C.39.WA:4.3 - Give each consequential transition its actual relation
Identify the subjects on both sides of a transition and the relation that permits the next claim. Use the following distinctions where they change the explanation or its appraisal.
| Transition | What must be recovered |
|---|---|
| A candidate falls under a kind | The candidate, the kind’s criterion and the basis for applying it; C.3 governs membership. |
| A narrower kind falls under a broader kind | The directed relation between criteria or the relevant exhaustive finite comparison; C.3.1 governs SubkindOf. |
| Contributions constitute a whole | The subject-specific composition relation, grounds of unity and conditions of the whole; A.14, B.1.5, C.2.1 and C.20 supply different constructions. |
| One contribution uses another’s result | The supplied result, receiving operation and conditions of use. This dependency has its own meaning alongside any composition. |
| Work enacts a Method | The reusable Method and the actual performer, occurrence and conditions; A.3.1 and A.15.1 govern these different subjects. |
| A description or model represents a subject | The original subject, representation objects and relations, claims, correspondence and the returned inference. C.2.1 and, for mathematical model use, C.29/C.29.1 preserve these distinctions. |
| A particular construction supports a more general operation | The retained premises, variable inputs, operation and grounds for the wider application; C.39.RO develops the generalization. |
| An abstraction serves a selected question | The retained distinctions and relations, the omitted detail, and the questions the selected representation can answer. |
A relation identifies how its participants are connected. A returned claim also needs an applicable inference rule. Separately, the resulting work must be compared with the original account question; C.39.QR:4.2–4.4 develops these two judgements. These relations can coexist. A reusable calculation can be a constituent of one Method and supply a result to another. A discipline can contain other disciplines and use results from fields that are not its constituents. A representation can preserve some structure, omit some and introduce useful constructed objects. Explain the relevant correspondence before returning a conclusion to the represented subject.
Grounding connects a case with an explained construction. Identify that construction and make its relevant objects, relations, operations and grounds available to the reader. Show which consequential moves in the case instantiate which operations, why the conditions select them, and what a change would reopen. In an account of a Method, distinguish the explained Method, its displayed performance and the subject worked on during that performance. For example, when explaining how to design an explanation, a calculation can be the material; selecting a contrast and revising the explanation are performances of the explained Method. E.8:4.2.1.1–1.3 and EXD.2 develop this correspondence for authoring explanations.
Choose meaningful variety from the account’s declared subject and use. Differences in objects, relations, premises or available means can require different branches. Retain cases that make those differences understandable. A running case helps trace connected operations; add or change cases where it hides a consequential distinction, and return from each application to what it reveals about the general account. The choice of examples follows the work they must do, with no fixed number applying to every account.
When generalizing, state what elements and relations are being generalized, the wider class, retained premises and grounds for the extension. Varied cases can support construction, expose limits and contribute evidence under the relevant inference method. A general proof, a qualified empirical inference and a demonstrated performance have different warrants. Explain the general contribution and the role of the cases in obtaining or understanding it.
Questions: What was the subject before this transition, and what is it now? Which relation connects them, and what inference does it support? What explained construction is grounded by the cases? Which material differences do their variations reveal? What is generalized, over which range and on what grounds?