The elementary proposition
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4.41 Der einfachste Satz, der Elementarsatz,
behauptet das Bestehen eines Sachverhaltes
The simplest proposition, the elementary
proposition, asserts the existence of facts
What is the simplest proposition? If I say 'either
Tom broke the clock or Harry did' is a complex
proposition made up of two simple
propositions,'Tom broke the clock' and 'Harry
broke the clock'
Complex
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But also 'Tom broke the clock' is a complex
proposition?
No, because there is not another that corresponds
to the proposition. Can be expressed by other
names, of course, (The clock was broken by
Tom)but the fact is the same as defined.
In fact, the names in close connection (4.221 in
unmittelbarer Verbindung) are the same
Tom,broken,clock.
Context
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True, also, to break and clock can be expressed by
other names, such as splitting, stopwatch, but it is
clear that the fact described imperceptibly turns.
The name also meant to be then take the other
names because it only makes sense in the
sentence, only in the context of the sentence has a
name meaning (3.3 nur im Zusammenhang des
Satzes hat ein Name Bedeutung)
In fact if I say 'Tom broke the clock' and 'The
clock was invented in the fifteenth century' the
clock changes its meaning.
Notation
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4.24Die Namen sind die Einfachen Symbole, ich
deute sie durch einzelne Buchstaben ( »x«, »y«,
»z«).Den Elementarsatz schreibe ich als Funktion
der Namen in der Form:»fx«, »φ(x.y)«, etc.Oder
ich deute ihn durch die Buchstaben p,q,r an.
The names are the simple symbols, I indicate
them by single letters («x», «y», «z»). The
elementary proposition, I write as a function of
names in the form: «fx»,«φ(xy)», etc.Or I indicate
it by the letters p, q, r to.
calculus
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We will deal almost exclusively the last way.
Even if we give some examples of the way first.
Wittgenstein seems to say that the two ways are
the same. But it is not so, because the last to rise
to the propositional calculus, the first in the
predicate calculus.
Our example: 'Either Tom broke the clock or
Harry did': Tom broke the clock= p ;'Harry broke
the clock' =q and the proposition 'Either Tom
broke the clock or Harry did' is pvq.