Basic issues in criterion-referenced measurement are addressed. In section II, issues involved in determining what a person does and can do are considered. A preliminary analysis of "can" is given which shows that there are several important senses of "can". In section III, results of an analysis of "ability" are given. The analysis is used to criticize current forms of "inductive" inference which employ the concept of "true score". It is argued that using the concept of "true score" lacks justification, and the difference between mathematical probability and inductive probability is explained; that is inductive probability does not conform to the normal multiplication and conjunction principles. Good judgment is shown as being centrally involved with all inductive inference. Alternative Bayesian and non-Bayesian approaches which place various, additional conditions on one's judgments are explored. In section IV, a description of the almost universally employed and traditional logical empiricist method is presented. It is stated that criterion referenced measurement (CRM) theory ought to employ a different method: imaginative participation. Throughout the essay implications are drawn for future CRM theory development and for the training of teachers. (Author/GK)