|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.
Schw 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.
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
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991