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SINGLE-TYPE ONTOLOGY 83
entities and propositions via (minimally informative) indices, and of representing partial
indices via sets of their extending total indices. The latter is a corollary of Stone’s Theorem
(Stone, 1936), (cf. Davey and Priestley, 2002). The possibility of representing partial indices
via sets of total indices also justifies the possibility of associating representations of entities
and propositions in the type with functions from partial indices to functions from
total indices to total truth-values. Note, however, that the resulting representations no longer
satisfy the intensionality requirement from Property 3.
This completes our identification of the suitable single basic types. We close the paper by
comparing Partee’s preliminary basic-type choice and with our newly identified single basic
types.
4. Single-Type Candidates and Partee’s Hypothesis
The above considerations disclose three interesting facts about Partee’s preliminary singletype
candidate:
1. Partee’s chosen type (i.e. properties of situations, type ) is a suitable single
basic type that satisfies the requirements from Properties 0–5.
2. Partee places more semantic constraints on single-type objects than necessary.
Granted her disregard of intensionality, Montagovian properties of possible worlds are
equally suitable.
3. Partee neglects an alternative type (for situation-to-proposition functions, type ), whose objects are semantically ‘richer’ than type- objects.
The observations from items (1) to (3) support Partee’s basic-type choice. However, they
point out the possibility of adhering more closely to Montague’s original ontology (cf. the
adoption of possible worlds; (2)), and of not prematurely excluding competing candidates (3).
More generally, the possibility of representing partial situations via sets of their extending
possible worlds (in Sect. 3.4) emphasizes the role of semantic operations and representational
strategies in ontology (as opposed to the identity of the different object types).
Kristina Liefke
Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität, München &
Tilburg Center for Logic and Philosophy of Science, Universiteit Tilburg
Kristina.Liefke@lrz.uni-muenchen.de
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