The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of (...) set theories due to Scott, Montague, Derrick, and Potter. (shrink)

In philosophical logic, a certain family of model constructions has received particular attention. Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke's least fixed point models of grounded truth. I develop a general formal theory of groundedness and explain how the well-founded sets, Cantor's extended number-sequence and Kripke's concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases. Then, I develop a new approach to a grounded theory (...) of proper classes. -/- However, the general concept of groundedness does not account for the philosophical significance of its paradigm instances. Instead, I argue, the philosophical content of the cumulative hierarchy of sets is best understood in terms of a primitive notion of ontological priority. -/- Then, I develop an analogous account of Kripke's models. I show that they exemplify the in-virtue-of relation much discussed in contemporary metaphysics, and thus are philosophically significant. I defend my proposal against a challenge from Kripke's “ghost of the hierarchy”. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and (...) a natural extension of BLT is definitionally equivalent with ZF. (shrink)

According to the iterative conception of set, sets are formed in stages. According to the purely iterative conception of set, sets are formed by iterated application of a set-of operation. The cumulative hierarchy is a mathematical realization of the iterative conception of set. A mathematical realization of the purely iterative conception can be found in Peter Aczel’s type-theoretic model of constructive set theory. I will explain Aczel’s model construction in a way that presupposes no previous familiarity with the (...) theories on which it is based. (shrink)

In the first part of the paper, I clarify what is at stake in the debate between accounts of the iterative conception based on the notion of metaphysical dependence and the minimalist account I have defended in previous work (Incurvati 2012; 2020). I argue that the debate concerns how to understand and motivate the central tenet of the iterative conception that every set occurs at some level of the cumulative hierarchy. This debate, I contend, should be distinguished from (...) the debate between actualist and potentialist accounts of the cumulative hierarchy. In the second part of the paper, I use the distinction drawn in the first part of the paper to assess an objection leveled by Mark Gasser (2015) against ante rem structuralism. In particular, this distinction makes it clear that there are two different objections in Gasser’s article. The first objection is that the iterative conception conflicts with dependence claims made by structuralists. As I have suggested in previous work, ante rem structuralists can address this objection by endorsing a minimalist account of the iterative conception. The second objection is that the indefinite extensibility of the set concept conflicts with the idea that the cumulative hierarchy is exhausted by the ZFC axioms. I chart various possible ways of addressing the second objection and show that by disentangling ante rem structuralism from the idea that mathematical structures ought to be given by implicit definitions opens up a novel way of addressing the second objection. I conclude by contending that although my arguments show that ante rem structuralism is compatible with the iterative conception, there are still reasons to favour a more deflationary understanding of structuralism, advocated by John Burgess, Joel Hamkins and Gasser himself. (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the (...) set of theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the so-called Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the primary bearers of truth and (...) reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. (shrink)

The success of set theory as a foundation for mathematics inspires its use in artificial intelligence, particularly in commonsense reasoning. In this survey, we briefly review classical set theory from an AI perspective, and then consider alternative set theories. Desirable properties of a possible commonsense set theory are investigated, treating different aspects like cumulative hierarchy, self-reference, cardinality, etc. Assorted examples from the ground-breaking research on the subject are also given.

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for the (...) existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed (...) by STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S (...) knows that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

This paper investigates how the credit incentive to engage in questionable research practices interacts with cumulative advantage, the process whereby high-status academics more easily increase their status than low-status academics. I use a mathematical model to highlight two dynamics that have not yet received much attention. First, due to cumulative advantage, questionable research practices may pay off over the course of an academic career even if they are not attractive at the level of individual publications. Second, because of (...) the role of bottleneck moments in academic careers, questionable research practices may be selected for even if they do not provide a benefit in expectation. I also observe that, within the model, the most successful academics are the most likely to have benefited from fraud. (shrink)

Applied Evolutionary Epistemology is a scientific-philosophical theory that defines evolution as the set of phenomena whereby units evolve at levels of ontological hierarchies by mechanisms and processes. This theory also provides a methodology to study evolution, namely, studying evolution involves identifying the units that evolve, the levels at which they evolve, and the mechanisms and processes whereby they evolve. Identifying units and levels of evolution in turn requires the development of ontological hierarchy theories, and examining mechanisms and processes necessitates (...) theorizing about causality. Together, hierarchy and causality theories explain how biorealities form and diversify with time. This paper analyzes how Applied EE redefines both hierarchy and causality theories in the light of the recent explosion of network approaches to causal reasoning associated with studies on reticulate and macroevolution. Causality theories have often been framed from within a rigid, ladder-like hierarchy theory where the rungs of the ladder represent the different levels, and the elements on the rungs represent the evolving units. Causality then is either defined reductionistically as an upward movement along the strands of a singular hierarchy, or holistically as a downward movement along that same hierarchy. Upward causation theories thereby analyze causal processes in time, i.e. over the course of natural history or phylogenetically, as Darwin and the founders of the Modern Synthesis intended. Downward causation theories analyze causal processes in space, ontogenetically or ecologically, as the current eco-evo-devo schools are evidencing. This work demonstrates how macroevolution and reticulate evolution theories add to the complexity by examining reticulate causal processes in space–time, and the interactional hierarchies that such studies bring forth introduce a new form of causation that is here called reticulate causation. Reticulate causation occurs between units and levels belonging to different as well as to the same ontological hierarchies. This article concludes that beyond recognizing the existence of multiple units, levels, and mechanisms or processes of evolution, also the existence of multiple kinds of evolutionary causation as well as the existence of multiple evolutionary hierarchies needs to be acknowledged. This furthermore implies that evolution is a pluralistic process divisible into different kinds. (shrink)

Cumulative cultural knowledge [CCK], the knowledge we acquire via social learning and has been refined by previous generations, is of central importance to our species’ flourishing. Considering its importance, we should expect that our best epistemological theories can account for how this happens. Perhaps surprisingly, CCK and how we acquire it via cultural learning has only received little attention from social epistemologists. Here, I focus on how we should epistemically evaluate how agents acquire CCK. After sampling some reasons why (...) extant theories cannot account for CCK, I suggest that things aren’t as bleak as they might look. I explain how agents deserve epistemic credit for how CCK is transmitted in cultural learning by promoting a central need of their social group: The efficient and safe transmission of CCK. A good initial fit exists between this observation and Greco’s knowledge-economy framework. Ultimately, however, Greco’s account doesn’t straightforwardly account for CCK because of its strict focus on testimony. I point out two issues in the framework due to this focus. The resulting view advocates giving epistemic credit to agents when they act to promote their communities’ epistemic needs in the right way and highlights the various ways in which agents come to do this. (shrink)

Two strong arguments have been given in favor of the claim that no selection process can play a role in explaining adaptations. According to the first argument, selection is a negative force; it may explain why the eliminated individuals are eliminated, but it does not explain why the ones that survived (or their offspring) have the traits they have. The second argument points out that the explanandum and the explanans are phenomena at different levels: selection is a population-level phenomenon, whereas (...) adaptation occurs on the individual level. Thus, selection can explain why individuals in a certain population have a certain trait, but it cannot explain why a certain indi- vidual has this trait. After pointing out that both arguments ignore the significance of the limitation of environmental resources, I will construe a positive argument for the claim that cumulative selection processes can, indeed, play a role in explaining adaptations. (shrink)

Contemporary evolutionary biology comprises a plural landscape of multiple co-existent conceptual frameworks and strenuous voices that disagree on the nature and scope of evolutionary theory. Since the mid-eighties, some of these conceptual frameworks have denounced the ontologies of the Modern Synthesis and of the updated Standard Theory of Evolution as unfinished or even flawed. In this paper, we analyze and compare two of those conceptual frameworks, namely Niles Eldredge’s Hierarchy Theory of Evolution (with its extended ontology of evolutionary entities) (...) and the Extended Evolutionary Synthesis (with its proposal of an extended ontology of evolutionary processes), in an attempt to map some epistemic bridges (e.g. compatible views of causation; niche construction) and some conceptual rifts (e.g. extra-genetic inheritance; different perspectives on macroevolution; contrasting standpoints held in the “externalism–internalism” debate) that exist between them. This paper seeks to encourage theoretical, philosophical and historiographical discussions about pluralism or the possible unification of contemporary evolutionary biology. (shrink)

In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic (...) is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

The attributes of gender in the media are disputable. This can be explained by a conflict generated by culturally acquired alternative imagined hierarchies which are not compatible or may be even contradictory. This article is a philosophical enquiry that examines the representation of gender and the environment in which it is conditioned.

Ce texte vise à proposer quelques arguments pour une critique empiriste de la hiérarchie des normes, c'est-à-dire pour les besoins d'une science du droit descriptive et explicative. La hiérarchie des normes est à la fois objet d’étude scientifique, et théorie construisant cet objet. Une approche empiriste nécessite la formalisation de quelques concepts et une justification minimale de la possibilité d'une science juridique empiriste : ce seront les objets des premiers points de ce texte. Il s'agira ensuite de proposer une formulation (...) de la conception de la hiérarchie des normes à laquelle l’empirisme peut conduire, permettant de réévaluer la théorie (normativiste) de la hiérarchie des normes proposée par Kelsen comme une théorie politique, qui ne décrit pas son objet mais le construit comme contrainte. (shrink)

The notion of “hierarchy” is one of the most commonly posited organizational principles in systems neuroscience. To this date, however, it has received little philosophical analysis. This is unfortunate, because the general concept of hierarchy ranges over two approaches with distinct empirical commitments, and whose conceptual relations remain unclear. We call the first approach the “representational hierarchy” view, which posits that an anatomical hierarchy of feed-forward, feed-back, and lateral connections underlies a signal processing hierarchy of (...) input-output relations. Because the representational hierarchy view holds that unimodal sensory representations are subsequently elaborated into more categorical and rule-based ones, it is committed to an increasing degree of abstraction along the hierarchy. The second view, which we call “topological hierarchy", is not committed to different representational functions or degrees of abstraction at different levels. Topological approaches instead posit that the hierarchical level of a part of the brain depends on how central it is to the pattern of connections in the system. Based on the current evidence, we argue that three conceptual relations between the two approaches are possible: topological hierarchies could substantiate the traditional representational hierarchy, conflict with it, or contribute to a plurality of approaches needed to understand the organization of the brain. By articulating each of these possibilities, our analysis attempts to open a conceptual space in which further neuroscientific and philosophical reasoning about neural hierarchy can proceed. (shrink)

Evidence hierarchies are widely used to assess evidence in systematic reviews of medical studies. I give several arguments against the use of evidence hierarchies. The problems with evidence hierarchies are numerous, and include methodological shortcomings, philosophical problems, and formal constraints. I argue that medical science should not employ evidence hierarchies, including even the latest and most-sophisticated of such hierarchies.

The paper examines the book Martin Buber’s Theopolitics and analyzes the conflict between the hierarchy in nature and in human society. Buber qualifies our relations to nature and to other non-living objects as darker than human relations. This creates an imbalance between the human You and the other type of You. This reflection allows us to think about the meaning of the principle of humanity in relation to personhood, and in relation to different forms of communities (natural, or inorganic (...) communities). It is an important question in the light of “conflicts” and tensions created by the environmental crisis we are facing today. The paper explains how to use the word “conflict” in this context and whether it is justified. (shrink)

Crime is a serious social problem, but its causes are not exclusively social. There is growing consensus that explaining and preventing it requires interdisciplinary research efforts. Indeed, the landscape of contemporary criminology includes a variety of theoretical models that incorporate psychological, biological and sociological factors. These multi-disciplinary approaches, however, have yet to radically advance scientific understandings of crime and shed light on how to manage it. In this paper, using conceptual tools on offer in the philosophy of science in combination (...) with theoretical work represented in this special volume of Psychology, Crime and Law, I provide some perspective on why explanatory progress in criminology has remained elusive and evaluate some positive proposals for attaining it. -/- . (shrink)

This paper argues against the claim that Frege is committed to an infinite hierarchy of senses. Carnap and Kripke, along with many others, argue the contrary; I expose where all such arguments go astray. Invariably these arguments assume (without citation) that Frege holds that sense and reference are always distinct. This is the fulcrum upon which the hierarchy is hoisted. The counter to this assumption is based on two important but neglected passages. The locution ‘indirect sense’ has no (...) ontological significance for Frege. It was just a ‘short expression’ (his term) to indicate that the customary relation between sign, sense, and reference is suspended in what he called the exception case of indirect context. Once the hierarchy is abandoned, the alleged problem of just what indirect sense is, as well as questions as to why Frege said so little about it and why he did not examine iterative indirect contexts are resolved. Of course, with no hierarchy, Davidson’s “unlearnability argument” turns out to be a non-starter. Some objections to my interpretation are considered and answered. Additionally, comparisons to Dummett’s one-level view of sense, which is similar to mine are made, as well as to some two-level views (Parsons and Skiba). (shrink)

Social egalitarianism holds that justice requires that people relate to one another as equals. To explain the content of this requirement, social egalitarians often appeal to the moral equality of persons. This leads to two very different interpretations of social egalitarianism. The first involves the specification of a conception of the moral equality of persons that is distinctive of the social egalitarian view. Social (or relational) egalitarianism can then claim that for people to relate as equals is for the relations (...) between them to conform to this conception of their moral equality. I will argue against this type of view. Instead, I will argue that social egalitarianism should propose a distinctive conception of social equality as a purely sociological phenomenon. I will show how this conception allows us to formulate the types of normative claims social egalitarianism should make. On this picture, social egalitarianism, instead of identifying social hierarchy as a distinctive kind of wrong, makes standard normative claims about a distinctive kind of social phenomenon. (shrink)

This paper seeks to resolve a fairly simple question in ethics: Why do seemingly reasonable people disagree about ethical problems? My paper seeks both to analyze this question and attempts to find a solution. My premise is that disagreement happens because of differences in hierarchical value ranking, or quite simply because some problems are more important to some people than others. Theories of choice, however, influenced by concepts such as "freedom of choice," conceal the hierarchical nature of our choices, leading (...) to confusion over the nature and degree of our ethical disagreements. I propose then that ethical disagreements can be reduced when we understand hierarchy as an essential element in moral choice theory. (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the (...) whole chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

The Hierarchy Problem in Physics and Its Resolution Through the Universal Law of Balance -/- The hierarchy problem in physics is a fundamental issue concerning the vast difference between the gravitational scale (Planck scale) and the electroweak scale. This discrepancy presents a challenge in understanding why the Higgs boson mass is so small compared to the Planck mass when quantum corrections should naturally drive it to much higher values. Various solutions have been proposed, such as supersymmetry, extra dimensions, (...) and composite Higgs models, but a definitive answer remains elusive. -/- Using the Universal Law of Balance, as formulated in my Universal Formula, the hierarchy problem can be understood as a manifestation of imbalance in the fundamental interactions governing the universe. The essence of the Universal Law of Balance is that all natural systems—whether physical, biological, or cognitive—must follow a dynamic equilibrium governed by interdependent feedback mechanisms. In this context, the extreme disparity between the fundamental forces indicates a state of disequilibrium that requires a deeper natural principle to restore balance. -/- The Universal Law of Balance and Hierarchical Scales -/- In nature, all stable systems—whether ecosystems, economies, or biological organisms—function within a balanced range of parameters. If an imbalance occurs, a natural feedback process either corrects it or results in structural instability and transformation. Applying this principle to physics, the discrepancy between the Planck scale and the electroweak scale suggests an underlying compensatory mechanism that has not yet been fully understood. -/- One possible interpretation within the Universal Formula is that the observed hierarchy reflects an inherent balance between different layers of reality, with each level influencing the other through feedback loops. The Higgs mass remains small not because of fine-tuning or accidental cancellations, but because nature inherently regulates hierarchical scales through self-balancing interactions. This could imply the presence of an as-yet-undiscovered feedback mechanism that dynamically stabilizes mass scales in a way that adheres to the universal balance principle. -/- Feedback Mechanisms in Fundamental Forces -/- In the biological and cognitive realms, decision-making and homeostasis operate under constant feedback loops. Similarly, in fundamental physics, the interactions between quantum fields must adhere to an intrinsic equilibrium. The hierarchy problem could be reinterpreted as a failure to recognize the hidden feedback process that naturally maintains the relative strength of forces. -/- This perspective aligns with theories that propose self-organized criticality, where nature fine-tunes itself dynamically rather than relying on arbitrary parameter adjustments. The universal balance principle suggests that rather than searching for a single missing component—such as a new symmetry or extra dimensions—we should look at how the interplay of known forces inherently maintains equilibrium. -/- Implications for the Future of Physics -/- If the Universal Law of Balance governs all interactions, then solutions to the hierarchy problem should focus on understanding how fundamental forces maintain equilibrium across different scales. Rather than assuming unnatural fine-tuning, physics should explore the possibility that the Higgs mass is a natural consequence of deeper balancing laws within the universe. -/- This could lead to new perspectives in high-energy physics, particularly in the search for a more unified framework that does not rely on artificial cancellations but instead follows a natural balancing principle inherent in all complex systems. The incorporation of the Universal Formula into theoretical physics could redefine how physicists approach unresolved problems, not just in the hierarchy of forces but also in the broader quest for a Theory of Everything. -/- In conclusion, the hierarchy problem is not merely a technical issue within particle physics—it reflects a deeper structural question about the balance of nature. By applying the Universal Law of Balance, we can gain a new perspective on why hierarchies exist and how they are maintained. This approach moves beyond fine-tuning paradoxes and points toward a more holistic understanding of physical reality, in which balance is the fundamental guiding principle of the universe. -/- . (shrink)

Despite a growing interest in and sympathy with Confucianism, there remains a stereotyped conception of Confucian civil order as a form of authoritarian hierarchy that is responsible for various oppressions in ancient China and is reprehensible from a modern egalitarian perspective. One central target of this modern criticism is the Confucian maxim of sangang 三綱, whose underlying idea is essential for regulating the relationship between sovereign and subject, father and son, and husband and wife in traditional Confucian society. Tu (...) Wei-ming translates sangang as the “Three Bonds” and argues that it is the “least defensible legacy of Confucian ethics” from the “modern egalitarian and liberal perspective.” For Tu.. (shrink)

Under which conditions are social relationships hierarchical, and under which conditions are they not? This article has three main aims. First, I will explain what this question amounts to by providing a more detailed description of the general phenomenon of social hierarchy. Second, I will provide an account of what social hierarchy is. Third, I will provide some considerations in favour of this account by discussing how it improves upon three alternative ways of thinking about social hierarchy (...) that are sometimes explicitly endorsed and sometimes suggested or presupposed in writings in philosophy and elsewhere. (shrink)

In my forthcoming book, How to Count Animals, More or Less (based on my 2016 Uehiro Lectures in Practical Ethics), I argue for a hierarchical approach to animal ethics according to which animals have moral standing but nonetheless have a lower moral status than people have. This essay is an overview of that book, drawing primarily from selections from its beginning and end, aiming both to give a feel for the overall project and to indicate the general shape of the (...) hierarchical position that I defend there. In this essay, I contrast the hierarchical approach with its most important rival (which holds that people and animals have the very same moral status), sketch the main idea behind one central argument for hierarchy, and briefly review three potentially troubling implications of the hierarchical view. I close with a discussion of a promising possible solution to the most worrisome of the three objections. (shrink)

It has recently become popular to suggest that questions of ontology ought be settled by determining, first, which fundamental things exist, and second, which derivative things depend on, or are grounded by, those fundamental things. This methodology typically leads to a hierarchical view of ontology according to which there are chains of entities, each dependent on the next, all the way down to a fundamental base. In this paper we defend an alternative ontological picture according to which there is no (...) ontological hierarchy. Such a picture appears counterintuitive (at least to many), in part because in the absence of a hierarchical structure to our world, there would be no structure apt to back metaphysical explanations. There are two reasons to suppose this is so. First, there would be no structure apt to back metaphysical explanations because there would be a fatal mismatch between the formal features of metaphysical explanation, on the one hand, and the structure of the world, on the other hand. Second, in the absence of an ontological hierarchy there would be no structure apt to back metaphysical explanations because the only connections that would obtain between relevant facts are mere correlational connections. But mere correlations are not the right kinds of relations to back metaphysical explanations: explanation requires something more. This paper aims to show that neither of these is a good reason to prefer a hierarchical view of ontology. (shrink)

Bryant’s paper, "A Logic of Multiplicities: Deleuze, Immanence, and Onticology," is useful for showing how the historical legacy of hierarchy in its many philosophical forms is still present, important, and, in fact, required even by those such as Bryant who would seek to deconstruct or ignore it. The following response will discuss Bryant’s presentation of his alternative position and throughout point out: a) the straw-man versions of hierarchy that Bryant employs; b) why what Bryant claims to be inherent (...) negatively in hierarchy is not the case; c) how Bryant’s position actually relies upon hierarchy for its own explication, and finally; d) the various principles of hierarchical metaphysics that are required in order to make sense of experience and reality. These latter include the notions that i) there are many kinds of hierarchy; ii) Being and Unity are prior to Multiplicity; iii) relation without substance is incoherent; iv) hierarchy is not inherently tyrannical; v) the distinction between essentially and accidentally ordered causal series is a real and useful one; and vi) the existence of hierarchy is more self evident than is flat ontology. (shrink)

In the early modern period the chain of being thesis was used by naturalists and philosophers to justify female subordination. My aim is to establish whether Catharine Trotter Cockburn's endorsement of this thesis entails that differences between sexes assigns differentiating places in the scale or not. I will review Locke’s formulation of the ontological scale first, because Cockburn refers to his description. Locke’s skepticism regarding our access to the real essence of substances hinders him from drawing unequivocal boundaries between species (...) and even within human species. However, he states that wives must subordinate to husbands on the basis of a higher capacity and strength naturally endowed to men. Cockburn’s understanding of the ontological scale rests on a realist conception where boundaries between species are clearly delimited because their nature is fixed and immutable. This insight into the ontological scale is employed to endorse natural equality between sexes, because if all members of a species share the same nature, they deserve equal treatment. Cockburn explains women subjection in terms of vicious notions and attitudes rooted in prejudice. (shrink)

This article deals with processes of accumulation of advantages and disadvantages in trajectories of social mobility from the working class, taking into account gender. In order to investigate how working-class trajectories in Buenos Aires Metropolitan Area are shaped by gender in terms of accumulation of (dis) advantages, we made biographical interviews to individuals with different social backgrounds within the working class. Families with more stable situations were able to transmit better conditions for spirals of accumulation of advantages to take place. (...) Among them, some men were able to take full advantage of them, while in women the obstacles to taking advantage were more recurrent. (shrink)

It is the focus of this paper to tackle the topic of how consumers affect their surrounding environment and, more specifically, how they can affect animal welfare. Through comparisons with the Darwinist survivalist consumption habits and Maslow´s hierarchy, our modern society´s needs and habits are evaluated. Finally a Utilitarian approach, with the goal of the rise of the conscious consumer, is suggested for our so-called advanced societies.

The paper places the work of G. Gaus into the tradition of political thought experimenting. In particular, his strategy of modeling moral decision by the heuristic device of idealized Members of the Public is presented as an iterated thought experiment, which stands in marked contrast with more traditional devices like the veil of ignorance. The consequences are drawn, and issues of utopianism and realism briefly discussed.

In both The Right and the Good and Foundations of Ethics, W. D. Ross maintains that any amount of the non-instrumental value of virtue outweighs any amount of the non-instrumental value of pleasure or avoidance of pain. The chapter raises two challenges to the status that Ross accords the value of virtue relative to the value of pleasure (pain). First, it argues that Ross fails to provide a good argument for thinking that virtue is always better than pleasure and that (...) it is in any case implausible to think that any amount of virtue (or avoidance of vice) is better than the avoidance of any amount of pain or suffering. Second, it argues that the inflexibility of Ross’s value theory exhibited in his claim about the relative value of virtue produces tension with and mars the attractive heterarchical structure of his theory of rightness or prima facie duties. (shrink)

The paper presents a truth-maker semantics for Strict/Tolerant Logic (ST), which is the currently most popular logic among advocates of the non-transitive approach to paradoxes. Besides being interesting in itself, the truth-maker presentation of ST offers a new perspective on the recently discovered hierarchy of meta-inferences that, according to some, generalizes the idea behind ST. While fascinating from a mathematical perspective, there is no agreement on the philosophical significance of this hierarchy. I aim to show that there is (...) no clear philosophical significance of meta-inferences above the first level. (shrink)

Some philosophers of fiction – most famously Jerold Levinson1 - have tried to argue that fictional narrators can never be identified with real authors. This argument relies on the claim that narration involves genuine assertion (not just the pretense of assertion that lacks truthfulness) and that real authors are not in a position to assert anything about beings on the fictional plain - given that they don’t rationally believe in their existence. This debate on the status of narrators depends on (...) the idea that fictional beings and beings in the real worlds reside, as it were, at different levels. The assumption that there is a gap separating the levels of fiction and reality serves as a rationale for the claim that real authors could not possibly be en rapport with the fictional characters that they create (e.g. entertain beliefs about them, etc.). (shrink)

This book begins with the question 'Who am I?' and immediately sets off in an astonishingly original direction. Why didn't anyone before Harding think of responding to this question like this? It's so obvious, once you see it. Harding presents a new vision of our place in the universe that uses the scientific method of looking to see what is true. It turns out that the truth about ourselves is not only true but also very good, and breathtakingly beautiful. We (...) live in a sacred, many-layered, living universe - or rather it lives in us. Though it was completed in 1950, this book is still ahead of its time. One day it will surely be widely recognised for its greatness: its all-encompassing vision, its originality and freshness, its depth of insight, its wide-ranging knowledge, the clarity and poetry of its language, its humanity. It is a world-view not dependent on local culture or religion, but on universally verifiable facts. It is also a world-view that respects our manifest differences whilst celebrating our underlying unity - the unity not just of oneself with other people but with all of life, indeed with the whole universe. Harding died in 2007 aged 97, leaving behind him an impressive body of work. He was a highly creative person who was passionate about - he was in love with - this living universe and the immortal treasure that abides at its centre - at our centre. "A work of the highest genius." C. S. Lewis. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using (...) analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

In 1655 La Peyrère was the first to substantially argue for and popularize polygenism—the view that God created multiple original human mating pairs in separate acts of creation with numerous created before Adam. Positing or rejecting polygenism has been central to modern theorizing about human types and origins. Prominent recent interpreters have maintained that La Peyrère’s polygenism does not imply a hierarchy of human types. This paper reconstructs La Peyrère’s account and, in opposition to the dominant view, argues that (...) his polygenism produces a human species hierarchy. The Adamite species is superior to the Pre-Adamite species in virtue of its material composition, mode of creation, and form. The upshot is that La Peyrère’s theological system posits a proto-racialist conception of human types. (shrink)

Quine’s way of dealing with the semantical paradoxes (Ways of Paradox, pp. 9-10) is criticized. The criticism is based on three premises: (1) no learnable language has infinitely many semantical primitives; (2) any language of which Quine’s theory is true has infinitely many semantical primitives; (3) English is a learnable language. The conclusion drawn is that Quine’s theory is not true of English.