Transcript QED - UiT

QED
What does that mean?
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Quod erat demonstrandum.
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Let us compare this Latin expression
with its equivalents in three other
languages.
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Quod erat demonstrandum.
Which was to be proved.
Vilket skulle bevisas.
Chto i trebovalos’ dokazat’.
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The easiest relation to establish is
the object relation.
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Quod erat demonstrandum.
Which was to be proved.
Vilket skulle bevisas.
Chto i trebovalos’ dokazat’.
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The next relation is most explicitly
expressed in Russian.
Chto i trebovalos’ dokazat’.
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Also in the Swedish equivalent
this meaning is expressed by a
separate word.
Vilket skulle bevisas.
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In Latin, this meaning is located to a
morpheme, namely the suffix
forming the gerundivum.
Quod erat demonstra<nd>um.
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In English, the carrier of the meaning is
the infinitive form of the verb be. To
express this we use the portmanteau
morpheme <INF>.
Which was (to be)<INF> proved.
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Note that the formants of the passive
voice need not be accounted for here;
they are always syntactic.
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The past tense meaning is represented
by a morpheme, which in all
languages, except Russian, is of the
portmanteau type: <PRET>. This
predicate has two valency positions,
one of which is occupied by the
implicit speech act verb «dico».
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«d.» Quod (erat)<PRET> demonstra<nd>um.
«d.» Which (was)<PRET> (to be)<INF> proved.
«d.» Vilket skulle<PRET> bevisas.
«d.» Chto i trebova<lo>s’ dokazat’.
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«Dico», in its turn, takes as its object
the whole sentence, represented by the
predicate corresponding to the finite
verbs in Russian and Swedish.
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«d.» Quod (erat)<PRET> demonstra<nd>um.
«d.» Which (was)<PRET> (to be)<INF> proved.
«d.» Vilket skulle<PRET> bevisas.
«d.» Chto i trebova<lo>s’ dokazat’.
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The relative pronoun remains to be
accounted for. It triggers the twoplace implicit predicate «i.e.». It is
sufficient to demonstrate this on one
example.
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«i.e.» Quod erat demonstrandum.
The stippled arrow points to the
theorem mentioned in the
preceding context.
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Now let us turn the relative pronoun into
an interrogative one. We can let the
question mark (the intonation) represent
the speech act verb.
Quod erat demonstrandum?
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This means that there are two object
relations pointing to the word quod.
Quod erat demonstrandum?
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A similar object position of the pronoun
we find in so-called objective
subordinate clauses.
Dixit, quod erat demonstrandum.
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In Latin, there is hardly any difference in
expression between the two uses of the
pronoun.
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In English, it is preferable to exchange
which for what:
He told us what was to be proved.
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A similar replacement takes place in
Swedish. In addition, the passive voice
of the objective sentence triggers the
insertion of a syntactic som.
Han meddelade vad (som) skulle bevisas.
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In Russian, finally, the new context
makes it necessary to drop the particle i,
which is connected with the function of
the relative pronoun.
On skazal, chto trebovalos’ dokazat’.
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In addition, the objective chto has a
considerably heavier stress than the
relative chto. This is still more evident if
we compare the pronoun chto with the
homonymous conjunction chto.
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Ja znaju, chtó ty kurish’.
Ja znaju, (chto) ty kúrish’.
In English: I know what you smoke (are
smoking) vs. I know that you smoke (are
smoking).
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The End
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