Tversky and Kahneman's demonstrations of people's inability to handle probabilities are examined in detail. The inherent ambiguity in the concept of probability and the rules of conversational logic are used to justify subjects' apparent fallacies. Moreover even in the framework of mathematical probability some of Tversky and Kahneman's subjects' behaviour is defended. The relevance of mathematical probability to everyday decisions is seen as being open to question. Conceptualizing a problem sensibly is held to be more important than having beliefs which are demonstrably consistent with a quantitative probabilistic model. The conceptualization should have regard to the sense in which probability is being used, how different possibilities should be categorized and the reliability of the presented information.