Axiomathes

ISSNs: 1572-8390, 1572-8390

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  1.  9
    Should Type Theory Replace Set Theory as the Foundation of Mathematics?Thorsten Altenkirch - 2023 - Axiomathes 33 (1):1-13.
    Mathematicians often consider Zermelo-Fraenkel Set Theory with Choice (ZFC) as the only foundation of Mathematics, and frequently don’t actually want to think much about foundations. We argue here that modern Type Theory, i.e. Homotopy Type Theory (HoTT), is a preferable and should be considered as an alternative.
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  2.  7
    Composition as Identity and the Logical Roots of Leibniz’s Nominalism.Filippo Costantini - 2023 - Axiomathes 33 (1):1-23.
    The paper deals with Leibniz’s ontology and the metaphysics of the aggregate. Concerning the ontology of aggregates, the main aim is to provide _a new argument_ in favor of the claim that an aggregate and its constituents have the same ontological import. This argument takes the form of a weakening of a principle known in the contemporary literature of mereology as ‘composition as identity’ (CAI). The paper shows that Leibniz’s nominalism toward aggregates is a direct consequence of two elements: the (...)
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  3.  12
    t.Jasper Doomen - 2023 - Axiomathes 33 (1):1-11.
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  4.  7
    Empirical Concepts: Their Meaning and its Emergence.Hans Radder - 2023 - Axiomathes 33 (1):1-23.
    This article presents a detailed, novel account of the emergence of (the meaning of) empirical concepts. Acquiring experience and empirical concepts is shown to be the result of multifaceted, cognitive processes, which require both material realization and conceptual interpretation. Generally speaking, the meaning of empirical concepts consists of several distinct components, but it includes at least a structuring and an abstracting component. These two meaning components are abstract entities, which can be justifiably interpreted as real objects. On this basis, I (...)
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  5.  6
    Davidsonian Metasemantics and Radical Interpretation.Maciej Tarnowski - 2023 - Axiomathes 33 (1):1-18.
    In the current debate on the metaphysical grounding of semantic properties Donald Davidson is usually taken to represent interpretationism, a stance according to which the meaning of expressions is metaphysically grounded by the process of assigning them semantic values which maximize certain parameters such as truth or rationality of the speaker. This stance is often contrasted with productivism, which takes circumstances of expression’s production, not interpretation, to ground its meaning. In this article, I argue that this widespread understanding of Davidson’s (...)
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  6. The Liar Paradox - A Case of Mistaken Truth Attribution.Jasper Doomen - 2023 - Axiomathes 33.
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