FORMAL / LOGICAL SYSTEMSARBITRARY MATHEMATICSSeminal Work on Math Expanded for Larger Formal SystemsPre-requisite: 2-d decimal system.Zero can have an area.Multiple origins are possible.Arbitrary mathematics.(Not just numbers, but also other formal ideas:not-just-number theory)As in philosophy, there is a need to define the rules.However, the rules can be mathematical.They can also be logical, where logic permits.In arbitrary mathematics, the biggest assumptions are logical.The biggest products are linguistic, chemical, biological, historical, fictional, etc.A model to uphold is the concept of a theoretic paradigm.The modification of the theoretical paradigm leads to different 'worlds'.As in Modal Realism, the worlds are different from one another in at least one way (whatever way that may be), but unlike MR, the differences are purely theoretical.In fact, in any given study of arbitrary mathematics, it may be that only one world is considered: the world under which the specific model of rules holds.Since the theory is so broad, it may be helpful to consider problems first. The extent to which problem-conditions are accepted can become a model for functions.Another possibility is to consider functions first. If functions can be based on problems, then positing functions may be just as strong as positing problems. Functions have the advantage that they are not necessarily problematic.Thus, the ideal system can be based on functions.If a particular system of functions is especially strong, then it defines a particular set of rules, and it is back to problems.Problems define functions define systems which define problems.All of this regardless of whether math is the only system involved.   BACK TO SYSTEMS