Neutrality Behind The Meaning

One of the principle in Aristotelian logic is that among any two contradictory statements, which describe the things in real world or the things that supposedly can be observed by the others, one of the statements is necessary false:

p&~p = either p orr ~p is false iff

is a description of the relations between things.

'p' – is presupposition of the statement.

Considering an introduction of the concept of presupposition (that hadn't been done by Aristotle at his time) it can be rewritten like:

~'p' |= {"(p&~p)" has no sense}

In Aristotelian logic we take p as a "some" statement or the statement that claims that "at least one x is/has...", but in modern logics with plural meanings there appears no need to stigma one variant of the meaning. We might say instead:

~'p'* |= {"(p&~p)" has sense in a *-context} or {the meaning of "(p&~p)" is *}

Despite of which version is correct (the traditional one or the modern one) it's important to accept that either the presupposition or "*" is taken as kind of a neutral element.

In other words, there's no meaning in anything without that neutral element behind them. We may not think about it or intentionally put in to the meaning, however it will be discovered through the set of interpretations:

~(~'p' |= {"(p&~p)" ...}) |= {"~'p' |= {"(p&~p)" ...}"}...

Each try would mean to find what we had plot to find before. Each act is pointing on a previous one, and so on. Every next step is to make us more neutral regarding our intentions.

Even trying to force it – to acknowledge that our intentions were not neutral, we had already accepted neutrality as a concept or a draw line between what is neutral and what is not.

It must made us perplexed, because it leads us to the thought: there is no neutral place between neutrality and non-neutrality. Previously we had already acknowledged that there must be. So, what kind of place is? – This is another question. And even this paradox shows that we have intention to observe it - the neutrality.

What is sufficient here is that the neutrality is indeed hidden behind the meaning.