The coordination of the truth or falsity of the whole proposition and the truth-combinations of the truth-arguments with lines in the following way:
This sign, e.g., would therefore present the proposition p → q. Now I will investigate on the strength of that whether, e.g., the proposition ~(p. ~p) (the Law of Contradiction) is a tautology. The form “~ξ” gets written in our notation as;
the form “ξ . η” thus:
So the proposition ~(p. ~q) goes thus:
If we put here “p” instead of “q” and investigate the combination of the outermost T and F with the innermost, then we get the result that the truth of the whole proposition is coordinated with all the truth-combinations of its arguments, its falsity with none of the truth-combinations.
A somewhat complicated way of demonstrating an obvious truth, but I suppose it’s the demonstration that matters here. Or maybe the point is that this is all that logic can be/do.