: The paper presents some mathematical aspects of the question of reducibility of relations. After giving a formal definition of reducibility we present the basic result (due to Herzberger) to the effect that relations of valency at least 3 are always reducible if the cardinality of the relation is at most equal to the cardinality of the underlying set (which is automatically the case if this set is infinite). In contrast to this, if the term "reduction" (...) is given a practicable form, relations on finite sets are "generically" irreducible, as is shown by a simple counting argument. Next we discuss the question of an "intrinsic" criterion for reducibility. Finally we propose a scheme for the graphic representation of reductions. (shrink)

Aufgrund seiner Bemerkungen über die Metaphysik und die Logik wird Leibniz oft die These, die Relationen seien auf Eigenschaften zurückführbar, zugeschrieben. Russell u. a. haben diese These, vorwiegend unter Bezugnahme auf asymmetrische Relationen, bestritten. Einige genaue Formulierungen der These erweisen sich in der Tat als falsch. Dennoch begründet die Leibnizsche Ontologie eine Version der Typenlogik, in der eine Form der Reduzierung bewiesen werden kann. Die hier verwendete Methode zeigt auch, wie zwei an sich mögliche Monaden nicht zusammen existieren können, also (...) wie die Inkompossibilität entstehen kann. (shrink)

Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of (...) equivalence modulo the nonstationary ideal restricted to regular cardinals in the space 2κ is Σ11-complete. We finish by showing that, for Π21-indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is Σ11-complete. (shrink)

We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

We study the Borel reducibility of isomorphism relations in the generalized Baire space. In the main result we show for inaccessible κ, that if T is a classifiable theory and is stable with the orthogonal chain property (OCP), then the isomorphism of models of T is Borel reducible to the isomorphism of models of.

A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to the partial case: every partially numbered set can be embedded in a set which results from (...) the given set by adding one point and which is enumerated by a total and complete numbering. As is shown, the degrees of complete numberings of the extended set also form an upper semilattice. Moreover, both semilattices are isomorphic.This is not so in the case of the usual, weaker reducibility relation for partial numberings which allows the reduction function to transfer arbitrary numbers into indices. (shrink)

This article reports a study carried out in order to measure how semantic factors affect reductions in the difficulty of the Chinese Ring Puzzle (CRP) that involves removing five objects according to a recursive rule. We hypothesised that semantics would guide inferences about action decision making. The study involved a comparison of problem solving for two semantic isomorphic variants of the CRP ( fish and fleas ) with problem solving for the puzzle's classic variant (the Balls and Boxes problem; Kotovsky (...) learning involves generalising the relations within a coherent, interconnected whole that makes up the puzzle's rules. It seems that semantics make it easier for the puzzle's elements to be grouped together within coherent, meaningful wholes, which reduces relational complexity and facilitates problem solving. (shrink)

Fifteen philosophers offer new essays exploring the metaphysics of relations from antiquity to the present day. They address topics as diverse as ancient and medieval reasons for scepticism about polyadic properties; recent attempts to reduce causal and spatiotemporal relations; recent work on the directionality of relational properties; powers ontologies and their associated problems; whether the most promising interpretations of quantum mechanics posit a fundamentally relational world; and whether the very idea of such a world is coherent. From those (...) who question whether there are relational properties at all, to those who hold they are a fundamental part of reality, The Metaphysics of Relations covers a broad spectrum of positions on the nature and ontological status of relations, from antiquity to the present day. (shrink)

We show that in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov–Hausdorff distance cannot be reduced to the equivalence relation defined by any Polish action.

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...) obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities. (shrink)

I am pleased to have been able to vindicate Plato from the oft-rehearsed charge of not having distinguished relations from qualities. Not only does Phaedo 102B7-C4 show quite clearly that he did make the proper distinction, but the theory of relations he adumbrated there is logically sound and ontologically viable. Furthermore, it is refreshing to think of relations not as Forms or universals, but as chains of ontologically tied universals.Naturally, now that we have a clear understanding of (...) Plato's Phaedo theory of relations and relational facts there is plenty of work to do. We must examine the other dialogues for alterations or even preservation of that theory. Moreover, there are those arguments of Aristotle that purport to reduce Plato's Theory of Forms to absurdity on account of relations. But of this I shall say more at some other time. (shrink)

We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and dark (...) degrees are definable in $\operatorname {\mathrm {\mathbf {ER}}}$. We show that every equivalence relation has continuum many self-full strong minimal covers, and that $\mathbf {d}\oplus \mathbf {\operatorname {\mathrm {\mathbf {Id}}}_1}$ needn’t be a strong minimal cover of a self-full degree $\mathbf {d}$. Finally, we show that the theory of the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ as well as the theories of the substructures of light degrees and of dark degrees are each computably isomorphic with second-order arithmetic. (shrink)

Negative self-referential processing has fruitfully been studied in unipolar depressed patients, but remarkably less in patients with bipolar disorder (BD). This exploratory study examines the relation between task-based self-referential processing and depressive symptoms in BD and their possible importance to the working mechanism of mindfulness-based cognitive therapy (MBCT) for BD. The study population consisted of a subsample of patients with BD (n = 49) participating in an RCT of MBCT for BD, who were assigned to MBCT + TAU (n = (...) 23) or treatment as usual (TAU) (n = 26). Patients performed the self-referential encoding task (SRET), which measures (1) positive and (2) negative attributions to oneself as well as (3) negative self-referential memory bias, before and after MBCT + TAU or TAU. At baseline, all three SRET measures were significantly related to depressive symptoms in patients with BD. Moreover, repeated measures analyses of variance revealed that negative self-referential memory bias diminished over time in the MBCT + TAU group, compared with the TAU group. Given the preliminary nature of our findings, future research should explore the possibly mediating role of reducing negative self-referential memory bias in preventing and treating depressive symptoms in BD through MBCT. (shrink)

Medical decision making when a patient cannot participate is complicated by the question of whose voice should be heard. The most common answer to this question is that “autonomy” is paramount, and therefore it is the voice of the unwell person that should be given priority. Advance care planning processes and practices seek to capture this sentiment and to allow treatment preferences to be documented and decision makers to be nominated. Despite good intentions, advance care planning is often deficient because (...) it is unable to facilitate a relational approach to decision making in cases when the patient’s competence is reduced. In this article we present findings from a study of the ways in which older people and their significant others understand decision making in such circumstances. Critical to the participants’ understanding was the emergent concept of “relational knowing,” a concept that is poorly articulated in the advance care planning literature. Our findings suggest that the dominant understanding of decision making in conditions of impaired competence is incomplete and obscures much of what matters to people. We conclude that, having recognized a broader set of ethical concerns, it is necessary to develop a relational and narrative based approach that applies in appropriate settings. (shrink)

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a (...) new characteristic of relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a (...) relation supervenes on its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations. (shrink)

We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or.

Abstract:This article builds on Bellucci’s and Murphey’s accounts of Peirce’s early logic of signs by making a pair of contributions to the literature on Peirce’s reduction of illation to the sign relation. First, I reinvesti-gate the connection between the structure of inference and the representative relation, relying here on Peirce’s early accounts of sign inference from 1865 and 1866. Second, with the development of Peirce’s theory of inquiry in mind, I elucidate the implications of Peirce’s early view of sign inference. (...) These contributions deepen our understanding of Fisch’s claim that the Illustrations series “is thought out within the framework of the doctrine of signs.”. (shrink)

Hume and Quine argue that human beings do not have access to general knowledge, that is, to general truths . The arguments of these two philosophers are premised on what Jaakko Hintikka has called the atomistic postulate. In the present work, it is shown that Hume and Quine in fact sanction an extreme version of this postulate, according to which even items of particular knowledge are not directly accessible in so far as they are relational. For according to their fully (...) realized systems, human beings do not initially perceive any relations, or similar epistemological elements that can associate or combine terms on which a relational or general knowledge claim may be based. Nor, likewise, do human beings perceive the relations or the associations themselves as separate entities. ;In Chapters 1 and 2, respectively, it is shown precisely why Hume and Quine deny that human beings initially perceive either such associative elements or associations in general. Concomitantly, it is made clear why Hume's and Quine's respective epistemologies preclude human beings from initially apprehending not only general knowledge, but particular relational knowledge as well. But this is not to say that Hume and Quine do not think we can eventually acquire such associative elements and correspondingly, knowledge. Rather, Hume and Quine do provide an account of knowledge, but one that holds all relational and connective elements to be constructed by the human mind. In Hume's case, they are constructed by the imagination. In Quine's case, we are never told quite how this construction occurs, although the evidence suggests that Quine implicitly relies on a faculty similar to Hume's imagination. ;In the final chapter of this thesis, it is argued that both Hume and Quine must be read as philosophers who justify knowledge by reducing its possibility to a psychological faculty of construction, as well as to a few concepts of intuitively grasped relations. By way of conclusion, it is shown that this makes Quine's naturalism the psychological heir to Carnap's Aufbau. (shrink)

We study the degree structure of the ω-c.e., n-c.e., and Π10 equivalence relations under the computable many-one reducibility. In particular, we investigate for each of these classes of degrees the most basic questions about the structure of the partial order. We prove the existence of the greatest element for the ω-c.e. and n-computably enumerable equivalence relations. We provide computable enumerations of the degrees of ω-c.e., n-c.e., and Π10 equivalence relations. We prove that for all the degree (...) classes considered, upward density holds and downward density fails. (shrink)

In the Deese-Roediger/McDermott paradigm, distinctive encoding of list items typically reduces false recognition of critical lures relative to a read-only control. This reduction can be due to enhanced item-specific processing, reduced relational processing, and/or increased test-based monitoring. However, it is unclear whether distinctive encoding reduces false recognition in a selective or global manner. To examine this question, participants studied DRM lists using a distinctive item-specific anagram generation task and then completed a recognition test which included both DRM critical lures and (...) either strongly related lures or weakly related lures. Compared to a read-control group, the generate groups showed increased correct recognition and decreased false recognition of all lure types. We then estimated the separate contributions of encoding and retrieval processes using signal-detection indices. Generation improved correct recognition by both increasing encoding of memory information for list words and by increasing memory monitoring at test. Generation reduced false recognition by reducing the encoding of memory information and by increasing memory monitoring at test. The reduction in false recognition was equivalent for critical lures and related lures, indicating that generation globally reduces the encoding of related non-presented items at study, while globally increasing list-theme-based monitoring at test. (shrink)

Background Retraction is a mechanism for alerting readers to unreliable material and other problems in the published scientific and scholarly record. Retracted publications generally remain visible and searchable, but the intention of retraction is to mark them as “removed” from the citable record of scholarship. However, in practice, some retracted articles continue to be treated by researchers and the public as valid content as they are often unaware of the retraction. Research over the past decade has identified a number of (...) factors contributing to the unintentional spread of retracted research. The goal of the Reducing the Inadvertent Spread of Retracted Science: Shaping a Research and Implementation Agenda (RISRS) project was to develop an actionable agenda for reducing the inadvertent spread of retracted science. This included identifying how retraction status could be more thoroughly disseminated, and determining what actions are feasible and relevant for particular stakeholders who play a role in the distribution of knowledge. -/- Methods These recommendations were developed as part of a year-long process that included a scoping review of empirical literature and successive rounds of stakeholder consultation, culminating in a three-part online workshop that brought together a diverse body of 65 stakeholders in October–November 2020 to engage in collaborative problem solving and dialogue. Stakeholders held roles such as publishers, editors, researchers, librarians, standards developers, funding program officers, and technologists and worked for institutions such as universities, governmental agencies, funding organizations, publishing houses, libraries, standards organizations, and technology providers. Workshop discussions were seeded by materials derived from stakeholder interviews (N = 47) and short original discussion pieces contributed by stakeholders. The online workshop resulted in a set of recommendations to address the complexities of retracted research throughout the scholarly communications ecosystem. -/- Results The RISRS recommendations are: (1) Develop a systematic cross-industry approach to ensure the public availability of consistent, standardized, interoperable, and timely information about retractions; (2) Recommend a taxonomy of retraction categories/classifications and corresponding retraction metadata that can be adopted by all stakeholders; (3) Develop best practices for coordinating the retraction process to enable timely, fair, unbiased outcomes; and (4) Educate stakeholders about pre- and post-publication stewardship, including retraction and correction of the scholarly record. -/- Conclusions Our stakeholder engagement study led to 4 recommendations to address inadvertent citation of retracted research, and formation of a working group to develop the Communication of Retractions, Removals, and Expressions of Concern (CORREC) Recommended Practice. Further work will be needed to determine how well retractions are currently documented, how retraction of code and datasets impacts related publications, and to identify if retraction metadata (fails to) propagate. Outcomes of all this work should lead to ensuring retracted papers are never cited without awareness of the retraction, and that, in public fora outside of science, retracted papers are not treated as valid scientific outputs. (shrink)

We introduce a game for Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.

In "Nondomination and the Limits of Relational Autonomy," Danielle Wenner aims to achieve the political goals of relational theorists through a more effective means. This is a worthy aspiration. She believes the neorepublican conception of freedom as nondomination "can best promote the aims embodied in the political project of feminist theorists", including reducing conditions of oppression, and do it in a way that avoids the conceptual problems inherent in relational autonomy. While I appreciate the pragmatism and clarity of her argument, (...) in this commentary I raise a challenge to the freedom as nondomination approach, specifically Wenner's claim that it can avoid making substantive value judgments. I... (shrink)

In a Realist ontology relations are subsisting or existing entities distinct from ordinary things. Idealists claim that the notion of relations is subject to a vicious infinite regress. Nominalists claim that relations are particularized instances. In an attempt to search for the roots of a Realist conception of relations and to meet these challenges I investigate Plato's conception of relations in the Phaedo. ;Against the current of a majority of Plato scholars, Castaneda finds evidence for (...) a distinction between relations and properties at Phaedo 102 b-d. I enter the debate on Castaneda's side and find support for his interpretation of the passage in the context of the dialogue as a whole. The relation--quality distinction resolves the paradox of Simmias being both taller than Socrates and shorter than Phaedo at the same time, since Plato possesses relational characteristics of tallness and shortness, which are not contraries unlike the the contrary properties of hot and cold which could not coexist in an individual. Gallop offers the alternative essence--accident distinction which also resolves the paradox since tallness and shortness as accidents may coexist. The latter distinction however Aristotelianizes Plato. I have shown how the essence--accident distinction is incompatible with Plato's theory of Forms, as it leads to such odd conclusions as the admittance of accidental Forms. ;Castaneda claims that Plato reduces relations to Form-chains in which individuals participate in pairs. I offer the alternative of Plato's positing of relational Forms as distinct from monadic Forms. I survey the corpus of Platonic dialogues in search of support for the distinction between relations and properties. I find that in the Statesman there is a distinction between two types of Forms which generates the distinction between monadic Forms and relational Forms. ;I conclude that there is ample evidence in Plato's dialogues and in Aristotle's assessment of Plato to ascribe this distinction to Plato. Plato's explanation of relations in terms of Forms, which have the highest grade of reality for him, sets up the basis for any Realist theory of relations--for reductionist theories reducing relations to relational properties or some other subsisting entities, as well as for the irreducible concept of relations as abstract subsisting entities. (shrink)

Although statistically significant correlations have been found among political, economic, and social indices, on the one hand, and measures of sociosexuality, on the other, it is likely that these correlations are second-order effects. Underpinning the reproductive freedom associated with higher sociosexuality are factors more closely related to biology, namely, easy access to safe, effective contraception and reproductive medical care.

Ash, C.J., Generalizations of enumeration reducibility using recursive infinitary propositional sentences, Annals of Pure and Applied Logic 58 173–184. We consider the relation between sets A and B that for every set S if A is Σ0α in S then B is Σ0β in S. We show that this is equivalent to the condition that B is definable from A in a particular way involving recursive infinitary propositional sentences. When α = β = 1, this condition is that B (...) is enumeration reducible to A. We establish further generalizations involving infinitely many sets and ordinals. (shrink)

Empirical evidence suggests that mindfulness, psychological flexibility, and addiction are interrelated in decision making. In our study, we investigated the relationship of the behavioral profile, composed of mindfulness and psychological flexibility, and smoking status on delay and probability discounting. We demonstrated the interaction of the behavioral profile of mindfulness and psychological flexibility and smoking status on delay discounting. We found that individuals who smoked and displayed higher mindfulness and psychological flexibility devalued rewards at a slower rate, compared to smokers with (...) a lower profile. Importantly, in those with a higher profile, smokers discounted rewards no differently than nonsmokers. Smokers with a lower profile did display, however, increased impulsivity, compared to nonsmokers. These results suggest that behavioral interventions aiming to modify the behavioral profile with regard to mindfulness and psychological flexibility can indeed support the regulation of elevated impulsivity in smokers to equate with that of nonsmokers. In probability discounting, we observed that individuals with a higher profile displayed lower discounting rates, i.e., were less risk-averse, with no other significant main effect or interaction. (shrink)

In order to apply known general theorems about the effective properties of recursive structures in a particular recursive structure, it is necessary to verify that certain decidability conditions are satisfied. This requires the determination of when certain relations, called back and forth relations, hold between finite strings of elements from the structure. Here we determine this for recursive reduced abelian p-groups, thus enabling us to apply these theorems.

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

Smell perception plays an important role in eating behavior and might be involved in body weight gain. Since a body of literature implies that olfactory perception and function is hampered in obesity, we here investigate neuroanatomical correlates of this phenomenon. We assessed olfactory bulb volume with magnetic resonance imaging in 67 healthy participants with a body mass index from 18.9 to 45.4 kg/m2. Moreover, we obtained psychophysiological data on olfactory ability and self-report measurements on eating behavior. Additionally, we collected parameters (...) associated with metabolic health in obesity to investigate recently proposed mechanistic explanatory models of why olfaction may be altered in obesity. We showed that OB volume was significantly lower in participants with obesity when compared to those of normal weight. Moreover, we found weak to moderate negative correlations between OB volume and BMI and related measures of metabolic health, especially leptin, body fat percentage, waist-height ratio and insulin resistance. However, neither OB volume nor BMI were related to olfactory function in our young and healthy sample. Nevertheless, our results provide first indications that obesity is associated with brain anatomical changes in the OBs. (shrink)

Most properties have comparatives, which are relations. For instance, the property of width has the comparative relation denoted by `_ is wider than _'. Let us say a property is reducible to its comparative if any statement that refers to the property has the same meaning as another statement that refers to the comparative instead. Width is not reducible to its comparative. To be sure, many statements that refer to width are reducible: for instance, `The Mississippi is wide' means (...) the same as `The Mississippi is wider than most rivers'. But some statements that refer to width are not reducible: for instance, `Electrons have zero width' is not. A property is not reducible to its comparative if it has absolute degrees, and specifically an absolute zero. A property's comparative relation places things in an order from those that have the property least to those that have it most. If there is an absolute zero point somewhere in this ordering, the property is not reducible to its comparative. For width, there is an absolute zero at one end of the ordering, so width is not reducible. The property of goodness is reducible to its comparative, betterness. In particular, there is no absolute zero of goodness. Things are ordered by betterness – some things are better than others – but nothing is absolutely good or absolutely bad. This is an exaggeration. In certain applications, goodness does have absolute degrees of a sort, and an absolute zero. For instance, it makes sense to say an event is good, and another event bad. These are absolute degrees of a sort, but they are themselves reducible to betterness. To say an event is good simply means the event is better than what would otherwise have happened. The goodness of lives has a different sort of absolute zero. Lives are ordered by betterness; some lives are better than others. We can make sense of the question `Where in this ordering is the division between lives that are good and those that are bad?' The division between good and bad lives is again reducible to betterness. To say a person's life is good means it is better that the person should continue living, rather than that she should die. Or it may mean it is better that her life should be lived rather than that it should never have been lived at all. As it is often put: a good life is a life worth living. Derek Parfit appears to attach a different sense to the idea of a good life. He appears to mean a life that contains a preponderance of good things (such as pleasure) over bad things (such as pain). If a life contains no good things and no bad things, it has zero goodness in this sense. In this sense, absolute goodness and the absolute zero of goodness are not reducible to betterness. However, this is a naturalistic sense of goodness, and it is subject to the open-question objection. If a life contains no good things and no bad things, it is an open question whether it has zero goodness. It might, for instance, be a bad thing that this life should be lived. In discussing the evil of death, some philosophers seem to have been searching for an absolute goodness that is not reducible to betterness. Thomas Nagel speaks of an asymmetry between what is good about life and what is bad about death. But if a person's life is good, that only means it would be better that she should continue living than that she should die. And if a person's death would be bad, that only means it would be worse that she should die than that she should continue living. So there can be no asymmetry. (shrink)

This article argues that blacks should reject integration on self-protective and solidarity grounds. It distinguishes two aspects of black devaluation: a ‘stigmatization’ aspect that has to do with the fact that blacks are subject to various forms of discrimination, and an aesthetic aspect (‘phenotypic devaluation’) that concerns the aesthetic devaluation of characteristically black phenotypic traits. It identifies four self-worth harms that integration may inflict, and suggests that these may outweigh the benefits of integration. Further, it argues that, while the integrating (...) process may reduce stigmatization, there is less reason to think that it can do the same for phenotypic devaluation. (shrink)

The present paper is a generalization and further development of the theory of Kernel measures of reducibility axioms formulated in [1], [2], [3] in. the years 1969–1973. In this paper logical connections of Kernel measures with some set-theoretical notions are studied and some suggestions related to these connections are formulated.

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.

We study the notion of polynomial-time relation reducibility among computable equivalence relations. We identify some benchmark equivalence relations and show that the reducibility hierarchy has a rich structure. Specifically, we embed the partial order of all polynomial-time computable sets into the polynomial-time relation reducibility hierarchy between two benchmark equivalence relations Eλ and id. In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.

We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.§1. Introduction. For X a Polish space and E a Borel equivalence relation on X, a classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c = c. To be of any value we would expect I and c to (...) be “explicit” or “definable”. The theory of Borel equivalence relations investigates the nature of possible invariants and provides a hierarchy of notions of classification.The following partial ordering is fundamental in organizing this study. Given equivalence relations E and F on X and Y, resp., we say that E can be Borel reduced to F, in symbolsif there is a Borel map f : X → Y with xEy ⇔ fFf. Then if is an embedding of X/E into Y/F, which is “Borel”.Intuitively, E ≤BF might be interpreted in any one of the following ways: The classi.cation problem for E is simpler than that of F: any invariants for F work as well for E. One can classify E by using as invariants F-equivalence classes. The quotient space X/E has “Borel cardinality” less than or equal to that of Y/F, in the sense that there is a “Borel” embedding of X/E into Y/F. (shrink)

Ever since the hard problem of consciousness (Chalmers, 1996, 1995) first entered the scene in the debate over consciousness many have taken it to show the limitations of a scientific or naturalist explanation of consciousness. The hard problem is the problem of explaining why there is any experience associated with certain physical processes, that is, why there is anything it is like associated with such physical processes? The character of one’s experience doesn’t seem to be entailed by physical processes and (...) so an explanation which can overcome such a worry must (1) explain how physical processes give rise to experience (explain the entailment), (2) give an explanation which doesn’t rely on such physical processes, or (3) show why the hard problem is misguided in some sense. Recently, a rather ambitious and novel theory of consciousness has entered the scene – Integrated Information Theory (IIT) of Consciousness (Oizumi et al., 2014; Tononi, 2008; Tononi et al., 2016) – and proposes that consciousness is the result of a specific type of information processing, what those developing the theory call integrated information. The central aim of this dissertation is to philosophically investigate IIT and see whether it has the ability to overcome the hard problem and related worries. I then aim to use this philosophical investigation to answer a set of related questions which guide this dissertation, which are the following: Is it possible to give an information-theoretic explanation of consciousness? What would the nature of such an explanation be and would it result in a novel metaphysics of consciousness? In this dissertation, I begin in chapter one by first setting up the hard problem and related arguments against the backdrop of IIT (Mindt, 2017). I show that given a certain understanding of structural and dynamical properties IIT fails to overcome the hard problem of consciousness. I go on in chapter two to argue that a deflationary account of causation is the best view for IIT to overcome the causal exclusion problem (Baxendale and Mindt, 2018). In chapter three, I explain IIT’s account of how the qualitative character of our experience arises (qualia) and what view of intentionality (the directedness of our mental states) IIT advocates. I then move on in chapter four to show why the hard problem mischaracterizes structural and dynamical properties and misses important nuances that may shed light on giving a naturalized explanation of consciousness. In the last and fifth chapter, I outline a sketch of a novel metaphysics of consciousness that takes the conjunction of Neutral Monism and Information-Theoretic Structural Realism to give what I call Information-Theoretic Neutral-Structuralism. (shrink)

Alcohol use and abuse play a major role in both crime and negative health outcomes in Scotland. This paper provides a description and ethical and legal analyses of a novel remote alcohol monitoring scheme for offenders which seeks to reduce alcohol-related harm to both the criminal and the public. It emerges that the prospective benefits of this scheme to health and public order vastly outweigh any potential harms.

Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. (...) There is an interesting system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification: one can't assimilate predication to functional application.<br>. (shrink)