Results for 'Digraph'

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  1. What Paradoxes Depend On.Ming Hsiung - 2018 - Synthese:1-27.
    This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I (...)
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  2.  56
    Spinoza's Ethics as a Mathematical Object.Herbert Roseman - manuscript
    Spinoza’s geometrical approach to his masterwork, the Ethics, can be represented by a digraph, a mathematical object whose properties have been extensively studied. The paper describes a project that developed a series of computer programs to analyze the Ethics as a digraph. The paper presents a statistical analysis of the distribution of the elements of the Ethics. It applies a network statistic, betweenness, to analyze the relative importance to Spinoza’s argument of the individual propositions. The paper finds that (...)
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  3. Some Open Questions About Degrees of Paradoxes.Ming Hsiung - manuscript
    We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the very condition. This paper aims at setting forth the theoretical framework of the theory of paradoxicality degree, and putting forward (...)
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