Library.Reference:1.2.1 - Related forms of thinking retain their questions

The holonic aspect of system thinking concerns Systems, the holonic aspect of methodological thinking concerns Methods, and the holonic aspect of reasoning about performed work concerns Work. These distinctions help explain the common contribution. The familiar names also have wider uses. A.1.STM connects the proposed system with its intended use, creators, Methods and cooperation; OPS.23 connects work with capacity, commitments, service, money and people’s conditions. Neither account becomes complete by identifying one holon kind.

Management and strategic reasoning connect several of these subjects. C.43 relates observations, choices and actions under the conditions of the same continuation. STR.18 relates worthwhile contributions, their obtaining ways, feasible means and commitments. Their holonic questions can concern systems, methods, work and knowledge together. “Strategic” and “operational” name different questions here; the words alone place neither the thinker nor the object at a particular system level.

Mathematical thinking also has several contributions. A proof account or theory can be considered as a connected whole of claims. A reusable proof Method can compose submethods. Mathematical thinking additionally constructs objects, operations, representations, witnesses and countermodels, and develops conjectures. A mathematical object that a claim concerns is different from the claim-bearing Episteme. MATH.Reference:1–3 develops that broader repertoire.

This distinction changes the next action. An adequate proof of existence may settle one mathematical question while a later use requires a way to obtain a witness. MATH.12 examines what construction the proof supplies; another mathematical contribution may be needed. Calling the proof an Episteme does not produce that contribution. A constructive account of mathematical work preserves the distinction between existence, a witness-producing operation and its execution; it need not exclude classical reasoning.

The synthesis connects these different contributions through what one supplies and another needs. It does not establish that all their originating disciplines are parts of one further discipline. C.20 supplies the stronger construction when that claim matters.