Was sollen wir tun? Was dürfen wir glauben? - bei DuEPublico ...

Statistical and Non-Statistical Normality
Corina Strößner
Logics of normality which have been suggested so far interpret normality non-statistically. In
this sense, something is normally the case if it is true in the most typical or plausible
circumstances. On the other hand, one might think of normality as majority. In this sense
something is normally the case if it is true in most circumstances. The paper argues that a
descriptive explication of normality must imply statistical majority. Finally it introduces a
formal logic of statistical normality and compares it to other approaches.
1. Principles of Normality Statements
“Normal” and “normally” are frequently used in natural language. We speak about normal
days, normal members of species, normal properties of someone or something etc. In this
discussion we define normality statements as nearly universal generalizations which allow for
exceptions. Not any statement with the word “normal”, “normality” or “normally” is a
normality statement in the sense of this investigation nor is any of these expressions a
necessary part of a normality statement. The word “normally” as a sentential modifier is a
sure indication for a normality statement, e.g. in “Birds can normally fly” or “John normally
sleeps long”. However, statements like “Birds can fly”, “A normal bird can fly” or “John is a
long sleeper” mean often the same as a sentence with “normally” and should be regarded as
normality statements too.
Normality statements are especially important to defeasible reasoning since they justify
predictions which can be revised when more information becomes available. This property of
normality statements can be explained by two different principles of normality statements:
statistical justification and epistemic ordering.
1.1 Statistical Justification
Why should one believe a normality statement like “Birds can normally fly”? Under which
circumstances should we reject such a sentence? One suggestion is that the acceptance of
normality statements should be justified by statistical reasons. Though the statistical reading
is not popular in non-monotonic logic, even Reiter, one father of default reasoning,
interpreted his defaults initially as statistical information: “Such facts usually assume the
form ‘Most P’s are Q’s’” (Reiter 1980: 82). 1
The plausibility of statistical justification for normality statements in natural language is
demonstrated by the obscurity of the following sentences:
(1) Normally, the train is on time; but mostly it is delayed.
(2) Bears are normally shy; but most bears are not shy.
Whoever utters these sentences makes a normality assumption against his statistical
knowledge. This seems to be incoherent. He violates the following principle:
1
Later Reiter strongly rejected this view. See (Reiter 1987).