Philosophy Lexicon of Arguments

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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Re III 104ff
Similarity Metrics/Stalnaker: smallest possible revision - i.e. the most similar world. Selection function: f(A, w) - "If you get a one, you will receive a scholarship" is true if the world in which you receive a scholarship is most similar to the world in which you are getting a one - possible world view: deviates from the probability function if the fore-link is wrong" - because all combinations can be realized in a possible world.
Re III 105
Similarity Metrics/Possible World/Conditional Sentence/Read: some classical logical principles fail here: e.g. contraposition that "if B, then not-A" follows from "if A, then not B" - the similar world in which it rains, can be very well one in which it rains only lightly. But the most similar world in which it rains violently cannot be one in which it does not rain at all.
Re III 106
Another principle that fails: the reinforcement of the if-sentence: "If A, then B. So if A and C, then B." - For example, when I put sugar in my tea, it will taste good. So when I put sugar and diesel oil in my tea, it will taste good. In the most similar world in which I put diesel oil like sugar in my tea, it tastes horrible - further: the results of the conditionality principle are invalid: - If A, then B. So if A and C, then B - and if A, then B. If B, then C. So if A, then C - Reason: the conditional sentence has become a modal connection. - We must know that these statements are strong enough in any appropriate modal sense - to ensure that the most similar A and C world is the most similar A-world, we must know that C is true everywhere.
III 108
Similarity Metrics/the conditionally excluded middle/Read: sentence of the conditionally excluded middle: one or other member of a pair of conditional sentences must be true - this corresponds to the assumption that there is always a single most similar world - (Stalnaker pro) - LewisVsStalnaker: e.g. Bizet/Verdi - all combinations are false - Stalnaker: instead of the only similar one at least one similar - LewisVs: set of possible world in which Lewis is 2 m + e tall, whereby e decreases appropriately, this has no boundary - Solution/Lewis: instead of selection function: similarity relation: he proposes, that "if A then B" is true in w if there is either no "A or non-B"-world, or any "A and B"-world that is more similar than any "A and not-B"-World.
Re III 110
Verdi-example: where there is no unique most similar world, the "would" conditional sentences are wrong because there is no most similar world for any of the most appropriate similar worlds in which they are country people, where Bizet has a different nationality. E.g. If you get a one, you will receive a scholarship: will be true, if there is for every world in which you get a one and do not receive scholarship, is a more similar world in which you get both (without conditional sentence of the excluded middle).
Re III 115
Similarity Metrics/Similarity Analysis/Possible World/ReadVsLewis: problem: e.g. (assuming John is in Alaska) If John is not in Turkey, then he is not in Paris - this conditional sentence is true according to the "similarity statement", because it only asks, whether the then-sentence is true in the most similar 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.
Logic Texts
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001

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Ed. Martin Schulz, access date 2017-08-23