## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
---|---|---|---|

Hintikka, J. Books on Amazon |
Impossible World | I 12 Impossible world/Hintikka: I believe that we must allow the impossible world to fight the problem of another kind of omniscience, the logical omniscience. --- I 63 Impossible worlds/Logical omniscience/semantics of possible worlds/Hintikka: Thesis: the problem of omniscience does not occur here at all! E.g. (1) A sentence of the form "a knows that p" is true in a world W iff. P is true in all a-alternatives. That is, in all worlds, which are compatible with the knowledge of a. Logical omniscience: their failure can be formulated like this: (2) There is a, p and q such that a knows that p, p implies logically q, but a does not know that q. Logical truth: is then analyzed model-theoretically: (3) A sentence is logically true, iff. it is true in every logically possible world. Problem: (1) - (3) are incompatible! However, they are not yet incompatible in the form given above, but only with the additional assumption: (4) Every epistemically possible world is logically possible. --- I 64 Problem: now it can be that in an epistemic a-alternative W'q is wrong! Problem: According to (4), these epistemic worlds are also logically possible. However, according to the logical truth of (p > q) ((s) in this example), q must be true in any logically possible world. This results in the contradiction. Solution: different authors have responded differently: Positivism: positivism takes refuge in the noninformative (tautological) logical truth. HintikkaVs: instead: semantics of possible worlds. (4): already presupposes omniscience! It assumes that a can only eliminate seeming possibilities. This is circular. Solution: there may be possibilities that appear only possible but contain hidden contradictions. --- I 65 Problem: the problem here is (4) and not (2)! Solution/Hintikka: we have to allow worlds that are logically impossible, but still epistemically possible. ((s) unlike the impossible worlds discussed in Stalnaker and Cresswell.) Then (1) - (3) can be true together. That is, in an epistemic world (p > q) can fail. Impossible world/Hintikka: Problem as how we can allow it. Impossible world/Cresswell/Hintikka: Cresswell proposes a reinterpretation of the logical constants. (Model theoretical). HintikkaVsCresswell: the real problem with omniscience is that people do not recognize all the logical consequences of their knowledge. And this takes place in classical logic. Non-standard logic: bypasses the problem. You could say it destroys the problem instead of solving it. --- I 65 Impossible world/Logical omniscience/Solution/Veikko RantalaVsHintikka: has solved some problems of this approach. --- I 66 Nonclassical models: nonclassical models are for first level sentences. Impossible world/Rantala: are not "impossible" according to Rantala, but they differ from normal possible worlds, in the way that they are "changing worlds" by allowing new individuals. However, in such a subtle way that they normally cannot be distinguished from invariant worlds (with always the same individuals). It is about: Urn model/Statistics/Omniscience/Hintikka: whereby the variant worlds are such worlds with which moves from the urn possibly get new individuals into the game. But only so few that you may not notice it. |
Hin I Jaakko and Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 W I J. Hintikka/M. B. Hintikka Untersuchungen zu Wittgenstein Frankfurt 1996 |

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Ed. Martin Schulz, access date 2017-03-25