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SINGLE-TYPE ONTOLOGY 79
compensate for this shortcoming. 5 In particular, their representational strategy follows the
strategy for the representation of entities in the type (cf. (1), (2)). Only, rather than
representing an entity via the set of its extensional properties at @, we represent the latter via
the set of true propositions at @ which carry information about it; or, equivalently, via the set
of indices at which all true propositions at @ which carry information about the entity are
true. An entity a is then represented by the set of indices from (8):
(8) {w s | for all p , if @ ∈ p & p ‘is about’ a, then w ∈ p}
To ease reference, we hereafter denote the representation of a from (8) by ‘a † @’.
We illustrate the above representation strategy by means of an example: Consider the
representation of John in a universe consisting of three indices @, w 1, and w 2, and two
distinct entities: John (abbreviated j) and Mary (abbreviated m). Assume further that, at the
current index, the propositions ‘John runs’ (Rj), ‘Mary runs’ (Rm) and ‘Mary doesn’t whistle’
(¬Wm) are true, that, at the index w 1, the propositions ‘John runs’, ‘John whistles’, ‘Mary
runs’ and ‘Mary doesn’t whistle’ are true (such that Rj, Wj, Rm, and ¬Wm obtain at w 1), and
that, at the index w 2, the propositions ‘John doesn’t run’, ‘Mary runs’, ‘John whistles’, and
‘Mary whistles’ are true (such that ¬Rj , Rm, Wj, and Wm obtain at w 2) (cf. Fig.1) .
Then, by the characterization of aboutness from Section 3.2, the proposition ‘John runs’ is the
only true proposition at @ which carries information about John. As a result, we represent
John at @ by the subset of the set {@, w 1, w 2} at whose members John runs. We identify the
latter with the set {@, w 1} (underbraced in Fig. 1). The latter encodes the information that
John runs at @.
Notably, the representation of entities along the lines of (8) presupposes the existence of the
represented entity a at the current index: If a does not exist at @, no proposition p will satisfy
the condition on the set from (8). Since a will thus be represented by the empty set of indices,
its type- representation at @ will be identified with the type- representations of all
other non-existing entities at @. But this is arguably undesirable.
To solve this problem, we hedge the condition, @ ∈ p & p ‘is about’ a, on the set a † @ from (8)
with the conjunct ‘a exists in w’. The entity a is then represented by the set of indices from
(9):
(9) {w s | a exists in w & for all p , if @ ∈ p & p ‘is about’ a, then w ∈ p}
Figure 2 illustrates the representation of John at an index in which he does not exist. In the
figure, we abbreviate ‘John exists’ as ‘Ej’.
5
Since they encode semantically ‘richer’ information than type- propositions, objects of the type
still satisfy the simplicity requirement from Property 5.