destin historique universel. Cette vision eschatologique, d'un réalisme éblouissant et pathétique, nous montre que la fin des temps et les temps nouveaux sont déjà commencés. (shrink)

v. 1. Truth of the world -- v. 2 Truth of God -- v. 3. The spirit of truth.

Religionskritik als Chance und Herausforderung für den christlichen Glauben - Selbstverantwortung und religiöse Mündigkeit - Dialog zwischen Religionen.

Cognitive Science, Volume 46, Issue 2, February 2022.

Most philosophers take Benacerraf’s argument in ‘What numbers could not be’ to rebut successfully the reductionist view that numbers are sets. This philosophical consensus jars with mathematical practice, in which reductionism continues to thrive. In this note, we develop a new challenge to Benacerraf’s argument by contesting a central premise which is almost unanimously accepted in the literature. Namely, we argue that — contra orthodoxy — there are metaphysically relevant reasons to prefer von Neumann ordinals over other set-theoretic reductions of (...) arithmetic. In doing so, we provide set-theoretical facts which, we believe, are crucial for informed assessment of reductionism. (shrink)

Language’s intentional nature has been highlighted as a crucial feature distinguishing it from other communication systems. Specifically, language is often thought to depend on highly structured intentional action and mutual mindreading by a communicator and recipient. Whilst similar abilities in animals can shed light on the evolution of intentionality, they remain challenging to detect unambiguously. We revisit animal intentional communication and suggest that progress in identifying analogous capacities has been complicated by (i) the assumption that intentional (that is, voluntary) production (...) of communicative acts requires mental-state attribution, and (ii) variation in approaches investigating communication across sensory modalities. To move forward, we argue that a framework fusing research across modalities and species is required. We structure intentional communication into a series of requirements, each of which can be operationalised, investigated empirically, and must be met for purposive, intentionally communicative acts to be demonstrated. Our unified approach helps elucidate the distribution of animal intentional communication and subsequently serves to clarify what is meant by attributions of intentional communication in animals and humans. (shrink)

A quantitative analysis of a trans-generational, conversational corpus of Chintang (Tibeto-Burman) speakers with community-wide bilingualism in Nepali (Indo-European) reveals that children show more code-switching into Nepali than older speakers. This confirms earlier proposals in the literature that code-switching in bilingual children decreases when they gain proficiency in their dominant language, especially in vocabulary. Contradicting expectations from other studies, our corpus data also reveal that for adults, multi-word insertions of Nepali into Chintang are just as likely to undergo full syntactic integration (...) as single-word insertions. Speakers of younger generations show less syntactic integration. We propose that this reflects a change between generations, from strongly asymmetrical, Chintang-dominated bilingualism in older generations to more balanced bilingualism where Chintang and Nepali operate as clearly separate systems in younger generations. This change is likely to have been triggered by the increase of Nepali presence over the past few decades. (shrink)

Cognitive Science, Volume 45, Issue 11, November 2021.

The language comprehension system preferentially assumes that agents come first during incremental processing. While this might reflect a biologically fixed bias, shared with other domains and other species, the evidence is limited to languages that place agents first, and so the bias could also be learned from usage frequency. Here, we probe the bias with electroencephalography (EEG) in Äiwoo, a language that by default places patients first, but where sentence-initial nouns are still locally ambiguous between patient or agent roles. Comprehenders (...) transiently interpreted nonhuman nouns as patients, eliciting a negativity when disambiguation was toward the less common agent-initial order. By contrast and against frequencies, human nouns were transiently interpreted as agents, eliciting an N400-like negativity when the disambiguation was toward patient-initial order. Consistent with the notion of a fixed property, the agent bias is robust against usage frequency for human referents. However, this bias can be reversed by frequency experience for nonhuman referents. (shrink)

Balthasar Hubmaier is often called ‘the theologian of the Anabaptists’ for he was the only early Anabaptist leader with an earned doctorate. The former Catholic priest embraced the reforming thought of Erasmus, Zwingli, and eventually Zwingli’s former pupils and led the Moravian city of Nikolsburg to become a bastion of Anabaptist thought and practice. The multi-dimensional religious landscape both afforded Hubmaier the opportunity and compelled him to author the first Anabaptist catechism. Through the work, Hubmaier articulated a clear and (...) succinct portrayal of Anabaptist theology and ecclesiology summed up in the Erasmian tenet of the love of God and neighbor. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BALTHASAR'S USE OF THE THEOLOGY OF AQUINAS }AMES J. BUCKLEY Loyola College in Maryland Baltimore, Maryland T HE AIM OF THIS essay is to raise some questions about the internal consistency of Hans Urs von Balthasar's use of the theology of Thomas Aquinas. These are genuine questions. That is, they are not questions ("Is Balthasar's use of Aquinas consistent?") disguising or masking answers ("Balthasar's use (...) of Aquinas is inconsistent"). While I hope the questions set an agenda for disputations between students of these two theologians, my aim is not to settle the many disputations between the theologies of Aquinas and Balthasar, but to propose some quaestiones disputatae. In Balthasar's terms, the aim is to set up the theater and put some characters on the stage, not to stage the drama itself. Why bother? First, Balthasar's theology arises out of a tradition critical of the theology of Aquinas, and students of Aquinas can only ignore such objections at the price of abandoning Aquinas's habit of responding to such criticisms. The locus classicus of this critique is Balthasar's claim that he omits Aquinas from his canon of theological aestheticians because Aquinas is one of those whose "deep and lucid philosophical aesthetics" has "failed to achieve a theological translation, that is, to be seen as the unfolding of a theology based on biblical revelation" (GL II, 21).1 Thomas Aquinas (Balthasar later says) "was more of a philosopher than a theologian" (GL III, 9). We shall see later that ' I shall use the following abbreviations: ST = Summa Theologiae. Latin text and English translation, ed. Thomas Gilby, various translators (New York: McGraw-Hill; London: Eyre & Spottiswoode, 1964-80). GL =The Glory ofthe Lord: A Theological Aesthetic, ed. Joseph Fessio, S.J., and John Riches, various translators, 7 vols. (San Francisco: Ignatius Press; New York: Crossroad Publications, 1982-91). 517 518 JAMES J. BUCKLEY Balthasar also mentions other objections to Aquinas. In fact, part of my argument will be that this central criticism of Thomas's aesthetics is intelligible only against the background of other even more important criticisms of Aquinas's theology. I ought also to note at this early stage, however, that Balthasar 's criticisms of Aquinas are almost always carefully qualified. For example, in the locus classicus just cited, Balthasar objects to Aquinas's aesthetics, not his ethics or metaphysics; indeed, it is a criticism of Aquinas's theological aesthetics, not his philosophical aesthetics. Still further, Balthasar even says it "would perhaps" be possible to develop the "implicit" theological aesthetics in Thomas's philosophical aesthetics; however, Balthasar (inexplicably, some would say at this point) thinks this could only be done "witn uncertain success" (GL II, 21). One reason for the frequent allusiveness of Balthasar's objections to Aquinas is a second reason for bothering with Balthasar's use of Aquinas: in and with the firmness of Balthasar 's criticisms of Aquinas, the vast majority of Balthasar's uses of Aquinas are constructive rather than critical. Indeed, if taking the measure of theological disputation were primarily a matter of weighing quotations, it could easily be shown that Balthasar's use of Aquinas is by far more positive than negative. More importantly, I shall propose that Balthasar notices features of Aquinas's theology not often noted (or still not noted often enough) by many students of Aquinas. This common ground between Balthasar and Aquinas recalls how, among Roman Catholics in the first part of this century, there was a sort of alliance among Catholic reformers-over against strains of Catholic traditionalisms-between some forms of Thomism and TD= Theodramatik, 4 vols. (Einsiedeln: Johannes Verlag, 1973-83). T-D =Theo-drama: Theological Dramatic Theory, various translators, 5 vols. planned (San Francisco: Ignatius Press, 1988-). TL= Theologik, 3 vols. (Einsiedeln: Johannes Verlag, 1985-87). For a summary of Balthasar's trilogy on beauty and goodness and truth, see his Epilog (Einsiedeln/Trier: Johannes Verlag, 1987) as well as My Work: In Retrospect, trans. Cornelia CapoI (San Francisco: Ignatius Press, 1993). BALTHASAR'S THEOLOGY OF AQUINAS 519 what was known as la nouvelle theologie (including Balthasar).2 It is this common ground that ought to make us wary of... (shrink)

The volume and diversity of Balthasar's output makes it hard to grasp his theological purpose. This article considers the aims of Herrlichkeit in particular. To take the beautiful seriously is ontologically important but evangelically more urgent still. The Gospel requires sensitivity to the form of Jesus Christ. If the anxieties of those who fear the aesthetic will displace the ethical and even the religious can be overcome, this approach permits a wonderful integration of apologetics and dogma, fundamental and systematic (...) theology. This primary aim of Herrlichkeit is supported by showing it is not unknown to the history of Christian thought. To gain a proper idea of its scope, however, requires exploration of pre‐Christian paganism's estimate of the beauty of being, and of the human capacity to register it. then, under the impact of revelation, it is possible to locate the climax of ontological thinking about beauty in the work of Aquinas—which integrated revealed and natural sources in an account of being as glorious because given away: supremely on the Cross, in self‐diffusion of the Trinitarian life. Balthasar's purpose now shifts. He will show how Western metaphysics declined from this high‐point of perception—but in such a way that the glory of being took refuge in the holy folly of the saints. Finally, he aims to show how re‐reading Scripture in the light of the above can generate the conviction that the message of the Bible is ultimately about the self‐giving divine glory as universal foundation of history and the world. (shrink)

L'A. étudie l'usage que Balthasar fait de la pensée grecque post-chalcédonienne. Le théologien allemand attire l'attention sur le style symphonique de la pensée grecque, sa concentration christologique et son caractère trinitaire. La première partie de ce travail est consacrée aux problèmes que soulève l'extension de l'usage de la pensée grecque post-chalcédonienne : peut-on mettre sur le même plan Maxime le Confesseur et le Pseudo-Denys ? L'A. montre ensuite que, si pour Balthasar le mérite de cette théologie tient à (...) sa propension à l'esthétique, cela n'exclut pas une doctrine christologique et trinitaire fouillée. La troisième partie est axée sur l'emploi critique que fait Balthasar de ses sources. (shrink)

(1993). Balthasar Bekker's Cartesian hermeneutics and the challenge of Spinozism. British Journal for the History of Philosophy: Vol. 1, No. 1, pp. 55-79.

In lieu of an abstract, here is a brief excerpt of the content:BALTHASAR AND ECKHART: THEOLOGICAL PRINCIPLES AND CATHOLICITY CYRIL O'REGAN Yale University New Haven, Connecticut Or pleas'd to wound, and yet afraid to strike, Just hint a Fault, and hesitate Dislike; Alike reserv'd to blame or to commend, A tim'rous Foe and a suspitious Friend 1 THE TENDENCY to avoid exclusion is a mark of the thought of Hans Urs von Balthasar. It represents an identifying habit, an (...) incorrigible feature of style and sensibility. His texts in which theologians, philosophers, poets, dramatists, and saints are christianly praised give testimony to a catholicity that barely brooks limits. Not only in true Gospel fashion are a multitude invited to the eschatological banquet, they constitute the vast medium of tradition, in which Maximus the Confessor rubs shoulders with Plato, in the company of Claudel, Calderon, and Therese of Lisieux. At different times Balthasar thinks of the tradition as one huge symphony in which notes sound only to be transcended and as a conversation between particular perspectives on the great mystery of redemption, no one of which is final and which meet only in the infinity of their object. The decision for plurality and variety in the tradition certainly validates difference and counts against its reduction.2 Yet at the same time tradition, precisely as a matter of variety, exhibits a measure of coherence or concordance that pro1 These couplets are from Alexander Pope's poem Atticus. See Minor Poems, ed. Norman Ault, completed by John Butt (London: Methuen & Co. Ltd.; New Haven: Yale University Press, 1954), p. 143. 2 See, for example, The Theology of Karl Barth, trans. Edward T. Oakes, S.J. (San Francisco: Ignatius Press, 1992), pp. 39, 187, 251. 203 204 CYRIL O'REGAN hibits difference from becoming truly excessive. It is this prohibition of excessive difference in Balthasar's reading of tradition that I would like to examine here. I take as my case study of Balthasar's rhetoric of reading his conflicted response to Meister Eckhart, about whose inclusion in the Christian tradition Balthasar expresses no doubts, yet whose theological message is such as to cause anxiety. We shall occupy ourselves in this paper with the way in which Eckhart's nonnegotiable inclusion within the tradition serves to repress the account of those features that present a fundamental challenge, that represent difference that would make the Christian field radically heterogeneous. In the first two sections, focusing mainly on the fifth volume of The Glory of the Lord (=GL),3 I shall offer outlines of both the positive and negative contributions Eckhart is deemed to have made to the theological tradition. Though I do not wish to give the impression of Scholastic pro and contra, Balthasar's positive remarks being imbricated with the negative and vice versa, it will be suggested that the elements adduced in both cases constitute mirror images of each other. Balthasar takes a bifocal, though not stereoscopic, view of a group of five elements: aesthetic disposition, the sameness of Being and God, the whylessness of the divine, Gelassenheit, and Gottesgeburt. This group is in effect read twice, once in a way that affirms and confirms Eckhart's unproblematic inclusion in the tradition (section 1), and again in a way that, in the light of basic Christian principles, raises serious questions about such inclusion (section 2). In a final section the question is raised whether the conflict in interpretation suggests a deeper underlying conflict between Balthasarian commitment to Catholic theological principles and catholicity. I. BALTHASAR'S AFFIRMATIVE RENDERING OF ECKHART On the surface there is little reservation about the approbation Eckhart receives in the fifth volume of The Glory of the 3 The Glory ofthe Lord: A Theological Aesthetics, vol. S, The Realm ofMetaphysics in the Modern Age, trans. Oliver Davies, Andrew Louth, Brian McNeil, C.R.V., John Saward, and Rowan Williams, ed. Brian McNeil, C.R.V. and John Riches (San Francisco: Ignatius Press, 1991). BALTHASAR AND ECKHART 205 Lord. If the depths of Balthasar's analyses of the medievals in his volumes on metaphysics (vols. 4 & 5) never reach the level of his account of Anselm and Bonaventure in volume two, it would be caviling to suggest that his intention at the... (shrink)

Hans Urs von Balthasar’s Christocentric philosophical anthropology is the premise not only of his religious epistemology, but also of his whole theological enterprise. The importance of his anthropology to the rest of his theology is often overlooked, because its fundamentals are set out in an early work to which little critical attention has been given: Das Betrachtende Gebet—a work which emphasises the ‘necessity of prayer’. According to von Balthasar, in praying, one encounters God, and it is through this (...) encounter that one can attain authentic personal identity and genuine fulfilment. In short, what this early work indicates is a conception of humanity as homo orans. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:PRZYWARA AND VON BALTHASAR ON ANALOGY ERICK PRZYWARA'S major work is entitled Analogia Entis: Metaphysil:,, Ur-Struktur und All-Rhythmus.1 As we will explain, it is especially the subtitle, " Basicstructure and Overall-rhythm", which is important in understanding the type of metaphysics he proposes. An explicit treatment of analogy by Hans Urs von Balthasar may be found in a se:des of two articles, " Analogie und Dialektik " and (...) " Analogie und Natur ", both of which carry the subtitle, " A clarification of the theological principles of Karl Barth " (1944-1945).2 They later become the basis of two important sections of Karl Barth: Darstellung und Deutung Seiner Theologie.3 The first becomes part of Balthasar's demonstration on Barth's "turn to analogy ".4 The second becomes part of presentation of Catholic" thought-form": "The concept of nature in Catholic theology". This context, the dialogue with Barth and Catholic theology in relationship to Barth, is essential for understanding Balthas,ar's views on analogy-as well as his relationship to Erich Przywara, anotheT dialogue partner of Barth. The "one concrete order of salvation", as 1 Anafogia En-tis. (AE) Einsiedeln: Johannes-Verlag, 1962. Second edition. The first edition (Munich: Koesel & Pustet, 1932), however, lacks this subtitle. It is called: Analogia Entis. JJfetaphysik. I. Prinzip. The new subtitle is a response to a "misunderstanding" (e.g., Barth's accusation) that analogia entis was only a metaphysical principle. Przywara also clarifies the sense in which analogy can be called a "principle" in the new forward to the second edition (p. 5), as well as in a new ending on p. 210. 2Both in Divus Thomas: the first in #22 (1944), 171-216; the second in # 23 (1945)' 3-56. 3 Cologne: Jakob Hegner Verlag, 1951. 4Cf. "Die Wendung zur.Analogie", 93-123; as well as "Die Vollgestalt der Analogie", 124-180. Balthasar acknowledges his indebtedness to Przywara in the enlarged treatment of analogy in Barth: cf. p. 10 ancl p. 404 n.3 (for the section on the" concept of nature in Catholic theology.") 473 474 JAMES V. ZEITZ, S.J. the place where analogy thinking must begin and end, is typical of both Przywarn and Balthasar-and reflects undoubtedly the influence of Barth on bot1h of these Catholic and (at the time) Jesuit theologians. To start at an earlier stage, however, the real issue of analogy, in both Przywa;ra and Balthasar's writings is the God question. How can we maintain God's transcendence as a true ' other ' in relation to immanence-the one concrete order where Jesus Christ is already present? This is first of all a prroblem for any theological method. The starting point and language which proceeds from this starting point must allow for transcendence within immanence. Thus Balthasar's aibove-mentioned work on analogy discusses the problem using the rubric of the time, a " concept of nacbure " in relationship to Ubernatur. His question is: what concept of nature is able bo relate to Ubernatur, while remaining truly a creaturely concept of nature? His thesis is that nature cannot be abstract or "pure " in an 18th century, secularized philosophical sense (e.g. Baius), but-in conformity with the whole tradition of the Ohurch Fathers, where nature means the whole human condition-the concept of nature is always already analogous, since ' rnan ' as creature can never stand aside from his already given, concrete nature within the order of salvation.5 Przywara had already prepared the way for this by insisting on a creaturely metaphysics leading to a theological metaphysics, where analogy is the adequate method. Besides the theological method, however, there is the problem of transcendence within one's understanding of Christ and the biblical revelation of the New Testament. Is there really a place for what can only be revealed and received? Or, to state the question in Balthasar's terms: how is the "one, concrete order", where Jesus Christ is already pa,rt of our history, 5 Cf. "Der Begriff der Natur in der Theologie ". Eine Diskussion zwischen Hans Urs von Balthasar und Engelbert Gutwenger. ZKTh vol. 75, 1953. 452461. In this debate, Balthasar further clarifies what he had said in Durstellung, in response to Gutwenger... (shrink)

In Hans Urs von Balthasar's 1947 Wahrheit, later republished as Theo-Logic I, he attempted to retrieve the notion that "truth is not just a property of knowledge but a transcendental quality of being as such". Villanova's D. C. Schindler enlists this retrieval in order to overcome "a metaphysics of presence," while also providing readers with an indispensable guide for navigating philosophical aspects of Balthasar's Werke. Although Schindler's text deals with notoriously dense subject matter, an undercurrent of pedagogical sense (...) controls his style and grants readers rewarding assimilation of a logic affirming both identity and difference within the concept of truth. (shrink)