Some time ago we discussed Andy Egan’s ‘Second-Order Predication and the Metaphysics of Properties’ (AJP 82 (2004), 48–67), at the St Andrews Metaphysics Reading Group in a couple of sessions.
In the paper, it is argued that properties should be identified with functions from worlds to extensions, as a way of solving the following problem: If properties are sets of (possible) instances, things that exist in more than one world can’t have any of their properties contingently. Properties like being green exists in more than one world, but have some properties contingently: being somebody’s favourite property.
Then, although more tentatively, it is argued that properties should be identified with functions from worlds and times to extensions, as a way of solving the following problem: If properties are functions from worlds to extensions, then things without temporal parts can’t have any of their properties at some but not other times. Properties like being bent don’t have temporal parts, but have some properties at some but not other times: being coinstantiated with being hungry.
I think I am generally sympathetic, but I was concerned that the same kind of reasoning would also motivate that properties should be identified with functions from worlds and times and places (or locations, for short) to extensions. After all, (i) “Second-order predication” of properties such as having many instances around seem to pose similar problems to the world-time proposal, by being possibly true at some places but not others; (ii) there seem to be parallel cases of spatially self-locating attitudes; and (iii) the response to Lewis' concern seems similarly effective as to defend the world-time-place proposal from the charge that these are relations rather than properties.
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