Principle of negation

If P then there exists a not-P

This states for every thing that exists there exists is an negative, an opposite. "For every action, there is an equal and opposite reaction"; "For every this, there is a that".

Excluded middle

For every P, there is a not-P such that not-(not-P) = P

This is a stronger case, it proposes that there for every this, there is an equal that. In other words, one can pass from the one to the other, and there is nothing else inbetween the two. This is a strong philosophical position, on which most of modern mathematical proofs are based. Now, in the realm of mathematics, the realm of ideals and thought, in which a certain purity is maintained, this might be possible. However, the real world, the world of existence is just not so neat, and there are many examples of this not being true.

In fact, for many experiments to be able to take place, one needs to ignore all the factors that might influence the purity needed to ensure that what is being focussed upon is clear, and anything that might affect that purity, must be excluded. In other words, ensuring that the excluded middle holds.

Included middle

Between P & not-P, there are infinite possibilities.

The excluded middle is just one possibility. Just as between any two points there are an infinite amount of lines possible, with the straight line—the one that is most convenient to us—being a single specific case.

Complimentarity - CounterSpace

This also illustrates the Principle of the Anti, or the: "For every action, there is an equal and opposite reaction", illustrated also in quantum theory, where for every sub-atomic particle, there exists an anti-particle.

I extend the statement to: "For every object in the universe, there is an equal and opposite object". And I use the example of the triangle to show this.