(for super-geeks)(math vs science)(unification of disciplines)(universal epistem

(for super-geeks)(math vs science)(unification of disciplines)(universal epistemological method) (human scale)

(read the comments with Davin and I.)

MATH VS SCIENCE?

Mathematics is not a science (theoretic system of external correspondence) but a logic (axiomatic system of internal consistency).

We are, almost universally, fooled by the fact that we cannot imagine all consequences of our axiomatic declarations, and equate this to the same phenomenon of our inability to imagine all consequences of our observations of reality. But axiomatic systems are declared (models) and theoretic systems are observed (reality). When our models and reality appear to correspond, we say that the model appears good or true.

For this reason mathematical (axiomatic systems) do not produce truths (ultimately parsimonious and completely correspondent descriptions of reality) , but proofs of internal consistency. Theories = True correspondence. Axioms = Proof of internal consistency. Both of which require that we are describing constant relations.

Until we discover the set of possible operations in the universe (causality or causal particulars) we must content ourselves with descriptions of the consequences of those operations (mathematics), by creating models with which we declare descriptive axioms as a general expression of the unknown causal operations.

Ergo we can use mathematics to create models of theoretic systems (reality) because axioms express constant relations and the universe operates deterministically (according to a set of rules that produce observably constant relations).

Science != to Empiricism (that the error of positivism). Instead, identity, logics, empiricism, operations, and morality when tested by limits, full accounting, and parsimony, assist us in removing error, bias, wishful thinking, suggestion, overloading, and deception from our thoughts, words, and deeds.

This is why mathematics generally succeeds in representing highly deterministic systems (constant relations of constant categories) but why mathematics fails us in slightly deterministic systems – in particular, heuristic systems (inconstant relations of inconstant categories.)

Mathematics is an abstraction of operations. A generalization for the expression of observations about which we do not know the operations.

Science on the other hand ensures that we use categories, sets, mathematical descriptions, empirical correspondence, causal operations, moral reciprocity (in matters of cooperation: social science) and then define limits, test for full accounting, and test for parsimony.

This process of ensuring is what we call falsification. if a description (theory) can survive all those tests, we can warranty that we have performed due diligence and speak truthfully.

In other words science provides us with a universal epistemology.