This paper argues that grammatical constructions, specifically argument structure constructions that determine the “who did what to whom” part of sentence meaning and how this meaning is expressed syntactically, can be considered a kind of relational category. That is, grammatical constructions are represented as the abstraction of the syntactic and semantic relations of the exemplar utterances that are expressed in that construction, and it enables the generation of novel exemplars. To support this argument, I review evidence that there are (...) parallel behavioral patterns between how children learn relational categories generally and how they learn grammatical constructions specifically. Then, I discuss computational simulations of how grammatical constructions are abstracted from exemplar sentences using a domain-general relational cognitive architecture. Last, I review evidence from adult language processing that shows parallel behavioral patterns with expert behavior from other cognitive domains. After reviewing the evidence, I consider how to integrate this account with other theories of language development. (shrink)

Theories of relational concept acquisition based on structured intersection discovery predict that relational concepts with a probabilistic structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate the learning of such categories. Experiment 1 showed that changing the task from a category-learning task to choosing the “winning” object in each stimulus greatly facilitated participants' ability to learn probabilistic relational categories. Experiments 2 and 3 further (...) investigated the mechanisms underlying this “who's winning” effect. Experiment 4 replicated and generalized the “who's winning” effect with more natural stimuli. Together, our findings suggest that people learn relational concepts by a process of intersection discovery akin to schema induction, and that any task that encourages people to discover a higher order relation that remains invariant over members of a category will facilitate the learning of putatively probabilistic relational concepts. (shrink)

In recent years scholars have begun to question the usefulness of the category of ''religion'' to describe a distinctive form of human experience and behavior. In his last book, The Ideology of Religious Studies (OUP 2000), Timothy Fitzgerald argued that ''religion'' was not a private area of human existence that could be separated from the public realm and that the study of religion as such was thus impossibility. In this new book he examines a wide range of English-language texts to (...) show how religion became transformed from a very specific category indigenous to Christian culture into a universalist claim about human nature and society. These claims, he shows, are implied by and frequently explicit in theories and methods of comparative religion. But they are also tacitly reproduced throughout the humanities in the relatively indiscriminate use of ''religion'' as an a priori valid cross-cultural analytical concept, for example in historiography, sociology, and social anthropology. Fitzgerald seeks to link the argument about religion to the parallel formation of the ''non-religious'' and such dichotomies as church-state, sacred-profane, ecclesiastical-civil, spiritual-temporal, supernatural-natural, and irrational-rational. Part of his argument is that the category ''religion'' has a different logic compared to the category ''sacred,'' but the two have been consistently confused by major writers, including Durkheim and Eliade. Fitzgerald contends that ''religion'' imagined as a private belief in the supernatural was a necessary conceptual space for the simultaneous imagining of ''secular'' practices and institutions such as politics, economics, and the Nation State. The invention of ''religion'' as a universal type of experience, practice, and institution was partly the result of sacralizing new concepts of exchange, ownership, and labor practices, applying ''scientific'' rationality to human behavior, administering the colonies and classifying native institutions. In contrast, shows Fitzgerald, the sacred-profane dichotomy has a different logic of use. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Concepts, Judgments, and Unity in Kant's Metaphysical Deduction of the Relational Categories CHARLES NUSSBAUM 1. INTRODUCTION TO ANY ATTENTIVEREADERof the section of the Critique of Pure Reason' known as the "Metaphysical Deduction of the Categories" (A67/B92-A83/B to9), one paragraph in that section stands out particularly by virtue of its special importance for Kant's developing argument: The same function Which gives unity to the various representations in (...) ajudgment also gives unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold of intuition in general.... (CPR A79/B loS) The importance of this paragraph is, however, more than equaled by its difficulties, which center on the question of how the function which operates by means of analytical unity can be the same as one that operates by means of the synthetic unity of the manifold of intuition in general. Put shortly, the problem is this. If the functions are really the same, then how do we distinguish at all between analytic and synthetic operations? But if they are different, then how can these forms of judgment serve as a clue for the discovery of the categories? ' Immanuel Kant, Critiqueof Pure Reason, trans. Norman KempSmith (London: Macmillan and Co., Ltd., 1963).Hereafter CPR. [89] 9~ JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 1990 The results of this dilemma which can be observed in the literature are not surprising: commentators tend to grasp one horn or the other. They either emphasize the difference between analysis and synthesis, and reject or dilute the claims as to sameness of function; or they take seriously Kant's argument concerning sameness of functions, and try to minimize the difference between analysis and synthesis. The major twentieth-century representant of the former approach is Kemp Smith," and of the latter, Paton. 3 This latter approach has found a formidable contemporary champion in the person of Henry Allison. By Allison's own admission,4 however, his position on this controversial topic was suggested (in part) by arguments first put forward over fifty years ago by Klaus Reich in a most remarkable book entitled Die Volls~ndigkeit der Kantischen Urteilstafel, 5 a book, by the way, also greatly admired by Paton. 6 In the first section of this paper I will try to show that Reich's arguments are rather more subtle than Allison apparently takes them to be, and that Reich is one commentator who attempts to go between the horns of the dilemma described above, and who essays an interpretation of our crucial paragraph that unifies its seemingly divergent tendencies. In the second section of the paper I will introduce some interpretive elements of my own. 2. Let us begin by reacquainting ourselves with Kant's notion of analytical unity, one aspect of this debate which is not particularly controversial and is largely agreed upon by all parties. For Kant, analytical unity is the sort of unity achieved by all general concepts (conceptus communes) insofar as they abstract from all differences that subsist between the objects under them, or the lower concepts subordinated to them. 7 A general concept unifies these objects or concepts by means of a common mark or set of marks. Thus Kant's example at CPR A69/B94 of the unification of bodies under the concepts 'body' and 'divisible' is a perfectly representative instance of unification via analytical unity, as the function upon which such concepts "rest." Let us note that the " Norman KempSmith,A CommentarytoKant's "Cr/t~rueofPureReason"(NewYork:HumanitiesPress, 196~). 3 H.J. Paton, Kant's MetaphysicofExperience, 2 vols.(London:George Allenand Unwin,Ltd., 1936). 4 Henry Allison,Kant's TranscendentalIdealum (NewHaven:YaleUniversityPress, 1983), 144 n. 3o. Hereafter KTI. 5 KlausReich,Die Vollst~ndigkeitderKantischenUrteilstafel,3rd. ed. (Hamburg: Meiner, 1986). Hereafter VKU. 6 Paton, Kant's Metaphysic, 1:302. Kant, we should note, does not makethis important logicaldistinctionbetweensubordination... (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)

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)

In model theory, a branch of mathematical logic, we can classify mathematical structures based on their logical complexity. This yields the so-called stability hierarchy. Independence relations play an important role in this stability hierarchy. An independence relation tells us which subsets of a structure contain information about each other, for example, linear independence in vector spaces yields such a relation.Some important classes in the stability hierarchy are stable, simple, and NSOP $_1$, each being contained in the next. For each of (...) these classes there exists a so-called Kim-Pillay style theorem. Such a theorem describes the interaction between independence relations and the stability hierarchy. For example, simplicity is equivalent to admitting a certain independence relation, which must then be unique.All of the above classically takes place in full first-order logic. Parts of it have already been generalised to other frameworks, such as continuous logic, positive logic, and even a very general category-theoretic framework. In this thesis we continue this work.We introduce the framework of AECats, which are a specific kind of accessible category. We prove that there can be at most one stable, simple, or NSOP $_1$ -like independence relation in an AECat. We thus recover (part of) the original stability hierarchy. For this we introduce the notions of long dividing, isi-dividing, and long Kim-dividing, which are based on the classical notions of dividing and Kim-dividing but are such that they work well without compactness.Switching frameworks, we generalise Kim-dividing in NSOP $_1$ theories to positive logic. We prove that Kim-dividing over existentially closed models has all the nice properties that it is known to have in full first-order logic. We also provide a full Kim-Pillay style theorem: a positive theory is NSOP $_1$ if and only if there is a nice enough independence relation, which then must be given by Kim-dividing.Abstract prepared by Mark Kamsma.E-mail:[email protected]:https://markkamsma.nl/phd-thesis. (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)

Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations.

While recognizing the theoretical importance of context, current research has treated naming as though semantic meaning were invariant and the same mapping of category exemplars and names should exist across experimental contexts. An assumed symmetry or bidirectionality in naming behavior has been implicit in the interchangeable use of tasks that ask subjects to match names to stimuli and tasks that ask subjects to match stimuli to names. Examples from the literature are discussed together with several studies of color naming and (...) basic emotion naming in which no such symmetry was found. A more complete model of naming is proposed to account for flexible mapping of names to items. Principles of naming are suggested to describe effects of stimulus sampling, differing access to terms, task demands, and other impacts on naming behavior. (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)

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 article puts into perspective Badiou’s differing approach to set theory and the theory of categories and shows how the distinctions and protocols specific to these fields affect his philosophical thought. It also questions the evolution of Badiou’s approach to these two mathematical theories. The article concludes with questions and examinations related to some of the key points of Badiou’s philosophical orientation that he has not yet addressed.

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.

ABSTRACTEmotion differentiation, the ability to describe and label our own emotions in a differentiated and specific manner, has been repeatedly associated with well-being. However, it is unclear exactly what type of differentiation is most strongly related to well-being: the ability to make fine-grained distinctions between emotions that are relatively closely related, the ability to make larger distinctions between very distinct emotions, or the combination of both. To determine which type of differentiation is most predictive of well-being, we performed a comprehensive (...) meta-analysis across six datasets. We examined the correlations between these three types of differentiation and several indicators of well-being. Results showed that individuals differentiated most between very distinct emotions and least between more related emotions, and that an index computed across emotions from both the same and di... (shrink)

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.

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.

This paper presents an analysis of conversational actions and category relations exhibited in an episode of argument between a brother and sister during a family meal. The paper is based on two sets of auspices: on a conversation analytic concern with the interconnection between the sequential and categorical ‘layers’ of organization to which parties to talk-in-interaction are demonstrably oriented, and on ‘Sacks’ Conjecture’ regarding children’s culture and adult—child ‘culture contact’. In terms of these auspices, the analysis shows that the children (...) use both sequential and categorical cultural resources to produce their argument. To adapt a concept of Garfinkel’s — the documentary method of interpretation — the category relationship between the children is the underlying matter that the sequential particulars are used to reflexively document and constitute. Specifically, through the sequentially organized particulars of degradation and resistance the children recognizably and reflexively constitute their category relationship. (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)

Porphyry’s Expositio per interrogationem et responsionem can help us to understand some obscure passages of chapter seven of Aristotle’s Categories, focused on the relative. The Porphyrian analysis of πρός τι presents indeed developments which are both useful for the understanding of the Aristotelian text and very innovative too. First, we can mention the general Porphyrian thesis according to which categories are predicates. This theory fits very well with πρός τι, which are predicates corresponding to properties that subjects only (...) possess because of an observed reciprocal relationship. This brings us to the second novelty of Porphyry’s analysis, really important for modern developments of the notion of relation, namely the difference between σχέσις and πρός τι, which depends on it. Finally, we will mention the important Porphyry’s contribution to the understanding of a particularly obscure issue concerning the relationship between the two definitions of πρός τι that Aristotle provides. Porphyry points out the Platonic origin of the first definition, without dismissing it though: instead, he will just consider it too vast and encompassing the true πρός τι, object of the second definition. (shrink)

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)

Values have always tended to play a central role in discourse on the environment, a tendency which is currently particularly evident in the biodiversity context. Traditionally, arguments about the environment have invoked instrumental value to highlight the necessity or utility of a healthy environment for people and intrinsic value to emphasize the importance of protecting nature for its own sake. More recently, this value dichotomy has been challenged, and the notion of a third value category – relational value – (...) has been introduced into the political and social conservation discussion. In the field of environmental philosophy, the idea of a third category of environmental value already has a longer tradition. This article describes and compares several philosophical accounts of third-category environmental value to contribute to a better characterization of relational value and thus to a better understanding of the role this type of value can play in environmental discourse and policy. (shrink)

This carefully argued book combines a phenomenological and rationalist account of the mind-body relation. Engelhardt avoids what he considers to be artificial analytic distinctions and employs the Hegelian dialectic to explain the mutual dependency of these concepts. "... The category of finite mind presupposes the category of body." The relationship is characterized as an identity in difference because the meaning of one depends on the other, but neither is reducible to the other. To show this, Engelhardt establishes a categorial domain (...) of relations and exemplifies the dialectic experientially in a phenomenological "founding—founded" structure. The mind is primary and transcendent, both experientially and rationally; there are no meaningful experiences without conscious thought but, concretely, mind is founded in a world-oriented body, whereas the body is not dependent on the mind for its founding but is dependent on mind for meaning. (shrink)