Abstract
Our uncertainty about matters of fact can often be adequately represented by probabilities, but there are also cases in which we, intuitively speaking, know too little even to assign meaningful probabilities. In many of these cases, other formal representations can be used to capture some of the prominent features of our uncertainty. This is a non-technical overview of some of these representations, including probability intervals, belief functions, fuzzy sets, credal sets, weighted credal sets, and second order probabilities.
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Notes
- 1.
It is sometimes unclear whether an agent’s uncertainty in a particular matter concerning herself is attributable to her lack of factual information or to the fact that she has not made some decision that could have resolved the uncertainty. This type of “ambiguous” uncertainty underlies several of the well-known decision-theoretical paradoxes [15].
- 2.
Let the credal set consist of all probability functions that assign to p(H) a value in either of the two intervals [0.1, 0.2] and [0.8, 0.9]. Then we still have \( \underline {p}(H) = 0.1\) and \(\overline {p}(H) =0.9\), but \(\overline {p}(HT) = 0.16\).
- 3.
For more information on decision rules, see Chap. 34.
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Asterisks (∗) indicate recommended readings.
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Acknowledgements
I would like to thank Richard Bradley and Karin Edvardsson Björnberg for very useful comments on an earlier version of this text.
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Hansson, S.O. (2018). Representing Uncertainty. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_19
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