Categorical Ontology I - Existence

The present paper approaches ontology and metaontology through mathematics, and more precisely through category theory. We exploit the theory of elementary toposes to claim that a satisfying “theory of existence”, and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category. This approach resembles, but is more general than, fuzzy logics, as most choices of E and thus of Ω E yield nonclassical, many-valued logics. Framed this way, ontology suddenly becomes more mathematical: a solid corpus of tech- niques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges’ famous paradoxes of Tlön’s “nine copper coins”, and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works

Categorical Ontology I - Existence

The present paper is the first piece of a series whose aim is to develop an approach to ontology and metaontology through category theory. We exploit the theory of elementary toposes to claim that a satisfying ``theory of existence'', and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category. This approach resembles, but is more general than, fuzzy logics, as most choices of \clE and thus of \Omega_\clE yield nonclassical, many-valued logics. Framed this way, ontology suddenly becomes more mathematical: a solid corpus of techniques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges' famous paradoxes of Tlön's ``nine copper coins'', and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works

Categorical Ontology I - Existence

The present paper is the first piece of a series whose aim is to develop an approach to ontology and metaontology through category theory. We exploit the theory of elementary toposes to claim that a satisfying ``theory of existence'', and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category. This approach resembles, but is more general than, fuzzy logics, as most choices of \clE and thus of \Omega_\clE yield nonclassical, many-valued logics. Framed this way, ontology suddenly becomes more mathematical: a solid corpus of techniques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges' famous paradoxes of Tlön's ``nine copper coins'', and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works

Categorical Ontology I - Existence

The present paper approaches ontology and metaontology through mathematics, and more precisely through category theory. We exploit the theory of elementary toposes to claim that a satisfying “theory of existence”, and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category. This approach resembles, but is more general than, fuzzy logics, as most choices of E and thus of Ω E yield nonclassical, many-valued logics. Framed this way, ontology suddenly becomes more mathematical: a solid corpus of tech- niques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges’ famous paradoxes of Tlön’s “nine copper coins”, and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works

Metaphor and Metanoia: Linguistic Transfer and Cognitive Transformation in British and Irish Modernism

This dissertation contributes to the critical expansions that Douglas Mao and Rebecca L. Walkowitz identify as New Modernist Studies. This expansion is temporal, spatial, and vertical. I engage with the effects Modernist texts have “above” the page: lived experience. I examine the structural similarity of linguistic metaphor and the mind as considered by cognitive scientists. Identifying the human mind as linguistic and language as an artifact of the human mind, my research extrapolates upon what I call the “psycho-ecology” of reading, a self-representational knot between text and mind that constitutes lived experience. Far from being an abstraction, psycho-ecology is concrete: atypical textual engagement is equated with a transformation in perception. The prologue traces a lineage between Modernism, phenomenology, and the cognitive sciences. The first chapter considers the relationship between two narrative levels in Oscar Wilde’s novel The Picture of Dorian Gray (1890). The second chapter considers temporal experimentation in Virginia Woolf’s novel To the Lighthouse (1927) in relation to Martin Heidegger’s formulation of being as that which discloses our experience with language as temporal and finite. The third chapter examines the “sentimental information” of James Joyce’s Finnegans Wake (1939) from a phenomenological approach to information theory. The final chapter analyzes Samuel Beckett’s Endgame (1957) as a zero-player game that discloses the limits of agency in psycho-ecology. The dissertation follows a trajectory beginning with the intimacy a reader has with alphanumeric text towards the increasing experience of illiteracy when encountering new languages such as digital code

Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat