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Conclusion of Part I

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Probability and Social Science

Part of the book series: Methodos Series ((METH,volume 10))

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Abstract

After the detailed examination of the main approaches to probability, the statistical inference that they imply, and their application to social science, we can now try to provide more detailed and better-informed answers to questions to which we have so far offered only partial answers: What is probability? What type of inference does it allow, particularly for social science? Can the three approaches be combined to any extent?

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Notes

  1. 1.

    Gradus certitudinis.

  2. 2.

    Leibniz is referring to the logic of probability that Aristotle links to the art of rhetoric in Rhetoric.

  3. 3.

    In fact, Gödel (1931) showed that the theories intended to provide a foundation for mathematics, such as Peano’s arithmetic and set theory, contain at least one proposition that can be neither proven nor rejected as false by the theory.

  4. 4.

    (1) die gleichen elektrodynamischen und optischen Gesetze gelten, wie diese für die Größen erster Ordnung bereits erwiesen ist, (2) das Licht im leeren Raume stets mit einer bestimmten, von Bewegungszustande des emittierenden Körpers unabhängigen Geschwindigkeit V fortpflanze.

  5. 5.

    Die Messungsergebnisse sind mit der lorentz-einsteinschen Grundannahme nicht vereinbar.

  6. 6.

    Quando-quidem calculus dicet, sortem Pauli infintum esse, nec tamen ullus sanae mentis, ut dicit, futurus sit, qui non libentissime spem suam vendiderit pro summa viginti ducatorum.

  7. 7.

    At the end of his presentation, given in 1731 but published in 1738, he notes that Cramer, the famous Swiss mathematician (1704–1752), had already described a similar theory in a letter to his cousin Nicolas in 1728, which Daniel Bernoulli quotes.

  8. 8.

    Cramer and Laplace still refer to this notion as moral expectation.

  9. 9.

    aestimari posse emolumentum lucri valde parvi summae bonorum reciproce proportionale.

  10. 10.

    Si decem habuerit ducatos, proxime tres valebit expectatio, and quatuor cum triente praeter propter si centum habuerit, ac denique sex cum mille habuerit. Facile hinc indicatu is quam immensas quis divitas possidere debeat, ut cum ratione viginti ducatis sortem Pauli emere possit.

  11. 11.

    Exponentiation relies on generating new lattice elements from old by grouping the old elements into sets called downsets. Downsets are constructed so that they contain their lower bound. That is, given any element in the downset, all elements included by this element are also members of the set (Knuth 2008).

  12. 12.

    Here we use the notations that we have adopted for the present book and not Knuth’s (2010a), which are slightly different.

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Courgeau, D. (2012). Conclusion of Part I. In: Probability and Social Science. Methodos Series, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2879-0_4

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