If it is, then we have the algorithm of generalization. It remains to write it in details and enter it into a computer.

But generalization was counted the greatest feature of human mind. I discovered the main part of the algorithm of technological singularity?!!!

]]>A middle is allowing defining predicates only which have no conjuntion at top level. Is this middle reasonable/effective?

]]>Obviously, this trouble could be solved by never defining any symbols (or defining some symbols but never defining predicate symbols).

However, this would lead to up to exponential on the number of defined symbols growth of size of theorem statements.

Which variant could be a reasonable middle between these two extremes?

]]>There is however a trouble (that could be classified as a trouble of too much freedom) that for example discovery of funcoids could be “eliminated” by using as presumptions predicates like X is a proximity (or even metrjc) space instead of an implicit conjunction of proximity axioms, making us unable (not willing) to eliminate superfluous axioms.

To solve this trouble, we could always trace a theorem to its primary implicants (“new axioms” of my system), but that would be indetermined by having multiple proofs (and even cycles of equivalent – implying each other – theorems) of an axiom, multiple definitions of a predicate.

How to eliminate (or make less harmful) this indeterminancy?

]]>Also using my logic partly solves the “wall” between fundamental and applied science, an important case of common goods tragedy (that works in fundamental science are important but workers oftentimes cannot obtain financing of research work, equipment, editing, subsidiaries, communication, and wide prestigious publication):

Removing superfluous axioms is expected to often make applied mathematical research much more fundamental and therefore much more useful without hindering (in short term) it’s monetary compensation.

]]>This in turn in some sense at least partly obsoletes my revolt because of my poverty and consequentially no degree:

My revolt was caused by non-publication of my algebraic general topology (and consequently of discontinuous analysis) and therefore stagnation of science.

But if we follow this new logic in “everyday” academic research, discovering and publishing theorems covering concepts and properties of funcoids, reloids, and even actions of partially ordered semigroups become inevitable (except of the case of ceased civilization) by the academic science even if the present irrational broken legal system, and broken traditions of academies and job hunting, that gives rights to receive salaries and grants paid, remain.

Now I speak as a scientific economist, not as a religious person fighting for justice. However the fact that injustice (that includes me having no degree and my pleas being not considered by courts) remain a serious economical trouble, also accordingly theories of many (most?) scientific economists.

]]>If it cannot, we get “logic without false”, “a truth-only logic”, “nothing can be falsified” (speaking like a propagandist) what looks like to be related with my Not Science project.

]]>So, mappings between funcoids that I discovered are mappings between sets defined by conjunctions of axioms. We could exclude axioms one-by-one and obtain bigger sets and wider mappings. However, the direct generalization of my theorems to wider mappings may be irrelevant (because false) generalizations. What is a good heuristic strategy in this case?

]]>This obsoletes my own formerly great discovery of Algebraic General Topology (such as funcoids and reloids). In the case of my theory of actions of partially ordered semigroups, the theory could be easily discovered by generalizing Kuratowski variant of topological spaces or theory of operator semigroups.

However axiomatic theories still make sense to describe sets of objects. In funcoids theory, it’s relevant in my theory of mapping between funcoids. How could we describe and discover such things as these mappings in a routine way rather than through my feat?

]]>Sorry, truth implies truth is not provable in intuitionistic logic.

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