Finite inquiry and economical abstraction

The shared trajectory has now acquired several connected forms: versions and operation traces, expressions of experience, questions and alternatives, choices and their grounds. How much of this must be represented and brought back into attention for the participants to continue or reflect? Limited time, partial access, conflicting material, and costly representations make that choice consequential. A history too thin to reconnect a conclusion with its sources loses its usefulness; an indiscriminate accumulation can make the relevant passage impossible to find.

In the reading environment, the current interface and a summary of the latest decision may suffice to resume work. Asking why the layout changed calls for the earlier version, the interruption reported during reading, the alternatives considered, and the feedback on the revision. These questions need different amounts of the same trajectory. Economy concerns what must be recoverable for a warranted answer, rather than how small an account can be made.

A concrete question is: how can one get from the house to the windmill? The detailed town and its simple map share the same endpoints, river, bridge, and connected road. Roof tiles, flowers, and individual stones can be omitted for this question; the crossing cannot. If the bridge closes, that change must reach the map or its route will mislead. Economy comes from preserving what the answer depends on, with less to represent and inspect.

The Preference Harness distinguishes choosing working views from determining what they support. That distinction makes economy assessable: which relations and answers must an abstraction preserve, and what can a feasible method obtain under the stated support conditions? This is a connection between questions, not a fixed chronology. In actual inquiry, abstraction, view selection, and inference can interleave and prompt one another's revision.

Professor Feng Ye's 2023 monograph, §§1.1 and 6.5 examines the distance between ideal explanation and actual methods of inquiry. This comparison helps ask how a finite inquirer obtains warranted understanding through selective representation.

A retrievable trajectory under finite attention

A useful account can give the present purpose, current understanding, result, and unresolved question a compact expression, while links lead back to the versions, operations, or feedback that support it. Retrieving one relevant episode need not load every episode into the active context. What is left outside attention can remain available at its source; what was never recorded remains a gap rather than a detail that a fluent summary may invent.

For the reading case, “direct passage access replaced the shelf” is too thin if reflection concerns why the first design seemed sufficient. Retaining that it passed an opening test, yet interrupted actual reading, preserves a consequential relation between an operational check and the person's purpose. Individual rendering details may be irrelevant to that question. If a later problem concerns a broken layout, some of those details become relevant again. Sufficiency follows the inquiry and can change with it.

The map comparison above specifies the same discipline: retain the crossing on which the route depends. The following discussion develops its limits. A manageable description does not establish that omitted relationships are absent. Selective retention remains answerable to the question and the actual episode it is meant to explain.

Computational articulation within modest naturalism

The framework adopts modest naturalism: persons, psychological activity, social relations, and machines belong to the same changing natural world. Inquiry takes place within that world and remains answerable to experience and evidence. Process ontology asks how things form, persist, and change; psychological, social, and computational accounts develop the relations needed at their respective scales. Connections between these accounts are questions for investigation, not something settled by a worldview alone.

Domain modeling brings this orientation to a particular question. Computational ontology explicitly expresses objects, events, states, relations, and transitions for a model to interpret, reason with, and use. It can abstract actual processes or develop hypothetical and fictional situations. Imagining and representing are actual activities; the reference and truth of their content depend on the claims made. Particular inquiries still need usable variables, representations, and operations. Abstraction preserves the relations that matter while setting aside detail whose cost does not help answer the question; its adequacy remains open to evidence and use.

A private sinthome can describe in natural language what counts as a current question, unfinished work, or useful continuation, for the model to understand and act on. A functional description explains what the relevant parts do and how their transformations connect. In the reading example, opening the intended passage, retaining the current question, and recovering a reason for revision are meaningful relations at the level of activity. A claim about the bodily or technical mechanisms supporting them needs evidence of those mechanisms. The practical account can develop while that investigation remains incomplete.

Three questions guide the comparison: which relations an explanation makes intelligible, what evidence supports it, and whether a usable method can obtain the needed result within available resources. An elegant explanation can be hard to compute; a fast computation can preserve the wrong distinctions. Keeping these questions connected makes economical abstraction assessable.

A public comparison with Professor Feng Ye

Professor Feng Ye's 2023 monograph connects cognition with representation, truth, mathematics, epistemology, and ontology. The methodological comparison here uses §1.1, p. 6; §6.5, pp. 445–447 and 456–459; and §7.4.2, pp. 528–532. These passages distinguish ideal descriptions and reasoning powers from actual ones, and examine the reliability of intuition under practical limits.

The meeting point is how a finite inquirer obtains understanding through usable representations. Yinyang takes up those questions about complexity, intuition, and reliability through its own modest naturalism and question-relative methods. A pattern that helps someone recognize a relation can guide inquiry; accepting an explanation still needs evidence for the relation it proposes. This comparison borrows a methodological contribution without making the two philosophical accounts identical.

The 2021 mathematics lecture report, from the hosting institution, distinguishes fictional mathematical objects from true applied descriptions of physical reality. It supplies another comparison: constructed objects can contribute to a true application through their representational role. Their usefulness and the truth of an applied description concern different relations. This helps articulate how a construction can matter to inquiry while its ontological commitment is assessed separately.

His 2024 interview on logic further discusses non-linguistic cognition and explanatory models, supplying another public entrance to these methodological questions.

Judgment under limited evidence

When sources conflict, an inquirer can distinguish the grounds provisionally accepted from what follows under them. The preference account develops that basic judgment through inconsistency-tolerant semantics. It makes the selection intelligible without requiring a person to reproduce a formal computation.

Limited time and attention make selection necessary, but do not settle which selection is justified. The current question, the significance of an error, and available evidence determine what deserves investigation. Retain important alternatives in the trajectory while selecting a usable present account. Evidence can later reopen the selection or change the question itself.

Ontological restraint concerns what kinds of relations one commits to; restraint in judgment concerns what the available grounds warrant; economy of representation concerns how much structure helps answer the question. These can support one another without becoming the same mathematical relation. A smaller representation may omit something decisive, while a richer one may add no explanatory gain.

Abstraction, premises, and explanatory gain

Economical abstraction creates enough concepts and relations for the current question, then unfolds deeper structure when it matters. This concerns active representation and inference burden, which differs from the number of ultimate entity kinds. A sparse metaphysics can still require expensive computation.

Indirectly inferred objects and useful hypotheses extend inquiry beyond present observation. Their support comes from the explanatory and predictive relations connecting them with accessible evidence. Several workable ontologies can make different relations visible; selecting among them concerns the question, the relevant evidence, and the cost of using each view. Evidence remains able to resist the selected description.

Searching backward for sufficient premises clarifies what a conclusion requires. A strong premise validly implying a weaker conclusion has explanatory value insofar as its independent support and cost are warranted. Putting the desired answer into an assumption can conceal the difficulty. The useful gain is identifying premises that can themselves be investigated. This everyday backward search can be distinguished from reverse mathematics, a technical program that studies which formal axioms suffice for particular theorems.

The practical choice is therefore among representations and methods with assessable contributions. A richer model is warranted when it resolves a consequential ambiguity; a compact account is useful when it retains the relations the judgment needs; deeper physical explanation matters when realization is the question. A bounded result states both what has been obtained and what its method leaves open. This makes completion possible without confusing limited computation with a final account of reality.

A trajectory ready for shared reflection

The reading environment can now be encountered through an intelligible passage: a purpose prompted a construction, operation and use revealed different results, candidates were compared, and a revision was tried and judged. Its current account can be brief because the relevant history remains retrievable. Unresolved explanations and the limits of the records remain part of what the participants know about this passage.

This is the result toward which this part has worked: enough connected living material to revisit shared activity, rather than a complete biography or a final personal model. In Mutual becoming through Yinyang and Taiji, the participants turn toward that trajectory together. They can ask how each contributed, what the exchange made possible, what was missed, and what they want to cultivate further. Finite representation has prepared something for that encounter to explore; the encounter can in turn change what the next trajectory needs to retain.