Synthese manuscript No. (will be inserted by the editor) Understanding Normality Corina Str¨ oßner Received: date / Accepted: date Abstract Many linguistic, logical and philosophical concepts are related to normality. In discussions on the semantics of normality in the last decades ma- jority was rarely considered as a necessary condition for normality statements. For one thing, logical systems which work with normality operations give usu- ally no statistical background semantics. For another thing, some philosophi- cal issues which are seen in partnership with normality are in no obvious way connected to statistical facts. This paper discusses different interpretations of normality and their relation to statistical statements. It will be argued that non-statistical normality interpretations face a problem when it comes to a justification of defeasible reasoning which is strongly related to normality statements. Only methodological considerations in communication contexts can justify these inferences. However this implies a rather non-descriptive interpretation of normality statements. It will be argued that a more ontic or descriptive understanding should be related but not reduced to statistical propositions. Keywords Normality · Typicality · ceteris paribus · Non-monotonic logic · Intermediate quantification 1 Preliminaries Normality is an important concept in different areas, e.g. medicine, sociology and in everyday life, as well. This paper focusses on a philosophical analysis of normality statements . Before we discuss the semantics of normality statements, we have to determine which of the numerous usages of the words “normal” and C.Str¨oßner Universit¨ at Konstanz 78457 Konstanz, Germany Tel.: +49 7531 88-5260 E-mail: corina.stroessner@uni.kn