Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non‐equivalent notions. In a hope to identify the “right” extension we consider the extensions appeared in the literature so far: the limit‐, level‐, Boolean and Wadge hierarchies of k ‐partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of Δ02‐measurable (...) k ‐partitions of the Baire space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (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)

" With this succinct formulation, Murray Bookchin launches his most ambitious work, The Ecology of Freedom.

Aquinas’ natural law theory contains a set of basic goods, such as survival, reproduction and the pursuit of truth. However, whether and how there is a hierarchical relationship among these goods remains disputed. Given the importance of Aquinas’ natural law theory for Christianity and the philosophy of law, this issue merits a closer investigation. By carefully examining various modern scholars’ theories and Aquinas’ texts, it is demonstrated that according to Aquinas, firstly, there are hierarchies of basic goods and sins; secondly, (...) these hierarchies are horizontal and vertical according to the order of participation and the dignity of substances, respectively.Contribution: This research reconsiders the modern debate over Aquinas’ hierarchical theory of basic goods and provides a more authentic understanding of Aquinas’ own view, which can be applied to his theory of sin. Aquinas’ natural law theory can hence be clarified in a more profound way. (shrink)

Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches (...) inevitably lead to the dilemma in question. In contrast, the present proposal sticks with classical semantic values, but allows the compositional rules associated with these to admit of exceptions. I show how such an approach can be developed systematically. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

This article shows that William E. Connolly’s work holds resources for projects of racial justice but must be revised to fully meet the challenge of racial inequality. There are two interrelated problems in Connolly’s theory: first, the drive to destabilize identity, for which he argues, rejects the need for collective identity, which is necessary in democratic politics. Furthermore, because domination renders identity unstable, the call to destabilize identity places too great a burden on already marginalized groups. The problem of destabilizing (...) identity is underwritten by a second problem: the white working class and its grievances occupy too important a position in Connolly’s analysis. This article uses insights provided by James Baldwin to amend Connolly’s contributions. The article argues that there is a need to destabilize the ‘we’ of American politics that allows white, male identity to occupy the ‘heart’ of liberal democracy. Baldwin’s insights help solve the problem of the ‘black hole’ at the center of liberal democracy which, Connolly argues, sustains fundamentalism and racial injustice. This article’s contribution is to amend Connolly’s work to meet the challenge of racial injustice, offer a novel reading of the place of political imagination in Baldwin’s work, and show how political imagination adds depth to conversations about democracy, racial justice, and pluralism. (shrink)

Large scale experiments at CERN’s Large Hadron Collider rely heavily on computer simulations, a fact that has recently caught philosophers’ attention. CSs obviously require appropriate modeling, and it is a common assumption among philosophers that the relevant models can be ordered into hierarchical structures. Focusing on LHC’s ATLAS experiment, we will establish three central results here: with some distinct modifications, individual components of ATLAS’ overall simulation infrastructure can be ordered into hierarchical structures. Hence, to a good degree of approximation, hierarchical (...) accounts remain valid at least as descriptive accounts of initial modeling steps. In order to perform the epistemic function Winsberg Model-based reasoning in scientific discovery. Kluwer Academic/plenum Publishers, New York, pp 255–269, 1999) assigns to models in simulation—generate knowledge through a sequence of skillful but non-deductive transformations—ATLAS’ simulation models have to be considered part of a network rather than a hierarchy, in turn making the associated simulation modeling messy rather than motley. Deriving knowledge-claims from this ‘mess’ requires two sources of justification: holistic validation :253–262, 2010; in Carrier M, Nordmann A Science in the context of application. Springer, Berlin, pp 115–130, 2011), and model coherence. As it turns out, the degree of model coherence sets HEP apart from other messy, simulation-intensive disciplines such as climate science, and the reasons for this are to be sought in the historical, empirical and theoretical foundations of the respective discipline. (shrink)

Through transatlantic contact and subsequent debates, the “humanity” of Amerindians was first established for Europeans according to the dictates of philosophical anthropology and theology. This hierarchical and colonial anthropology is problematic precisely because it normalizes a singular, indigenous way of “being human” as the only correct and universal formulation of the “human being,” i.e., Man. Consequently, people that live outside this constructed definition are exposed to dispossession, dehumanization, and genocide because they are deemed outside the bounds of Mankind. Through a (...) three-part analysis, this work will examine Bartolomé de Las Casas’ categorization of Amerindians though his formulation of “barbarianism,” compare this taxonomy with Orson Scott Card’s “Hierarchy of Foreignness,” and finally argue that Indigenous traditions of thought—as seen in “grounded normativity” and “place-thought”—allow not only for the dissolution of colonial anthropologies but also permit for a teleological suspension of Man. (shrink)

I analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings. I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todorčević’s square at the appropriate level. I also establish connections between these (...) hierarchies and the hierarchies of bounded and weak bounded forcing axioms. (shrink)

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. (...) Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight. (shrink)

The idea that nature is governed by laws and that the goal of science is to discover and formulate these laws, rose to prominence during the Scientific Revolution of the seventeenth century. It was manifestly held by the most significant actors of that revolution such as Galileo, Descartes, Kepler, Boyle, and Newton. But this idea was not new. In fact, it made an appearance in the Middle Ages, and it is likely to have emerged already in Antiquity.1In this paper we (...) pay close attention to the concept of law of nature in the writings of Roger Bacon, the outspoken Franciscan who promoted experimental science. We will be using Bacon as a test case to show that long before the... (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)

In spite of feminist recognition that hierarchical organizations are an important location of male dominance, most feminists writing about organizations assume that organizational structure is gender neutral. This article argues that organizational structure is not gender neutral; on the contrary, assumptions about gender underlie the documents and contracts used to construct organizations and to provide the commonsense ground for theorizing about them. Their gendered nature is partly masked through obscuring the embodied nature of work.jobs and hierarchies, common concepts in organizational (...) thinking, assume a disembodies and universal worker. This worker is actually a man; men's bodies, sexuality, and relationships to procreation and paid work are subsumed in the image of the worker. Images of men's bodies and masculinity pervade organizational processes, marginalizing women and contributing to the maintenance of gender segregation in organizations. The positing of gender-neutral and disembodied organizational structures and work relations is part of the larger strategy of control in industrial capitalist societies, which, at least partly, are built upon a deeply embedded substructure of gender difference. (shrink)

This paper argues for two propositions. (I) Large asymmetries of power, status and influence exist between economists. These asymmetries constitute a hierarchy that is steeper than it could be and steeper than hierarchies in other disciplines. (II) This situation has potentially significant epistemic consequences. I collect data on the social organization of economics to show (I). I then argue that the hierarchy in economics heightens conservative selection biases, restricts criticism between economists and disincentivizes the development of novel research. (...) These factors together constrain economics’ capacity to develop new beliefs and reduce the likelihood that its outputs will be true. (shrink)

The question whether Frege’s theory of indirect reference enforces an infinite hierarchy of senses has been hotly debated in the secondary literature. Perhaps the most influential treatment of the issue is that of Burge (1979), who offers an argument for the hierarchy from rather minimal Fregean assumptions. I argue that this argument, endorsed by many, does not itself enforce an infinite hierarchy of senses. I conclude that whether or not the theory of indirect reference can avail itself (...) of only finitely many senses is pending further theoretical development. (shrink)

T i 2 = S i +1 2 implies ∑ p i +1 ⊆ Δ p i +1 ⧸poly. S 2 and IΔ 0 ƒ are not finitely axiomatizable. The main tool is a Herbrand-type witnessing theorem for ∃∀∃ П b i -formulas provable in T i 2 where the witnessing functions are □ p i +1.

The paper is a study of the logic of existence, negation, and order in the Neoplatonic tradition. The central idea is that Neoplatonists assume a logic in which the existence predicate is a comparative adjective and in which monadic predicates function as scalar adjectives that nest the background order. Various scalar predicate negations are then identifiable with various Neoplatonic negations, including a privative negation appropriate for the lower orders of reality and a hyper-negation appropriate for the higher. Reversion to the (...) One can then be explained as the logical inference of hyper-negations from mundane knowledge. Part I develops the relevant linguistic and logical theory, and Part II defends Wolfson and the scalar interpretation against the more traditional Aristotelian understanding of Whittaker and others of reversion as intensional abstraction. (shrink)

The complexity class of [Formula: see text]-polynomial local search problems is introduced and is used to give new witnessing theorems for fragments of bounded arithmetic. For 1 ≤ i ≤ k + 1, the [Formula: see text]-definable functions of [Formula: see text] are characterized in terms of [Formula: see text]-PLS problems. These [Formula: see text]-PLS problems can be defined in a weak base theory such as [Formula: see text], and proved to be total in [Formula: see text]. Furthermore, the [Formula: (...) see text]-PLS definitions can be skolemized with simple polynomial time functions, and the witnessing theorem itself can be formalized, and skolemized, in a weak base theory. We introduce a new [Formula: see text]-principle that is conjectured to separate [Formula: see text] and [Formula: see text]. (shrink)

The paper provides a new argument against the classical invariance criterion for logical terms: if all terms with a permutation invariant extension qualify as logical, then for any arbitrary true contingent sentence K of the meta-language, there would be a logically true object-language sentence 'φ' such that K follows from the sentence 'φ is true'. Thus, many logically true sentences would be a posteriori. To prevent this fatal consequence, we propose to alter the invariance criterion: not only the term's extension, (...) but also its semantic clause must satisfy certain invariance conditions. The paper ends with the observation that the new criterion makes explicit the dependency of the classification of terms into logical and non-logical ones at the different levels of the Tarskian hierarchy of languages. (shrink)

In the context of [Formula: see text], we analyze a version of Hindman’s finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the [Formula: see text].

Four classes of naturally rare vascular plant species are described and classified, based on parameters of spatial distribution and longevity. Properties intrinsic to these time/space parameters are explored and an importance hierarchy of causes of rarity is proposed for each class. These hierarchies serve as the basis for a predictive classification. Human causes of rarity such as habitat destruction and taxonomic difficulties are not considered in detail here but are discussed as confounding factors in the elucidation of rarity in (...) vascular plants. Several examples are provided to illustrate this classification and provide testable hypotheses concerning the origins of natural rarity in plant species. (shrink)

Most biologists use the Linnaean system for constructing classifications of the organic world. The Linnaean system, however, has lost its theoretical basis due to the shift in biology from creationist and essentialist tenets to evolutionary theory. As a result, the Linnaean system is both cumbersome and ontologically vacuous. This paper illustrates the problems facing the Linnaean system, and ends with a brief introduction to an alternative approach to biological classification.

Incels (involuntary celibates) are part of a broader misogynistic culture known as the manosphere. Some communities within the manosphere, including incels, promote gender-based violence through misogynistic rhetoric and ideology. Incels are men who struggle to form romantic relationships and thus seek solace in online forums to find a sense of purpose and community. The community is organised around an ideology and a hierarchical classification of members. This paper presents a computational linguistic analysis of the utterances made within the community. We (...) analyse the linguistic patterns of six different ranks of users: paragons, high-rank users, low-rank users, greycels, banned users, and self-banned/deleted users. We conducted an analysis of the sentiments expressed between ranks and of the affective attitude of posters when discussing a variety of topics. We then we analysed linguistic features, also conditioned on the rank of the poster. These analyses reveal qualitative differences between users of different ranks in how they express themselves and their sentiments. Finally, we trained models based on the linguistic features of users’ posts and show that already based on this information it is possible to predict the rank of users. Overall, our results indicate that the incel community has developed distinctive linguistic patterns to disseminate their ideology and that these linguistic patterns vary according to the rank of an incel within the community. This methodology offers a robust framework for studying similar echo chamber-like communities. (shrink)

We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.

A trenchant defense of hierarchy in different spheres of our lives, from the personal to the political All complex and large-scale societies are organized along certain hierarchies, but the concept of hierarchy has become almost taboo in the modern world. Just Hierarchy contends that this stigma is a mistake. In fact, as Daniel Bell and Wang Pei show, it is neither possible nor advisable to do away with social hierarchies. Drawing their arguments from Chinese thought and culture (...) as well as other philosophies and traditions, Bell and Wang ask which forms of hierarchy are justified and how these can serve morally desirable goals. They look at ways of promoting just forms of hierarchy while minimizing the influence of unjust ones, such as those based on race, sex, or caste. Which hierarchical relations are morally justified and why? Bell and Wang argue that it depends on the nature of the social relation and context. Different hierarchical principles ought to govern different kinds of social relations: what justifies hierarchy among intimates is different from what justifies hierarchy among citizens, countries, humans and animals, and humans and intelligent machines. Morally justified hierarchies can and should govern different spheres of our social lives, though these will be very different from the unjust hierarchies that have governed us in the past. A vigorous, systematic defense of hierarchy in the modern world, Just Hierarchy examines how hierarchical social relations can have a useful purpose, not only in personal domains but also in larger political realms. (shrink)

The unreduced solution to the arbitrary interaction problem, absent in the standard theory framework, reveals many equally real and mutually incompatible system configurations, or "realizations". This is the essence of universal dynamic undecidability, or multivaluedness, and the ensuing causal randomness (unpredictability), non-computability, irreversible time flow (evolution, emergence), and dynamic complexity of every real system, object, or process. This creative undecidability of real-world dynamics provides causal explanations for "quantum mysteries", relativity postulates, cosmological problems, and the huge efficiency of high-complexity phenomena, such (...) as life, intelligence, and consciousness, giving rise to extended applications, far beyond the critical limits of usual science paradigm. (shrink)

Abstractabstract:This paper intervenes in a contemporary debate on the animal ethics of the Brethren of Purity's (Iḫwān al-Ṣafāʾ) epistle on animals. I argue that they present a case for justice for animals by rejecting the fallacious link between ontological superiority and moral superiority. Since human beings are vice-regents of God and since the rational soul is the vice-regent, the Brethren's account of human beings as superior in virtue of their rationality establishes a moral obligation toward animals. The Brethren develop this (...) account partially under the influence of the Muʿtazilī theological tradition, and as a result, their position falls in line with other positions on justice for animals found during their time. Even on the issue of animal use, the Brethren maintain that the human need for animal labor emphasizes the obligation to treat animals justly. In the end, the greater rational capacity of human beings entails greater moral responsibility toward animals, not moral impunity. (shrink)

Gynecological surgery prompts women to consider the meanings of their uteruses and ovaries, generally taken for granted as “natural” components of female bodies. Analysis of 44 in-depth interviews with women who underwent hysterectomy indicates that a preponderance of respondents conceptualized a socially constructed hormonal hierarchy based on the degree to which ovaries were excised in the course of surgery. While retained ovaries may not always produce actual physiological benefits, respondents placed great symbolic value on ovaries as the source of (...) female normality. This reflects cultural understandings that hormones produced by the ovaries are the essential determinants of sexual difference. The interweaving of social constructionist and biological perspectives in respondents' narratives helps to elucidate the complicated interaction between the material body and the social body. (shrink)