|Boer, Steven E.
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Opacity/description dependent/Boer: 1. This is usually a question of hidden parameters, additional arguments in the logical form, which do not appear in everyday language.
The hidden parameters would be the kind of representations quantified in (D5):
(D5) R is a concept-dependent relation = for each object x and y that x has the relation R to y, entails for a representation z and one behavior-determining relation Q:
A) a has Q to z and
(i) z forms y (i.e., z is or contains something that represents y for x)
(ii) z expresses y (i.e., z is a representation with a fulfillment condition which they have from y) and
C) for each representation r which maps y or expresses whether x has q to r depends on whether r has one or more intrinsic properties of a certain domain (i.e. there is a set F of intrinsic features of x' representations, for each representation r which maps y for x, x has Q to r iff r exemplifies a feature from F).
Or any entities that could be gained from such representations.
This explains why the alleged breach of (T2)
(T2) For arbitrary objects x, y, z and every two-digit relation R: if y = z and x has R to y, then x has R to z.
is only an apparent one: for the fact that b = c and that R (a, b, r) need not to contain R (a, c, r'), if this is not made explicit, it seems to be a two-digit relation that violates (T2).
2. Another possibility is that R itself is context-dependent: that "b = c" and "R (a, b)" would be logically compatible with "~R (a, c)" if the contexts are only different enough. E.g. "R" could be analyzed as the complex binary predicate "[λxy (Er) Gyrx]" whereby the domain of the questionable quantifier is a contextual set of mediating representations,
which differ in the applications "b = c", "R (a, b)" and "~ R (a, c)".
3. Strategy: Thesis that the alleged relations of R are not the real relations. It is not guaranteed that "b" in the various uses always stands for the same object here.
For example, if a name appears in a sentence both inside and outside of quotes, it is natural to assume that it refers once to the bearer, but also to a wordtype. Thus, in our case, different referents of "b" could also be assumed.
4. "about": can also be ambiguous. This can lead to that identity fails in the belief of something.
(A) In one sense, a belief about the evening star is at the same time also a belief about the morning star
B) in another sense, it is not. ((s) de re/de dicto).
Weaker/Boer: "For a G, A believes that N is G."
"From"/de re/Boer/(s): is stronger and, together with the identity of morning star and evening star, implies that the belief "of" the morning star equals the belief of the evening star.
Steven E. Boer
Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010
Steven E. Boer
Knowing Who Cambridge 1986