FORMAL SYSTEMSPRINCIP-PUZZLEPrinciple-Puzzle or Princip-Puzzle is a rare logic drawn from the analogy that principle occupies one of any number of geometric categories.So, for example, in a 2-d typology such as a bounded Cartesian Coordinate system similar to a truth-table, except exclusive, principle might occupy one of the four categories of a system (say, in generating proofs, for example). Think of principle as a kind of description of the necessity for logical ingredients.Now, we can analogize that the presence of principle defines that two categories within the same diagram can oppose principle, but that one category can no more than cancel it out. Thus, we can see that some sort of irrationality is required in 1/2 of the categories if we are to oppose the idea of having principle. Incidentally, the 1/2 ratio (maximum) is precisely the point at which reason becomes diametrically opposed to madness, thus reducing the system to a pair of opposites and eliminating the logic. Thus, principle becomes provably a figure of logic. And, at the same time, we can see that when 1/2 is madness, principle composes 1/2 of reason, thus, there still remains 1/2 of reason which may be not yet defined. Thus, combining some further idea with principle is what creates reason.That's the full description of what Princip-Puzzle means for a 2-d typology. Here is the diagram:                  PRINCIP-PUZZLE 1 (2-D)A second princip-puzzle which I hit upon recently inspired this writing. It relates to analogizing between 4-d metaphysics and a 3-part typology. Once again, principle is one geometric category, but in this case it is left unstated, and simply rounds out the 3-typology to make it adequate for 4-d metaphysics. In other words, it is creating an application of 3-d categories that has a principle of 4-d by having a 4th category that represents principle.The 4-d construction is 3-d because it is a construction based on principles, and the variable called 'principles' already counts as one dimension, when it is taken seriously (i.e. when it is quantifiable like all typological categories theoretically are).The three further categories I came up with are:1. Root / origin: Identity.2. Connector / conjunction: Balance.3. Structure / filler: Infinity.Make sense? Here is the diagram in that order. Notice that the nodes have different interpretations of what principle means, and are fairly exclusive for the set.   PRINCIP-PUZZLE 2   (4-D METAPHYSICS)             BACK TO SYSTEMS