Systems Expressed in Modulo 2

Historical Theories (dialectic structure)

1. History is a material progression.
2. Critical theory implies a dialectic of history.

Math (linear structure)

1. + / - operators define space.
2. The result is meaningful, because it expresses numeric values in two dimensions.
3. Two-dimensionality allows mapping of more complex equations.
4. Because math is more useful than before, math must be useful.

Coherent Categorical Deduction (logical structure)

1. Opposites are exclusive of all but neutrals.
2. The only pure neutral is zero.
3. All words have opposites, however absurd.
4. A word can be found for anything that has a concept.
5. Opposites must be opposed diagonally, to have the longest possible distance.
6. Either comparisons cancel out (opposite vs. opposite), or direct comparisons must take place between non-opposites within the set.
7. In quadra, therefore, there are only two combinations (with A arbitrarily selected as primary, and secondary choices having no express set order): AB-CD and AD-CB, since opposites must remain in opposite positions, but secondary opposites can exchange places.
8. Since no other combinations are possible in term of the expressed categories without producing either opposition or a different, equally exclusive, and non-contradicting category set (since only opposites contradict, and opposites are always expressed within the existing set no matter how many sets there are), the two combinations can be deemed coherent for quadra.

This writing was a product of the question What is Theoretical Justification? on Quora: https://www.quora.com/What-is-theoretical-justification/answer/Nathan-Coppedge