Philosophy Dictionary of ArgumentsHome
| |||
|
| |||
| Impossible World: possible worlds are determined by counterfactual descriptions, specifying conditions for the existence of objects or laws, or a listing of instanced properties. The existence of an impossible world is already excluded by the concept. However, an impossible world can e.g. be characterized by the fact that in it all propositions are true. Then, for an arbitrary sentence A applies A is true and non-A is true. Thus, existence is excluded for every object and property. See also possible worlds, modal logic, necessity, possibility, possible world semantics._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
| Author | Concept | Summary/Quotes | Sources |
|---|---|---|---|
|
Jaakko Hintikka on Impossible World - Dictionary of Arguments
II 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. >Logical omniscience. II 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. The failure of the logical omniscience 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. The 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. II 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. II 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: how we can allow a possible world? 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. II 65 Impossible World/logical omniscience/solution/Veikko RantalaVsHintikka: Hintikka has solved some problems of this approach. II 66 Nonclassical models: nonclassical models are for first level sentences. Impossible World/Rantala: impossible worlds 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, they differ 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: in the urn model, 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. >Possibility, >Logical possibility, >Metaphysical possibility, >Possible worlds._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
||
> Counter arguments against Hintikka
> Counter arguments in relation to Impossible World
Ed. Martin Schulz, access date 2024-04-28