According to one standard semantic definition of a contradiction, a sentence is a contradiction if (and only if) it is false in every model, whereas a sentence is a tautology if (and only if) it is true in every model. This dissertation explores three reinterpretations of these definitions, each of which seeks to extend the coverage of these definitions to new phenomena in natural language. The first reinterpretation excludes all models in which a term is undefined, and is used to classify certain Existential There Sentences as either contradictions or tautologies. The second reinterpretation excludes the very few models in which a sentence whose subject is a but-phrase that is headed by a non-universal determiner is true. The final reinterpretation requires that we shift our focus from models, to the more inclusive concept of an interpretation, and classifies a sentence whose meaning is compatible with only one interpretation that is always false as a contradiction. An example of this strategy is any statement of support for the position that all quantification is restricted in natural language, e.g. I am not quantifying over everything. The dominant focus of these reinterpretations has been the behaviour of the data in the sanctioned models (or interpretations). A strategy, I will argue, that does not yield nearly as much insight into the semantic properties of natural language as a close study of these constructions in the excluded models (or interpretations). The topics covered include the odd truth value assignment to Existential There Sentences in which a term is undefined, the influence of Grice's maxims of conversation on the distribution of DPs in but-phrases, and the possibly related phenomenon of sentences in which the subject is modified by a sentence initial only, and finally, the impossibility of expressing the content of the view that all quantification is restricted in natural language.