Towards the coalescing of a reliable World Hypothesis, cognitive refinement requires evidence be increasingly convincing. This occurs through increasing precision and increasing scope.
> ยง2. _Scope and precision_ [....] [p. 74] > The cognitive value of such hypotheses is generated directly out of the mode of cognitive refinement which requires them. Structural corroboration cannot get along at all except by the aid of hypotheses which connect together the evidence that is corroborative. [p. 75]
A single item of evidence is weak. Through corroboration, items of evidence support each other. Pepper illustrates this through the example of belief of a chair's strength.
> Even in our earlier common-sense example of structural corroboration having to do with the strength of a chair, the evidence would not have been convincing but for a set of hypothetical connections, mostly causal, which brought together the evidence toward the belief in the chair's strength. > * For instance, take the evidences of wear on the chair which were accepted as evidences of the chair's strength. > * Consider what an amount of hypothetical construction based on what an amount of more or less rough observation was necessary to bring that perception forward as an item of evidence. > * Consider, furthermore, how weak this evidence would be if not supported by the other items of corroborative evidence. Notice how every item mutually supports every other through some sort of implied structure, so that each gains in weight as the evidence accumulates. > * And notice -- what is particularly interesting after our discussion in the previous chapter -- how, after all this circumstantial evidence has been accumulated and organized, the sitting of a man in the chair becomes simply one more (though certainly weighty) circumstance to be added to the structure of other circumstances justifying the belief in the chair's strength. [p. 75, editorial paragraphing added]
If we start from the premise of doubt, knowledge comes from building up the corroborative evidence. Pepper continues the focus on structural corroboration of danda, and temporarily puts aside the multiplicative corroboration of data.
digraph PepperCh04ScopePrecision { // Global setup rankdir = BT // Node list rcog [shape=oval color="blue" label="Refining Cognition via\nCorroborating Structurally"] 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 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"] }
> If we wished to increase the reliability of this crude hypothesis (and for the moment we shall minimize the aid of multiplicative corroboration), we could do so by developing it in either of two directions, either > * by discriminating more carefully the nature of a chair and its strength or > * by extending the range of circumstances which bear upon its strength. > * The first may be called the development of the precision of the hypothesis; > * the second, the development of its scope. > These two marks of a good structural hypothesis are so closely allied that often they can scarcely be separated, and the greater the refinement of the hypothesis the less they can be separated. [pp. 75-76, editorial paragraphing addded]
Developing precision increases scope. And developing scope increased precision.
> ... the accumulation of these facts to increase the precision of the hypothesis automatically increases its scope. They constitute so many more circumstances organized and brought to bear upon the cognitive situation. > Similarly, an attempt to increase the scope of the hypothesis, to find more corroborative facts for it, will inevitably lead to more precise analysis of the individual facts and their connections. We find out what facts bear, or most strongly bear, on the situation, and automatically the precision of the hypothesis is increased. [p. 76]