Which is the difference between Sache and Sachverhalt in the Tractatus?

Question

As far as I know, When Russell asked to Wittgenstein to tell him the difference between Sache and Sachverhalt, Wittgenstein answered that "Sachverhalt" is what corresponds to an elementar sätze (an atomic statement, an atomic meaningful declarative sentence) if it is true, whereas "Sache" is all that correspond to the logical product (that is conjonctions, as we say today) of elementary propositions when this product is true.

• Is it correct to say that Sache is the elementary proposition when it's true, whereas Sachverhalt is the compound sentence when it's true? Why did Wittgenstein need to specifically connote true elementary and molecular propositions?

Answer 1

Yes; writing to Russell from Monte Cassino in 1919, Wittgenstein explained Sachverhalt as what corresponds to an elementary proposition if it is true, and a Tatsache as what corresponds to the logical product (i.e. the conjunction) of elementary propositions when this product is true. [GEM Anscombe, An Introduction to Wittgenstein's Tractatus (2nd ed - 1963), page 30].

2 What is the case — a fact [die Tatsache] — is the existence of states of affairs [Sachverhalten].

4.25 If an elementary proposition is true, the state of affairs [Sachverhalt] exists: if an elementary proposition is false, the state of affairs does not exist.

Thus, a Sachverhalt is an atomic fact, or elementary situation, that corresponds to a true elementary proposition.

A non-existent Sachverhalt correspons to a false elementary proposition (see: 2.06 We also call the existence of states of affairs a positive fact, and their non-existence a negative fact.)