If there is a good wellordering of the reals, then there is a wellfounded relation for which the comparison relation is not projective.

We show that it is relatively consistent with ZFC that there is a projective wellfounded relation with rank higher than all projective prewellorderings.

If there is a good $\Delta^1_3$ wellordering of the reals, then there is a $\Pi^1_1$ wellfounded relation for which the comparison relation is not projective.

In a previous article on cosmological arguments, I have put forward a few examples of complete infinite and circular explanations, and argued that complete non-wellfounded explanations such as these might explain the present state of the world better than their well-founded theistic counterparts (Billon, 2021). Although my aim was broader, the examples I gave there implied merely causal explanations. In this article, I would like to do three things: • Specify some general informative conditions for complete and incomplete non- (...) class='Hi'>wellfounded causal explanations that can be used to assess candidate explanations and to generate new examples of complete non-wellfounded explanations. • Show that these conditions, which concern chains of causal explanations, easily generalize to chains of metaphysical, grounding explanations and even to chains involving other “determination relations” such as supervenience. • Apply these general conditions to the recent debates against the existence of nonwellfounded chains of grounds and show, with a couple of precise examples, that the latter can be complete, and that just like in the case of causal explanations, non-wellfoundedness can in fact be an aset rather than a liability. (shrink)

We prove that if I is a partially ordered set in a countable transitive model M of ZFC then M can be extended by a generic sequence of reals a i , i ∈ I, such that ℵ M 1 is preserved and every a i is Sacks generic over $\mathfrak{M}[\langle \mathbf{a}_j: j . The structure of the degrees of M-constructibility of reals in the extension is investigated. As applications of the methods involved, we define a cardinal invariant to distinguish (...) product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω 2 -iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds. (shrink)

Ross Cameron (2022) argues that metaphysical infinitists should reject the generally accepted idea that metaphysical determination relations back metaphysical explanations. Otherwise it won’t be possible for them to come up with successful explanations for the existence of dependent entities in non-wellfounded chains of dependence. I argue that his argument suffers from what he calls the finitist dogma, although indirectly so. However, there is a better way of motivating Cameron’s conclusion. Assuming Cameron’s principle of Essence, explanations for the existence of (...) dependent entities turn out to be circular if determination relations back explanations. This latter argument provides a stronger case as it puts the foundationalist under significant pressure, besides putting the infinitist under some pressure, to deny the idea that determination relations back explanations. (shrink)

The philosophies of education serve as the guide of the teachers in handling the teaching-learning process. However, a belief will remain as a belief unless it is practiced. This study aimed to find the relationship between the philosophical beliefs and practices of the 30 teachers of the schools in San Roque, Mabini, Bohol - San Roque Elementary School and San Roque National High School, S.Y. 2019-2020. The study utilized a quantitative method descriptive survey research design. The research instrument used was (...) a self-constructed questionnaire in which the reliability was tested by a Cronbach’s Alpha using Statistical Package for the Social Science (SPSS) software. Simple percentage and weighted mean were some of the statistical treatments used. Kendall’s tau_b, a non-parametric test, was used to determine the correlation between philosophical beliefs and their equivalent pedagogical practices. All of the statistical treatments were also run using the SPSS software. Further, the researcher assured the proper observation of the research ethics protocol. Based on the results, the philosophies of Progressivism (3.63) and Perennialism (3.31) were the most and least prevailing philosophical beliefs, respectively. On the other hand, the most and least prevailing philosophies practiced are Progressivism (3.69) and Essentialism (3.19), respectively. Moreover, research findings revealed that there was a significant relationship between the philosophical beliefs of teachers and their pedagogical practices. In conclusion, this study claims that teachers’ pedagogical practices are dependent to their philosophical beliefs; and as the teachers believed on a particular philosophy of education, they practice it accordingly to the extent of their adherence to the belief. (shrink)

Barbarism was by no means unique to the past 100 years, Jonathan Glover tells us, but ''it is still right that much of 20th-century history has been a very unpleasant surprise.'' This was the century of Passchendaele, Dresden, Nanking, Nagasaki and Rwanda; of the Final Solution, the gulag, the Great Leap Forward, Year Zero and ethnic cleansing -- names that stand for killings in the six and seven figures and for suffering beyond comprehension. The technological progress that inspired the optimism (...) of the Victorians turned out also to multiply the effects of old-fashioned evil and criminal stupidity. (shrink)

Presents the fundamental ideas of Indian thinkers that have shaped the mind of Indian from 1770 to the post-modern era in the middle of 20th century in India. Lists the most Indian influential figures in the field of philosophy, political theory, activicism such as Rabindranath Tagore, Ram Mohan Roy, Swami Vivekananda, and Mohandas Karamchand Gandhi.

The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems (...) is essentially the same as for plain unconstrained FO 2 , namely non-deterministic exponential time. In contrast FO 2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings, wellorderings, or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO 2 and computation tree logic CTL. (shrink)

We consider foundational questions related to the definition of functions by corecursion. This method is especially suited to functions into the greatest fixed point of some monotone operator, and it is most applicable in the context of non-wellfounded sets. We review the work on the Special Final Coalgebra Theorem of Aczel [1] and the Corecursion Theorem of Barwise and Moss [4]. We offer a condition weaker than Aczel's condition of uniformity on maps, and then we prove a result relating (...) the operators satisfying the new condition to the smooth operators of [4]. (shrink)

In [10] Friedman showed that is a conservative extension of <ε0for-sentences wherei= min, i.e.,i= 2, 3, 4 forn= 0, 1, 2 +m. Feferman [5], [7] and Tait [11], [12] reobtained this result forn= 0, 1 and even with instead of. Feferman and Sieg established in [9] the conservativeness of over <ε0for-sentences for alln. In each paper, different methods of proof have been used. In particular, Feferman and Sieg showed how to apply familiar proof-theoretical techniques by passing through languages with Skolem (...) functionals.In this paper we study the same choice principles in the presence of theBar Rule, which permits one to infer the scheme of transfinite induction on a primitive recursive relation ≺ when it has been proved that ≺ is wellfounded. The main result characterizes + as a conservative extension of a system of the autonomously iterated-comprehension axiom for-sentences. Forn= 0 this has been proved by Feferman in the form that + is a conservative extension of <Γ0; this was first done in [8] by use of the Gödel functional interpretation for the stronger systemZω+μ+ + and then more recently by the simpler methods of [9]. Jäger showed how the latter methods could also be used to obtain the general result of Theorem 1 below. (shrink)

A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. (...) These algebras, however, generate the variety of all ( ,f) with f a hemimorphism on ). (shrink)

Building on previous work by Mints, Buchholz and Schwichtenberg, a simplified version of continuous normalization for the untyped λ-calculus and Gödel’s is presented and analysed in the coalgebraic framework of non-wellfounded terms with so-called repetition constructors.The primitive recursive normalization function is uniformly continuous w.r.t. the natural metric on non-wellfounded terms. Furthermore, the number of necessary repetition constructors is locally related to the number of reduction steps needed to reach the normal form and its size.It is also shown how (...) continuous normal forms relate to derivations of strong normalizability in the typed λ-calculus and how this leads to new bounds for the sum of the height of the reduction tree and the size of the normal form.Finally, the methods are extended to an infinitary λ-calculus with ω-rule and permutative conversions and this is used to derive a strong form of normalization for an iterative version of Gödel’s system , leading to a value table semantics for number-theoretic functions. (shrink)

This paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel’s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a (...) variant of the Mitchell order called the internal relation. (shrink)

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and (...) are compared to classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

In this paper we present and study a categorical formulation of the W-types of Martin-Löf. These are essentially free term algebras where the operations may have finite or infinite arity. It is shown that W-types are preserved under the construction of sheaves and Artin gluing. In the proofs we avoid using impredicative or nonconstructive principles.

We study the non-wellfounded sets as fixed points of substitution. For example, we show that ZFA implies that every function has a fixed point. As a corollary we determine for which functions f there is a function g such that . We also present a classification of non-wellfounded sets according to their branching structure.

The paper explores the proof theory of non-wellfounded mereology with binary fusions and provides a cut-free sequent calculus equivalent to the standard axiomatic system.

Abstract: The paper provides a general account of value relations. It takes its departure in a special type of value relation, parity, which according to Ruth Chang is a form of evaluative comparability that differs from the three standard forms of comparability: betterness, worseness and equal goodness. Recently, Joshua Gert has suggested that the notion of parity can be accounted for if value comparisons are interpreted as normative assessments of preference. While Gert's basic idea is attractive, the way he (...) develops it is flawed: His modeling of values by intervals of permissible preference strengths is inadequate. Instead, I provide an alternative modeling in terms of intersections of rationally permissible preference orderings. This yields a general taxonomy of all binary value relations. The paper concludes with some implications of this approach for rational choice. (shrink)

In the foundations of Fechner's psychophysics, the concept of “functional relation” plays a highly relevant role in three different respects: (1) in respect to the principles of measurement, (2) in respect to the mind-body problem, and (3) in respect to the concept of a law of nature. In all three cases, it is important to explain the difference between a functional dependency of a variable upon another and a causal relationship between two (or more) variables. In all three respects, (...) Ernst Mach developed Fechner's ideas further and tried to extend the lessons he had learned from using the concept of a functional relation in psychophysics to the whole of science. For all three cases, I explain why they are still relevant for psychophysics and philosophy today. (shrink)

‘Relational value’ (RV) has intuitive credibility due to the shortcomings of existing axiological categories regarding recognizing the ethical relevance of people’s relations to nature. But RV is justified by arguments and analogies that do not hold up to closer scrutiny, which strengthens the assumption that RV is redundant. While RV may provide reasons for ethically considering some relations, much work remains to show that RV is a concept that does something existing axiological concepts cannot, beyond empirically describing relations people have (...) to environmental areas and places. (shrink)

The evidence is overwhelming that members of particularly wealthy and industry-owning segments of Western societies have much larger carbon footprints than most other humans, and thereby contribute far more than their “fair share” to the enormous problem of climate change. Nonetheless, in this paper we shall counsel against a strategy focused primarily on blaming and shaming and propose, instead, a change in the ethical conversation about climate change. We recommend a shift in the ethical framework from a focus on the (...) role of individual agents and a conversation about guilt; in its place, we propose a relational approach to public health ethics that is centered around the idea of relational solidarity. We begin by briefly reviewing the most common—and woefully inadequate—approach in the West to reducing emissions and responding to the health-related impacts of climate change. We then go on to propose a relational approach to public health ethics as an alternative ethical framework that better fits the moral problems associated with climate change and holds promise for a more meaningful response. (shrink)

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (...) (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations. (shrink)

This article contributes to the critical engagement with luck egalitarianism by advancing two arguments. Firstly, it questions the cogency of the dichotomies – e.g., luck/choice, person/circumstance, agency/structure – and the accompanying moral ideal of pure voluntarism. This makes it difficult for luck egalitarianism to dissect appropriately the inequalities embedded in social relations, such as social networks and involuntary associations, in which voluntariness and contingency as well as agency and structure are intertwined. Secondly, it suggests that the relational approach, which has (...) been developed, inter alia, in the empirical study of inequality, provides a morally and practically adequate perspective on egalitarian justice. The relational approach achieves this by converging upon those in‐between social relations that are irreducible to the macro‐level structure and to micro‐level agency. Moreover, a relationally sensitive perspective on inequality can adeptly respond to the difficulties that luck‐egalitarian theories encounter. (shrink)

In past and modern psychophysics there are several unresolved methodological and philosophical problems of human and animal perception, including the outstanding question of the relational basis of whole psychophysics. Here the main issue is discussed: if, and to what extent, there are viable bridges between the traditional “gestalt” oriented approaches and the modern perceptual-cognitive perspectives in psychophysics. Thereby the key concept of psychological “frame of reference” is presented by pointing to Hermann Ebbinghaus' geometric-optical illusions, on the one hand, and Max (...) Wertheimer's treatment of the traditional transposition phenomenon, on the other hand. A much-needed theoretical reorientation of future research may help to overcome the philosophical narrowness of present-day human and comparative psychophysics. (shrink)

I argue that the phenomenon underlying Bernard Williams’ (1976) “agent-regret” is considerably broader than appreciated by Williams and others. Agent-regret— an anguished response that agents have for harms they have caused, even if faultlessly— I maintain, is a species of a more general response to harms that need not be one’s fault, but which nonetheless impact one’s practical identity in a special way. This broader genus includes as a species what I call “relation-regret”, a pained response to harm caused (...) by a person to whom one is intimately related, as a co-member of a group partly constitutive of one’s practical identity (e.g. one’s family). After providing an account of the moral psychology of relation-regret, I attend to its normative significance, proposing in particular that acceptance of relation-regret provides us with reasons for accepting a novel form of moral luck, namely associative luck: the luck of being vulnerable to responsibility-responses in virtue of one’s attachments to others, despite one’s personal faultlessness. (shrink)

It is often argued that relational egalitarianism has a fundamental problem with intergenerational justice when compared to other theories of justice such as utilitarianism, prioritarianism, and luck egalitarianism. Recently, Timothy Sommers argued that there is no such comparative disadvantage for relational egalitarianism. His argument is quite modest: it merely aims to reject the claim that there could be no way to extend relational egalitarianism to intergenerational justice. This may be called the ‘No Comparative Disadvantage Thesis’. The present article challenges Sommers’s (...) argument in two ways. First, I show that Sommers fails to provide a reasonable constraint on causal efficacy, which is crucial to his argument for our relation (not relationship) to future generations. Second, I show that the chain-relatedness problem casts a shadow over Sommers’s argument for the No Comparative Disadvantage Thesis. More specifically, compared to the other theories of justice, relational egalitarianism (as it stands) can less easily justify that present persons have duties to future others. This is because relational egalitarianism cannot appeal to a specific principle in regard to the duties in question, because its principle is sensitive to current context and practice. I conclude that the No Comparative Disadvantage Thesis does not hold much promise. (shrink)

Most recent accounts of personal autonomy acknowledge that the social environment a person lives in, and the personal relationships she entertains, have some impact on her autonomy. Two kinds of conceptualizing social conditions are traditionally distinguished in this regard: Causally relational accounts hold that certain relationships and social environments play a causal role for the development and on-going exercise of autonomy. Constitutively relational accounts, by contrast, claim that autonomy is at least partly constituted by a person’s social environment or standing. (...) The central aim of this paper is to raise the question how causally and constitutively relational approaches relate to the fact that we exercise our autonomy over time. I argue that once the temporal scope of autonomy is opened up, we need not only to think differently about the social dimension of autonomy. We also need to reconsider the very distinction between causally and constitutively relational accounts, because it is itself a synchronic (and not a diachronic) distinction. (shrink)

In this article I draw on resources from the African philosophical tradition to construct a theory of human rights grounded on dignity that presents a challenge to the globally dominant, autonomy-based approach. Whereas the latter conceives of human rights violations as degradations of our rational nature, the former does so in terms of degradations of our relational nature, specifically, our capacity to be party to harmonious or friendly relationships. Although I have in the past presented the basics of the Afro-relational (...) approach, in this article I defend it from objections and also go on the offensive by arguing that understanding the human rights violations of torture and rape to be (roughly) behavior that treats innocent parties in an extremely discordant or unfriendly way is, if not more plausible than standard Kantian understandings, then at least a promising alternative to them. (shrink)

The long-term success of organizations is mainly attributable to employees’ psychological health. Organizations focusing on promoting and managing the flow may enhance employees’ well-being and performance to an optimum level. Surprisingly, the literature representing the role of HRM practices for their effect on work-related flow is very sparse. Accordingly, by drawing primarily on the job demands-resources model and HRM specific attribution theory, this paper develops a theoretical framework that unravels the effectiveness of specific organizational level High Involvement HRM practices in (...) activating the individual level work-related flow with beneficial effect and mediating role of affective commitment. In addition to highlighting the underlying mechanisms that may cause HIHRM practices to be regarded as resources and sometimes as demands, this paper especially proposes that these practices implemented with a focus to promote employee well-being are perceived as job resources and may positively influence affective commitment and flow, whereas these practices used as a demand to increase performance are perceived as job demands and may hinder affective commitment and flow. It is further significant to understand the possible moderating effects of emotional intelligence on the relationships among HIHRM practices, affective commitment, and flow. The paper augments the knowledge and understanding of the impact process of HIHRM practices, in particular how the HIHRM effect is sensed by the workers and thus, influences their succeeding job attitude and work experience. Finally, this work, as the first paper to link HIHRM practices with work-related flow, promotes the concept of positive psychology in the workplace. (shrink)

Sometimes, there are reasons for which we believe, intend, resent, decide, and so on: these reasons are the “bases” of the latter, and the explanatory relation between these bases and the latter is what I will call “the basing relation.” What kind of explanatory relation is this? Dispositionalists claim that the basing relation consists in the agent’s manifesting a disposition to respond to those bases by having the belief, intention, resentment, and so on, in question. Representationalists (...) claim that the basing relation consists in the agent’s representing the bases as justifying the belief, intention, resentment, and so on, in question. This article shows that an adequate account of the basing relation requires a particular refinement and combination of these two views. On the hybrid account defended here, the basing relation involves a disposition exercise that is individuated by the agent’s object-involving de se representation of that very exercise as justifying. (shrink)

Recent work on complex adaptive systems in the natural sciences, and the growing relational turn in the social sciences both reject the "systems theories" of earlier generations. This book builds on these entities to advance a relational processual approach to the comparative study of historical and contemporary international systems.

Heil wants us to be ‘ontologically serious’. Because if we’re ontologically serious we won’t take relations seriously. Here’s one of the lines of thought that runs through Heil’s Relations. It’s go...

Predication and the problems of universals and individuation have preoccupied philosophers from Plato (if not before) to the present. Concerns about relations and the special problems posed by relational predication came later - along with the explicit recognition of facts as purported entities that make a judgment true, rather than false, and resultant questions about the structure of such grounds of truth. The essays in the volume explore aspects of the history of the classic issues raised as well as alternative (...) attempts to deal with such issues. (shrink)

Contrary to widely shared opinion in analytic metaphysics, E.J. Lowe argues against the existence of relations in his posthumously published paper There are probably no relations (2016). In this article, I assess Lowe’s eliminativist strategy, which aims to show that all contingent “relational facts” have a monadic foundation in modes characterizing objects. Second, I present two difficult ontological problems supporting eliminativism about relations. Against eliminativism, metaphysicians of science have argued that relations might well be needed in the best a posteriori (...) motivated account of the structure of reality. Finally, I argue that, by analyzing relational inherence, trope theory offers us a completely new approach to relational entities and avoids the hard problems motivating eliminativism. (shrink)

In this revised edition of his 1979 classic Political Theory and International Relations, Charles Beitz rejects two highly influential conceptions of international theory as empirically inaccurate and theoretically misleading. In one, international relations is a Hobbesian state of nature in which moral judgments are entirely inappropriate, and in the other, states are analogous to persons in domestic society in having rights of autonomy that insulate them from external moral assessment and political interference. Beitz postulates that a theory of international politics (...) should include a revised principle of state autonomy based on the justice of a state’s domestic institutions, and a principle of international distributive justice to establish a fair division of resources and wealth among persons situated in diverse national societies. (shrink)