The Trope Coextension Problem
DOI link for The Trope Coextension Problem
The Trope Coextension Problem book
Trope theory has traditionally been thought to mark an improvement over object class nominalism (OCN). According to OCN, property types are natural classes of objects meeting a certain condition (‘naturalness’ is either further analyzed in terms of resemblance or taken as a primitive). Certain critical objections directed at the latter have seemed not to apply to the former, including the coextension problem (CP) (see, for example, Armstrong (1989, 125-126)). CP involves situations in which non-identical property types, P and P’ , are assessed as identical to the same class of objects by OCN, thus giving the wrong result that these property types are identical. 1 For example, if all and only spheres are red (the Red-Sphere Case ), then OCN seems to entail that redness and sphericalness are each identical to the class of red spheres and, hence, to each other. 2 Trope theory takes property types to consist in classes of tropes, not objects, so no such false type-type identity implication is attached to these CP-situations. However, it may be that CP-style problems can be generated for trope theory. Suppose, for example, that all red objects are crimson, a superdeterminate shade of red, so that the class of red tropes is identical to the class of crimson tropes (the Red-Crimson Case ) 3 According to traditional trope theory, in these circumstances, (1) the determinable property type redness is the class of crimson tropes and (2) the property type crimsonness is also identical to that class. So, the property type redness is identical to the property type crimsonness under these conditions. 4 But the property type redness is not identical to the property type crimsonness, the objection goes, no matter the circumstances (the trope coextension problem (TCP)). The trope theorist thus seems to lose one of his advantages over object class nominalism. This lack of advantage is compounded by the apparent fact that these theories are on a par with respect to a solution to their respective coextension problems. The close-to-standard approach to CP for the object class nominalist-with respect to contingently coextensive properties-involves the possibilia of modal realism (Rodriguez-Pereyra 2002, 99-100). If redness is identifi ed with the class of all possible red objects, including merely possible red objects that are not spherical, there is no implication on the part of that
theory that redness is identical to sphericalness even if all actual spheres are red and all actual red things are spheres. Trope theory, however, also seems to require modal realism to solve its coextension problem (Manley 2002, 86). If redness is identifi ed with the class of all possible red tropes, including some non-crimson red tropes, then the problematic type-type identity implication fails. But then trope theory has no advantage over OCN. 5 Both theories have coextension problems and both theories require modal realism, a metaphysical theory many philosophers fi nd to be unacceptable (Manley 2002). My goal in this chapter is to show that this assessment is wrong. I will try to show that trope theory can retain an advantage over OCN with respect to coextension issues if trope theory is combined with property counterpart theory without modal realism.