In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. I (...) shall argue this point by examining four basic ideas embraced by von Neumann in his foundational considerations: a) the conservative attitude to assume in mathematics; b) the role that mathematics and the axiomatic approach have to play in all that is science; c) the notion of success as an alternative methodological criterion to follow in scientific research; d) the empirical and, at the same time, abstract nature of mathematical thought. Once these four basic ideas have been accepted, Hilbert’s spirit in von Neumann’s methodology of science will become clear. (shrink)

The paper deals with the controversial issue of realism in Wittgenstein’s Tractatus. Most of the problems are grounded in the logical-linguistic foundation of important ontological notions given within the text (such as object, state of affairs, fact, etc.). This has led some scholars to think that there is no conception of the world in the Tractatus that is independent of language and that in his work Wittgenstein is simply engaged in a logical investigation of what it is essential for any (...) language to represent reality. Therefore, no conclusions about a transcendent world can be drawn from it. Here we argue that it is true that the author of the Tractatus is engaged in a logical investigation, conducted a priori and internal to language, on the conditions that are (or have to be) satisfied by any significant language. However, what such an investigation reveals, given one of these languages, is the necessity to presuppose a world made in a certain way and transcendent to the language that pretends to describe it. Two issues are considered to clarify the sense of the realism of the Tractatus — that of the existence of simple objects, and that of the truth of propositions — and a new interpretative schema for the text is advanced. (shrink)

Shortly after Kurt Gödel had announced an early version of the 1st incompleteness theorem, John von Neumann wrote a letter to inform him of a remarkable discovery, i.e. that the consistency of a formal system containing arithmetic is unprovable, now known as the 2nd incompleteness theorem. Although today von Neumann’s proof of the theorem is considered lost, recent literature has explored many of the issues surrounding his discovery. Yet, one question still awaits a satisfactory answer: how did von Neumann achieve (...) his result, knowing as little as he seemingly did about the 1st incompleteness theorem? In this article, I shall advance a conjectural argument to answer this question, after having rejected the argument widely shared in the literature and having analyzed the relevant documents surrounding his discovery. The argument I shall advance strictly links two of the three letters written by von Neumann to Gödel in the late 1930 and early 1931 (i.e. respectively that of November 20, 1930 and that of January 12, 1931) and finds the key for von Neumann’s discovery in his prompt understanding of the Gödel sentence A – as the documents refer to it – as expressing consistency for a formal system that contains arithmetic. (shrink)

In "La science et l’hypothèse" Henri Poincaré scrive: «Compito dello scienziato è ordinare; si fa la scienza con i fatti, come si fa una casa con le pietre; ma un cumulo di fatti non è una scienza, proprio come un mucchio di pietre non è una casa» . Oltre a richiamare qualcosa che a molti potrebbe persino apparire ovvio – cioè che la scienza non possa in alcun modo ridursi ad un mero agglomerato di fatti che il ricercatore registra in (...) ambito osservativo, ma richieda piuttosto un attento processo di elaborazione razionale sia in fase preventiva rispetto al contesto dell’esperienza, sia in fase di valutazione dei dati sperimentali raccolti – questa affermazione ha il merito di ricordarci qualcosa che spesso viene passato sotto silenzio, vale a dire il fatto che durante il nostro tentativo di comprendere il mondo si dia alla conoscenza una materia, un complesso di "oggetti", tale da risultare determinante nella costruzione e nella formulazione delle nostre teorie. Se questo è vero, si può quindi parlare di una materia, e di una forma da essa distinta, della conoscenza scientifica, sebbene con alcune precisazioni. Nel contributo si preciserà questa distinzione facendo riferimento alle assiomatizzazioni di alcune discipline scientifiche condotte nella prima metà del secolo scorso. (shrink)

Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andréka-Németi group use several formal axiomatic theories together to re-capture, predict, recover or explain the phenomena of special relativity, general relativity (...) and classical kinematics. Their scientific methodology is close to Hilbert’s conceptions of how science should be done ideally. In this paper, we compare Formica’s reading of Hilbert’s axiomatic method to the method used by the Andréka-Németi group. (shrink)

ANALOGY has not just to do with the abstruse details and niceties of metaphysics but rather underlies the structure of all metaphysical thought. It is the heart of metaphysics. No system of metaphysics can discard it, without prejudice to the richness and variety of being. Without analogy there is elimination and over-simplification. Metaphysics is far from being a straightforward science; it is highly complex and its method and style of argument are not easy to master. Its field of inquiry is (...) wide. It is the task of the metaphysician to reduce the world of things to an intelligible unity. (shrink)

Pada 11 Oktober 2012 Gereja Katolik merayakan 50 tahun dibukanya Konsili Vatikan II. Namun demikian, 16 dokumen yang dihasilkan selama Konsili itu berlangsung (11 Oktober 1962-7 Desember 1965) belum dikenal oleh semua umat Katolik. Bahkan ada tidak sedikit umat Katolik yang belum pernah melihat dokumen-dokumen tersebut. Ada pula yang mengatakan bahwa kendati sudah membacanya, namun merasakan sangat sulit untuk memahaminya. Ada pula yang ketika melihat buku tebal yang memuat dokumen-dokumen tersebut langsung merasa terintimidasi dan ketakutan (intimadated), lalu tidak berani membukanya. (...) Sudah ada berbagai macam upaya untuk menyampaikan isi dan semangat dari Konsili Vatikan II kepada seluruh anggota Gereja Katolik. Salah satu cara adalah menerbitkan buku untuk mengulas isi dokumen-dokumen tersebut. Salah satu dari sekian banyak buku yang pantas dibaca adalah karya Maureen Sulivan, seorang assistant professor ilmu Teologi di Saint Anselm College, Manchester, New Hapshire, Amerika Serikat. Buku yang ditulis dalam bentuk tanya jawab ini dibagi menjadi 9 bab. Bab 1 berbicara mengenai “Pengumuman” diadakannya Konsili yang menggemparkan para pemimpin Gereja, khususnya anggota Dewan Kardinal dan Kuria di Vatikan, yang merasa bahwa Konsili tidak diperlukan. Dalam bab ini dibicarakan tentang arti dari Konsili yang disebut sebagai ekumenis dan pastoral, alasan perlu diadakannya Konsili, persiapan yang dibutuhkan, serta tujuan yang ingin dicapai dengan diadakannya Konsili Vatikan II. Secara khusus disebutkan peran almarhum Paus Johanes XXIII, yang ketika mengumumkan untuk mengadakan Konsili, beliau baru tiga bulan diangkat menjadi Paus. Lewat Konsili ini beliau menginginkan agar Gereja mampu menemukan cara agar iman Kristiani dapat disampaikan kepada dunia dan dimengerti oleh dunia. Demi tujuan itu Gereja perlu “membuka jendela” agar “angin segar memasuki dirinya (hlm. 29).” Gereja perlu melakukan aggiornemento, pembaruan diri. Bab 2 mengulas mengenai orang-orang yang berperan dalam KonsiliVatikan II, ketegangan-ketegangan yang muncul antara mereka yang ingin mengadakan pembaruan dengan mereka yang ingin mempertahankan status quo Gereja, serta peran media massa. Selain sekitar 2200 peserta (Kardinal, Uskup, dan Abas), juga terdapat ratusan teolog yang berperan sebagai penasihat bagi para peserta Konsili (periti), antara lain dengan memberikan seminar-seminar mengenai topik-topik teologis kepada para peserta Konsili (hlm. 35-36). Selain itu juga terdapat para pengamat dari Gereja Ortodoks, Gereja-gereja Protestan main streams (Lutheran, Episkopalian, Anglikan, Metodis, Presbyteran, dan Quakers), dan Yudaisme. Hadirnya para pengamat dari kalangan khusus ini merupakan sesuatu yang baru dan revolusioner dalam Konsili. Secara khusus ditampilkan seorang tokoh pembaru: Kardinal Bea, ketua Sekretariat untuk Kesatuan Umat Kristiani. Ia begitu dikenal dengan ucapannya yang sangat menggemparkan di depan para wartawan: “Members of the other Christian Churches who are living today never ’left’ the Church. So they cannot ‘return,’ can they? We are talking about going together, hand in hand, toward a new future” (hlm. 33). Tokoh pembaru lain adalah Kardinal Achile Liénart, seorang Kardinal senior dari Prancis, yang pada hari ketiga Konsili menolak untuk memilih dari daftar nama yang sudah disiapkan (kebanyakan adalah anggota Kuria) untuk menjadi ketua dari 10 komisi yang akan mengendalikan agenda Konsili. Ia mengusulkan supaya para peserta Konsili memilih orang-orangnya sendiri. Usulan ini didukung oleh Kardinal Josef Fring dari Jerman, dan kemudian diterima oleh semua perserta Konsili. Tokoh pembaru lain adalah Kardinal Jan Alfrink dari Belanda, dan Kardinal Leo Josef Suenens dari Belgia (hlm. 38-38). Di pihak lain, ada tokoh sangat konservatif yang mencoba menghambat jalannya Konsili: Kardinal Alfredo Ottaviani, seorang anggota Kuria dan ketua The Holy Office (sekarang dikenal sebagi Kogregasi untuk Ajaran Iman), yang terkenal dengan ucapannya “Semper idem” (Selalu sama). Ia antara lain melawan hadirnya para pengamat dalam Konsili (hlm. 33), mencoba melarang kuliah-kuliah yang diberikan kepada para peserta Konsili oleh para Yesuit dari Institut Biblis di Roma, bahkan meminta Paus Yohanes XXIII untuk mengusir teolog Yesuit, Karl Rahner dari Roma, yang tentu saja ditolak oleh Paus (hlm. 35). Ia menolak penggunaan bahasa-bahasa lokal untuk Misa, yang intinya adalah pemindahan kekuasaan dari hierarki kepada Umat (hlm. 43), menghambat disahkannya kolegialitas para Uskup dan menandaskan bahwa Komisi Teologi yang ia pimpin memiliki otoritas di atas Konsili (hlm. 55). Dalam bab ini juga disebutkan hal yang baru dalam Konsili ini adalah hadirnya para wartawan dari pelbagai media massa dari seluruh dunia........................................... Sebagai penutup, dalam bab 9, Sullivan menegaskan bahwa ada dua hal yang benar-benar perlu diperhatikan untuk zaman ini sebagai agenda yang belum selesai dari Konsili Vatikan II: kolegialitas (relasi atara Paus dan Uskup) dan peran kaum perempuan dalam Gereja. Akhirnya, pada awal abad ke-21 ini Sullivan mengajak kita semua untuk bertanya: Apakah Gereja kita sungguh-sungguh dapat menjawab tantangan-tantangan pada zaman ini?; Apakah Gereja kita dapat membuat pesan Injil relevan untuk zaman ini?; Apakah Gereja kita dapat membangkitkan entusisme baru yang dapat membangun sebuah generasi baru?; Apakah Gereja dapat meredakan berbagai macam ketegangan yang akhir-akhir ini menggoncang “bahtera Petrus?” Dengan bijak Sullivan mengatakan bahwa kita perlu terus berharap, dan harapan itu akan menjadi semakin produktif kalau kita selalu berpegang pada nasihat almarhum Yohanes XXIII: “Untuk hal-hal yang mendasar, kesatuan; untuk hal-hal yang meragukan, kebebasan; dan untuk segala sesuatu, cinta kasih” (hlm. 124). Buku ini sangat komprehensif mengulas Konsili Vatikan II dan disampaikan dengan bahasa yang sederhana. Buku ini sangat membantu para pembaca karena dilengkapi dengan daftar isi yang mendetil, daftar semua dokumen yang dihasilkan oleh Konsili Vatikan II beserta dengan waktu promulgasinya, daftar istilah-istilah yang penting berkaitan dengan Konsili Vatikan II, serta indeks subjek. Semoga dengan membaca buku ini para pembaca terdorong untuk membuka dan menemukan pesan-pesan penting dari dokumen-dokumen Konsili Vatikan II. (Ignatius Madya Utama, Program Studi Ilmu Teologi, Sekolah Tinggi Filsafat Driyarkara, Jakarta). (shrink)

I teoremi di Gödel suscitano un interesse sempre crescente nella riflessione filosofica contemporanea. Rimane però in discussione fra gli studiosi come si sia arrivati alla loro scoperta e quale sia il loro significato per il dibattito sui fondamenti delle scienze. Nel volume si ripercorrono le vicende che portarono alla formulazione dei teoremi di incompletezza, a partire dall’incontro tra von Neumann e Gödel al Congresso di Königsberg nel 1930, e si indaga, riferendosi in particolare al lavoro di von Neumann, sull’impatto che (...) questi teoremi hanno avuto per il progetto hilbertiano di fondazione della matematica e delle scienze più in generale. Ne risulta un’immagine delle indagini di Hilbert meno rigida di quella finora corrente, in linea con le più recenti acquisizioni della storiografia, e soprattutto più rispettosa della stessa prassi assiomatica, che oscillava per Hilbert tra ambizioni fondazionaliste e istanze pragmatiche. È stato von Neumann a rendere esplicita, dopo la scoperta dei teoremi di Gödel, quella che si può definire come la “svolta pragmatica” nell’assiomatica. Il libro propone inoltre un chiarimento riguardo alla scoperta di von Neumann del secondo teorema di incompletezza. (shrink)

This article proposes a 'fusion of horizons' in constructing urban public theologies in South Africa. This is done through the introduction of five interrelated themes that have emerged from the on-going knowledge and idea production by a distinguishable counterpoint in contemporary scholarly, intellectual and activist engagement with the urban, in the authors' own South African context but also wider internationally. In advancing a praxis-agenda for urban public theology, the authors subsequently identify the following, albeit not exhaustive, themes: southern urbanisms and (...) the factor of unprecedented urban migration; 'right to the city' and urbanisation from below; a reclaiming of the commons; the making of 'good cities'; and actors of faith in relation to urban social life. (shrink)

Is it possible to provide context-relevant education to a diverse and dispersed body of students via online presented courses? Contextual relevance is called for by students and the public alike, as can also be seen in the #fallist movements. More traditional academics and institutions argue for retaining excellence from the past and known knowledge still to be taught. In this conceptual article, education is seen as a mastery of knowledge expanses by integrating Data and Information into Knowledge and Wisdom (D-I-K-W). (...) Departing from the learning sciences, especially mind, brain and education science and its application in culturally appropriate learning, it is argued that including effective learning strategies in online courses, especially application-oriented strategies, can help students to apply knowledge from the past to contexts in the present, thereby attaining context-relevant education. However, the application of learnt material to situations brings forward another dimension, namely, the future, which is Volatile, Uncertain, Complex and Ambiguous (VUCA). In applying and making decisions, it is helpful to attend to the Cynefin framework, attending to the domains of the obvious, the complicated, the complex, the chaotic and the disorder. Excellence from the past and relevance in the present should, therefore, be augmented by abilities aimed at future readiness. Context-relevant online education should therefore attend to the past, the present and the future. (shrink)

This article proceeded from the assumption that the theme of service delivery in present-day South Africa could well be qualified by the notion of 'crisis', to the extent that this qualification, from a theological perspective and on the basis of comparative social analysis, well recalls the statements in such critical and profound theological documents as The Kairos Document and Evangelical Witness in South Africa on the 'crisis' in the latter years of apartheid. The further recognition that the theme of service (...) delivery constitutes an essentially new focus for practical-theological scholarship in South Africa led the author, who has a pertinent interest in the field of Christian diaconia, to thereupon go the full circle of practical-theological interpretation in developing such a focus. This was done by, firstly, attempting to develop a deeper contextual understanding of the problem of service delivery in the country on the basis of the prevailing debate on service delivery in South Africa, after which the ideas from conceptualisations of two different modes of diaconal practice within contexts of endemic poverty in the practical-theological literature were explored. The discussion concluded with a more pertinent consideration of the extent to which these two conceptualisations could be taken as providing direction in conceptualising a transformational diaconal response to the current service-delivery problem. (shrink)

This article presents a missional perspective on the complex interplay between socio-political realities, religious vulnerability and the formation of political ideologies among Western Christians, drawing insights from the biblical narrative of the choice of Barabbas at Jesus’s trial. In today’s world, Western Christians are confronted with numerous socio-political challenges that can compromise their spiritual discernment, leading to religious delusion and, potentially, the adoption of politicised ideologies. Through a deep dive into the Jewish choice of Barabbas over Jesus, we seek to (...) unravel the underlying dynamics. By examining the socio-political context of Roman occupation and Jewish societal pressures, we illuminate how these external factors influenced the religious vulnerability of the Jewish people. Furthermore, we explore how this vulnerability manifested in the decision to prefer Barabbas, a figure representing worldly resistance, over Jesus Christ, the embodiment of divine grace. From a missional perspective, we reflect on the implications of this historical event for contemporary Western Christian engagement with socio-political issues. We argue that understanding the delicate interplay between socio-political context, religious vulnerability and political ideology is essential for Western Christians seeking to embody the transformative mission of Christ in today’s world.Contribution: This article contributes to missional theology by offering insights into how believers can navigate socio-political complexities with spiritual discernment and faithful witness. (shrink)

The construction of body image consists of the ways in which the body is considered, perceived, and evaluated. The ideal body image has been changing considerably over the centuries; the discrepanc...

Hilbert’s methodological reflection has certainly shaped a new image of the axiomatic method. However, the discussion on the procedural character of the method is still open, with commentators subs...

Change is the new normal, but so it has been for ages. Experience to navigate change is something you get just after you needed it, unless you tap into age-old experience. The Fourth Industrial Revolution (4IR) is bringing about wide-ranging changes. With people having to adjust, the question is whether Christianity, with its roots in preindustrial times, may support people to navigate these changes. This conceptual article focusses on the relationships amongst constructs, exploring logical arguments about how these constructs are (...) associated. The 4IR is briefly described from differing vantage points, as to whether it is a valid description thereof. Whether a revolution or evolution, it is a complex system, and therefore the theory of complex systems is used, with the conclusion that one may merely participate in such systems. Being novel situations, one needs to participate creatively, based on a cognitive understanding of creativity. Creative solutions do not materialise out of thin air but are the novel use of existing knowledge structures. Christian traditions include institutional memories of how people managed situations of radical change, as reflected in Genesis 1 and Lamentations 4. These passages provide building blocks that may be used in creative coping strategies during times of change. Both passages suggest the strategy to juxtapose order and chaos, and borrowing from that, a ‘Grip-Grapple-Grow’ scaffolding system is suggested. To test the usability thereof, the issue of face masks during the Coronavirus Disease 2019 pandemic was touched upon, to evaluate how the interplay amongst 4IR, disruption, (Christian) beliefs and technological advancement may play out. Contribution: The Fourth Industrial Revolution is speeding up the pace of change, with people having to adapt. This article explores processes of change management, juxtaposing the theory of complex systems, the cognitive science understanding of creativity and institutional memories afforded by some Christian traditions reflecting on how people managed order and chaos. (shrink)

Christians who got married want to have a happy family life. They also want their family life become a sacrament. Yet, their dreams do not always come true. One of the obstacles that prevent their dreams become a reality is domestic violence that takes place in their family life. On the one hand, the ones doing the violence sometimes even justify their behavior by quoting some teachings from the Scriptures and other Church’s documents. Other factor that supports domestic violence is (...) patriarchical and kyriarchical culture. On the other hand, the life of Jesus, the practice of early Christian communities, as well as other teachings of the Church, especially since the second Vatican Council, challenge us to eracidicate domestic violence as a very serious threat for a happy family life. (shrink)

INTRODUCTION The subtitle of this dissertation, "Brahman, the pure unity of thought within itself", which epitomizes Hegel's view of Indian philosophy and ...

Purpose:This study is meant to appraise philosophically the notion of family in Igbo African society. The study will also show the distinguishing features between the Igbo African society and the western societies in relation to the notion of family. This paper will attempt to discuss the notion of family in the Igbo-African society with a particular interest in analyzing the components that make the family in the Igbo-African society stand out.Methodology:The applicable methodology in any study is determined largely by the (...) objectives or purposes which the study is meant to achieve. For the purpose of this study, the applicable methodology will be a form of review of relative literatures, peer reviewed journals and internet sources which treated the concepts and issues relating the subject matters to be appraised by this study.Findings: The study finds that family is the smallest unit of society. The study also found that the concept of family is part and parcel of man, and it is as old as man himself. Furthermore, the study observed that there is a general assumption that the overall dispositions of conducts and characters in any given society can be traced to the conducts and characters at the family level. The study also found that the notion of family in the Igbo African society is distinct in several features and factors when compared to the one in the western cultures.Unique contribution to theory, practice and policy: Although several authors have devoted the time and scholarly efforts in researching about the concept of family; there are dearths of scholarly researched literatures which narrows the concept to the Igbo African society. It implies that there are few or no academic publications where the notion of family is philosophically appraised with specific interest to its features, and factors in the Igbo African society. It is on this note that this study comes in to fill the voidness by making a philosophical appraisal of the notion of family in the Igbo African society. (shrink)

The experiences of clinicians who care for the sick and dying after withdrawal of treatment are rarely documented. This may be because these narratives, which offer insight into the intentionality and character of the clinician, do not lend themselves to clinical reports. The experience of palliative care touches clinicians in different ways and often confronts them with complex ethical dilemmas about care and treatment. This article explores the character of the clinician in relation to the telos of medicine and the (...) experience of accompanying the dying after withdrawal of treatment. (shrink)

The Calabrian Mafia seems to be animated by a hunger for power with no precedent in other crime organizations, and an ability to hide its presence so much to make it an obvious and inevitable component of the decreed social system, deeply crept into the community cohabitation norms. In the study, we have aimed at investigating the Reggio Calabria flying squad policemen's representations and lived experiences. The qualitative analysis of the text, carried out through dedicated software, has pointed out two (...) super codes. In other words, “solitude” as lived experience is spatially contained in “aggression to connections” and “the absence of freedom” encloses the lived experience of constant and systematic danger. This means that the emotional elaboration on Mafia, carried out during the group process, has highlighted thinking categories connected to the coercion of relational space which articulate themselves along t.. (shrink)