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)

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 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)

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)

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)

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.

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)

Research programs in empirical psychology from the past two decades have revealed implicit biases. Although implicit processes are pervasive, unavoidable, and often useful aspects of our cognitions, they may also lead us into error. The most problematic forms of implicit cognition are those which target social groups, encoding stereotypes or reflecting prejudicial evaluative hierarchies. Despite intentions to the contrary, implicit biases can influence our behaviours and judgements, contributing to patterns of discriminatory behaviour. These patterns of discrimination are obviously wrong and (...) unjust. But in remedying such wrongs, one question to be addressed concerns responsibility for implicit bias. Unlike some paradigmatic forms of wrongdoing, such discrimination is often unintentional, unendorsed, and perpetrated without awareness; and the harms are particularly damaging because they are cumulative and collectively perpetrated. So, what are we to make of questions of responsibility? In this article, we outline some of the main lines of recent philosophical thought, which address questions of responsibility for implicit bias. We focus on (a) the kind of responsibility at issue; (b) revisionist versus nonrevisionist conceptions of responsibility as applied to implicit bias; and (c) individual, institutional, and collective responsibility for implicit bias. (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)

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)

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)

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)

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)

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)

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.

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)

In both The Right and the Good and The 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)

Le contrôle de constitutionnalité, dont la magistrature parlementaire de l’Ancien Régime revendiquait le plein droit, n’était pas fondé uniquement sur les lois fondamentales du royaume, mais sur l’ensemble des principes (« les maximes ») tirés de la « Tradition ». Cette dernière était composée en premier lieu par le droit divin et le droit naturel, c’est-à-dire par des systèmes juridiques qui nécessitaient, tous les deux, une interprétation juridictionnelle ‘sapientiale’. Cette activité interprétative était ‘révélatrice’ d’un corpus de valeurs métaphysiques à laquelle (...) seule la Scientia Juris des magistrats pouvait puiser. Mais dans la sphère de la Tradition juridique rentraient aussi le « dépôt légal », c’est-à-dire l’ensemble de toutes les lois, même des lois ainsi dites « ordinaires », c’est-à-dire celles qui avaient été produites par la simple manifestation de volonté souveraine d’un roi prédécesseur « car tel avait été son plaisir » (moderne formulation du brocarde de droit romain : « quidquid principi placuit legis habet vigorem »). Ainsi la juridiction parlementaire donnait lieu à un jugement de constitutionnalité qui était normalement exercé de manière très flexible par le corps de la magistrature, dépendant des circonstances et des intérêts politiques momentanés des situations juridiques qu’elle voulait protéger. La hiérarchie des normes était ainsi un formidable instrument de protection de cet ordre juridique dont les legum doctores se sentaient les tuteurs. Elle était, donc, directement liée au gouvernement politique des juges. (shrink)

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)

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.

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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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)

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.

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)

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)

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized conceptual dimensions: (...) prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (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.

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)

Implicatures are described as particular forms reasoning from best explanation, in which the para-digm of possible explanations consists of the possible semantic interpretations of a sentence or a word. The need for explanation will be shown to be triggered by conflicts between presumptions, namely hearer’s dialogical expectations and the presumptive sentence meaning. What counts as the best explanation can be established on the grounds of hierarchies of presumptions, dependent on dialogue types and interlocutors’ culture.

Both mindreading and stereotyping are forms of social cognition that play a pervasive role in our everyday lives, yet too little attention has been paid to the question of how these two processes are related. This paper offers a theory of the influence of stereotyping on mental-state attribution that draws on hierarchical predictive coding accounts of action prediction. It is argued that the key to understanding the relation between stereotyping and mindreading lies in the fact that stereotypes centrally involve character-trait (...) attributions, which play a systematic role in the action–prediction hierarchy. On this view, when we apply a stereotype to an individual, we rapidly attribute to her a cluster of generic character traits on the basis of her perceived social group membership. These traits are then used to make inferences about that individual’s likely beliefs and desires, which in turn inform inferences about her behavior. (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)

Abstract: Without directly taking sides in the design/anti-design debate, this paper defends the following position: the assertion that biological evolution “is” design-free presupposes the possibility to model biological evolution in a design-free way. Certainly, there are design-free models of evolution based on cumulative selection. But “to model” is a verb denoting “modeling” as the process leading to a model. So any modeling – trivially – needs “previous human design.” Nevertheless, contrary to other scientific activities which legitimately consider models while (...) ignoring the process leading to them, evolution theory must take into account the human activity of modeling required by its corresponding models. (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)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different (...) inferential level. Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)