#brexit, #language, #mathematics, #pseudoscience, #rhetoric, #style

Brand-new and remarkable: #today, in a speech before #industry-representatives, chancellor Angela #Merkel used an old-fashioned, and,I think, INAPPROPRIATE,mathematical term to describe the #Brexit discussions..
.. in the #UK.

On 20180925, 9:50 CET, (cf. bdi.eu/der-bdi/termin…), chancellor Merkel said the following: "Wesentlich hängt es natürlich auch davon ab, was Großbritannien denn wirklich möchte. Auch da ist ja die Diskussion nicht so ganz eineindeutig [sic],
und, das muss ich..
.. allerdings sagen: Man kann nicht zum Binnenmarkt gehören, wenn man in EINEM Teil nur zum Binnenmarkt gehören will, aber in drei ANDEREN Teilen nicht zum Binnenmarkt gehört, und da müssen wir verschiedene, äh, vernünftige Wege [ rest drowned out by applause ]."
My translation.
'It also depends in an essential way on what Great Britain actually wants.
There, too, the discussion is not quite injective, and, this I have to say
though: one cannot belong to the [single European] domestic market if one
wants to only belong to ONE part..
.. of this domestic market, but in three OTHER parts does not belon to the domestic market, and in this regard, different, reasonable ways must [rest drowned out by applause].'

Now, my gripe is with the chancellor's use of the word "eineindeutig". Let me first mention that ..
.. the once critical, but increasingly uncritical, fawning and propagandistic German newspaper 'Zeit', implicitly praised the chancellor for her choice of words in zeit.de/news/2018-09/2… . There, the chancellor's statement is quoted,and then it is casually remarked that Merkel..
.. has studied physics. (By the, one COULD construe the omission of a mention of the chancellor's doctorate as a slight, though I don't think that this is intentional.) Then, the newspaper explains 'eineindeutig' as 'a term from set-theory', which supposedly means 'unique in ..
.. both directions'. While these explanations aren't entirely beside the point, they seem not to have been written by a mathematician.The term 'eineindeutig' is a somewhat old-fashiod German synonym for what today is called 'injective'. Is sometimes ALSO considered as a synomym..
.. of the term 'bijective'. There isn't a precise answer which of the two is the correct translation, for a simple reason: in the old days(when this term was used often), the #codomain of a map was not given much attention, at least not as a mathematical object in its own right..
.., in particular, the codomain was seldom precisely defined as a set,which is why is often impossible to tell for sure whether an author in the old days has defined an injective non-surjective map, or even a bijective map. I think it is fair to say that the meaning 'injective'..
.. is the predominant meaning. For example, in Gödel's famous 1931 paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", Gödel uses 'eineindeutig' on page 179 for a map which obviously is injective but not bijective (as a map with..
.. codomain IN, that is.) (Needless to say, every injective map defines a bijective map to its own image.) Now, what did the chancellor mean? I contend that she didn't mean anything more than to say 'Auch da ist ja die Diskussion nicht so ganz frei von Widersprüchen.' Thus..
.., the question reduces to: 'how to model contradictory statements by way of a non-injective map'. Of course, what immediately comes to mind is to have any finite set $S$ such that $S$ is inconsistent be mapped by the 'discussion' (Merkel says she wants to model a 'Diskussion'..
.. as a map) to a set which is strictly smaller than $S$ (and hence the map 'discussion' in non-injective). However, there isn't any canonical way to carry out this construction. This exegesis of Merkel's statement, as well as any other I can think of, seems contrived and ..
.. unnecessary. I think it is fair to say that the Chancellor's use of 'eineindeutig' in this context is not natural and does NOT convey any more meaning than if she had simply said that the Brits are still making contradictory statements in their #Brexit discussions. Merkel's..
.. use of 'eineindeutig' seems to not add anything to her speech, except some confusion, and perhaps the possibility to impress some uneducated members of the audience.
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