A single primitive trope relation

Abstract

sense treated here. Whilst there may be systematic metaphysical reasons why a theory of tropes as "thin" properties and relations is more fruitful than a theory of tropes as states of affairs (though I doubt it), the issue is not joined here. 33. Ontological economy. The main point is now gained: trope structures can be replaced by trope cascades, themselves slight elaborations of the simplest sort of trope structure, the degenerate monadic trope structure. The latter, in turn, is nothing but a reflexive, symmetric relational structure. This result forces a revision of the metaphysical assessment of Bacon (xz28). He found modal models based on trope structures to be more baroque than other approaches, though still attractive on other grounds. Now that we have reduced the possible infinity of trope relations in trope structures to one similarity relation in a trope cascade, the corresponding models appear far more streamlined. Both from a metaphysical and a semantic point of view, trope theory now survives Ockham's razor handily. Relationes non multiplicatae sunt praeter necessitatem. 34. Ontological options. To be sure, the ontologically serious recourse to trope cascades conflicts with what I take to be one of the principal attractions of trope theory: the vision of 1-tropes as ontologically basic. As Williams puts it, ... entities like our fine parts or abstract components are the primary constituents of this or any possible world, the very alphabet of being. They nor only are actual but are the only actualities . . . (1953, p. 78) This raises the question whether our logical reduction to trope cascades and 3-tropes should be taken as an ontological reduction too. In any case, it would sorely try the tonsorial skill of an Ockhamite to shave off the tangle of 1-relations while leaving their relata unnicked. (It mightn't trouble a nominalist, I suppose; but trope theory is not inherently nomanilistic.) Whether being is aptly spelt out in 1-tropes and abbreviated in 3-tropes or vice versa, trope cascades clarify the alphabetic options. This content downloaded from 207.46.13.33 on Sat, 26 Nov 2016 04:20:32 UTC All use subject to http://about.jstor.org/terms PRIMITIVE TROPE RELATION 153