|Existential generalization, logic: if an object that can be named, has a certain property, then there is at least one object with this property. See also universal generalization, universal instantiation.|
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|Existential Generalization||I 42
Existing Generalization/EG/HintikkaVsParsons, Terence: his criterion of the existential generalization is wrong, because it can fail for reasons that have nothing to do with non-existence.
(1) Queen Victoria knew that Lewis Carroll is Lewis Carroll.
From this one cannot infer, even though Caroll existed, and this was known by the Queen that
(2) (Ex) Queen Victoria knew that Lewis Carroll is x.
(3) Someone is so that Queen Victoria knew that he was Lewis Carroll.
(2) and (3) say the same as
(4) Queen Victoria knew who Lewis Carroll is.
But this is not entailed by (1).
Existential Generalization/EG/Hintikka: the equivalence of (2) - (3) with (4) is, however, quite independent of whether the quantifiers go only about existent or non-existent objects.
The reason for the failure of the existential generalization is not a failure of the unambiguousness.
Unambiguity, however, fails because in various situations, which are compatible with the knowledge of the queen, the name Lewis Carroll can be applied to different people. Therefore, not only a single specific object can function as the value of "x".
Therefore, the existential generalization does not apply in (1) and yet it can be understood that it obliges the one who utters it to the existence of Lewis Carroll. Therefore, Parsons criterion fails.
Existential Generalization/EG/Hintikka: the existential generalization entitles us to move from one sentence S (b) to a singular term "b" to the existence statement (Ex) S (x).
This fails in intensional (epistemic) contexts.
Transition from "any" to "some". (> Existential Generalization)
E.g. epistemic context:
(10) (premise) George IV knew that (w = w)
(11) (tentatively concluding) (Ex) George IV knew that (w = x)
Problem: the transition from (10) to (11) fails because (11) has the strength of (12)
(12) George IV knew who w is.
Existential generalization/failures/Solution/Frege/Hintikka: assumed that we are dealing with ideas of speakers in intensional (opaque) contexts.
HintikkaVsFrege: Problem: then (11) would in any case follow from (10) ((s) And that is just not desired). For one would have to assume that there is in any case any meaning under which George IV imagines an individual w.
Problem: "w" picks out different individuals in different worlds.
Semantics of Possible Worlds/Solution/Hintikka: E.g. Suppose
(13) George knows that S (w)
(14) (Ex) George knows that S (x)
Whereby S (w) does not contain expressions that create opaque contexts.
Then we need an additional condition
(15) (Ex) in all relevant worlds (w = x)
But this is not a well-formed expression in our notation. We must say what the relevant worlds are.
Definition relevant world/Hintikka: are all those which are compatible with the knowledge of George.
Thus, (15) is the same with
(16) (Ex) George knows that (w = x).
This is the additional premise. That is, George knows who is w. (knowing-that, knwing-who, knowing-what).
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996