Abstract:
situations are the mathematical (albeit ontologically impoverished) counterparts of real situations, and unlike the latter, are amenable to symbolic manipulation. Given a real situation s, the set f' j s j= 'g is taken to be the corresponding abstract situation. (This set will be nonwellfounded when s is a circular situation. However, this need not concern us in this paper.) Let s be a given situation. Following the standard practice, we require the availability of some device for making reference to arbitrary objects of a given type 3 , viz. parameters. If x is a parameter and I is a finite set of infons (involving x), then there is a type [ x j s j= V '2I ']. This is the type of those objects to which x may be anchored 4 in s, so that all the conditions in I obtain. We refer to this process of obtaining a type---from a parameter x, a situation s, and a set I of infons---as type abstraction. Here x is the abstraction parameter and s is the `grounding' situation. In situati...
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