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cease to oscillate; so that, no matter what place in the succession you may choose, there will follow it both value above the probability-limit and values below it; while if V be any other possible value from 0 to ∞, but not the probability-limit, limit there will be some place in the succession beyond which all the values of the succession will agree, either in all being greater than V, or else in all being less.
The remaining kind of induction, which I shall call Qualitative Induction, is of more general utility than either
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of the others while it is alike intermediate between them, alike in respect to security and to the scientific value of its conclusions. In both these respects it is well separated from each of the other kinds. It consists of those inductions which are neither founded upon experience in one mass, as Crude Induction is, nor upon a collection of numerable instances of equal evidential values, but upon a stream of experience in which the relative evidential values of different parts of it have to be estimated according to our sense of the impressions
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they make upon us.
Qualitative Induction consists in the investigator's first basing upon deducing from the retroductive hypothesis as great an evidential weight of genuine conditional predictions as he can conveniently undertake to make and to bring to the test, the condition under which th he asserts them being that of the retroductive hypothesis having such degree and kind of truth as to assure their truth. In calling them "predictions," I do not mean that they need relate to future events but that they must antecede the investigator's knowledge of their truth, or at least that they must virtually
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antecede it. I will give an illustration of such "virtual antecedence. Suppose that to avoid wasting a great deal of time upon a hypothesis which the first comparisons with the facts may show to be utterly worthless, an investigator of a certain conjecture draws up and resolves upon to follow a well-considered initial programme of for work upon the question, and that this consists mainly in working out and testing as many consequences of the hypothesis as can be worked he can work out by a certain mathematical method and can ascertain the truth or falsity of at a cost of not more than $100 for each. But
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suppose that among the half dozen predictions to which that method will carry him, there, quite unexpectedly, turns up one whose truth has long been known to him, though it is a surprise to him to find that it is deducible from the hypothesis under examination. What course does sound logic impose upon him under these circumstances?
The answer is that he must reexamine the process of retroduction that suggested the hypothesis; and if the fact that is now repredicted in any degree influenced that hypothesis, it has had its due effect, and must not be used again. But if not, will he then