12 found

Year:

Forthcoming articles
  1.  84
    David Ellerman (forthcoming). On Adjoint and Brain Functors. Axiomathes:1-21.
    There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory and (...)
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  2. Moti Mizrahi (forthcoming). Why Be an Intellectually Humble Philosopher? Axiomathes:1-14.
    In this paper, I sketch an answer to the question “Why be an intellectually humble philosopher?” I argue that, as far as philosophical argumentation is concerned, the historical record of Western Philosophy provides a straightforward answer to this question. That is, the historical record of philosophical argumentation, which is a track record that is marked by an abundance of alternative theories and serious problems for those theories, can teach us important lessons about the limits of philosophical argumentation. These lessons, in (...)
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  3.  31
    Seungbae Park (forthcoming). Against Mathematical Convenientism. Axiomathes:1-8.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine-Putnam indispensability (...)
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  4. Francis Beauvais (forthcoming). “Memory of Water” Without Water: Modeling of Benveniste’s Experiments with a Personalist Interpretation of Probability. Axiomathes:1-17.
    Benveniste’s experiments were at the origin of a scientific controversy that has never been satisfactorily resolved. Hypotheses based on modifications of water structure that were proposed to explain these experiments were generally considered as quite improbable. In the present paper, we show that Benveniste’s experiments violated the law of total probability, one of the pillars of classical probability theory. Although this could suggest that quantum logic was at work, the decoherence process is however at first sight an obstacle to describe (...)
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  5.  4
    Noel L. Clemente (forthcoming). A Virtue-Based Defense of Mathematical Apriorism. Axiomathes:1-17.
    Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, (...)
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  6. L. Dappiano (forthcoming). La holologia come progetto di metafisica descrittiva. Le parti e l'intero nella concezione di Aristotele. I'. Axiomathes.
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  7.  7
    Wojciech Krysztofiak (forthcoming). Representational Structures of Arithmetical Thinking: Part I. Axiomathes:1-40.
    In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a (...)
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  8.  4
    Wojciech Krysztofiak (forthcoming). Algebraic Models of Mental Number Axes: Part II. Axiomathes:1-33.
    The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed (...)
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  9.  5
    Vassilis Livanios (forthcoming). Beyond Platonism and Nominalism? Axiomathes:1-7.
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  10.  2
    John R. Shook (forthcoming). Abduction, Complex Inferences, and Emergent Heuristics of Scientific Inquiry. Axiomathes:1-30.
    The roles of abductive inference in dynamic heuristics allows scientific methodologies to test novel explanations for the world’s ways. Deliberate reasoning often follows abductive patterns, as well as patterns dominated by deduction and induction, but complex mixtures of these three modes of inference are crucial for scientific explanation. All possible mixed inferences are formulated and categorized using a novel typology and nomenclature. Twenty five possible combinations among abduction, induction, and deduction are assembled and analyzed in order of complexity. There are (...)
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  11.  42
    Jairo José Silvdaa (forthcoming). Structuralism and the Applicability of Mathematics. Axiomathes.
    In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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  12. Valerio Velardo (forthcoming). Recursive Ontology: A Systemic Theory of Reality. Axiomathes:1-26.
    The article introduces recursive ontology, a general ontology which aims to describe how being is organized and what are the processes that drive it. In order to answer those questions, I use a multidisciplinary approach that combines the theory of levels, philosophy and systems theory. The main claim of recursive ontology is that being is the product of a single recursive process of generation that builds up all of reality in a hierarchical fashion from fundamental physical particles to human societies. (...)
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