Hierarchy of Constant Relations
1 – identity: tests of intra-reference constant relations
2 – logic: tests of inter-reference constant relations.
3 – mathematics: operations on positional relations, which by definition remain constant.
4 – construction: operational construction (arithmetic)
5 – deduction: deduction from a construction. (geometry/algebra)
6 – elimination (subtraction): deduction by falsification of all alternatives. (fields – effectively trial and error) the problem is that mathematical trial and error is cheap while verbal and existential trial and error is prohibitively expensive.
We are trained in construction, deduction, induction, abduction, guessing, and free association.
But mathematicians are trained in the trial and error method.
In science we practice the trial and error method.
In law we practice the trial and error method.
It’s only (silly) justificationism that construction and deduction have any function, and even then that function, like the formal logics is of very limited value: it tells us only that something is false.
You don’t prove anything (non trivial) with logic.
You just falsify with it.