Abstract
According to Aristotelian doctrine, there are two kinds of inference or modes of deriving one judgement from others without contradiction: from a more general to a more particular judgement, by syllogism; and from particular judgements to the general one that comprises them, by what is now called induction. Judgements that form a science or system are perfectly adapted to each other without contradiction, if they can be derived from each other according to these modes. This alone shows that the opening up of new sources of knowledge cannot be the task of the rules of logic, which rather serve only to examine whether findings drawn from other sources agree or disagree, and, if the latter, to point to the need to secure full agreement.
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Notes
J. S. Mill, System der deduktiven und induktiven Logik, translated by Gomperz, 1884, I, pp. 209 f.
Ibid., p. 235.
Kant, Prolegomena zu einer jeden künftigen Metaphysik, Pt. 1.
Beneke, System der Logik als Kunstlehre des Denkens I, pp. 225 f.
Cf. Ch. XXI of the present volume.
Ibid.
Cf. note 1 above.
A. Stöhr (Leitfaden der Logik) treats induction in the section ‘Erwartungslogik’ (=logic of expectation), pp. 94f., which seems to me to mark the proper point of view.
Wallis, Arithmetica infinitorum, Oxford 1655.
Cavalieri, Geometria indivisibilibus continuorum nova quadam ratione promota, Bologna 1635.
Jac. Bernouilli, Acta Eruditorum 1686, pp. 360, 361.
This example worked out by Kunze in Weimar is mentioned in Apelt, Theorie der Induktion, pp. 34, 35. We readily see how this leads to integral calculus. Take n very large and the lower powers vanish compared with the higher, and the expression differs only in notation from ∫ x 2 dx=x 3/3. In the formula of the text dx is represented by 1.
J. S. Mill, Logik I, pp. 331–367.
Whewell, Philosophy of Discovery, pp. 238–291.
Apelt, Theorie der Induktion, pp. 62f., 143 f.
Whewell, l.c., p. 284.
Whewell, The Philosophy of the inductive sciences II, p. 92.
J. Müller, Phantastische Gesichtserscheinungen, pp. 95 f.
Liebig, Induktion und Deduktion, 1874.
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© 1976 D. Reidel Publishing Company, Dordrecht, Holland
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Mach, E., Hiebert, E.N. (1976). Deduction and Induction Psychologically Viewed. In: Knowledge and Error. Vienna Circle Collection, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1428-1_18
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