The intervention validity of cognitive assessment batteries is considered within an historical context to identify what the evidence supports (knowns), what cannot be known (unknowables), and what is not yet known (unknowns). Two ways cognitive batteries could inform intervention are identified: a disordinal (i.e., aptitude-treatment interaction) model and an ordinal (i.e., "g") model. Existing research provides little support for disordinal models and modest to strong support for ordinal models when applied to conditions of incomplete instruction. Limitations to what can be known (e.g., a failure to prove is not proof of failure) are identified to avoid holding intervention validity research to inappropriate evidential standards. Finally, issues that are within the realm of knowledge but for which there is currently insufficient or no evidence are identified as logical next steps toward understanding the intervention validity of cognitive assessment batteries. (Contains 2 figures.)