This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

In an earlier paper the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut (...) relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure , where I is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36 519–530]. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...) [Formula: see text], proofs of [Formula: see text] sentences in [Formula: see text] can be translated into proofs in [Formula: see text] at a polynomial cost in size. Moreover, the [Formula: see text]-conservativity of [Formula: see text] over [Formula: see text] can be proved in [Formula: see text], a fragment of bounded arithmetic corresponding to polynomial-time computation. For [Formula: see text], this answers a question of Clote, Hájek and Paris. (shrink)

The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in$$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1$$\end{document}-Foundation + V=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V=L$$\end{document} is enough to carry out finite injury arguments in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:AQUINAS AND HEIDEGGER: THE QUESTION OF BIDLOSOPHICAL THEOLOGY VINCENT GUAGLIARDO, O.P. Dominican School of Philosophy and Theology Graduate Theological Union Berkeley, Oalifornia I N IDS BOOK, Hediegger and Aquinas: An Essay on Overcoming Metaphysics, John D. Caputo recommends a " deconstruction" of Aquinas' philosophical theology in order to let.the true ·element orf his thought, mysticism, come to the fore. Caputo argues persuasively that Aquinas' thought, expressed ·as.it is in (...) the garh of metaphysics, cannot escape Heidegger':s critique of met:aiphysfos as "onto-theo-logioal ". Aquinas, no more thoo.any other thinker of the West, has succeeded mavoiding this iorgorttenness. Those Thomi:sts who have tried to argue that Aquinas.is an exception rto this critique, Caputo oontends, have not succeeded in presenting their case. The verdict o.f Heidegger stainds. The on:ly reoourrse left is thart of deconstruction, which Capurto presents ais gaining mther than losing the true Aquinas precisely because deconstruction.allows us to move from the said (the metaphysical dimension) fo rbhe uil!said (the mystical dimension) of Aquinas' thought. The uns1aiid is the kernel, the center a;ro:und which whatever Aquinas says moves. It is the true dimension which his thinking il'eally seeks: union with God, in wh~ch both the union and God 1are themselves rineff1a;ble.1 There is, however,.a disturbing problem which I find wti:th Capui;o's conclusion. This problem does not have to do with his oonte!lltion that the true kernel of St. Thomas' thought!is mysticail. Ra.ther, the problem concerns what is being disen1 See John D. Caputo, Heidegger and Aquinas: An }j}ssay on Overcoming Metaphysics (N.Y.: Fordham University Press, 1982), pp. 211 & 247-8. 407 408 VINCENT GUAGLIARDO; O.P. gaged and put out of play tin the deconstrrucrb.ion, namely: philosophical thoology.2 What are the iimplicatfons of such a movie? Are they desirable for theology? Ought we and oan we, 1a;s Caputo suggests, disengage,and leave behind St. Thomas' philosophical theology because metaphysical without there being any true loss? Might we be facing a;n impoverishment of another kind: in a moI"e " radical " seeking of the dii.vine might we not be losing something m'a foI"getfulness of ourselves as,.after 1 all, omy human? ls not this something precisely the,realm of the humanitas of the homo huma,nus, which Heidegger 's thinking seeks Ito point out and draw us closer to, where humanitas refers to our necessary trelation to Heing, from whlch relation we as humans cannot detach ourselves so long as we are " auf die Erde "? 3 The ~oblematic In beginning our inquiry I would like to distinguish three different regions of human engagement in which the over1appii.ng of one onto the other ii.s not.always easy to discern: philosophy, phl1osopihioal theology and mysticism.. I want to say "iphilosophical theology " and not simply " theology " because I think that it ii.s not possible to thoologize without 1 at the same time also philosophiizing. I 1think St. Tihomas thought this as well. 'l\hat is why his theology was always philosophioa ;l, 1in dialogue wiith :the philosophers: Aristotle, the Platonists, Ma~monides and the Ail1abs. In saying this, however, I do not mean to,say that philosophy 1and theology 1 are 1 the same. Now the altemativce which Caputo would ha,ve us embrace, because presumably not onto-theo-logioal, is that of a "reli2 See Caputo, op. cit., 11 & 283. a" Die Wahrheit des Seins denken, heisst zugleich die humaniitas des homo humanus denken " (" Brief iiber den Humanismus," in W egmarken (Frankfurt am Main: Vittorio Klostermann, 1978), p. 349). This Latin expression is a.lso used by St. Thomas in De ente et essentia, III, to designate the formal principle (rationality) by which. the whole (an individual human being) becomes a whole. Also see In Met., VII, Leet. 5, nn. 1378-1380. THE QUESTION OF PHILOSOPHICAL THEOLOGY 409 giious 1alerthi0Jogy" of mysticism.4 One is.then led to ask whether and if,so, how, the same person could ibe hoth a philosopher and 1a mystic, i.e. both!a thinker and a person of [aith. Do they remain " existentially " opposed,,as... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE MUNUS OF TRANSMITTING HUMAN LIFE: A NEW APPROACH TO I-IUMANAE VITAE JANET E. SMITH University of Dallas Irving, Texas 'TIRE ONLY ACQUAINTANCE 1bhat most rea;ders have with the Latin of Humanae Vitae is the tit1le. It is likey that fow laymen and perhaps eV'en fow schofars make ire:ferenoe to the Latin text; indeed, it is ireported that I-Iumanae Vitae was originally composed in ltalian, and it seems that (...) aH available translations of the text al'e based primarily on the Italian V'ersion. But since the official text of Humanae Vitae is in Latin and since translations are necessa11ily deficient, we shouild not be surprised that the ava:ilahle translations fail to convey a:M the nuances of the official text. (Latin, of course, is tihe langua:ge in which all official documents of the Church are written.) This study seeks to show that attenti¥eness to certain words fa the Latin text, most particularly the word munus, uncovers important eonnections between Humanae Vitae and pe['spect[ves of the Church, perspectives particularly highlighted in the documents of Vatican II. It also seeks to show that the La.tin provides greater philosophical precision for certain key teaohings of the text, most particularly section 11: "each and every maritail act must remain open to proc11eation." It is ii.mportant to note that some of the crucial Latin words of the document cal'ry connotations tihat cannot possibly be captured ihy 1any one English word. Indeed, some of the words convey concepts and attitudes that are quite foreign to speak:iers of modern English; to convey the meaning of some terms requires a. fairly lengthy expl,ication of notions not immed :iate1ly and directly graspaible hy ail readers. Even to the reade[' of Latin, the text does not 'easily ~eld its secrets. The 385 386 JANET E. SMITH Latin of the document has no identifiahle souTee of reliabJe deoipherment; it is a kind of " modern " 0 1 r " Church " Latin, which is an odd comhinat~on of elassical Latin and the lang1uage the Ohurch ha:s deve1oped oveil.' the centuries. The method of translation employed here has invo1 lved consultation of classical and medieval dictionaries, reference to arguably rep-!l1esentative classical and medieval 1 authors, tracing of the word 'being ioonsidered through t1he documents of Vatican II, con- 'sideration of 1appearance of the word in other Church documents, cross-reference to other uses of the word within Huma,nae Vitae itself, and reference to the Italian" 1 original." 1 l In preparation for this article reference was made to six English translations : (a) the translation done by the NC News Service, made widely available by the Daughters of Saint Paul, Of Human Life (Boston, Mass.: Daughters of St. Paul, 1968), hereafter referred to as the "usual translation" and designated by HY; (b) the translation by the Catholic Truth Society printed in John Horgan, Humanae Vitae and the Bishops (Shannon, Ireland: Irish University Press, 1972), 33-53; this translation was modified and reprinted in (c) The Pope Speaks 13 (1969): 329-346, and in (d) the Vatican Press Office translation, " Encyclical Letter on the Regulation of Births " in Vatican II: More Post-Conciliar Doauments, ed. Austin Flannery, O.P. (Northport, N. Y.: Costello Publishing Company, 1982), 397-416; (e) the translation by Rev. Marc Calegari, S.J., Humanae Vitae (San Francisco: Ignatius Press, 1978), which has undergone a further, as of yet unpublished, revision. 'There is one translation (f) that was made entirely from the Latin, by Rev. A. J. Durand, Humanae Vitae: A New Translation (Bethlehem, Pa.: Catechetical Communications; no date given); it is, though, not widely available. Rev. Calegari, in private communication with this author, noted that the document was originally written in Italian, though the Latin text is the official text. He also stated that the modern language versions were made from the Italian text. My comparisons of the translations of Humanae Vitae with the Italian and the Latin versions indicate that Rev. Calegari is correct in saying that most modern versions are based on the Italian, though a few, most notably that by the Catholic Truth Society, have clearly made reference to the... (shrink)

The notion of trustworthy AI has been proposed in response to mounting public criticism of AI systems, in particular with regard to the proliferation of such systems into ever more sensitive areas of human life without proper checks and balances. In Europe, the High-Level Expert Group on Artificial Intelligence has recently presented its Ethics Guidelines for Trustworthy AI. To some, the guidelines are an important step for the governance of AI. To others, the guidelines distract effort from genuine AI regulation. (...) In this chapter, we engage in a critical discussion of the concept of trustworthy AI by probing the concept both on theoretical and practical grounds, assessing its substance and the feasibility of its intent. We offer a concise overview of the guidelines and their vision for trustworthy AI and examine the conceptual underpinnings of trustworthy AI by considering how notions of 'trust' and 'trustworthiness' have been discussed in the philosophical literature. We then discuss several epistemic obstacles and moral requirements when striving to achieve trustworthy AI in practice before concluding with an argument in support of the establishment of a trustworthy AI culture that respects and protects foundational values. (shrink)

The purpose of this study was to explore whether the performance of the green innovation brought positive effect to the competitive advantage. This study found that the performances of the green product innovation and green process innovation were positively correlated to the corporate competitive advantage. Therefore, the result meant that the investment in the green product innovation and green process innovation was helpful to the businesses. This study argued that the businesses should cognize the correct value and positioning of the (...) green innovation. (shrink)

Background The use of lengthy, detailed, and complex informed consent forms is of paramount concern in biomedical research as it may not truly promote the rights and interests of research participants. The extent of information in ICFs has been the subject of debates for decades; however, no clear guidance is given. Thus, the objective of this study was to determine the perspectives of research participants about the type and extent of information they need when they are invited to participate in (...) biomedical research. Methods This multi-center, cross-sectional, descriptive survey was conducted at 54 study sites in seven Asia-Pacific countries. A modified Likert-scale questionnaire was used to determine the importance of each element in the ICF among research participants of a biomedical study, with an anchored rating scale from 1 to 5. Results Of the 2484 questionnaires distributed, 2113 were returned. The majority of respondents considered most elements required in the ICF to be ‘moderately important’ to ‘very important’ for their decision making. Major foreseeable risk, direct benefit, and common adverse effects of the intervention were considered to be of most concerned elements in the ICF. Conclusions Research participants would like to be informed of the ICF elements required by ethical guidelines and regulations; however, the importance of each element varied, e.g., risk and benefit associated with research participants were considered to be more important than the general nature or technical details of research. Using a participant-oriented approach by providing more details of the participant-interested elements while avoiding unnecessarily lengthy details of other less important elements would enhance the quality of the ICF. (shrink)

The rising tide of corporate scandals and audit failures has shocked the public, and the integrity of auditors is being increasingly questioned. It is crucial for auditors and regulators to understand the main causes of audit failure and devise preventive measures accordingly. This study analyzes enforcement actions issued by the China Securities Regulatory Commission against auditors in respect of fraudulent financial reporting committed by listed companies in China. We find that auditors are more likely to be sanctioned by the regulators (...) for failing to detect and report material misstatement frauds rather than disclosure frauds. Further analysis of the material misstatements indicates that auditors are more likely to be sanctioned for failing to detect and report revenue-related frauds rather than assets-related frauds. In sum, our results suggest that regulators believe auditors have the responsibility to detect and report frauds that are egregious, transaction-based, and related to accounting earnings. The results contribute to our knowledge of auditors’ responsibilities for detecting frauds as perceived by regulators. (shrink)

The relationship between career counselling and widening participation is increasingly capturing the attention of educational researchers, especially those interested in its social justice implications. International research on first-in-family students demonstrates the continual class-based barriers they are faced with which influence their progression into and through higher education. Career counselling has an important role to play in both supporting first-in-family students to not only enter university but also set them on a career trajectory which allows them to fulfil their aspirations. However, (...) access to effective forms of career counselling remains fragmented and highly dependent on social class. This article explores how first-in-family students engage in what we call ‘DIY career counselling,’ where they draw on their informal networks and the internet to enhance their understanding of their future prospects and possible trajectories. Their efforts suggest a strong desire to learn more about what university can offer them and how they can position themselves advantageously in the job market; furthermore, their efforts also suggest a consumerist awareness that the career counselling on offer in their secondary schools was lacking. (shrink)

Vietnam has seen fast-rising debts, both domestic and external, in recent years. This paperreviews the literature on credit market in Vietnam, providing an up-to-date take on the domesticlending and borrowing landscape. The study highlights the strong demand for credit in both therural and urban areas, the ubiquity of informal lenders, the recent popularity of consumer financecompanies, as well as the government’s attempts to rein in its swelling public debt. Given thehigh level of borrowing, which is fueled by consumerism and geopolitics, (...) it is inevitable that theamount of debt will soon be higher than the saving of the borrowers. Unlike the conventional wisdom that creditors have more bargaining power over the borrowers, we suggest that—albeitlacking a quantitative estimation—when the debts pile up so high that the borrowers could not repay, the power dynamics may reverse. In this new politics of debt, the lenders fear to lose the money's worth and continue to lend and feed the insolvent debtors. The result is a toxic lending/borrowing market and profound lessons, from which the developing world could learn. (shrink)

This data collection comprises of Amazon reviews of the book titled “Wild Wise Weird.” These reviews will be analyzed and updated to identify factors driving people to love a fiction book. Wild Wise Weird is a collection of 42 fables that blends traditional storytelling with modern sensibilities, weaving together life lessons, humor, and social commentary.

A phenomenon is that which appears. In his phenomenology, Jean-Luc Marion shows how a phenomenon that appears in and out of itself evades the metaphysical demand of grounding. Classical philosophy has acknowledged phenomena only in so far as they can be sanctioned by the concepts of the intellect. This holds good also of Husserl’s constitutive ego. Now, Marion distinguishes between such intuitively “poor phenomena” and the “saturated phenomena” that exceed the intentional consciousness; they are given not by the consciousness but (...) to the consciousness in an excess of intuition. This “gift of appearance” is Marion’s main concern, in the visible in general, and in painting in particular. But whereas idols only reflect our own desire to see and to be seen, icons surprise us by the gaze the saint directs on us. A picture is the scene of a possible revelation; and the revelation is nothing but the phenomenon taken in its fullest meaning: intuitive saturation at its maximum. A crucial question, nonetheless, remains: What is the relation between revelation as a phenomenological possibility, and Revelation as a theological dogma of the utmost importance? (shrink)

The present study investigates the dynamics of emotional processing and awareness using an affective facial priming paradigm in conjunction with a multimodal assessment of awareness. Key facial primes are visually masked, and are presented for brief and extended durations. Using a preference measure, we examine whether the effects of the primes differ qualitatively . We show that: unconscious affective priming with faces emerges strongly in initial presentations and diminishes rapidly with repetition; conscious affective priming also emerges strongly in initial presentations, (...) however it persists in strength with repetition; and in contrast to other reports on the salience of negative stimuli, happy faces appear more salient than sad faces when presented outside awareness. We discuss the limits and extensions of unconscious affective priming with faces, and consider several methodological and conceptual questions concerning emotional processing out of awareness. (shrink)

Jun Otsuka, in his recent work Thinking About Statistics (2023), undertakes a philosophical investigation of fundamental statistical methodologies, with a particular emphasis on causal inference. In his ontological analysis of causal inference, Otsuka posits that causal analysis, within a given causal model, requires the modification of the underlying probabilistic distribution. This modification, he argues, effectively constitutes a transition between possible worlds. Consequently, Otsuka identifies the objective of causal inference as the discovery of inter-world laws that govern the relationships between these (...) distinct probabilistic models (Otsuka 2023, p.168). Granting Otsuka’s ontological commitments regarding causal and probabilistic models, his interpretation of certain causal analyses as inherently inter-worldly is indeed compelling. This perspective merits particular attention given the prevailing tendency to view such analyses to mere rules for estimating causal effects. While this review does not directly challenge Otsuka’s position, it aims to further explore and contribute to this stimulating concept. (shrink)

Since the emergence of Pakistan the history of Pak-Afghan relations can best be analyzed from conflict to cooperation. Some of the early problems are mainly responsible for conflict and cooperation in both countries relations. After the establishment of democratic setup in both states, different CBMs indicate positive sign in Pak-Afghan diplomatic relationship. The drawdown of US forces has created security concern for Pakistan and Afghanistan that the creation of power vacuum can push the country again into civil war like situation. (...) In such state of security Pakistan’s engagement to bring the Taliban to the negotiation table will smooth the way for a broad-based government in Afghanistan. Some of the Afghan domestic political issues also created mistrust i.e., the refugee’s problem, cross border militant’s infiltrations, drug problem and issue of the Taliban. However, the paper will highlight the measures to keep intact the reconciliation more effective and replace the mistrust by trust. How domestic political issues effect their bilateral relations and why various methods taken in the prescribe time not effective in bilateral relations of the two states. (shrink)

Response to Floridi et al, 2008/2009. Based on insufficient evidence, and inadequate research, Floridi and his students report inaccuracies and draw false conclusions in their Minds and Machines evaluation, which this paper aims to clarify. Acting as invited judges, Floridi et al. participated in nine, of the ninety-six, Turing tests staged in the finals of the 18th Loebner Prize for Artificial Intelligence in October 2008. From the transcripts it appears that they used power over solidarity as an interrogation technique. As (...) a result, they were fooled on several occasions into believing that a machine was a human and that a human was a machine. Worse still, they did not realise their mistake. This resulted in a combined correct identification rate of less than 56%. In their paper they assumed that they had made correct identifications when they in fact had been incorrect. (shrink)

In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost (...) from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about. (shrink)

This is a critical discussion of Paul Humphreys's fusion view of emergence, focusing on the basal loss feature of his ontology. The discussion yields some general morals for special science ontology.