Knowledge of the backgrounds of students of behaviour working in the field of applied animal behavior science may help us to recognize their influence on conclusions reached in a particular study and on more general points of view. This recognition may result in a speed up of the progress in this science, to the benefit of science and animals. Some types are: (1) Eco-ethologists (ethologists of the hunters-type). They like to stalk healthy wild animals in their natural environment. They are (...) less interested in the abnormal behavior of domestic animals under husbandry circumstances. (2) Behaviorists. These are psychologists that still think in a man-animal dichotomy. They are not interested in animals for their own sake but as models for human behavior. (3) Behavior physiologists. These biologists are not primarily interested in behavior. Because of the type of experiments they perform they have an aversity against animal protectionists. (4) Ethologists of the farmers type. These ethologists want to posses animals, collect animal species, take care of them and breed them. They are able to speak on approximately the same wavelength as farmers as well as animal protectionists. (5) Zootechnicians of the farmers type. These scientists want to make a living out of animals and like to take care for them. They are also able to speak at approximately the same wavelength as farmers and animal protectionists. (shrink)

Recent pleas for more heterodoxy in explaining economic action have been defending a pluralism for economics. In this article, I analyse these defences by scrutinizing the pluralistic qualities in the work of one of the major voices of heterodoxy, Tony Lawson. This scrutiny will focus on Lawson's alternatives concerning ontology and explanation to mainstream economics. Subsequently, I will raise some doubts about Lawson's pluralism, and identify questions that will have to be addressed by heterodox economists in order to maintain the (...) claim of pluralism. (shrink)

The development of ever smaller integrated circuits at the sub-micron and nanoscale—in accordance with Moore’s Law—drives the production of very small tags, smart cards, smart labels and sensors. Nanoelectronics and submicron technology supports surveillance technology which is practically invisible. I argue that one of the most urgent and immediate concerns associated with nanotechnology is privacy. Computing in the twenty-first century will not only be pervasive and ubiquitous, but also inconspicuous. If these features are not counteracted in design, they will facilitate (...) ubiquitous surveillance practices which are widely available, cheap, and intrusive. RFID technology is an instructive example of what nanotechnology has in store for privacy. (shrink)

In a recent paper on realism and pragmatism published in this journal, Osmo Kivinen and Tero Piiroinen have been pleading for more methodological work in the philosophy of the social sciences—refining the conceptual tools of social scientists—and less philosophically ontological theories. Following this de-ontologizing approach, we scrutinize the debates on social explanation and contribute to the development of a pragmatic social science methodology. Analyzing four classic debates concerning explanation in the social sciences, we propose to shift the debate away from (...) (a) the ontologizing defenses of forms of social explanation, and (b) a winner-takes-all-approach. Instead, we advocate (c) a pragmatic approach towards social explanation, elaborating a rigorous framework for explanatory pluralism detached from the debates on social ontology. (shrink)

Instances of explanatory reduction are often advocated on metaphysical grounds; given that the only real things in the world are subatomic particles and their interaction, we have to try to explain everything in terms of the laws of physics. In this paper, we show that explanatory reduction cannot be defended on metaphysical grounds. Nevertheless, indispensability arguments for reductive explanations can be developed, taking into account actual scientific practice and the role of epistemic interests. Reductive explanations might be indispensable to address (...) some epistemic interest answering a specific explanation-seeking question in the most accurate, adequate and efficient way. Just like explanatory pluralists often advocate the indispensability of higher levels of explanation pointing at the pragmatic value of the explanatory information obtained on these higher levels, we argue that explanatory reduction—traditionally understood as the contender of pluralism—can be defended in a similar way. The pragmatic value reductionist, lower level explanations might have in the biomedical sciences and the social sciences is illustrated by some case studies. (shrink)

An introduction to a special issue on computer ethics.

The current study investigated how work-related disagreements—coined as conflicts—relate to workplace bullying, from the perspective of the target as well as the perpetrator. We hypothesized a positive indirect association between task conflicts and bullying through relationship conflicts. This process accounted for both for targets and perpetrators of bullying. Targets are distinguished from perpetrators in our assumption that this indirect effect is boosted by distributive conflict behavior, being yielding for targets and forcing for perpetrators. Results in a large representative sample of (...) the Flemish working population confirmed our hypotheses. Additionally, our study also revealed a direct effect from task conflicts to bullying in the analyses regarding the indirect as well as the conditional indirect effects. For perpetrators, both the indirect and direct relationships are moderated by forcing, underlining the importance of distributive conflict behavior particularly for the enactment of bullying behaviors. (shrink)

We present a Reformed view on the relation between Christianity and non-Christian religions. We then explore what this view entails for the question whether Christians and non-Christian religious believers refer to, believe in, and worship the same God. We first analyze the concepts of worship, belief-in, and reference, as well as their interrelations. We then argue that adherents of the Abrahamic religions plausibly refer to the same God, whereas adherents of non-Abrahamic religions do not refer to this God. Nonetheless, it (...) would be wrong to say that adherents of all Abrahamic religions believe in and worship the same God. (shrink)

The development of ever smaller integrated circuits at the sub-micron and nanoscale—in accordance with Moore’s Law—drives the production of very small tags, smart cards, smart labels and sensors. Nanoelectronics and submicron technology supports surveillance technology which is practically invisible. I argue that one of the most urgent and immediate concerns associated with nanotechnology is privacy. Computing in the twenty-first century will not only be pervasive and ubiquitous, but also inconspicuous. If these features are not counteracted in design, they will facilitate (...) ubiquitous surveillance practices which are widely available, cheap, and intrusive. RFID technology is an instructive example of what nanotechnology has in store for privacy. (shrink)

Common sense philosophy holds that widely and deeply held beliefs are justified in the absence of defeaters. While this tradition has always had its philosophical detractors who have defended various forms of skepticism or have sought to develop rival epistemological views, recent advances in several scientific disciplines claim to have debunked the reliability of the faculties that produce our common sense beliefs. At the same time, however, it seems reasonable that we cannot do without common sense beliefs entirely. Arguably, science (...) and the scientific method are built on, and continue to depend on, common sense. This collection of essays debates the tenability of common sense in the face of recent challenges from the empirical sciences. It explores to what extent scientific considerations--rather than philosophical considerations--put pressure on common sense philosophy. The book is structured in a way that promotes dialogue between philosophers and scientists. Noah Lemos, one of the most influential contemporary advocates of the common sense tradition, begins with an overview of the nature and scope of common sense beliefs, and examines philosophical objections to common sense and its relationship to scientific beliefs. Then, the volume features essays by scientists and philosophers of science who discuss various proposed conflicts between commonsensical and scientific beliefs: the reality of space and time, about the nature of human beings, about free will and identity, about rationality, about morality, and about religious belief. Notable philosophers who embrace the common sense tradition respond to these essays to explore the connection between common sense philosophy and contemporary debates in evolutionary biology, neuroscience, physics, and psychology. (shrink)

In the literature on scientific explanation two types of pluralism are very common. The first concerns the distinction between explanations of singular facts and explanations of laws: there is a consensus that they have a different structure. The second concerns the distinction between causal explanations and uni.cation explanations: most people agree that both are useful and that their structure is different. In this article we argue for pluralism within the area of causal explanations: we claim that the structure of a (...) causal explanation depends on the causal structure of the relevant fragment of the world and on the interests of the explainer. (shrink)

The rapid dynamics of COVID-19 calls for quick and effective tracking of virus transmission chains and early detection of outbreaks, especially in the “phase 2” of the pandemic, when lockdown and other restriction measures are progressively withdrawn, in order to avoid or minimize contagion resurgence. For this purpose, contact-tracing apps are being proposed for large scale adoption by many countries. A centralized approach, where data sensed by the app are all sent to a nation-wide server, raises concerns about citizens’ privacy (...) and needlessly strong digital surveillance, thus alerting us to the need to minimize personal data collection and avoiding location tracking. We advocate the conceptual advantage of a decentralized approach, where both contact and location data are collected exclusively in individual citizens’ “personal data stores”, to be shared separately and selectively, voluntarily, only when the citizen has tested positive for COVID-19, and with a privacy preserving level of granularity. This approach better protects the personal sphere of citizens and affords multiple benefits: it allows for detailed information gathering for infected people in a privacy-preserving fashion; and, in turn this enables both contact tracing, and, the early detection of outbreak hotspots on more finely-granulated geographic scale. The decentralized approach is also scalable to large populations, in that only the data of positive patients need be handled at a central level. Our recommendation is two-fold. First to extend existing decentralized architectures with a light touch, in order to manage the collection of location data locally on the device, and allow the user to share spatio-temporal aggregates—if and when they want and for specific aims—with health authorities, for instance. Second, we favour a longer-term pursuit of realizing a Personal Data Store vision, giving users the opportunity to contribute to collective good in the measure they want, enhancing self-awareness, and cultivating collective efforts for rebuilding society. (shrink)

This article examines whether the involvement of stakeholders in the design of corporate codes of conduct leads to a higher implementation likelihood of the code. The empirical focus is on Occupational Safety and Health (OSH). The article compares the inclusion of OSH issues in the codes of conduct of 30 companies involved in International Framework Agreements (IFAs), agreed upon by trade unions and multinational enterprises, with those of a benchmark sample of 38 leading Multinational Enterprises in comparable industries. It is (...) found that codes of the IFA group have a higher implementation likelihood in OSH than the codes of the benchmark group. Further, European firms, culturally more used to stakeholder involvement, score higher than their US and Japanese competitors, and hence are more capable of addressing the safety and health issues in international supply chains. The implementation likelihood of codes seems closely related to the type of corporate CSR approach. (shrink)

In this article, we inquire into two contemporary participatory formats that seek to democratically intervene in scientific practice: the consensus conference and participatory technology assessment. We explain how these formats delegitimize conflict and disagreement by making a strong appeal to consensus. Based on our direct involvement in these formats and informed both by political philosophy and science and technology studies, we outline conceptions that contrast with the consensus ideal, including dissensus, disclosure, conflictual consensus and agonistic democracy. Drawing on the notion (...) of meta-consensus and a distinction between four models of democracy, we elaborate how a more positive valuation of conflict provides opportunities for mutual learning, the articulation of disagreement, and democratic modulation—three aspirations that are at the heart of most pTAs and consensus conferences. Disclosing the strengths and weaknesses of these different models is politically and epistemically useful, and should therefore be an integral part of the development of participation theory and process in science and technology. (shrink)

This paper presents the first bibliometric mapping analysis of the field of computer and information ethics (C&IE). It provides a map of the relations between 400 key terms in the field. This term map can be used to get an overview of concepts and topics in the field and to identify relations between information and communication technology concepts on the one hand and ethical concepts on the other hand. To produce the term map, a data set of over thousand articles (...) published in leading journals and conference proceedings in the C&IE field was constructed. With the help of various computer algorithms, key terms were identified in the titles and abstracts of the articles and co-occurrence frequencies of these key terms were calculated. Based on the co-occurrence frequencies, the term map was constructed. This was done using a computer program called VOSviewer. The term map provides a visual representation of the C&IE field and, more specifically, of the organization of the field around three main concepts, namely privacy, ethics, and the Internet. (shrink)

Knowledge of the backgrounds of students of behaviour working in the field of applied animal behavior science may help us to recognize their influence on conclusions reached in a particular study and on more general points of view. This recognition may result in a speed up of the progress in this science, to the benefit of science and animals. Some types are: (1) Eco-ethologists (ethologists of the hunters-type). They like to stalk healthy wild animals in their natural environment. They are (...) less interested in the abnormal behavior of domestic animals under husbandry circumstances. (2) Behaviorists. These are psychologists that still think in a man-animal dichotomy. They are not interested in animals for their own sake but as models for human behavior. (3) Behavior physiologists. These biologists are not primarily interested in behavior. Because of the type of experiments they perform they have an aversity against animal protectionists. (4) Ethologists of the farmers type. These ethologists want to posses animals, collect animal species, take care of them and breed them. They are able to speak on approximately the same wavelength as farmers as well as animal protectionists. (5) Zootechnicians of the farmers type. These scientists want to make a living out of animals and like to take care for them. They are also able to speak at approximately the same wavelength as farmers and animal protectionists. (shrink)

In projects concerning big data, ethical questions need to be answered during the design process. In this paper the Value Sensitive Design method is applied in the context of data-driven health services aimed at disease prevention. It shows how Value Sensitive Design, with the use of a moral dialogue and an ethical matrix, can support the identification and operationalization of moral values that are at stake in the design of such services. It also shows that using this method can support (...) meeting the requirements of the General Data Protection Regulation. (shrink)

Is epistocracy epistemically superior to democracy? In this paper, I scrutinize some of the arguments for and against the epistemic superiority of epistocracy. Using empirical results from the literature on the epistemic benefits of diversity as well as the epistemic contributions of citizen science, I strengthen the case against epistocracy and for democracy. Disenfranchising, or otherwise discouraging anyone to participate in political life, on the basis of them not possessing a certain body of (social scientific) knowledge, is untenable also from (...) an epistemic point of view. Rather than focussing on individual competence, we should pay attention to the social constellation through which we produce knowledge to make sure we decrease epistemic loss (by ensuring diversity and inclusion) and increase epistemic productivity (by fostering a multiplicity of perspectives interacting fruitfully). Achieving those epistemic benefits requires a more democratic approach that differs significantly from epistocracy. (shrink)

When thinking about ethics, technology is often only mentioned as the source of our problems, not as a potential solution to our moral dilemmas. When thinking about technology, ethics is often only mentioned as a constraint on developments, not as a source and spring of innovation. In this paper, we argue that ethics can be the source of technological development rather than just a constraint and technological progress can create moral progress rather than just moral problems. We show this by (...) an analysis of how technology can contribute to the solution of so-called moral overload or moral dilemmas. Such dilemmas typically create a moral residue that is the basis of a second-order principle that tells us to reshape the world so that we can meet all our moral obligations. We can do so, among other things, through guided technological innovation. (shrink)

Information technology is an integral part of the practices and institutions of post-industrial society. It is also a source of hard moral questions and thus is both a probing and relevant area for moral theory. In this volume, an international team of philosophers sheds light on many of the ethical issues arising from information technology, including informational privacy, digital divide and equal access, e-trust and tele-democracy. Collectively, these essays demonstrate how accounts of equality and justice, property and privacy benefit from (...) taking into account how information technology has shaped our social and epistemic practices and our moral experiences. Information technology changes the way that we look at the world and deal with one another. It calls, therefore, for a re-examination of notions such as friendship, care, commitment and trust. (shrink)

In computer ethics, as in other branches of applied ethics, the problem of the justification of moral judgment is still unresolved. I argue that the method which is referred to as “The Method of Wide Reflective Equilibrium” (WRE) offers the best solution to it. It does not fall victim to the false dilemma of having to choose either case‐based particularist or principle‐based universalist approaches to the problem of moral justification. I claim that WRE also provides the best model of practical (...) moral reasoning available for computer ethics. It does not pretend to provide quasi‐algorithmic procedures for moral decision‐making, but neither does it abandon the regulative ideal of communicative transparency in discursive public justification. (shrink)

In Printing Spinoza Jeroen van de Ven systematically examines all seventeenth-century printed editions of Spinoza's writings, published between 1663 and 1694, as well as their variant 'issues'. In focus are Spinoza's 1663 adumbration of René Descartes's 'Principles of Philosophy' with his own 'Metaphysical Thoughts', the 'Theological-Political Treatise' (1670), and the posthumous writings (1677), including the famously-known 'Ethics'. Van de Ven's descriptive bibliography studies, contextualizes, and records all aspects of the publication history of Spinoza's writings from manuscript to print and (...) assesses their immediate reception. It discusses the printed books' codicology, philology, typographical and textual relationships, illustration programmes, as well as their dissemination in early Enlightenment Europe, in view of the physical aspects of 1,246 extant copies and their provenance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Herman Daly’s Economics for a Full World: His Life and Ideas by Peter VictorJeroen Van Den Bergh (bio)Victor, Peter (2022). Herman Daly’s Economics for a Full World: His Life and Ideas. Routledge, Oxon UK and New York USA (ISBN: 978–0–367-55694-5).Herman Daly (1938–2022) spent a lifetime thinking about how to achieve a sustainable economy. In an inclusive biography, Canadian economist and environmental scientist Peter Victor discusses his ideas, critiques (...) and debates with others, while clarifying his motivations and struggles. Daly has greatly influenced others, as reflected by numerous prizes awarded to him. This influence is confirmed by original text boxes in the book that contain statements of many colleagues about his work and person, obtained through a questionnaire survey by the author.As a young man, Daly decided to study economics as he imagined it combined humanities and science. He was disappointed in it being less scientific than hoped, but his environmental concern motivated him to work on reestablishing the foundations of the field in environmental science and ethics. Daly is best known for his critique of economic growth and his alternative of the “steady-state economy.” He contributed, however, many other novel concepts and ideas during his lifetime, such as the ends-means spectrum, empty vs full world, uneconomic growth and optimal scale.Victor explains these ideas in a calm pace, showing a deep knowledge of Daly’s work. He, moreover, is able to connect it to ongoing sustainability research. He does all this in the course of thirteen chapters, covering Daly’s early life, education and career, his views on economics, his personal philosophy and the role of religion, his proposal for a steady-state economy, and his opinions on economic growth, population and migration, money and banking, and the perils of trade. [End Page 117]Ultimate endsMany consider Herman Daly to be a heterodox and even heretic economist. He associates himself with ecological economics, the field he co-founded. But while some of his ideas seem radical, many of his core proposals do not deviate substantially from mainstream economics. For instance, his “ultimate ends” concept is perfectly consistent with the broad notion of “welfare” in standard economics. In line with this, many welfare economists—such as Samuelson (1961), Mishan (1967), Hirsch (1976), Sen (1976), Scitovsky (1976) and Frank (1985)—have expressed themselves as critical of GDP (gross domestic product) dominance and growthmania (van den Bergh 2009). In fact, neoclassical economics is not married to economic growth—this is more the empirical side of macroeconomics. While Daly recognizes these subtleties, some of his followers do not.Daly sees his Protestant religion as delivering the ultimate ends, but Victor notes that this has not led to concrete suggestions. Ultimate ends based in Christian religion may be motivated by the promise of eternal (after)life, which in effect means gratifying selfish preferences. Instead, a humanistic perspective—which Daly also seems to embrace—would stress solidarity with future generations and a bioethical view of solidarity with other species. These distinct viewpoints, combined with diversity of human preferences and experiences, suggest that it will be difficult if not impossible for democratic societies to agree upon ultimate means.The Index of Sustainable Economic Welfare (ISEW), a kind of greened or sustainable GDP metric, is Daly’s most concrete elaboration of ultimate means (Daly and Cobb 1989). For many OECD (Organization for Economic Cooperation and Development) countries, it indicates a stabilization of welfare, despite continued GDP growth (Lawn 2003; Posner and Costanza 2011). As clarified by Victor, The ISEW remains close to GDP, produces a monetary measure, has a simple and transparent calculation method, and received considerably attention from theoretical and empirical angles. In view of this, it may well represent the best candidate for a beyond-GDP metric that can replace the GDP. What urgently fails is an effective institutional procedure to achieve its widespread adoption (van den Bergh 2022).Religion, evolution and biodiversityDaly’s religious standpoint make him skeptical of the modern scientific worldview which regards the world to be governed by materialism and evolution, with no role for a higher purpose or an ultimate end. This led him... (shrink)

Contrary to economics or history, for example, there does not exist an organized field dedicated to the philosophy of political science. Given that the philosophical issues raised by political science research are just as pressing and vibrant as those raised in these more organized fields, fostering a field that labels itself Philosophy of Political Science (PoPS) is important. PoPS is advanced here as a fruitful meeting place where both philosophers and practicing political scientists contribute and discuss—with philosophical discussions that are (...) close to and informed by actual developments in political science, making philosophy of science continuous with the sciences in line with contemporary naturalist philosophy of science. The topics scrutinized in the different chapters of the Handbook will figure prominently in PoPS, as we lay out in this chapter. (shrink)

In the age of Big Data, companies and governments are increasingly using algorithms to inform hiring decisions, employee management, policing, credit scoring, insurance pricing, and many more aspects of our lives. Artificial intelligence systems can help us make evidence-driven, efficient decisions, but can also confront us with unjustified, discriminatory decisions wrongly assumed to be accurate because they are made automatically and quantitatively. It is becoming evident that these technological developments are consequential to people’s fundamental human rights. Despite increasing attention to (...) these urgent challenges in recent years, technical solutions to these complex socio-ethical problems are often developed without empirical study of societal context and the critical input of societal stakeholders who are impacted by the technology. On the other hand, calls for more ethically and socially aware AI often fail to provide answers for how to proceed beyond stressing the importance of transparency, explainability, and fairness. Bridging these socio-technical gaps and the deep divide between abstract value language and design requirements is essential to facilitate nuanced, context-dependent design choices that will support moral and social values. In this paper, we bridge this divide through the framework of Design for Values, drawing on methodologies of Value Sensitive Design and Participatory Design to present a roadmap for proactively engaging societal stakeholders to translate fundamental human rights into context-dependent design requirements through a structured, inclusive, and transparent process. (shrink)

Bullying is one of the most impactful deviant actions that affects workers' personal health and work experience. Bullying is a quite distinctive deviant behavior as targets are subjected to transgressions that could last for months or longer. Even though a number of actions can be taken to resolve bullying between all parties, from the viewpoint of the target it is hard to resolve the situation. As a result, hierarchical influence may be necessary to prevent bullying in the first place. A (...) possible solution, therefore, is focusing on how leaders can impact the bullying behavior. This research argued and showed that ethical leadership is negatively associated with being bullied through tackling one of its most important antecedents of bullying: the design of the work environment. That is, ethical leaders could be shown to improve employees' workload (quantitative work environment) and poor working conditions (qualitative work environment), which was related to decreased bullying. (shrink)

Starting from the plurality of explanatory strategies in the actual practice of socialscientists, I introduce a framework for explanatory pluralism – a normative endorsement of the plurality of forms and levels of explanation used by social scientists. Equipped with thisframework, central issues in the individualism/holism debate are revisited, namely emergence,reduction and the idea of microfoundations. Discussing these issues, we notice that in recentcontributions the focus has been shifting towards relationism, pluralism and interaction, awayfrom dichotomous individualism/holism thinking and a winner-takes-all approach. (...) Then, thechallenge of the debate is no longer to develop the ultimate individualistic approach ordefending the holist approach, but rather how to be combine individualism and holism; howcan they co-exist, interact, be integrated or develop some division of labour, while making thebest out of the strengths and limitations of the respective explanatory strategies of holists andindividualists? Thus, the debate shifts to how exactly pluralism should be understood as thenext leading question, going beyond the current individualism/holism debate. The paper endswith a discussion and evaluation of different understandings of explanatory pluralismdefended in the literature. (shrink)

Commenting on recent articles by Keith Sawyer and Julie Zahle, the author questions the way in which the debate between methodological individualists and holists has been presented and contends that too much weight has been given to metaphysical and ontological debates at the expense of giving attention to methodological debates and analysis of good explanatory practice. Giving more attention to successful explanatory practice in the social sciences and the different underlying epistemic interests and motivations for providing explanations or reducing theories (...) (which ask for different kinds of explanatory information to be found on the social or on the individual level) might lead to real progress in the debate on methodological individualism, and away from the unending battles of (metaphysical) intuitions. Key Words: methodological individualism • nonreductive materialism • pluralism • pragmatics of explanation. (shrink)

In this article we characterize a countable ordinal known as the big Veblen number in terms of natural well-partially ordered tree-like structures. To this end, we consider generalized trees where the immediate subtrees are grouped in pairs with address-like objects. Motivated by natural ordering properties, extracted from the standard notations for the big Veblen number, we investigate different choices for embeddability relations on the generalized trees. We observe that for addresses using one finite sequence only, the embeddability coincides with the (...) classical tree-embeddability, but in this article we are interested in more general situations. We prove that the maximal order type of some of these new embeddability relations hit precisely the big Veblen ordinal ϑΩΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vartheta \Omega^{\Omega}}$$\end{document}. Somewhat surprisingly, changing a little bit the well-partially ordered addresses, the maximal order type hits an ordinal which exceeds the big Veblen number by far, namely ϑΩΩΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vartheta \Omega^{\Omega^\Omega}}$$\end{document}. Our results contribute to the research program on classifying properties of natural well-orderings in terms of order-theoretic properties of the functions generating the orderings. (shrink)