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According to the language Wittgenstein builds in the Tractatus, you start with the set of atomic facts, pick some subset of them, negate all of the members of the subset (using nand), and then add the new fact to your bag of facts. The process can be repeated ad infinitum.

So assume we start with atomic facts p, q, and r. A new statement would be p|q, or not p and not q. Then another statement could be (p|q)|(p|q), or not (not p and not q), or p or q.

My question is, assuming that all the atomic facts are true, does this mean that all negations of atomic facts are false? Does this mean negation (when you adjust for the possibility of multiple uses of negation, so that not (not p) is the same as p) is always wrong?

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No, negation is not always false. At 2.06, Wittgenstein says:

The existence and non-existence of of atomic facts is the reality.

(The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)

When we include atomic fact p in the starting set (our bag of all atomic facts), what it's saying is "Atomic fact p exists."

Some atomic facts are true, others are false. If a false atomic fact is negated, the new statement is true.

I think.

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