|Similarity metrics: a measure of similarity. It is a problem in relation to possible worlds that it is not always determinable which one of two worlds is closer in relation to a third._____________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. |
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Similarity metric/Possible worlds/Po.wo./Similarity/Lewis: order assumption: weak order: whenever two worlds can be accessed from the the world i in question, either one or the other is more similar to world i. - Decreasing or increasing similarity is transitive. - In contrast, partial order: not all couples are distinguishable.
Compatibility/Possible world/Lewis: B is compatible with A in world i if an A world is closer to i than any non-B-world. - (Reversal of rather true) - then A were>>would C is true if C follows from A together with auxiliary hypotheses B1...Bn. - E.g. natural laws are compatible or completely incompatible with every assumption - thesis: then laws of nature are generalizations of what we consider to be particularly important. - Then conformity with Laws of Nature should be important for the similarity relation between possible worlds - (> similarity metric).
Similarity metric/Possible worlds/Lewis: sphere/Similarity sphere: E.g. S sphere around the world i: exists, if any S world is accessible from i and closer than any ~ S world): admitting A: a sphere contains an A world. - Degree: spheres represent degrees (comparative, unlike neighborhood in topology). Compatibility/Compatible/(s): B is compatible with A if there is an A world in the B sphere. - Definition A were>>would C is true if A>C applies in an A permitting sphere around i, if such a sphere exists. ((s) implication).
Definition Then were A>>would C would be true if AC applied in every A permitting sphere around i ((s) conjunction) - Definition A impossible worlds: Impossible World.
Similarity metric/Similarity/Possible world/Lewis: It is not about any particular similarity relation that you happen to have in mind. - Problem: if some aspects do not even count, the centering assumption would be violated. - I.e. worlds that differ in an unnoticed aspect, would be identical with the actual world. - Lewis: but such worlds do not exist.-
Similarity relations: must be distinguished: a) for explicit judgments - b) for counterfactual judgments.
Revision/Possible world/Similarity metrics/Stalnaker/Lewis: every revision will select the most similar antecedent world.
Schwarz I 160
Lewis: E.g. a single particle changes its charge: then it behaves differently. - Because a possible world in which not only the charge but also the role were exchanged would be much less similar (> next world)._____________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.
Clarence Irving Lewis
Collected Papers of Clarence Irving Lewis Stanford 1970
Die Identität von Körper und Geist Frankfurt 1989
Konventionen Berlin 1975
Philosophical Papers Bd I New York Oxford 1983
Philosophical Papers Bd II New York Oxford 1986
Clarence Ivar Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991
David Lewis Bielefeld 2005