Even though human speech is, by default, filled with ambiguity, competent speakers of a natural language generally manage to communicate with each other without having to request clarification after every second sentence. In fact, most linguistic ambiguity is not even noticed by speakers of a language, unless they are made explicitly aware of it or are asked to clarify some particular point, possibly by a less competent speaker of the language in question. In certain situations, linguistic ambiguity can cause headaches for people, but it does not make human communication impossible. Context, knowledge of the world, and common sense generally make it clear which interpretation of an ambiguous statement is appropriate. While the word "bank" in the statement "I"ve got some money in the bank" is lexically ambiguous - a "bank" in English can be a financial institution, the land alongside a river or a lake, or an airplane manoeuvre - semantics only allow for one interpretation. People suffering from aphasia - the partial loss of language skills due to brain damage - have to deal with more linguistic ambiguity than others. Aphasia affects people's capability to correctly interpret morphology and syntax, stripping away the much needed context competent speakers of a language need to correctly interpret human language. This paper details the handling of ambiguity in text simplification software aimed at patients of this illness.