The premise of this paper is that the goal of signifying Being central to ontological phenomenology has been tacitly subverted by the semiotic structure of conventional phenomenological writing. First it is demonstrated that the three components of the sign—sign-vehicle, object, and interpretant (C. S. Peirce)—bear an external relationship to each other when treated conventionally. This is linked to the abstractness of alphabetic language, which objectifies nature and splits subject and object. It is the subject-object divide that phenomenology must surmount if (...) it is to signify Being. To this end, we go beyond alphabetic convention and explore the use of iconic signs. Following the lead of Merleau-Ponty, the iconic expression of Being is seen as entailing paradox, and we are directed to the fields of visual geometry and topology, where we work with three paradoxical figures: the Necker cube, Moebius strip, and Klein bottle. While the Necker cube and Moebius prove to have their limitations in fully signifying Being, the Klein bottle, possessing an added dimension (made palpable via a stereogram), can embody Being more intimately, provided that it is approached in a radically non-classical way. The essay closes with the realization that the most concrete signification of Being must be a self-signification. Here the author removes his cloak of anonymity and makes his presence tangibly felt in the text. (shrink)

This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For (...) the second case, we investigate how the development of new representational forms influenced the development of the theory of exponentiation. For the third case, we analyze the connection between the development of commutative diagrams and the development of both algebraic topology and category theory. Our main conclusions are that semiotic scaffolding indeed plays a role in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding. (shrink)

A topological model of elementary semiotic schemes is presented. Implications are discussed with respect to the establishment of abstract terms and the search for ultimate meaning.

Our greatest certainty and greatest mystery is our mortality. In this book, Steven M. Rosen explores the profound mystery of death and rebirth from psychological, philosophical, and alchemical perspectives. To model, embody, and contain the paradoxical transformations involved in the death-rebirth enigma, Rosen employs a paradoxical form of mathematics: the topology of the Moebius strip and Klein bottle. As we follow this alchemical odyssey, the author makes himself transparent through his dreams and brings himself tangibly into his text so as (...) to enact a dialectic of ego and Self. "In tackling the subject of death and rebirth Steven Rosen writes about our modern state of mind, how we got like this and where we need to go from here. He does all this with a psychotherapeutic insight that begins with his own subjectivity--and his own dreams--and ends with the subjectivity of the modern world. Using myths, dreams, and alchemical symbolism as well as psychological research and Jungian insights, Rosen speaks to us all from the self and the Self. A book to be read immediately, and then read again." --Christopher Hauke, Jungian analyst and author of Jung and the Postmodern: The Interpretation of Realities "How does a mental-spiritual ego, the creation of our post-Renaissance world, embrace the body as a living partner? In Dreams, Death, Rebirth, Steven M. Rosen offers a topological analysis that meets the challenge of this daunting endeavor. It is a remarkable accomplishment, and vital for the advancement of psychotherapy." --Nathan Schwartz-Salant, Jungian analyst and author of The Black Nightgown: The Fusional Complex and the Unlived Life Steven M. Rosen is professor emeritus of psychology at the College of Staten Island of the City University of New York. After receiving his PhD in psychology in 1971, he began exploring the foundations, frontiers, and poetics of science, and his work became transdisciplinary and philosophical in nature. His essays have appeared in journals and collections spanning the fields of psychology, philosophy, theoretical physics, education, semiotics, and ecology. He is the author of Science, Paradox, and the Moebius Principle (1994), Dimensions of Apeiron (2004), Topologies of the Flesh (2006), and The Self-Evolving Cosmos (2008). (shrink)

As the accompanying articles in the Special Issue on Semiotic Scaffolding will attest, my colleagues in biosemiotics have done an exemplary job in showing us how to think about the critically generative role that semiotic scaffolding plays “vertically” – i.e., in evolutionary and developmental terms – by “allowing access to the upper floors” of biological complexity, cognition and evolution.In addition to such diachronic considerations of semiotic scaffolding, I wish to offer here a consideration of semiotic scaffolding’s synchronic power, as well (...) – and in particular the ability that it can afford its users to access new and other sign relations “horizontally” as a function of the way that multiple semiotically scaffolded relations intertwine to result in a “definite semantic topology that determines the ways that symbols modify each other’s referential functions in different combinations”.Taking up, in turn, Terrence Deacon’s later challenge that what the sciences of cognition – and biology more generally – needs to “come to grips with [is] the process of semiosis; the dynamic of interpretive activity by which semiotic relationships emerge from other semiotic relationships [as] intrinsically dynamic phases in a generative process”, I attempt here to show how Deacon’s own Peirce-inspired matrix of referential sign relations as presented in The Symbolic Species, when viewed as a semiotic scaffold of interactional constraints and possibility biases, provides the key to understanding the essentially thirdness-manifesting nature of symbol reference, formation and growth. (shrink)

This paper aims to understand how and why tree diagrams are of central importance to microbiome scientists in their practices of meaning making. The interfaces that scientists use are, in fact, topological structures that organize the genetic data generated by sequencing technology. They establish relationships among microbes and also between microbes and the conditions of the ecological niche they help construct. The tree structure is a powerful _topos_ of knowledge organization in Western culture. However, biomolecular research has revealed the (...) existence of horizontal gene exchange among microbes and other merging forms; these cast doubt on the tree as a valid representational metaphor for the tangle of the microbial world and help to overcome neo-Darwinism. This essay analyzes the software and interfaces used by microbiome scientists as tools for organizing knowledge that shape how we see human-microbe relationships, while escaping a representational function. While trees have long been considered representative forms of visualization of an evolutionary paradigm, we emphasize the non-illustrative and heuristic power of these interfaces, which, although steeped in centuries of reflection and debate on evolutionary theories, respond more to a diagrammatic logic: tools for discovering the new from genetic “black matter” and for exploring new forms of relationships between microbes and humans. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

We all intuitively know what a diagram is, and still it is surprisingly difficult to describe it as a semiotic function or type. In this article, we present four groups of hypotheses in view of a clarification. We hypothesize: (1) That diagrams are signs of a distinct type, unknown to classical semiotics; (2) That the elementary graphs of a diagram are all derived fromlines and pointsintopologicalmental spaces. The mind applies these diagrammatic spaces to referential spaces in many ways, but (...) basically through conceptual integration (blending). The mind blends topology and reference, which makes the topology unnoticeable; (3) That elementary diagrammatic graphs constitute a natural, phenomenological, spatiotemporal, figurative and dynamic but informal geometry in the embodied, thinking mind; (4) That diagrammatic signs are the active components of the abstract mental figuration in working memory that accompany perception and deliver the schematizing ideas which invest and connect our categories and construe proper descriptive, narrative, patterns of inferentialthoughtand programs of sensorimotor and social action. (shrink)

The aim of this article is to tackle the sociosemiotic strategies through which the relation between power and visibility is articulated in today’s metropolitan São Paulo. Drawing on the theoretical-methodological framework of Greimasian and post-Greimasian semiotics, the following hypotheses are put forth: (1) contemporary São Paulo is characterized by a true visual hypertrophy, which manifests itself, all at once, in both its architectural and mediatic landscapes; (2) in São Paulo, power is hypervisible and apparently transparent; (3) the excess of (...) images, gazes, and perspectives produces, in São Paulo, dense and wide areas of topological, mediatic, and social invisibility; (4) the predominant visibility in São Paulo can be qualified as a “populist” visibility. Based on these assumptions, this article intends to contribute to the consolidation of a critical debate on the visual matrices of power and on social processes of exclusion and inclusion currently in place in global metropolises. Likewise, it is intended to contribute to the elaboration of a theoretical-methodological framework capable of understanding and addressing the complexity of the phenomena that characterize such debate. (shrink)

ABSTRACT Recently, children’s books have used augmented reality as a resource, being called 4D books. Augmented reality allows the user to see through the world while interacting in real-time with images produced digitally, resulting in interactivity. The present study aims to introduce the results of a brief reflection on the illustrated book O reino encantado do pôneis 4D under the approach of the semiotics of culture, departing from the notion of semiosis and semiosphere. The semiosphere, drawn by Lotman (1990), (...) in analogy with the biosphere, can help understand the topology of the real and virtual worlds, referred to as the real subsemiosphere and virtual subsemiosphere, located in the interior of the broader semiosphere of the Brazilian culture. In 4D/Augmented reality books, the elements from the virtual subsemiosphere are placed into the real subsemiosphere, crossing their borders. (shrink)

The book explores Peirce's non standard thoughts on a synthetic continuum, topological logics, existential graphs, and relational semiotics, offering full mathematical developments on these areas. More precisely, the following new advances are offered: (1) two extensions of Peirce's existential graphs, to intuitionistic logics (a new symbol for implication), and other non-classical logics (new actions on nonplanar surfaces); (2) a complete formalization of Peirce's continuum, capturing all Peirce's original demands (genericity, supermultitudeness, reflexivity, modality), thanks to an inverse ordinally iterated (...) sheaf of real lines; (3) an array of subformalizations and proofs of Peirce's pragmaticist maxim, through methods in category theory, HoTT techniques, and modal logics. The book will be relevant to Peirce scholars, mathematicians, and philosophers alike, thanks to thorough assessments of Peirce's mathematical heritage, compact surveys of the literature, and new perspectives offered through formal and modern mathematizations of the topics studied. (shrink)

This article consistently elaborates the extra‐contextual nature of metaphysical knowledge. Metaphysicsis seen as a semantic construction of culture that produces a certain type of thinking, memory, and identification: that is, subjectivity, and sociality as an ethical and axiological model of interaction with the world and the Other. The paper argues that metaphysics is a kind of orientation in space and that culture is a semiotic way of world orientation, or collection of spaces into an intelligible structure, a specific characteristic of (...) human existence in the universe. Indeed, metaphysics through the space of culture allows one to experience the universe empirically as unity, to assume the presence of meaning. Based on the analysis, the paper summarizes the definition of the phenomenon of culture as a specifically human way of mastering space and controlling time, consciousness as a topology of reflective practices, and virtual reality technology as a space of pure metaphysics. (shrink)

The question of “time” is a worthy topic of psychoanalytic inquiry, concerning at least three different levels: technical, epistemological, and existential. However, if subjective well-being is the ultimate purpose of the analytic experience, it is immediately clear that the last level also defines the previous ones. In this perspective, we can attribute an innovative role to Lacan’s inquiry on time, in receiving the Freudian psychoanalytical legacy and in participating in the contemporary thought about subjective consciousness of time. Indeed, starting from (...) the paper entitled “Logical time”, Lacan completely abandons a linear notion of time: what concerns psychoanalysis is not the “real” past sequence of events in themselves, but the way these events exist “now” in memory, and the way the patient reports them. This dynamic idea of subjective temporality was immediately received not only by clinical therapy but also by other branches of knowledge. Nevertheless, in his late teaching Lacan directly engages the epistemological level of time analysis, trying to offer constants to the dynamic of time consciousness. Therefore, in the last years of his Seminar, he introduces into his work the mathematical concept of topological space, and begins to delineate a close relationship between time and space from the immanent point of view of discourse theory. If “rhythm” seems to be the ultimate horizon opened by Lacan’s teaching on time toward the end of his career, this perspective could mark the definitive return to Freud and anticipate some of the current most valid research in semiotics and physics. Unfortunately, the death of the French psychoanalyst resulted in this perspective remaining only barely sketched out. (shrink)

This research on the morphogenesis of the city uses conjointly morphodynamic semiotic theory and structural theory of the urban form to elaborate the existence of a non-trivial topology, stemming from a process of stratification. The basic thesis of this work is the following: On the one hand, the form of a city emerges from the choice of its physical site; on the other hand, it modifies itself through geo-historical actualization. The theory of urban form proposes a global theory of the (...) engendering of forms and their relationships to spatial positions. Morphodynamic semiotics adopts a dynamic conception of the modal phenomenon. These theoretical influences offer our study a morphogenetic conception of meaning that is reconstituted through spatial stratification. This model thus proposed enables us to reconstitute the form of the city in general. (shrink)

We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic (...) geometry a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

Recursion or self-reference is a key feature of contemporary research and writing in semiotics. The paper begins by focusing on the role of recursion in poststructuralism. It is suggested that much of what passes for recursion in this field is in fact not recursive all the way down. After the paradoxical meaning of radical recursion is adumbrated, topology is employed to provide some examples. The properties of the Moebius strip prove helpful in bringing out the dialectical nature of radical (...) recursion. The Moebius is employed to explore the recursive interplay of terms that are classically regarded as binary opposites: identity and difference, object and subject, continuity and discontinuity, etc. To realize radical recursion in an even more concrete manner, a higher-dimensional counterpart of the Moebius strip is utilized, namely, the Klein bottle. The presentation concludes by enlisting phenomenological philosopher Maurice Merleau-Ponty’s concept of depth to interpret the Klein bottle’s extra dimension. (shrink)

Merrell's task in this work is to transform the Peircean tradition of semiotics in the light of more recent work in such research areas as chaos physics, topological theory, and the newer quantum theories. Relying on the theories of David Bohm, among others, Merrell develops a conventionalist conception of semiotics that stresses the constructive power of signs to shape space, time, and the basic contours of the human process. The approach is an evolutionary one, but it is (...) not confined to the neo-Darwinian biological framework. Evolution is seen in terms of the movement from a primal state of pure firstness to the determinate world of interaction. (shrink)

Möbian Nights: Literary Reading in a Time of Crisis develops a new understanding of literary reading: that in the wake of disasters like the Holocaust, death remains a premise of our experience rather than a future. Challenging customary "aesthetic" assumptions that we write in order not to die, Sandor Goodhart suggests (with Kafka) we write to die. Drawing upon analyses developed by Girard, Foucault, Blanchot, and Levinas (along with examples from Homer to Beckett), Möbian Nights proposes that all literature works (...) "autobiographically", which is to say, in the wake of disaster; with the credo "I died; therefore, I am"; and for which the language of topology (for example, the "Möbius strip") offers a vocabulary for naming the "deep structure" of such literary, critical, and scriptural sacrificial and anti-sacrificial dynamics. (shrink)

Oleg B. Zaslavskii. The little in a non-Euclidean world: On the artistic space in Tom Stoppard's film and play “Rosencrantz and Guildenstern are dead”. It is shown that quite different aspects of Tom Stoppard’s work — spatial organization, relationship between reality and the conditional character of events, causality and narrative links, the problems of choice and personality — are united by the spatial one-sided model like the Möbius strip or Klein bottle. The artistic space turns out to be not orientable, (...) the time being cyclic. This enables us to explain the mutual exchange of names between Rosencrantz and Guildenstern and a number of other paradoxical features in the plot and composition. The model like the Möbius strip embodies the absence of a free choice: there is no other side in the world and there is no chance to escape from the fate indicated in the title of Tom Stoppard’s work. The relevance of topology, e.g. the property of a globalnature, is connected with the fact that a bearer of danger is the world as a whole. Apart from this, it points to the fact that such a structure of the world is essentially “non-Euclidean” and cannot be understood on the basis of observations from every-day life or “obvious” experiments like those carried out by Rosencrantz. (shrink)

Autopoietic theory is increasingly seen as a candidate for a radical theory of law, both in relation to its theoretical credentials and its relevance in terms of new and emerging forms of law. An aspect of the theory that has remained less developed, however, is its material side, and more concretely the theory’s accommodation of bodies, space, objects and their claim to legal agency. The present article reads Luhmann’s theory of autopoietic systems in a radical and material manner, linking it (...) on the one hand to current post-structural theorisations of law and society, and on the other hand extending its ambit to accommodate the influx of material considerations that have been working their way through various other disciplines. The latter comprises both a materialisation of the theory itself and ways of conceptualising the legal system as material through and through. This I do by further developing what I have called Critical Autopoiesis, namely an acentric, topological, post-ecological and posthuman understanding of Luhmann’s theory, that draws on Deleuzian thought, feminist theory, geography, non-representational theory, and new material and object-oriented ontologies. These are combined with some well-rehearsed autopoietic concepts, such as distinction, environment and boundaries; Luhmann’s earlier work on materiality continuum; more recent work on bodies and space; as well as his work on form and medium in relation to art. The article concludes with five suggestions for an understanding of what critical autopoietic materiality might mean for law. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...) point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

In this paper I want to show that topology has a bearing on the theory of tropes. More precisely, I propose a topological ontology of tropes. This is to be understood as follows: trope ontology is a „one-category”-ontology countenancing only one kind of basic entities, to wit, tropes. 1 Hence, individuals, properties, relations, etc. are to be constructed from tropes.

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological (...) models of knowledge and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

NOTE: Series number is not an integer: n/a.

Scholars often argue that Charles Sanders Peirce was responsible for Josiah Royce's semiotic turn in _The Problem of Christianity_ of 1913. Thus scholars tend to assume that a _Roycean_ approach to semiotics was a later development and derives almost entirely from Peirce's semiotics. Far from a later development, Royce probably read Peirce much earlier. Indeed, even before Royce had read Peirce, the kernel of a Rocyean approach to semiotics is found in the dissertation of 1878. Thus the (...) present essay will prove that a Roycean approach to semiotics did not have a basis in Peirce's semiotics, whether early or later, but rather grew out of Royce's earliest writings. The first part will reconstruct the early pragmatism in the dissertation of 1878 and find that the kernal of a Roycean approach to semiotics was the idea of a _mediating third_. The second part will show how the disseration's pragmatism develops into a phenomenology of time that contains Royce's earliest semiosic insights. The third part will explain how the early pragmatism and phenomenology come together in the argument on the possibility of error from Royce's _The Religious Aspect of Philosophy_ of 1885. The possibility of error is Royce's original argument for absolute idealism, so the essay will conclude that a Roycean approach to semiotics entails a semiotics of the absolute. (shrink)

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the (...) topological indices of different structures. (shrink)

The purpose of this paper is to present a very versatile family of logical systems ofpositionalortopologicallogic. These systems—obtained by generalizing the existing systems of chronological logic—are to have a very general nature, capable of reflecting the characteristics of a wide range of logical systems, including not only chronological (alsotemporalortense) logic, but also what we may call locative or place logic, and even a logic of “possible worlds”.

The completeness of the modal logic S4 for all topological spaces as well as for the real line , the n-dimensional Euclidean space and the segment etc. was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvili with a further simplification. The proof strategy is to embed a finite rooted Kripke structure for S4 into a (...) subspace of the Cantor space which in turn encodes . This provides an open and continuous map from onto the topological space corresponding to . The completeness follows as S4 is complete with respect to the class of all finite rooted Kripke structures. (shrink)

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorčević theory in the more general context of automorphism groups of not necessarily countable structures. One of the main points is a description of the universal ambit as a certain space of types in an expanded language. Using this, we recover results of Kechris et al. (Funct Anal 15:106–189, 2005), Moore (Fund Math 220:263–280, 2013), Ngyuen Van Thé (Fund Math 222: 19–47, 2013), in the context of automorphism groups of not (...) necessarily countable structures, as well as Zucker (Trans Am Math Soc 368, 6715–6740, 2016). (shrink)

Most contemporary approaches to meaning presume the limitation of semiotics (Didi-Huberman, Gumbrecht, Belting). The question of what kind of “semiotics” is required has not been asked. However, without some general science of meaning it is impossible to reform theory without committing past errors or ignoring progress. In the interest of reconnecting contemporary interests in “presence” to long-evolving needs, I review the ossification and decline of one theory of semiotics that serves as the tacit model rejected today. I (...) return to problems of the nature of the sign – whether it is “digital” or “analog” and conceived as “communication” or merely “meaning.” I then reconstitute a workable visual cognitive semiotics based on phenomenological premises. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is (...) to show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing (...) between natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)