A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational (...) class='Hi'>structures that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the (...) first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. (...) This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

In this paper I argue for the Atlas-Kempson Thesis that sentences of the form The A is not B are not ambiguous but rather semantically general (Quine), non-specific (Zwicky and Sadock), or vague (G. Lakoff). This observation refutes the 1970 Davidson-Harman hypothesis that underlying structures, as full semantic representations, are logical forms. It undermines the conception of semantical presupposition, removes a support for the existence of truth-value gaps for presuppositional sentences (the remaining arguments for which are viciously circular), (...) and lifts the Russell-Strawson dispute of 1950–1964 from stalemate to a formulation in which a resolution is possible for the first time. Suggestions of Davidson, Montague, Stalnaker, Kaplan and H. P. Grice are shown to be inadequate semantic descriptions of negative, presuppositional sentences. I briefly discuss the radical Pragmatics view of my 1975 publications and suggest that it too fails to do justice to the linguistic data. I speculate that Semantic Representations should be given the form (more or less) of computer programs, describable in Dana Scott's mathematical semantics for programming languages. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational (...) class='Hi'>structures that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category (...) theory does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects2 The Set-theoretic Peril for Radical Ontic Structural Realism3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism4 Throwing out the Relations with the Relata5 Categorial and Set-theoretical Structures6 Radical Suggestions from Topological Quantum Field Theory?7 Sheaves of Einstein Algebras as Radical Structures?8 Conclusions. (shrink)

The standard presentation of topological spaces relies heavily on (naïve) set theory: a topology consists of a set of subsets of a set (of points). And many of the high-level tools of set theory are required to achieve just the basic results about topological spaces. Concentrating on the mathematical structures, category theory offers the possibility to look synthetically at the structure of continuous transformations between topological spaces addressing specifically how the fundamental notions of point and open come about. (...) As a byproduct of this, one may look at the different approaches to topology from an external perspective and compare them in a unified way. Technically, the category of sober topological spaces can be seen as consisting of (co)algebraic structures in the exact completion of the elementary category of sets and relations. Moreover, the same abstract construction of taking the exact completion, when applied to the category of topological spaces and continuous functions produces an extension of it which is cartesian closed. In other words, there is one general mathematical construction that, when applied to a very elementary category, generates the category of topological spaces and continuous functions, and when applied to that category produces a very suitable category where to deal with all sorts functions spaces. Yet, via such free constructions it is possible to give a new meaning to Marshall Stone’s dictum: “always topologize” as the category of sets and relations is the most natural way to give structure to logic and the category of topological spaces and continuous functions is obtained from it by a good mix of free – i.e. syntactic – constructions. (shrink)

The arguments that Fodor (1987: 150-52) gives in support of a Language of Thought are apparently straightforward. (1) Linguistic capacities are "systematic", in the sense that if one understands the words 'John loves Mary' one also understands the form of words 'Mary loves John'. In other words, sentences have a combinatorial semantics, because they have constituent structure. (2) If cognitive capacities are systematic in the same way, they must have constituent structure also. Thus there is a Language of Thought. The (...) essential connection between language and thought that the argument requires is: Since the function of language is to express thought, to understand a sentence is to grasp the thought that its utterance standardly conveys. So from the systematicity of sentences it follows that anyone who can grasp the thought that John loves Mary can grasp the thought that Mary loves John. Thought must be as systematic as language, for the best empirical explanation of the psychological fact that one who grasps the thought that John loves Mary can grasp the thought that Mary loves John is that grasping a thought is standing in some thinking relation to a complex entity whose constituents are MARY, X LOVES Y, and JOHN and semantic relations among MARY, X LOVES Y, and JOHN. So sayeth Fodor (1987). (shrink)

We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere “intervals cum description”.1 On the other hand, in ordinary circumstances the point of talking about time is to talk about (...) what actually happens or might happen at some time or another. We talk about ‘now’ and ‘then’ in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy. This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above—in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time.3 It is this second question that we intend to focus on here.. (shrink)

The purpose of this research is to highlight the relationship between green product attributes and consumer trust that influence consumers’ decision to purchase green products in the context of Pakistan. This study contributes to determining quantitatively how green product attributes such as physical, perceptual, and reflexive attributes influence consumers’ trust to purchase a green product and investigates the mediating role of green marketing. Data was collected from different industrial sectors through a survey questionnaire. We employed Structural Equation Modeling using the (...) SMART-PLS software to check the reliability and validity of the constructs, and to test the hypotheses. This study reveals variations in terms of shaping the sustainable consumers’ buying behavior by modifying product attributes and green marketing strategies that are in congruence with the proposed hypotheses of this study. In the end, the findings and interpretations of the results are given which can guide the managers to develop effective green marketing campaigns in reshaping the purchase intentions of consumers toward their green products. (shrink)

The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...) known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (shrink)

The research is focused on the role of two related key concepts, namely variables and data, in the impact evaluations of public projects. A difficult task of the evaluators and researchers is to select the appropriate variables to ensure the best model of reality and satisfy the evaluation methods' needs. Therefore, the paper aims to look at the current knowledge and discuss how variables and data could be best used to connect the evaluation models, the particularities of the intervention with (...) the potential of the advanced quantitative assessment methods. The results emphasise that evaluations operate with data with different levels of granularity, as required by the intervention logic. Structuring data in clusters and categories, performing evaluability assessments are useful in assessing data quality and limitations and improving them. In line with the existing literature, we demonstrate that data accessibility is a key constraint and imposes adjustment of the desired evaluation model to a feasible one. While Big Data and Open Data systems significantly improved data quality in evaluations in recent years, blockchain, as a ledger technology with default features related to decentralisation and security, is expected to bring large benefits to evaluation. For evaluators and policymakers, blockchain potential is an area of further research looking for additional advantages that could enhance the use of quantitative methods. (shrink)

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied (...) to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support (a): the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b): standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful. (shrink)

We present and study the category of formal topologies and some of its variants. Two main results are proven. The first is that, for any inductively generated formal cover, there exists a formal topology whose cover extends in the minimal way the given one. This result is obtained by enhancing the method for the inductive generation of the cover relation by adding a coinductive generation of the positivity predicate. Categorically, this result can be rephrased by saying that inductively generated (...) formal topologies are coreflective into inductively generated formal covers. The second result is that unary formal covers are exponentiable in the category of inductively generated formal covers and hence, thanks to the coreflection, unary formal topologies are exponentiable in the category of inductively generated formal topologies. From a localic point of view the exponentiability of unary formal topologies means that algebraic dcpos are exponentiable in the category of open locales. But, the coreflection theorem states that open locales are coreflective in locales and hence, as a consequence of well-known impredicative results on exponentiable locales, it allows to prove that locally compact open locales are exponentiable in the category of open locales. (shrink)

Social epistemology studies knowledge and justified belief acquisition through organized group cooperation. To do this, the way such group cooperation is structured has to be modeled. The obvious way of modeling a group structure is with a directed graph; unfortunately, most types of social cooperation directed at epistemological aims are variably implementable, including in their structural expression. Furthermore, the frequency with which a practice is implemented in a certain way can vary with topology. This entails that the topology (...) of social practices directed toward epistemological ends has to be modeled by a set of directed graphs, or their equivalent, together with a probability distribution over that set. In theory, this is eminently possible; however, there are considerable practical obstacles to the specification of a practice’s topology in this way. This paper examines these practical difficulties and concludes that todays sampling protocols are either far too slow to handle pratices with 10 or more participants, or else prone to produce misleading evaluations. (shrink)

We present and study the category of formal topologies and some of its variants. Two main results are proven. The first is that, for any inductively generated formal cover, there exists a formal topology whose cover extends in the minimal way the given one. This result is obtained by enhancing the method for the inductive generation of the cover relation by adding a coinductive generation of the positivity predicate. Categorically, this result can be rephrased by saying that inductively generated (...) formal topologies are coreflective into inductively generated formal covers. The second result is that unary formal covers are exponentiable in the category of inductively generated formal covers and hence, thanks to the coreflection, unary formal topologies are exponentiable in the category of inductively generated formal topologies. From a localic point of view the exponentiability of unary formal topologies means that algebraic dcpos are exponentiable in the category of open locales. But, the coreflection theorem states that open locales are coreflective in locales and hence, as a consequence of well-known impredicative results on exponentiable locales, it allows to prove that locally compact open locales are exponentiable in the category of open locales. (shrink)

Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.

In the last decades there has been a great controversy about the scientific status of emotion categories. This controversy stems from the idea that emotions are heterogeneous phenomena, which precludes classifying them under a common kind. In this article, I analyze this claim—which I call the Variability Thesis—and argue that as it stands, it is problematically underdefined. To show this, I examine a recent formulation of the thesis as offered by Scarantino (2015). On one hand, I raise some issues regarding (...) the logical structure of the claim. On the other hand, and most importantly, I show that the Variability Thesis requires a consensus about what counts as a relevant pattern of response in different domains, a consensus that is lacking in the current literature. This makes it difficult to assess what counts as evidence for or against this thesis. As a result, arguments based on the Variability Thesis are unwarranted. This raises serious concerns about some current empirical theories of emotions, but also sheds light on the issue of the scientific status of emotion categories. (shrink)

The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural (...) rules. Next, Hubert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.The first part of the paper, which follows, contains the first two sections, which deal with sequent-systems and Hubert-formulations. The second part, due to appear in the next issue of this journal, will contain the third section, which deals with groupoid models. (shrink)

The purpose of this paper is to connect the proof theory and the model theory of a family of prepositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related to BCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the (...) structural rules. Next, Hilbert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.Below is the sequel to the first part of the paper, which appeared in the previous issue of this journal (vol. 47 (1988), pp. 353–386). The first part contained sections on sequent-systems and Hilbert-formulations, and here is the third section on groupoid models. This second part is meant to be read in conjunction with the first part. (shrink)

A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. A set equipped with a convergent cover relation is a predicative counterpart of a locale, where the given set plays the role of a set of generators, typically a base, and the cover encodes the relations between generators. A positivity relation enriches the structure of a locale; among other things, it is a tool (...) to study some particular subobjects, namely the overt weakly closed sublocales. We relate the category of locales to that of positive topologies and we show that the former is a reflective subcategory of the latter. We then generalize such a result to the category of suplattices, which we present by means of cover relations. Finally, we show that the category of positive topologies also generalizes that of formal topologies, that is, overt locales. (shrink)

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...) pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

We analyse the category-theoretical structures involved with the notion of continuity within the framework of formal topology. We compare the category of basic pairs to other categories of “spaces” by means of canonically determined functors and show how the definition of continuity is determined in a certain, canonical sense. Finally, we prove a standard adjunction between the algebraic approach to spaces and the category of topological spaces.

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)

We re-evaluate existing data that demonstrate a large amount of variability in the content of categories considering the fact that these data have been obtained in a specific task: the production of features of single isolated categories. We present new data that reveal a large consensus when participants have to judge whether or not a given feature is characteristic of a category and we show that classification tasks produce an intermediate level of consensus. We argue that the differences observed between (...) tasks are due to the extent of implied context and we propose a reinterpretation of typicality effects, demonstrating that they are compatible with the existence of a stable conceptual core. In order to explain how the existence of a conceptual core is consistent with variability due to context, we present a theory of categorisation based on a property tree organisation. Within a domain of description, we distinguish between semantic implications (flying → moving) and empirical implications (flying → having wings) as well as between properties used to describe objects. Semantic implications serve to build property lines and Galois lattices are used to reveal category structures according to empirical implications. We show that variability in the category content may be explained by the fact that some properties are emphasised while others are masked according to the context. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on (...) fronts, generalizing the Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

L’atlas linguistique finnois de Lauri Kettunen (1940), accessible en ligne, a été initialement conçu par son auteur en fonction de variables de phonologie diachronique. Cependant, en raison de l’intrication de la phonologie dans la morphologie flexionnelle nominale et verbale du finnois, ces données se prêtent aisément à une lecture en termes de taxinomie morphologique. Le finnois apparaît alors comme bien moins « agglutinant » sur le plan typologique, et bien plus inférentiel, ou de type fusionnel. Nous appliquons le modèle (...) PFM (Paradigm Function Morphology) dans cette perspective, en proposant une modélisation diasystémique des classes flexionnelles du finnois. L’approche diachronique de Kettunen, fondée sur des étymons et des schèmes concaténatifs « agglutinants » invite par ailleurs à remonter plus haut dans l’histoire de la langue. On voit alors, comme d’un système somme toute simple de bipartition entre radicaux thématiques et athématiques, de disyllabes et d’imparisyllabiques, le diasystème finnois a évolué vers une complexification croissante, tout en préservant les structures fondamentales héritées. (shrink)

The distinction between abstract and concrete concepts is fundamental to cognitive linguistics and cognitive science. This distinction is commonly operationalized through concreteness ratings based on the aggregated judgments of many people. What is often overlooked in experimental studies using this operationalization is that ratings are attributed to words, not to concepts directly. In this paper we explore the relationship between the linguistic properties of English words and conceptual abstractness/concreteness. Based on hypotheses stated in the existing linguistic literature we select a (...) set of variables and verify whether they are statistically associated with concreteness ratings. We show that English nouns are rated as more concrete compared to other parts of speech, but mass nouns are rated as less concrete than count nouns. Furthermore, a more complex morphological structure is associated with abstractness, and as for etymology, French- and Latin-derived words are more abstract than words of other origin. This shows that linguistic properties of words are indeed associated with the degree of concreteness that we attribute to the underlying concepts, and we discuss the implications that these findings have for linguistic theory and for empirical investigations in the cognitive sciences. (shrink)

A pattern of interaction that arises again and again in programming is a 'handshake', in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent--the client or Angel--and concluded by the other--the server or Demon. We present a category in which the objects--called interaction structures in the paper--serve as descriptions of services provided across such handshaken interfaces. The morphisms--called (general) simulations--model components that provide one such service, (...) relying on another. The morphisms are relations between the underlying sets of the interaction structures. The proof that a relation is a simulation can serve (in principle) as an executable program, whose specification is that it provides the service described by its domain, given an implementation of the service described by its codomain. This category is then shown to coincide with the subcategory of 'generated' basic topologies in Sambin's terminology, where a basic topology is given by a closure operator whose induced sup-lattice structure need not be distributive; and moreover, this operator is inductively generated from a basic cover relation. This coincidence provides topologists with a natural source of examples for non-distributive formal topology. It raises a number of questions of interest both for formal topology and programming. The extra structure needed to make such a basic topology into a real formal topology is then interpreted in the context of interaction structures. (shrink)

For G a group definable in some structure M, we define notions of “definable” compactification of G and “definable” action of G on a compact space X , where the latter is under a definability of types assumption on M. We describe the universal definable compactification of G as View the MathML source and the universal definable G-ambit as the type space SG. We also point out the existence and uniqueness of “universal minimal definable G-flows”, and discuss issues of amenability (...) and extreme amenability in this definable category, with a characterization of the latter. For the sake of completeness we also describe the universal compactification and universal G-ambit in model-theoretic terms, when G is a topological group. (shrink)

This study investigates global properties of three categories of English text: canonical fiction, non-canonical fiction, and non-fictional texts. The central hypothesis of the study is that there are systematic differences with respect to structural design features between canonical and non-canonical fiction, and between fictional and non-fictional texts. To investigate these differences, we compiled a corpus containing texts of the three categories of interest, the Jena Corpus of Expository and Fictional Prose. Two aspects of global structure are investigated, variability and self-similar (...) patterns, which reflect long-range correlations along texts. We use four types of basic observations, the frequency of POS-tags per sentence, sentence length, lexical diversity, and the distribution of topic probabilities in segments of texts. These basic observations are grouped into two more general categories, the lower-level properties and, which are observed at the level of the sentence, and the higher-level properties and, which are observed at the textual level. The observations for each property are transformed into series, which are analyzed in terms of variance and subjected to Multi-Fractal Detrended Fluctuation Analysis, giving rise to three statistics: the degree of fractality () of the fractal spectrum. The statistics thus obtained are compared individually across text categories and jointly fed into a classification model. Our results show that there are in fact differences between the three text categories of interest. In general, lower-level text properties are better discriminators than higher-level text properties. Canonical fictional texts differ from non-canonical ones primarily in terms of variability in lower-level text properties. Fractality seems to be a universal feature of text, slightly more pronounced in non-fictional than in fictional texts. On the basis of our results obtained on the basis of corpus data we point out some avenues for future research leading toward a more comprehensive analysis of textual aesthetics, e.g., using experimental methodologies. (shrink)

We offer a topological treatment of scattered theories intended to help to explain the parallelism between, on the one hand, the theorems provable using Descriptive Set Theory by analysis of the space of countable models and, on the other, those provable by studying a tree of theories in a hierarchy of fragments of infinintary logic. We state some theorems which are, we hope, a step on the road to fully understanding counterexamples to Vaught's Conjecture. This framework is in the early (...) stages of development, and one area for future exploration is the possibility of extending it to a setting in which the spaces of types of a theory are uncountable. (shrink)

This essay is an exploration of the relationship between Agamben's 1995 text, Homo Sacer, and Derrida's 1992 “Force of Law” essay. Agamben attempts to show that the camp, as the topological space of the state of exception, has become the biopolitical paradigm for modernity. He draws this conclusion on the basis of a distinction, which he finds in an essay by Walter Benjamin, between categories of life, with the “pro‐tagonist” of the work being what he calls homo sacer, or bare (...) life—life that is stripped of its humanity and value. Five years earlier, in 1990, Derrida had given a lecture at UCLA (later published in its entirety as “The Force of Law”) in which he had analyzed the very same essay by Benjamin and had highlighted the distinction between “base life” and “just life.” The implications of his analysis show a discomforting prox‐imity between Benjaminian messianism and the Nazi “final solution,” a conclusion that Agamben dismisses entirely. In this paper, however, I demonstrate that the structures of the two works are quite similar in many important ways. I argue that, though the broad scope of Agamben's work is original in many respects, and I would not wish to reduce Agamben's work to Derridean repetitions, he nevertheless utilizes much more of Derrida's analysis, specifically with respect to the categori‐zation of life, than he would like the reader to believe. (shrink)

High‐throughput genomic technologies are revolutionizing human genetics. So far the focus has been on the 1.5% of the genome, which is coding, in spite of the fact that the great majority of genomic variants fall outside the coding regions. Recent efforts to annotate the non‐coding sequence show that over 80% of the genome is biochemically active. The genome is divided into regulatory domains consisting of sequence regions that enhance and/or silence the expression of nearby genes and are, in some cases, (...) separated by boundaries with insulator activity. In this paper, we review the recent advances in the identification of variations that influence gene regulation and their consequences for human disease. We hypothesize that structural variations outside of the coding genome can interfere with normal gene regulation by disrupting the regulatory landscape. Therefore, the regulatory landscape of the genome has also to be taken into consideration when investigating the pathology of human disease. (shrink)

Hrushovski's suggestion, given in [3], to capture the structure of the 1-analysable covers of a theory T using simplicial groupoids definable in T is realized here. The ideas of Haykazyan and Moosa, found in [“Functoriality and uniformity in Hrushovski's groupoid-cover correspondence,” Annals of Pure and Applied Logic, 2018] are used, and extended, to define an equivalence of categories. Finally, a couple of examples are studied with these new tools.

The concept of rhetorical predicates reveals significant information about Anggor semantic structure. Still greater generality comes from introducing the theoretical concept of a topologically based time index. This topological handling of time provides a tool for studying universal aspects of the cognition of time. Time indexing provides an adequate means of indicating temporal relations in semantic structure without being compelled to consider particular surface manifestations of temporal relations as basic, and also provides a means of relating intralinguistic and extralinguistic temporal (...) reference. Time indexing appears to go more appropriately with propositions than with variables. (shrink)

“Is logic a physical variable?” This thought-provoking question was put forward by Michael Heller during the public lecture “Category Theory and Mathematical Structures of the Universe” delivered on 30th March 2017 at the National Quantum Information Center in Sopot. It touches upon the intimate relationship between the foundations of physics, mathematics and philosophy. To address this question one needs a conceptual framework, which is on the one hand rigorous and, on the other hand capacious enough to grasp the (...) diversity of modern theoretical physics. Category theory is here a natural choice. It is not only an independent, well-developed and very advanced mathematical theory, but also a holistic, process-oriented way of thinking. (shrink)

Vocal bursts are non-linguistic affectively-laden sounds with a crucial function in human communication, yet their affective structure is still debated. Studies showed that ratings of valence and arousal follow a V-shaped relationship in several kinds of stimuli: high arousal ratings are more likely to go on a par with very negative or very positive valence. Across two studies, we asked participants to listen to 1,008 vocal bursts and judge both how they felt when listening to the sound (i.e. core affect (...) condition), and how the speaker felt when producing it (i.e. perception of affective quality condition). We show that a V-shaped fit outperforms a linear model in explaining the valence-arousal relationship across conditions and studies, even after equating the number of exemplars across emotion categories. Also, although subjective experience can be significantly predicted using affective quality ratings, core affect scores are significantly lower in arousal, less extreme in valence, more variable between individuals, and less reproducible between studies. Nonetheless, stimuli rated with opposite valence between conditions range from 11% (study 1) to 17% (study 2). Lastly, we demonstrate that ambiguity in valence (i.e. high between-participants variability) explains violations of the V-shape and relates to higher arousal. (shrink)

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces (...) are introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this book. (shrink)

We present the paradigm of categories-as-syntax. We briefly recall the even stronger paradigm categories-as-machine-language which led from -calculus to categorical combinators viewed as basic instructions of the Categorical Abstract Machine. We extend the categorical combinators so as to describe the proof theory of first order logic and higher order logic. We do not prove new results: the use of indexed categories and the description of quantifiers as adjoints goes back to Lawvere and has been developed in detail in works of (...) R. Seely. We rather propose a syntactic, equational presentation of those ideas. We sketch the (quasi-equational) categorical structures for dependent types, following ideas of J. Cartmell (contextual categories). All these theories of categorical combinators, together with the translations from -calculi into them, are introduced smoothly, thanks to the systematic use of– - an abstract variable-free notation for -calculus, going back to N. De Bruijn, – - a sequent formulation of the natural deduction. (shrink)

Beyond their linguistic and rhetorical uses, the mental epistemic verbs to knowand to believe reveal a basic conceptual system for human intentionality and the theory of representational mind. Numerous studies, particularly in the field of child development, have been devoted to the conditions under which knowledge and belief are acquired. Upstream of this empirical approach, this paper proposes a topological model of the conceptual structure underlying the linguistic use of to know and to believe. A cusp model of catastrophe theory (...) is chosen to model the formation of epistemic states. Its main characteristic is considering to believe as an intermediate state which lacks stability and presents the delayed effect of hysteresis. The attribution of mental states to the other (viewpoint of the third person) is obtained by the crossing of first and third person knowledge and belief, which gives rise to new categories (to know if and to falsely believe) and closes the system. Another merging of the beliefs of persons A and B, using the butterfly catastrophe, provides a model of interpersonal belief appreciated by an independent observer along a potential evolving from agreement to disagreement. (shrink)

This paper is about the most important technical problem faced by Structured Meanings Semantics: the reiteration of hyperintensional functors (i.e., functors of -categorial languages of the sort defined by Max Cresswell in [6]). A way to solve this problem in a general and natural way by using Scott's Domains is both suggested and shown. The result is a semantics which unrestrictedly allows reiterations of hyperintensional functors. The semantics is also extended to accommodate -categorial languages with variables.

Lacan postulated that the psyche can be understood by means of certain structures, which control our lives and our desires, and which operate differently at different logical moments or stages of formation.Jacques Lacan and the Logic of Structure offers us a reading of the major concepts of Lacan in terms of his later topological theory and aims to show how this was always a concern for Lacan and not only an issue in the last seminars. Ellie Ragland discusses how (...) various stages of formation can be uncovered topologically within language itself, and operate to place certain properties – fantasy, the drive, jouissance, discourse and ethics in language itself. In this way she explores not only how language actually works in tandem with the properties, but also gives a different idea of what knowledge actually is and what implications that may have for reimagining and reworking differential/diagnostic structures. Jacques Lacan and the Logic of Structure is a compelling exponent of the innovative approaches Lacan takes to rethinking what psychoanalysis is and what it can do to enlighten psychoanalysts and treat patients. It will be essential reading to psychoanalysts, psychoanalytic psychotherapists, training graduate students in the fields of film, literary, gender and cultural studies. (shrink)

Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class sized mathematical structures (...) need to be allowed for in constructive set theory because the powerset axiom and the full separation scheme are necessarily missing from constructive set theory. We also consider the notion of a formal topology, usually treated in Intuitionistic type theory, and show that the category of set-generated locales is equivalent to the category of formal topologies. We exploit ideas of Palmgren and Curi to obtain versions of their results about when the class of formal points of a set-presentable formal topology form a set. (shrink)

An incline S is a commutative semiring where r+1=1 for any r \in S . We note that the ideal lattice of an S-semimodule is naturally an S-semimodule and so is its congruence lattice when S is transitive. We prove that the categories of complete S-semimodules, together with dual functor, internal hom and tensor product, is a ⋆-autonomous category. We define the locally and globally maximal congruences which are related to Birkhoff subdirect product decomposition. We show that the categories of (...) S-semimodules, algebraic S-semimodules and topological S-semimodules are equivalent. Finally, we get a sheaf representation of any S-semimodule. (shrink)

Concerning race and its intertwinements with gender, sexual orientation, class, accents, or ability there is a scarcity of social psychological research in Europe. With an intersectional approach studying racism in Europe it is possible to detect specific experiences of discrimination. The prevalent understanding of European racism is connected to migration from the former colonies to the European metropoles and the post-Second-World-War immigration of ‘guest workers.’ Thus, the focus of this research is on work-related discrimination. Against the background of a short (...) historical review, we present the results of the few existing studies on intersectional discrimination within the labor market in Europe and discuss their implications. The pattern of findings is more complex than the assumption that individuals belonging to two or more marginalized social categories are always the most discriminated ones. Gender, sexual orientation, and origin rather interact with the specific job context. These interactions determine whether minority individuals are discriminated against or even preferred over individuals belonging to the majority group. We argue that considering the stereotype content model and social-identity theory helps to structure the sometimes contradictory results of intersectionality research. Therefore, the review presents new perspectives on racism in Europe based on current research, develops hypotheses on the interplay of intersecting identities, and identifies four novel research questions based on racist attributions considering situational variables: These are the role of concrete job contexts in explaining discrimination, the influence of different stereotypes regarding marginalized groups, the explanatory value of sexual orientation as well as class or socioeconomic-status and age in terms of some patterns of results. (shrink)