Philosophy Lexicon of Arguments

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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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I 129
Counterfactual Conditional/Valuation/Valuation Function/Valuation Rules/Bigelow/Pargetter:
V9 If a = (ß would be > weould be γ) then V (a) is the set of all possible worlds w ε w so that there is a possible world u where β is true and γ is true and every possible world v in which ß is true and γ is false, is less accessible from w than u. ((s) > similarity metrics.)
Resemblance/possible worlds/similarity metrics/counterfactual conditional/Bigelow/Pargetter: rule V9 states that a counterfactual conditional (β would be > would be γ) is true in a possible world if the next ß-worlds are all γ-worlds.
For example, Violet says: "If I were a blackbird, I would sing" this is true in the actual world, because the next worlds where Violet is a blackbird are possible worlds where she sings.
Similarity metrics/Bigelow/Pargetter: the possible worlds in which Violet is a blackbird on the tree or on the mailbox can be possibly at the same distance from the actual world.
Connection/Possible worlds: the question of whether such "connections" can exist is discussed in connection with the conditionally excluded middle (see above).
Complexity/Bigelow/Pargetter: the complexity of V) is due to the desired generality.
I 130
Resemblance/similarity metrics/counterfactual conditional/proximity/possible worlds/Bigelow/Pargetter: we want a possible world, in which the fore link and back link of the counterfactual conditional are both true, to be closer than one in which only the fore links are true, and the back links are false.
I 209
Possible World/Variant/Bigelow/Pargetter: we could also specify individuals by describing their position in the course of their existence. Through an infinite sequence of quadruples.
There are many variants, including more economical ones.
We can combine all the positions of a particle into one function. This is also possible for other properties that we attribute to a particle. So we can combine a particle not only with numbers, but also with whole functions.
Function: these functions could describe the changes of the particle.
Book/Bigelow/Pargetter: a book for such a described world could be a Hilbert space. But a book is not a world yet! A book for the actual world would consist of
two components:
1. a world property, or a maximum specific structural universal
2. to something that instantiates this universal, that is the world itself.
This applies to the actual world!
Other possible worlds correspond to a universal, but this is not instantiated, so there is no world here.
Representation/Bigelow/Pargetter: now the numbers representing these world properties could seem all too abstract.
I 210
But they are not! They represent the proportions in which the properties of the parts that we have chosen as units are related to each other.
Crossworld-relations/world properties/property theory/Bigelow/Pargetter: now it seems as if our theory is making a surprising turn: it seems to provide a measure for the distance between possible worlds that we have been unable to gain so far. And that measure would not be arbitrary!
Accessibility: could we get it under control with this? (see below)
If the possible worlds contain the same individuals, it is even easy to construct a similarity metrics for them.
If the individuals are different, it is more difficult.

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.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

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Ed. Martin Schulz, access date 2018-04-23