|Similarity: conformity of one or more - but not all - properties of two or more objects._____________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. |
Accessibility/Lewis: Accessibility between possible worlds: their degrees should be understood as degrees of similarity.
Similarity/possible worlds/Lewis: here we have to recognize the relevant similarity. More important is the one concerning certain laws! This presupposes laws in the explanation. (Lewis 1979,1986a - JacksonVsLewis: Jackson 1977a: Causality instead of similarity)
Accessibility/Bigelow/Pargetter: Example 3 worlds
1. World u: Darwin asks his father for permission to sail away, receives it and writes his book, of which we have all heard
2. World w: Darwin does not get permission, does not sail away and does not write his book.
3. World e v: Darwin does not get permission to sail away, but still sails off... and his father forgot what he said.
Accessibility/Lewis/Bigelow/Pargetter: according to our semantics (and that of Lewis) the corresponding counterfactual conditional is only true in w, if possible worlds like u are the most accessible of w (next world most similar possible world).
Lewis: so u has to be more similar than w v is similar. u and w must be closer to each other.
If v and w were closer together, the following counterfactual conditional would be true:
If Darwin's father had not given permission, Darwin would not have obeyed and his father would have forgotten.
And that is not true in w. So u w is closer than v u is close.
Similarity/possible worlds/relevance/Bigelow/Pargetter: what kind of similarity is the relevant one? It cannot be about certain facts (as in this story). That would not be enough.
Definition similarity/similarity metrics/possible world/Lewis: by fewer exceptions in a possible world with laws that apply in the other possible world. > Miracles.
For example, Darwin: "Miracles" would be the false acoustic transmission of the father's statement and the forgetting through the father.
Miracles/Lewis: but also world u could contain miracles: the prehistory is the same as in v, but the father's decision is different, but the causal situation would be the same and the miracle of the other decision would perhaps be just as great as that of erasure of memory and mishearing.
Natural Laws/Worlds/Lewis/Bigelow/Pargetter: so it could be that other laws apply there as well.
Obey/Laws/Possible Worlds/Bigelow/Pargetter: we can also say that a world obeys the laws of another possible world to a certain extent.
For example, there might be a possible world z that obeys the laws of w better than u?
z: assuming there are laws here that make the refuse of the permission probable. Suppose the father has heard of a conflict with France in the sea area. This does not require any change in the laws.
Then we would be forced to assume that the following counterfactual conditional is true in w: (according to our semantics and that of Lewis):
If Darwin's father had refused, war would have broken out between England and France or there would have been another factor that would have led to rejection.
However, it is wrong in w in at least one way of reading.
Similarity metrics/relevance/similarity/Lewis: this shows that similarity of laws is not the only relevant factor.
Solution/Lewis: Similarity between worlds must be explained
a) by similarity in terms of laws,
b) by similarity in relation to certain facts.
Weighting/Lewis: For example, the same facts over a long period of time have more weight than obeying the same certain laws.
But compliance with laws has more weight than certain consistent facts.
LewisVsBigelow: VsModal theory.
Bigelow/Pargetter: we explain laws by accessibility
Lewis: explains accessibility by law.
Bigelow/Pargetter: if Lewis is right, our theory is circular.
Solution/Lewis: see below
BigelowVsVs/BigelowVsLewis: we deny that accessibility must be explained by similarity. The easiest accessible world does not have to be the most similar world! This is shown by the above examples (Darwin's father).
But even if it were not the case, it would not refute the modal theory of the laws of nature.
Similarity/Possible World/Bigelow/Pargetter: we are challenged to construct a better theory than Lewis._____________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.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990