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Coordinate-free logic

Review of Symbolic Logic 9 (3):522-555 (2016)

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  1. Explaining the differential application of non-symmetric relations.Maureen Donnelly - 2021 - Synthese 199 (1-2):3587-3610.
    Non-symmetric relations like loves or between can apply to the same relata in non-equivalent ways. For example, loves may apply to Abelard and Eloise either by Abelard’s loving Eloise or by Eloise’s loving Abelard. On the standard account of relations, different applications of a relation to fixed relata are distinguished by the direction in which the relation applies to the relata. But neither Directionalism nor its most popular rival, Positionalism, offer accounts of differential application that generalize to relations of arbitrary (...)
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  • Relations.Fraser MacBride - 2016 - Stanford Encyclopedia of Philosophy.
    In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...)
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