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Conceptual dependency/conceptual/strong metaphysical intentionality/Boer: is the second feature of strong intentionality: is much more problematic:
For example, Oedipus would like to marry Iokaste.
marry. Must then be conceptually dependent, because he certainly does not want to marry his mother.
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Conceptual dependency/Boer: it seems that we should characterize it by (CD):
(CD) R is a concept-dependent relation = it is possible that for some objects x and y and properties F and G, x R to y, qua has the thing that is F, but x has R not to y qua the thing which is G.
Vs: this makes conceptual dependency easily to something paradox. It can happen that the identity of terms is no longer respected: E.g. objects a, b and x, so that b = c and a has R to b, but a does not have R to c. This would follow logically from (CD), if the definiens of (CD) was merely symbolized as
M (Ex) (Ey) (EF) (EG) (y = the F & y = the G & R (x, the F) & R (x, the G)).
That would be fatal.
Relation/Boer: the mere idea of a relation, which does not recognize the identity of its terms, violates the following two principles (in referential quantification):
(P2) For objects x and y: if x = y, then for every property F applies, x has F iff Y has F.
(Leibniz's law)
(P3) Neccessary, for each double-digit relation R and objects x and y: x has R to y iff y has the relational property of being a thing z such that x has R to z (formal: "[λzRxz]").
This is the principle of abstraction/concretion.
Both principles are indisputable and have (T2) as a consequence:
(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.
For according to (P3) there is then a property [λzRxz] which is exemplified by y. And
because of y = z, z must have it itself, then it follows from (T2) that x has R to z. This derivation of T2) is not circular, because from the formula φ
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and equation [a = b] we derive with standard substitution for identity:
Φ (a//b).
Substitutability/Identity/Conceptual dependency/Boer: those who think that conceptually dependent
relations do not respect the identity of their terms, would not the recognize substitutability.
