Simplicity is necessary in mathematics since mathematical symbols and operations

Simplicity is necessary in mathematics since mathematical symbols and operations itself (state and operators) are necessary to allow us to remember state with sufficient precision that we can conduct comparisons between states.

However, if we restated the foundations of mathematics operationally (constructively – analogous to gears), and we stated the foundations of mathematical deduction negatively, as geometry, we would be able to show that it is convergence between the via-positiva construction, and the via-negative deduction that leads us to truth.

Unfortunately, man discovered (logically so) geometry prior to gears, and as such, we retain the ‘superstitious’ language of geometry (and algebra) of the superstitious era in which both were invented.

Reality has only so many dimensions. By adding and removing dimensions from consideration we simplify the problem of describing the constant relations within it.

Mathematics specializes in the removal of (a) scale, and (b) time, and (c) operations (and arguable (d) morality) from consideration, leaving only identity, quantity, and ratio, to which we add positional naming (numbers). We then construct general rules of arbitrary precision (scale independence) and apply those to reality wherein we must ‘hydrate’ (reconstitute) scale, time, and operations(actions).

So just as philosophy is ‘stuck’ in non contradiction instead of increasing dimensions in order to test theories, mathematics is ‘stuck’ in non-contradiction instead of re-hydrating (restoring dimensions) to justify propositions.

In other words, fancy words like ‘limits’ or ‘non-contradictory’ or ‘axiom of choice’ and various other terms in the field are just nonsense words that prevent the conversion of mathematics from a fictionalism into a science.