We claimed that the categories of rational judgement are three: the necessary, the impossible and the possible. However, an opponent may ask: “how do you know that there are only three categories?”
We respond: if a statement can be neither affirmed nor negated, then this statement is not a proposition. It is therefore impossible for a proposition to not accept both of affirmation and negation. This means that a proposition either does not accept one of affirmation or negation, or it accepts both of affirmation and negation.
If a proposition does not accept one of affirmation or negation, then either it does not accept negation, or it does not accept affirmation.
If a proposition does not accept negation, then it must be affirmed. This is a necessary proposition.
If a proposition does not accept affirmation, then it must be negated. This is an impossible proposition.
If a propositions accepts both affirmation and negation, then it may or may not be affirmed. This is a possible proposition.
Thus, a proposition must be one of necessary, impossible or possible.