This dissertation consists of two parts, related in that the first part motivates the mathematical questions addressed by the second. The first part treats the concepts vulnerability (to climate change) and probability, as well as the method of formalization. Formalization is here considered to be a translation of concepts from everyday language or scientific terminologies into mathematical concepts. The result of such a formalization is a mathematical model of a concept. An advantage of using

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... athematical concepts is that they do not have implicit connotations. The concept probability, with its different interpretations and mathematical models, is considered as an example of formalization. A subjective probability interpretation is of interest for climate change related research because, unlike the frequentist interpretation, it makes probability applicable also in cases where long data series are not available. The subjective interpretation is presented using de Finetti's model of coherent probability assignments. Different mathematical models of probability are related to the concept itself in differing ways: de Finetti's model explains its meaning and provides a rule for measuring probabilities, whereas Kolmogorov's model mainly serves as a basis for the mathematical theory; it specifies neither meaning nor measurement of probability. All in all, the example concept probability shows that formalization is not a miracle cure against conceptual unclarity, but that it can support clarification. Conceptual clarification was one aim of a formalization of vulnerability and related concepts developed at the Potsdam Institute for Climate Impact Research. This work presents the formalization and uses it for clarifying a terminology for which the literature states a 'Babylonian confusion'. Many similar theoretical definitions of vulnerability exist, but there are different interpretations and approaches to assessing it. With the help of precise but nevertheless general mathematical definitions of vulnerability, the com [...]