Continuing improvement of Scope and Precision in a System of Structural Hypotheses, at some point, reaches a level that may be declared as adequate.
> §3. _World hypotheses demanded by structural corroboration_ -- It thus becomes clear that, in the pursuit of re liability, structural corroboration does not stop until it reaches unlimited scope. For as long as there are outlying facts which might not corroborate the facts already organized by the structural hypothesis, so long will the reliability of that hypothesis be questionable. The ideal structural hypothesis, therefore, is one that all facts will corroborate, a hypothesis of unlimited scope. Such a hypothesis is a world hypothesis.
Pepper had previously introduced the phrase "systems of structural corroboration" [p. 73]. Whether that system is adequate or inadequate is a judgement, both through (i) the refining of the strength of the structural corroboration and (ii) the assuring the absence of disturbing facts from outside the limited field.
digraph PepperCh04AdequateInadequate { // Global setup rankdir = BT // Node list wh [shape=box color="green" label="World\nHypotheses"] inad [shape=box style="rounded" color="brown" label="Inadequate"] ad [shape=box style="rounded" color="brown" label="Adequate"] subgraph cluster_SSH { color="green" labelloc=t label="System of Structural Hypotheses" {rank = same inad ad} } rcog [shape=oval color="blue" label="Refining Cognition via\nCorroborating Structurally"] and [shape=oval color="blue" label="Assuring\nthe\nAbsence\nof\nDisturbing\nFacts\nfrom\nOutside\nthe\nLimited\nField"] dp [shape=oval color="blue" label="Developing\nthe\nPrecision\nof\nthe\nHypothesis"] ds [shape=oval color="blue" label="Developing\nthe\nScope\nof\nthe\nHypothesis"] dn [shape=oval color="blue" label="Discriminating\nthe\nHypothesis\nin\nGreater\nDetail"] er [shape=oval color="blue" label="Finding\nMore\nCorroborative\nFacts\nfor the\nHypothesis"] // Adding edges ad -> wh [ltail=cluster_SSH arrowhead="curve" arrowsize="1.5" label="is\nexhibited\nby"] and -> rcog [arrowhead="odot" label="is\nrequired\nby"] inad -> rcog [arrowhead="onormal" arrowsize="0.8" label="state\nchanges\nthrough"] rcog -> ad [arrowhead="onormal" arrowsize="0.8" label="changes\n\state\nto"] dp -> rcog [arrowhead="onormal" arrowsize="1.5" label="is part of\n(consists)"] ds -> rcog [arrowhead="onormal" arrowsize="1.5" label="is part of\n(consists)"] dn -> dp [arrowhead="curve" arrowsize="1.5" label="is\nexhibited\nby"] er -> ds [arrowhead="curve" arrowsize="1.5" label="is\nexhibited\nby"] }
> ... facts gathered in a limited field may acquire a certain degree of autonomy through the aid of multiplicative corroboration; but in terms of structural corroboration the hypotheses covering such facts and even the facts themselves are only tentative and provisional. > The hypotheses are adequate and the facts genuine if there are no disturbing facts bearing on them outside the arbitrarily limited field. And how can it be known that there probably are no disturbing facts outside of the limited field, unless the areas outside are explored to see? > * This does not mean that an utterly precise account could not be given of an isolated fact. > * It does mean that in terms of structural corroboration the only way of assuring ourselves of the isolation of a fact is to find that other facts are not connected with it and that they thereby confirm its isolation; and > * we can only believe that the fact is truly isolated if we believe that no other fact in the universe could affect it, > * which is the same as saying that we have a hypothesis of world-wide scope on the basis of which we judge that the description of this isolated fact as isolated is entirely adequate. > However we turn it, structural corroboration drives us eventually to hypotheses of unlimited scope -- to world hypotheses. [pp. 77-78, editorial paragraphing added]
Towards expanding beyond a limited scope, rough danda may be refined (through increasing Scope and Precision) in pursuit of a World Hypothesis.
> > Tentative structural hypotheses with limited scope are, of course, not devoid of cognitive value, especially when partly supported, as they generally are, with some degree of multiplicative corroboration. The facts they generate are rough danda and are cognitively in the same condition as rough data. What may actually be their cognitive value (apart from a guess that it is pretty good) can only be established reliably in terms of the refined danda of world theories (or in terms of refined data). The strength of the chair in terms of circumstantial evidence and one or two experiences of sitting in it is a good example of a rough dandum. [p. 78]
The paths from data to danda would seem to be covered in _§4. World hypotheses include data_