QED

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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 demonstraltndgtum.
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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 ltINFgt.
Which was (to be)ltINFgt 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 ltPRETgt. 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)ltPRETgt demonstraltndgtum.
d. Which (was)ltPRETgt (to be)ltINFgt proved.
d. Vilket skulleltPRETgt bevisas.
d. Chto i trebovaltlogts 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)ltPRETgt demonstraltndgtum.
d. Which (was)ltPRETgt (to be)ltINFgt proved.
d. Vilket skulleltPRETgt bevisas.
d. Chto i trebovaltlogts dokazat.
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The relative pronoun remains to be accounted for.
It triggers the two-place 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