Normality and Majority: Towards a Statistical Understanding of Normality Statements

Abstract

Normality judgements are frequently used in everyday communication as well as in biological and social science. Moreover they became increasingly relevant to formal logic as part of defeasible reasoning. This paper distinguishes different kinds of normality statements. It is argued that normality laws like “Birds can normally fly” should be understood essentially in a statistical way. The argument has basically two parts: firstly, a statistical semantic core is mandatory for a descriptive reading of normality in order to explain the logical features of normality laws. Secondly, a statistical justification of normality statements can be derived by game theoretic considerations if the normality law is understood as communication convention.

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Fig. 1

Notes

  1. 1.

    The examples illustrate that different words and grammatical constructions might be used to speak about normality: “normal”, “typical”, “usual”, “regular” or generics.

  2. 2.

    I will not consider the normativity of normality in this paper. The view that normality is essentially normative is a misunderstanding that is caused by the appearance of the words. Obviously one can easily use the word in normative contexts. Furthermore, stating that something is abnormal might be condemnatory act. However, almost any word can be used in normative contexts and there are many normality statements which are clearly not normative. Considerations of normality might matter in a normative discourse and this is worth to be considered. A clarification of normality outside of normative contexts must precede this consideration.

  3. 3.

    For an overview on the history and different usages of ceteris paribus see Reutlinger et al. (2014).

  4. 4.

    Note, however, that such statements are no contradictions in logical systems without centering axioms (cf. Leitgeb 2012). Still it holds that (weak) centering, and in the course modus tollens, are much more desirable for counterfactuals than for normality statements.

  5. 5.

    Of course, you might state what is normally the case in similar situations.

  6. 6.

    Schurz distinguishes between fundamental and derived prototypical traits. Fundamental prototypical traits are causes for the overwhelming selection in favour of some reprotype while derived traits are rather side effecs. This distinction can be important in response to Wachbroit who claims that any evolution theoretic account has to presuppose normality to capture the difference between function and malfunction.

  7. 7.

    Schurz continues his argument and deduces SC, the final version of the statistical consequence thesis (cf. Schurz 2001, 495). I will not go in the details of the further argumentation. The idea, I think, is sufficiently clear in conclusion 2.

  8. 8.

    He argues that natural-historic judgements, which are Aristotelian oriented, should logically behave like universal laws (cf. Thompson 2008, 69).

  9. 9.

    This is not only problematic for academic disciplines that need to work with normality statements (like biology). One should also consider ethical implications. Our prejudices about other social and ethnical groups usually take the form of normality judgements. Lack of testability seems to imply the right to stay with ones prejudices no matter how many counterexamples or statistical data is provided.

  10. 10.

    A quote from the Wikipedia entry on “Tooth (human)”. The example is mentioned in (2008, 68).

  11. 11.

    Admittedly, the entire framework of update semantics eliminates truth conditions in favour of belief change conditions (cf. Veltman 1996, 221). It still is enlightening that he chooses this framework to introduce a formal operator for normality laws.

  12. 12.

    Prototypicality effects arise whenever a category has more and less salient members. A brief characterization is given in Rosch (1978).

  13. 13.

    According to Lewis, a convention is a regularity in the behaviour which is widely spread in a community. Furthermore it is in the best interest of everyone that everyone conforms to this regularity. However, there is another possible regularity such that everyone would prefer that everyone else conforms to it, if a majority of people acted according to this rule. All this is commonly known by the members of the group. For a full and refined definition of convention see (Lewis 1969, 79). The definition of common knowledge is given in (Lewis 1969, 56). Most importantly, common knowledge of A in the Population P implies not merely that everyone in P knows A but also that everyone knows that anyone else knows that A. This is again known by everyone and so on...

  14. 14.

    These equilibria are Nash-equilibria. They are also special cases of pareto optimality in a scenario without conflicting interessts. During the following text I will stick to Lewis’ terms.

  15. 15.

    Such relation has often been denied, most notably by Reiter (1987).

  16. 16.

    Personally, I think there are good reasons to reject agglomeration of normality laws as too strong, especially in addition to statistical justification. Though statistical justification and agglomeration are in principle consistent both together reduce the acceptibility of normality laws considerably: Most things have to be completely normal with respect to the normality laws you accept.

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Acknowledgments

The paper was written in the course of an Emmy Noether project on formal epistemology supported by the German Research Foundation. It partly builds on my PhD thesis that was written at the Saarland University and published in German as Strößner (2014). I am grateful to Joanna Kuchacz and Franz Huber for their comments. I also thank the anonymous referees.

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Strößner, C. Normality and Majority: Towards a Statistical Understanding of Normality Statements. Erkenn 80, 793–809 (2015). https://doi.org/10.1007/s10670-014-9674-1

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Keywords

  • Normality statements
  • Ceteris paribus
  • Normic laws
  • Commonsense reasoning