Abstract
Among fallible inferences, that is to say, ones in which the truth of the premises is not in fact decisive for the truth of the conclusion are included probabilifying inferences.1 Probabilifying inferences are those in which, when we start from true premises it is not impossible that we may come to a false conclusion, but we expect rationally the conclusion to be true. Of the various types of probabilifying inferences we are going to discuss reductive inferences and a particularly important variety of these—inference by incomplete induction. We shall also discuss inference by analogy; although the latter does not have the traits of reductive inference.
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There are also inferences quite worthless from the point of view of methodology.
The second example is even more complicated in that we have to accept a conclusion concerning every solid and every temperature rise. This requires the introduction of a more complicated, but more general pattern of inference by way of incomplete induction. The premises would be various, successive substitutions of the function: f(x, y) ? g(x, y)—where f stood for being a solid; g, for being subject to expansion of volume; x, for a variable indicating particular objects, and y, a variable indicating temperature increments within some interval. The conclusion attained by way of induction would correspondingly have the form: II x, y: f(x, y) ? g(x, y).
Methodologists usually distinguish simple historical generalizations of propositions concerning individual facts (for example, that in the nineteenth century each national uprising in Poland was unsuccessful) from universal scientific laws. The latter are defined as stating some universal regularities observed in any given field of facts (for example, that in each group that has come to power the percentage of ‘climbers’ is growing—persons who hold their careers to be of primary importance). Cf., e.g., A. Malewski and J. Topolski, Studia z metodologii historic, Warszawa 1960, pp. 15 ff.; J. Pelc, Prawa nauki, Warszawa 1957, pp. 30 ff. It is, however, quite a complex problem. Cf. J. Such, O uniwersalnosci praw nauki, Warszawa 1972, p. 399.
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© 1976 Springer Science+Business Media Dordrecht
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Ziembiński, Z. (1976). Probabilifying Inferences. In: Practical Logic. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-5604-4_14
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DOI: https://doi.org/10.1007/978-94-017-5604-4_14
Publisher Name: Springer, Dordrecht
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