November, 6, 2020, h. 17-19 CET

Traditionally we distinguish between relations and their converses, e.g., above and below or before and after. This distinction poses a dilemma. Is a relation really distinct from its converse or are they one and the same? There are contrasting arguments that favor one or the other reply, both of them in Russell, who first opted for the former (in Principles of Mathematics) and then for the latter (in Theory of Knowledge). Since then accounts of relations that side with one or the other option have flourished, e.g., standard set-theoretical accounts, Geach, Grossmann, Tegtmeier, Van Inwagen on the one hand; Castañeda, Williamson, Fine, Dorr, MacBride, Orilia on the other hand. I shall argue that a hybrid approach to properties and relations (attributes), according to which there are both sparse and abundant attributes, offers a satisfactory way out of the dilemma, whereby distinct converses are acknowledged at the semantic and intentional level of abundant attributes and rejected at the truthmaker or ontological level of sparse attributes. I shall also show how distinct converses can be appropriately accommodated, not by endorsing the directionalist approach with which they are usually associated, but rather within a positionalism that appeals to thematic roles such as agent, patient, source, destination, location, etc.

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