II 194
Substitutability of Identity/intensionality/Hintikka: a sure indicator of intensionality is the failure to preserve the identity of the individual domain.
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Intentionality.
If it happens that the identity fails from one possible world to another, we have a counter-example to the known law ((s) Leibniz's law):
(Substitutability of identity) (x)(y) (X = y > F[x] > F[y])).
((s) identical objects have all properties in common).
This is sometimes called the "bound variable form of identity".
Equivalent to:
(x)(y) ( x = y > neccessary (x = y))
((s) What is identical is necessarily identical).
Hintikka: this failure of the substitutability of the identity is to be distinguished from the failure for any singular terms. Here it can simply be because a singular term refers to another thing in another possible world.
II 195
Identity/individuals/Hintikka: it is much less clear how the identity can fail for certain individuals in the transition to another possible world. That is, that world lines can branch (> separation).
Separation/KripkeVsSeparation/substitutability of identity/SI/Hintikka: Kripke excludes separation because the substitutability of identity is valid for him. A separation would violate the transitivity of the identity according to him. After a separation, the individuals would not be identical, even if they were identical after the transition. Therefore, the substitutability of identity is inviolable to Kripke.
HintikkaVsKripke: that is circular:
Transitivity of Identity/Hintikka: can mean two things:
A) transitivity within a world or
B) transitivity between worlds.
The plausibility of transitivity belongs to the former, not to the latter.
Transitivity of the identity between possible worlds is simply to exclude separation. This is the circularity in Kripke's argument.
Substitutability of Identity/Hintikka: many authors have noted that identity and quantification remain meaningless in intensional contexts unless we have the substitutability of identity.
HintikkaVs: that is simply wrong: after the world lines are defined, we can formulate the truth conditions for sentences with arbitrary intensional expressions. And then, independently of the behavior of the world lines.
Modal Logic/substitutability of identity/Hintikka: it is double ironic that the defenders of conventional modal logic want to save the substitutability of identity by saying that without it, possible worlds and intensional logic makes no sense. This is because substitutability of identity excludes separation.
Fusion/Hintikka: to exclude it, we need the reverse form instead substitutability of identity we need identity of substitutability:
(identity of substitutability) (x)(y) (possible (x = y) > x = y)
((s) possible identity is identity, i.e. ultimately it is necessary).
Problem/Hintikka: identity of substitutability is not valid in some conventional systems of the quantified modal logic, including that of Ruth Barcan Marcus.
For these systems, we must allow separation when we go from possible worlds to the actual worlds (travel home).
Direction/interpretation/Hintikka: however in interpretation there is nothing to distinguish between the directions.
II 196
It is only a coincidence that these systems do not contain retrospective operators (Saarinen, see above).
That is, every defender of these conventional systems secretly defends the possibility of separation. That is, the rejection of substitutability of identity.
II 196
Separation/Hintikka: separation is useful in a few models of cross-world identification, re-identification in time. E.g. a computer could be dismantled and two computers could be built from it. This could be revised later.
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Cross world identity.
Re-Identification/Hintikka: re-identification is the key to cases of separation and fusion.
Separation/Hintikka: there is a structural reason why it is so rare: if world lines are composed of infinitesimal elements as the solutions of differential equations, the separation of a singularity corresponds - this is a rare phenomenon.
Separation/Hintikka: the arguments against them are circular in a deep sense. They are based on the idea that for quantification the individual domain should remain fixed (HintikkaVsKripke).
Possible World/individual area/HintikkaVsKripke: one should not demand that the individuals must remain the same when changing from world to world. The talk of worlds is empty, if there are no possible experiences that could distinguish them.
