In Aristotle on the Category of Relation, Pamela Hood challenges the view that Aristotle's conception of relation is so divergent from our own that it does not count as a theory of relation at all. This book presents compelling evidence that Aristotle's theory of relation is more robust than originally suspected.

Roderick T. Long - Aristotle on the Category of Relation - Journal of the History of Philosophy 45:1 Journal of the History of Philosophy 45.1 149-150 Muse Search Journals This Journal Contents Reviewed by Roderick T. Long Auburn University Pamela M. Hood. Aristotle on the Category of Relation. Lanham, MD: University Press of America, 2004. Pp. xi + 154. Paper, $28.00. It is often assumed that Aristotle cannot have an adequate understanding of relations, and in particular (...) that "his substance-accident ontology and his reduction of propositions to the logical structure of subject-predicate form" compel him to treat relations as monadic properties of the relata. But as Hood shows in this book, Aristotle's theory does indeed make room for dyadic predicates—meaning not just that he employs such.. (shrink)

Within the context of an involutive monoidal category the notion of a comparison relation ${\mathsf{cp} : \overline{X} \otimes X \rightarrow \Omega}$ is identified. Instances are equality = on sets, inequality ${\leq}$ on posets, orthogonality ${\perp}$ on orthomodular lattices, non-empty intersection on powersets, and inner product ${\langle {-}|{-} \rangle}$ on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with “tame” relations as morphisms. Examples include familiar categories in the (...) foundations of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation. (shrink)

As with the problem of universals, late medieval thinkers were very concerned with the ontological status of relations, for they were central to numerous theological and philosophical problems. These relations were of various types: relations of identity, qualitative similarity, quantitative equality, causal relations, and intentional relations, such as those between knower and the object known. Each of these relations was taken to be an Aristotelian accident. Does it differ from the substance which is related? Broadly speaking, I have discovered four (...) alternative theories: as sentence of the form "a is related by a real relation R to b" is true only if the relation R is an extra-mental thing really distinct from a and b ; R only exists as a concept in a mind ; a and b exist in a certain real way ; the term "R" is connotative, signifying a directly and connoting b . Using printed sources and my critical edition of various codices, I ask the following thinkers whether a real relation is distinct from that which is related: Thomas Aquinas, Giles of Rome, Henry of Ghent, Richard of Middleton, John Duns Scotus, Henry of Harclay, Hervaeus Natalis, and Peter Aurioli. (shrink)

We make some beginning observations about the category Eq of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations R and S is a mapping from the set of R-equivalence classes to that of S-equivalence classes, which is induced by a computable function. We also consider some full subcategories of Eq, such as the category Eq(Σ01) of computably enumerable equivalence relations (called ceers), the category Eq(Π01) of co-computably enumerable equivalence relations, and (...) the category Eq(Dark*) whose objects are the so-called dark ceers plus the ceers with finitely many equivalence classes. Although in all these categories the monomorphisms coincide with the injective morphisms, we show that in Eq(Σ01) the epimorphisms coincide with the onto morphisms, but in Eq(Π01) there are epimorphisms that are not onto. Moreover, Eq, Eq(Σ01), and Eq(Dark*) are closed under finite products, binary coproducts, and coequalizers, but we give an example of two morphisms in Eq(Π01) whose coequalizer in Eq is not an object of Eq(Π01). (shrink)

This is a précis of a forthcoming book which expounds and defends Kant's claim to the derivation of the categories from the principle of apperception in the vein of Klaus Reich.

The publication of Frege’s Begriffsschrift in 1879 forever altered the landscape for many Western philosophers. Here, Sebastian Rödl traces how the Fregean influence, written all over the development and present state of analytic philosophy, led into an unholy alliance of an empiricist conception of sensibility with an inferentialist conception of thought. -/- According to Rödl, Wittgenstein responded to the implosion of Frege’s principle that the nature of thought consists in its inferential order, but his Philosophical Investigations shied away from offering (...) an alternative. Rödl takes up the challenge by turning to Kant and Aristotle as ancestors of this tradition, and in doing so identifies its unacknowledged question: the relation of judgment and truth to time. Rödl finds in the thought of these two men the answer he urges us to consider: the temporal and the sensible, and the atemporal and the intelligible, are aspects of one reality and cannot be understood independently of one another. In demonstrating that an investigation into the categories of the temporal can be undertaken as a contribution to logic, Rödl seeks to transform simultaneously our philosophical understanding of both logic and time. (shrink)

We investigate a certain system of intuitionistic set theory from three points of view: an elementary set theory with bounded separation, a topos with distinguished inclusions, and a category of classes with a system of small maps. The three presentations are shown to be equivalent in a strong sense.

This comparative paper analyses in detail the contexts in which the “contingency” category was used by the philosophers mentioned in its title. While Odo Marquard and Richard Rorty situated contingency within the antifundamentalist discourse, especially in the sphere of philosophical anthropology, epistemology and ethics, Jürgen Habermas drew his conception of the contingency of human birth from the “human nature”— related discourse against modern-day genetic engineering. Marquard’s and Rorty’s theories differ in their philosophical assumptions. Among others, the author shows that (...) none of the mentioned thinkers accepted the radically relativistic consequences of the debate around the “contingency” conception. In his analyses, he also makes frequent use of Marquard’s distinction between “arbitrarily accidental” and “fatefully accidental.”. (shrink)

In the course of this paper, I shall argue that an absolute ineffable God of Islam is contradictory beyond the ordinary categories (substantive or insubstantive) of truth. In order to demonstrate my thesis, I shall refer to a metaphysical and epistemological inquiry. In virtue of both of these inquires, I shall establish that the contradictory assumption ‘the God of Islam is absolutely ineffable’ cannot be false in a substantive or an insubstantive sense. The metaphysical inquiry shall comprise of two related (...) phases. The first phase includes logical realism and anti-realism, while the second phase includes ontological realism and ontological deflationism. I demonstrate that the contradictory assumption ‘the God of Islam is absolutely ineffable’ cannot be considered false in virtue of these outlooks for different reasons. The epistemological inquiry refers to epistemicism. I demonstrate that although this particular view infers an indeterminate truth-value of the contradictory assumption ‘the God of Islam is absolutely ineffable’, it is incompatible with the notion of an absolute ineffable God of Islam. In light of both these inquires, it will become apparent that the contradictory assumption of an absolute ineffable God of Islam cannot be false in a substantive or insubstantive sense. This is because an absolute ineffable God of Islam transcends beyond these very categories of falsehood and truth. (shrink)

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic (...) R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics. (shrink)

Audio features such as inharmonicity, noisiness, and spectral roll-off have been identified as correlates of “noisy” sounds. However, such features are likely involved in the experience of multiple semantic timbre categories of varied meaning and valence. This paper examines the relationships of stimulus properties and audio features with the semantic timbre categories raspy/grainy/rough, harsh/noisy, and airy/breathy. Participants rated a random subset of 52 stimuli from a set of 156 approximately 2-s orchestral instrument sounds representing varied instrument families, registers, and both (...) traditional and extended playing techniques. Stimuli were rated on the three semantic categories of interest, as well as on perceived playing exertion and emotional valence. Correlational analyses demonstrated a strong negative relationship between positive valence and perceived physical exertion. Exploratory linear mixed models revealed significant effects of extended technique and pitch register on valence, the perception of physical exertion, raspy/grainy/rough, and harsh/noisy. Instrument family was significantly related to ratings of airy/breathy. With an updated version of the Timbre Toolbox, we used 44 summary audio features, extracted from the stimuli using spectral and harmonic representations, as input for various models built to predict mean semantic ratings for each sound on the three semantic categories, on perceived exertion, and on valence. Random Forest models predicting semantic ratings from audio features outperformed Partial Least-Squares Regression models, consistent with previous results suggesting that non-linear methods are advantageous in timbre semantic predictions using audio features. Relative Variable Importance measures from the models among the three semantic categories demonstrate that although these related semantic categories are associated in part with overlapping features, they can be differentiated through individual patterns of audio feature relationships. (shrink)

Working within the Aristotelian tradition, I argue that relation is not a category but a transcendental property of being. By this I mean that all substances are actualized, and hence defined, relationally: all actuality is interactuality. Interactuality is the locus for the relational categories of substance, action, being-affected, number, and most types of quality. The interactuality of corporeal beings is further conditioned by relations of setting; here we find the relational categories of place (where), quantity in the sense (...) of size, quality in the sense of shape, and time (when). In offering a relational account of substance, I distinguish between external relata (physical environment, objects of sensation and knowledge as external) and internal relata (one’s body, objects of sensation and knowledge as internal. This distinction between external and internal relata is transcended in the case of the Trinity, insofar as the divine persons are both perfectly distinct and perfectly united. (shrink)

This paper considers a principal concept of metaphysics – the category of substance – as it figures in Kant’s critical program of establishing metaphysics as a science. Like Leibniz, Kant identifies metaphysical concepts through logical reflection on the form of cognitive activity. He thus begins with general logic’s account of categorical judgment as an act of subordinating predicate to subject. This categorical form is then considered in transcendental logic with reference to the possibility of its real use. Transcendental reflection (...) reveals that the categorical form, in its potential for such use, constitutes the category of substance and accident, representing a first real subject and a determination of its existence. But to qualify for objective, scientific employment, metaphysics’ concepts must admit of real definitions, which show their objects to be possible, and such possibility, pace Leibniz, can be established only in relation to possible experience. Thus, relying on his doctrine of the schematism, Kant shows the category to figure constitutively in experience, as the ground of the first law of nature, that in all change substance persists. (shrink)

Background There is ongoing debate regarding how moral distress should be defined. Some scholars argue that the standard “narrow” definition overlooks morally relevant causes of distress, while others argue that broadening the definition of moral distress risks making measurement impractical. However, without measurement, the true extent of moral distress remains unknown. Research aims To explore the frequency and intensity of five sub-categorizations of moral distress, resources used, intention to leave, and turnover of nurses using a new survey instrument. Research design (...) A mixed methods embedded design included a longitudinal, descriptive investigator-developed electronic survey with open-ended questions sent twice a week for 6 weeks. Analysis included descriptive and comparative statistics and content analysis of narrative data. Participants Registered nurses from four hospitals within one large healthcare system in Midwest United States. Ethical considerations IRB approval was obtained. Results 246 participants completed the baseline survey, 80 participants provided data longitudinally for a minimum of 3 data points. At baseline, moral-conflict distress occurred with the highest frequency, followed by moral-constraint distress and moral-tension distress. By intensity, the most distressing sub-category was moral-tension distress, followed by “other” distress and moral-constraint distress. Longitudinally, when ranked by frequency, nurses experienced moral-conflict distress, moral-constraint distress, and moral-tension distress; by intensity, scores were highest for moral-tension distress, moral-uncertainty distress, and moral-constraint distress. Of available resources, participants spoke with colleagues and senior colleagues more frequently than using consultative services such as ethics consultation. Conclusions Nurses experienced distress related to a number of moral issues extending beyond the traditional understanding of moral distress (as occurring due to a constraint) suggesting that our understanding and measurement of moral distress should be broadened. Nurses frequently used peer support as their primary resource but it was only moderately helpful. Effective peer support for moral distress could be impactful. Future research on moral distress sub-categories is needed. (shrink)

This edited volume is a comprehensive presentation of views on the relations between metaphysics and logic from Aristotle through twentieth century philosophers who contributed to the return of metaphysics in the analytic tradition. The collection combines interest in logic and its history with interest in analytical metaphysics and the history of metaphysical thought. By so doing, it adds both to the historical understanding of metaphysical problems and to contemporary research in the field. Throughout the volume, essays focus on metaphysica generalis, (...) or the systematic study of the most general categories of being. Beginning with Aristotle and his Categories , the volume goes on to trace metaphyscis and logic through the late ancient and Arabic traditions, examining the views of Thomas Aquinas, Duns Scotus, and William Ockham. Moving into the early modern period, contributors engage with Leibniz's metaphysics, Kant's critique of metaphysics, the relation between logic and ontology in Hegel, and Bolzano's views. Subsequent chapters address: Charles S. Peirce's logic and metaphysics; the relevance of set-theory to metaphysics; Meinong's theory of objects; Husserl's formal ontology; early analytic philosophy; C.I. Lewis and his relation to Russell; and the relations between Frege, Carnap, and Heidegger. Surveying metaphysics through to the contemporary age, essays explore W.V. Quine's attitude towards metaphysics; Wilfrid Sellars's relation to antidescriptivism as it connects to Kripke's; the views of Putnam and Kaplan; Peter F. Strawson's and David M. Armstrong's metaphysics; Trope theory; and its relation to Popper's conception of three worlds. The volume ends with a chapter on transcendental philosophy as ontology. In each chapter, contributors approach their topics not merely in an historical and exegetical fashion, but also engage critically with the thought of the philosophers whose work they discuss, offering synthesis and original philosophical thought in the volume, in addition to very extensive and well-informed analysis and interpretation of important philosophical texts. The volume will serve as an essential reference for scholars of metaphysics and logic. (shrink)

Objective. Study of the Covid-19 related quarantine concept as an emerging category of linguistic consciousness of Ukrainians. -/- Materials & Methods. The strategy of the study is based on the logical and methodological concept of inductivism. Respondents were asked to write down their own understanding of the quarantine, formulate an appropriate definition and describe the situation, which in their opinion is the exact opposite to quarantine. Respondents also assessed how much their psychological well-being, their daily lifestyle during quarantine had (...) changed, and ranked their preferences for the quarantine strategies proposed to them. A discursive analysis was applied to the obtained texts, as a result of which nine discourses were identified. These data, along with some socio-demographic characteristics were subjected to multidimensional mathematical and statistical processing. -/- Results. Covid-19 related quarantine is represented in the linguistic consciousness of Russian-speaking Ukrainians by a discursive field, which includes at least nine recognizable, semantically autonomous discourses. Empirically discovered such phenomenon as – inter-discourse semantic dissociation. Its essence is a statistically significant reduction in the probability of some discourses appearing in the texts when others are being actualized there. This feature is associated with the innate negativity of the language and determines the semantic biasing of the quarantine concept. Inter-discourse semantic dissociation, as well as the influence of non-discursive factors constitute the discursive formation of the quarantine concept, which is qualitatively characterized by the hierarchical relationship of its components. At the same time, it was revealed that part of the discourses interacting “horizontally” are indirectly associated “vertically”, which forms the stable semantic core of the quarantine concept. Partial empirical confirmation has been found of the previously put forward assumptions about: a) the existence of such a relationship between discourses and psychological defense mechanisms (as character-forming factors) that contributes to the hierarchical structure construction of discursive formations; b) the differential nature of discourses and mechanisms of psychological defenses interaction, which makes it possible to single out the discursive aspect in a characterological profile and consider a discourse as an operator of characterological semantics. -/- Conclusions. An empirical study made it possible to form a primary idea of the substantive and structural semantic features of the quarantine concept, as an emerging category of linguistic consciousness of Ukrainians. The results obtained have a potentially useful application perspective. Thus, when implementing anti-epidemiological measures, it is important to consider the studied features of the discursive formation hierarchical structure of the quarantine concept, since discursive semantics are associated with cognitive focusing, which, in turn, affects the behavior direction and its upshots. (shrink)

It is a commonplace that, to a great extent, the way we think depends upon the categories we think with. In this paper I propose to introduce a group of related categories which, if they do not obviously lead to new discoveries, at least provide new ways of understanding and interrelating old ideas. The basic category I am concerned with is that of imperceptibles: not particularly a new one, but always previously a confused one because proper definition of it (...) requires specification of the perceiver. I wish to propose a set of definitions which cures such ambiguities, and then to examine some of the uses to which it may be put. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of (...) intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)

In this study, edited on the basis of a critical review of domestic and foreign literature, as well as authors’ own analyzes, previously presented in several articles (Słodowa-Hełpa 2015; Gorynia 2021 and 2022), mainly in two shorter texts published in popular magazines with a range of Poland (Gory-nia and Słodowa-Hełpa 2022a, 2022b), selected aspects of the concept of the common good from the perspective of the Covid-19 pandemic were presented. The authors’ conviction that in the process of searching for cures (...) to overcome civilization turbulences, the common good cannot be eliminated from the social, political, economic and moral space, was the inspiration to take up this issue. Therefore, the search for answers to the following four questions was considered leading: Will pandemic experiences catalyze a better understanding of the common good? How can they reduce its deficit? To what extent can a return to the concept of the common good, offering real forms of participation and shared responsibility, help in overcoming the painful effects of the present and future threats to civilization? Can respecting the principles of the common good be considered an imperative in the process of overcoming problems of an increasingly global scope? In view of the ambiguity of the category of the common good and the related interpretation difficulties, it was deemed necessary to place the main part of the study in the background of the most general approach to the essence of the analyzed category and its status in philosophical and economic terms. The summary outlines conclusions and postulates concerning the conditions for the functioning of global common goods and the possibility of using them in international cooperation. (shrink)

Hanna Kulagina-Stadnichenko in her article “Category of Love as a axiological marker by individual religiosity of the Orthodox believer” is examines the love category in the theological context of the present, to determine its axiological and praxeological potential value to the implementation of individual religious Orthodox believer, identify certain impacts related to the practical implementation of the concept of "love" in Orthodoxy.

A classification of models of reduction into three categories — theory reductionism, explanatory reductionism, and constitutive reductionism — is presented. It is shown that this classification helps clarify the relations between various explications of reduction that have been offered in the past, especially if a distinction is maintained between the various epistemological and ontological issues that arise. A relatively new model of explanatory reduction, one that emphasizes that reduction is the explanation of a whole in terms of its parts is (...) also presented in detail. Finally, the classification is used to clarify the debate over reductionism in molecular biology. It is argued there that while no model from the category of theory reduction might be applicable in that case, models of explanatory reduction might yet capture the structure of the relevant explanations. (shrink)

This edited volume is a comprehensive presentation of views on the relations between metaphysics and logic from Aristotle through twentieth century philosophers who contributed to the return of metaphysics in the analytic tradition.

We can perceive not only low-level features of events such as color and motion, but also seemingly higher-level properties such as causality. A prototypical example of causal perception is the ”launching effect’: one object moves toward a stationary second object until they are adjacent, at which point A stops and B starts moving in the same direction. Beyond these motions themselves --- and regardless of any higher-level beliefs --- this display induces a vivid visual impression of causality, wherein A is (...) seen to cause B’s motion. Do such percepts reflect a unitary category of visual processing, or might there be multiple distinct forms of causal perception? While launching is often simply equated with causal perception, researchers have sometimes described other phenomena such as ”triggering’ and ”entraining’. We used psychophysical methods to determine whether these labels really carve visual processing at its joints, and how putatively different forms of causal perception relate to each other. Previous research demonstrated retinotopically specific adaptation to causality: exposure to causal launching makes subsequent ambiguous events in that same location more likely to be seen as non-causal ”passing’. Here, after replicating this effect, we show that exposure to triggering also yields retinotopically specific adaptation for subsequent ambiguous launching displays, but that exposure to entraining does not. Collectively, these results reveal that visual processing distinguishes some types of causal interactions. (shrink)

When addressing the Muslim women question, one of the problematic issues is the centrality of a religious tradition or a political ideology as a primary subject of inquiry. Muslim women are seen as the embodiment of a singular tradition or ideology, as in the case of Turkey, where the contemporary headscarf-wearing women are represented as ‘Islamist’. In this project, I aim to problematise this stereotyping categorisation through ontological conceptualisations, inspired by the French thinker Gilles Deleuze. To implement the relational ontology (...) of Deleuze, I examine headscarf contestations in Turkey through interviews conducted in two women’s organisations in Turkey: Capital City Women’s Platform (Baskent Kadin Platformu) and Hazar. I argue that the world constantly ‘becomes’ through flows of relations between multiple elements; therefore, it is a multiplicity, an intensity and fractured. With this Deleuzian ontology in mind, I consider the quotidian physical, material and social resources of my interviews with the aim of elucidating relations between a female body and the commodities produced by multiple socio-economic and political factors in Turkey. Then I address a Deleuzian understanding of categorisations such as class, gender, race and ideology. These categorisations, for Deleuze, are aggregations of multiplicities and fluidities forming specific fixations according to a range of ascribed characteristics, such as income, education, employment or dress codes. In this regard, I conclude that the label ‘Islamist’ restrains the relational and multiple characters of headscarf practices within a unifying category by attributing certain features to particular embodiments and materials. (shrink)

Rather than approaching Kant's moral theory in the normal way through a consideration of The Groundwork of the Metaphysics of Morals and The Critique of Practical Reason, I do so from the perspective of an extended analysis of other aspects of his work that bear on his moral philosophy . Consideration of the Doctrine of Right suggests that the universal principle of Right Kant identifies is a restricted version of the CI applied to the limited domain of relations between persons (...) at issue in this context. Given that duties of Right deriving from this principle are also regarded as perfect ethical duties, an analysis of the nature and scope of the universal principle of Right can, I argue, be expected to be informative with respect to our understanding of perfect duties and the contradiction in conception from which these are said to derive. Allowing for the more limited scope of merely external duties of Right, analysis of these duties suggests that ethical duties of Right are obligations concerned with ensuring the capacity of rational agents to govern themselves on the basis of reason . This kind of analysis, I argue, is both confirmed and clarified by Kant's subsequent discussion of perfect and imperfect duties of virtue we owe to ourselves under the rubric of concerns with our moral health and moral prosperity. ;The resulting view is, I claim, a promising one that allows us to integrate the different treatments of duties in these two works and accommodate the various duties Kant discusses. In particular, understood in terms of the notions of moral health and prosperity, the concerns engendered here require careful consideration of the particular nature and psychology of human agency and yield a much more subtle and interesting account of duty and of the moral life than those typically associated with Kant. (shrink)

Elementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results (...) are proved. Relations between categories and sets, the latter defined as discrete categories, are described, and applications to foundations are discussed. (shrink)

Drawing on Membership Categorization Analysis, we aim to tease out how narrators talk into being the social group constellations in their storyworlds and how these – potentially shifting – constellations can be related to the narrator’s identity constructions. We investigate two World War II-testimonies narrated by Belgian concentration camp survivors and scrutinize whether the expected Standardized Relational Pair of victim-perpetrator – viz. the camp prisoners versus the Nazis – is in operation, how these two categories are talked into being, whether (...) other social groups are mentioned and how all these processes affect the narrators’ identity work. It proved to be the case that, even though the victim-perpetrator Standardized Relational Pair is indeed present in both testimonies, it functions very differently in both stories, resulting in almost opposing identity work by the two narrators. (shrink)

In the second part of the Critique of Judgment, Immanuel Kant provides a transcendental analysis of the bases of our right to employ teleological conceptions in biology. A living organism exemplifies the conception of a natural end insofar as the organization of the parts to form a whole is the result of a process in which the organism is both cause and effect of itself. Kant’s analysis of the concept of a natural purpose is guided, in part, by his general (...) theory of logic. By examining the manner in which the logical modes of relation are used as a basis for analyzing the concept of a natural purpose, I hope to accomplish two goals: to compare Kant’s analysis of the category of community to the analysis of the concept of a natural purpose; to evaluate some of the strengths and weaknesses ofKant’s account of community and natural purpose; to consider one criticism of Kant’s use of the logical form of the disjunctive as a basis for the analysis of these conceptions that is developed by Charles Sanders Peirce. Peirce indicates that Darwin’s theory of biological evolution was one of the primary causes that led him revisit Kant’s logic and his analysis of the categories of relation. (shrink)

Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K • relating integral residuated lattices with 0 with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about an adjunction between Heyting and Nelson algebras, which is an enrichment of the basic adjunction between lattices and Kleene algebras. The lifting of the functor to the category of residuated lattices leads us to (...) study other adjunctions and equivalences. For example, we treat the functor C whose domain is cuRL, the category of involutive residuated lattices M whose unit is fixed by the involution and has a Boolean complement c. If we restrict to the full subcategory NRL of cuRL of those objects that have a nilpotent c, then C is an equivalence. In fact, C M is isomorphic to C e M, and C e is adjoint to, where assigns to an object A of IRL0 the product A × A 0 which is an object of NRL. (shrink)

ABSTRACTThe aim of this study was to examine the extent to which cognitive emotion regulation strategies were “common or transdiagnostic correlates” of symptoms of depression and anxiety and/or “specific correlates” distinguishing one problem category from the other. The sample comprised 582 13- to 16-year-old secondary school students. Symptoms of depression and anxiety were measured by the SCL-90, and cognitive emotion regulation strategies were measured by the CERQ, in a cross-sectional design. Multivariate regression analyses were performed. Before controlling for comorbidity, (...) the same cognitive emotion regulation strategies that were related to symptoms of depression were also related to symptoms of anxiety. However, after controlling for comorbid anxiety symptoms, rumination, self-blame, positive reappraisal, and positive refocusing were uniquely associated with depression symptoms; and after controlling for comorbid depression symptoms, ca... (shrink)

A recent article in this journal attempts to link categories of sport competition to appropriate psychologies of participants in the different sorts of competition. It criticises accounts of competition which understand it in relation to a very restricted range of psychologies because the purposes and psychologies with which people enter and engage in competition vary enormously. So, taking as a starting point a consensus view among sport philosophers of the key conditions governing competition, work is undertaken to identify fundamental (...) distinctions drawing from the conditions, which are said to result in a fourfold typology of competitions. The final step is to suggest psychologies most suited to the components of the typology. My article examines this project and produces reasons to doubt its success. (shrink)

ABSTRACTThe aim of this study was to examine the extent to which cognitive emotion regulation strategies were “common or transdiagnostic correlates” of symptoms of depression and anxiety and/or “specific correlates” distinguishing one problem category from the other. The sample comprised 582 13- to 16-year-old secondary school students. Symptoms of depression and anxiety were measured by the SCL-90, and cognitive emotion regulation strategies were measured by the CERQ, in a cross-sectional design. Multivariate regression analyses were performed. Before controlling for comorbidity, (...) the same cognitive emotion regulation strategies that were related to symptoms of depression were also related to symptoms of anxiety. However, after controlling for comorbid anxiety symptoms, rumination, self-blame, positive reappraisal, and positive refocusing were uniquely associated with depression symptoms; and after controlling for comorbid depression symptoms, ca... (shrink)

This paper traces the history of uses of the word “gender”. It suggests that though “gender” has been recuperated and become commonplace, many issues persist around the way “women” and “men”, and the power relations between them, are defined and are evolving. Provided it still allows us to question the meanings attached to the sexes, how they are established and in what contexts, gender remains a useful, because critical, analytical category.

Many arguments for flexible type assignment to syntactic categories have to do with the need to account for the various scopings resulting from the interaction of quantified DPs with other quantified DPs or with intensional or negated verb contexts. We will define a type for arbitrary arity relations in polymorphic type theory. In terms of this, we develop the Boolean algebra of relations as far as needed for natural language semantics. The type for relations is flexible: it can do duty (...) for the whole family of types t, e → t, e → e → t, and so on. If we use this flexible type for the interpretations of verbs, we can perform a ‘flexible lift’ on DP interpretations, so that DPs get interpreted as operations on verb meanings. This leads to an elegant implementation of Keenan’s proposal for polyadic quantification in natural language (‘Beyond the Frege Boundary’). It turns out that scope reorderings are particularly easy to implement in this framework. (shrink)

In this article, the categories of literary, dramatic, musical and artistic (LDMA) works in which copyright subsists are considered, and an argument made that the legislature’s division of protected works into categories is appropriate given the psychology of art appreciation, and the fact that in order to perceive a work qua work one must perceive it in relation to a category of work. Nonetheless, an argument is also made that the statutory definitions of LDMA works suffer from the (...) defects of formalist theory. Those defects are outlined, and an alternative theory of works proposed, drawing on the scholarship of art theorist Kendall Walton and the intentional, historical view of the work developed in a recent publication (J Pila, ‘An Intentional View of the Copyright Work’ (2008) 71 MLR 535–58). According to that theory, LDMA works are constituted in part by their properties of form and in part by the history of their individual production. Consistent with this, the statutory categories of work are cast as denoting authorial traditions: evolving practices of LDMA expression that exist and are experienced in a particular social context. In addition to its general explanatory and normative value for copyright, this theory has specific implications for the legislature’s expression of the categories of works in which copyright subsists. (shrink)

A network of aligned ontologies is a distributed system, whose components are interacting and interoperating, the result of this interaction being, either the extension of local assertions, which are valid within each individual ontology, to global assertions holding between remote ontology syntactic entities through a network path, or to local assertions holding between local entities of an ontology, but induced by remote ontologies, through a cycle in the network. The mechanism for achieving this interaction is the composition of relations. In (...) this perspective, we introduce the notions of local composable relations, which relate ontology entities belonging to the same ontology, remotely induced composable relations, which relate ontology entities belonging to remote ontologies through a path of ontologies and alignments in the network, and network induced local composable relations, which relate ontology entities belonging to the same ontology, but through a path of ontologies and alignments forming a cycle starting and ending at the same ontology, to characterize the logical consequences extracted from a network of aligned ontologies, and we propose a category-based methodology for detecting semantic inconsistencies in networks of aligned ontologies, which is based on contravariant representable functors and on the definition of two composition operators suitable for propagating local knowledge through the network. (shrink)

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

The concept of tolerance is one of the basic ethical categories of Buddhism. Showing conscious tolerance, you control a situation and do not allow feelings, such as anger or arrogance to take top above reason. Besides, the tolerance to other people and different situation shows your wide scope and common emancipation. The tolerance is one of qualities inherent to bodhisattvas - sacred Buddhists. These qualities are called paramita, and paramita of tolerance - kshanti-paramita. Kshanti-paramita is triple: tolerance to other alive (...) beings, tolerance to vital circumstances and tolerance coming with wisdom and penetration into essence of things and the phenomena. The man practicing tolerance, sympathizes with living creatures, understands their problems, mental condition and level of consciousness development. He can understand the true reasons of their behaviour. Buddhist tolerance is based on respect of other alive essences, by their potentially and permanently actualized trueness. Concept of tolerance propagates equality and peaceful coexistence of various essences. The tolerance in relation to vital circumstances helps the man to keep positive mood without dependence from modus of possession and external conditions. In this sense thespiritual sermons are very important drawing attention of a man to values of the internal world, his unity with the universe. (shrink)

When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids. In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proof-irrelevant family F of setoids. The objects of the categories form the index setoid I of the family, whereas the definition of arrows differs. The first (...) class='Hi'>category has for arrows triples →F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\rightarrow \,F)$$\end{document} where f is an extensional function. Two such arrows are identified if appropriate composition with transportation maps makes them equal. In the second category the arrows are triples 2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2)$$\end{document} where R is a total functional relation between the subobjects F,F↪Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F, F \hookrightarrow \Sigma $$\end{document} of the setoid sum of the family. This category is simpler to use as the transportation maps disappear. Moreover we also show that the full image of a category along an E-functor into an E-category is a category. (shrink)

This paper traces the history of uses of the word “gender”. It suggests that though “gender” has been recuperated and become commonplace, many issues persist around the way “women” and “men”, and the power relations between them, are defined and are evolving. Provided it still allows us to question the meanings attached to the sexes, how they are established and in what contexts, gender remains a useful, because critical, analytical category.