thanks for the contributions from all of you, indeed. Meanwhile I have
realized that my question was somewhat improper, as it is very difficult
to say if two similar tongues can be considered dialects of the very
same languages or two separate languages. Separate statehood of
the speakers might contribute to considering them separate
languages, just as in case of the split of the former Yugoslavia, the
once indivisible Serbo-Croat today is considered to be 3 separate
languages, such as Bosnian, Croatian and Serbian, though difference
may be less significant between Bosnian and Serbian than Swiss
German and Hochdeutsch (the latter two are thought to be the same
language).
It could have been similar in the age of shifting from common-Germanic
to Western-Germanic languages and Old Norse. Since this was
continuous we could only set a symbolic date or estimate a longer
period during which it could have happened. But of course mutual
intelligibility does not end at the time when the dialects split into
separate languages, e.g. written Dutch is more or less intelligible to
German-speakers, or Estonian is also understandable to Finns in some
extent. But because of the mutual intelligibility no one would say that
these are dialects of the very same language, any longer.
The reason for my question was that I wanted to when the Old Norse
word lög acquired the meaning law. According to my presumption #
1, this must have happened after that Old Norse and West Germanic
languages split form each other, because the English cognate lay and
German cognate Lage do not have the same meaning as lög.
But again (presumption #2) since dialects can be well different
before formally splitting into different languages it could have
happened that in the Northern dialects of the common-Germanic the
proto-Germanic *lag (or whatever the correct form may have been)
already had the meaning law (or some kind of commonly accepted
social custom etc.), but not in the West or East dialects.
This latter argument could be supported by the fact that German and
OE both use words (Gesetz and gesetnys) with the similar original
meaning: setzen and to set also have the same primary meaning
as Swedish lägga (to lay) and ON leggja, both having the primary
meaning to lay, to put, to set etc.. I presume that the Northern
dialects and Western dialects meant the same thing, but one of the
dialects shifted to an other word, though a secondary meaning
(i.e. law) of *lag could have been intelligible to the Western dialects
or a secondary meaning of the word *set or *geset (or whatever
the correct proto-Germanic may have been) could have been
understandable to the speakers of the Northern dialects, e.g. Swedish
still has the verb sätte with a similar meaning as German setzen
and English to set.