Translating Negations

We place the tilde in front of a wff, so the most obvious translation involving the tilde is one where the English phrase is "it is not the case that", as in:

Translation:	Commentary:
It is not the case that France is in South America.	English sentence to be translated
A: France is in South America	Sentence letter abbreviation for simple sentence
It is not the case that A	Replacement of simple sentence by sentence letter
~A	Full translation

Negations don't always occur at the beginning of a sentence, however, and this very sentence is a great example!

Translation:	Commentary:
Negations don't always occur at the beginning of a sentence, however, and this very sentence is a great example!	English sentence to be translated
A: Negations always occur at the beginning of a sentence B: This very sentence is a great example.	Sentence letter abbreviations for simple sentence
It is not the case that A, and B	Replacement of simple sentence by sentence letter
(~A & B)	Full translation

In this sentence, the negation is buried in "don't. So we move it outside in the second step to make it explicit. But in doing so, we have to take care to in respect the proper scope of the negation sign. By that we mean that we're only negating the left half of the conjunction, not the whole conjunction.

When negations have a wider scope than a single sentence letter or its negation, that is usually signalled by the use of a grouping indicator in English. For conjunctions, look for the grouping indicator "both." For disjunctions, look for the grouping indicator "either." Here is an example of the use of negation and "either" to produce the negation of a disjunction:

Translation:	Commentary:
It is not the case that either war is justified or aggression warranted.	English sentence to be translated
A: War is justified. B: Aggression is warranted.	Sentence letter abbreviations for simple sentence
It is not the case that either A or B	Replacement of simple sentence by sentence letter
~(A v B)	Full translation