What is "fairness" in the context of educational assessment? I apply this question to a number of contemporary educational assessment practices and policies. My approach to philosophy of education owes much to Wittgenstein. A commentary set apart from the main body of the paper focuses on my style of philosophising. Wittgenstein teaches us to examine in depth the fine-grained complexities of social phenomena and to refrain from imposing abstract theory on a recalcitrant reality. I write philosophy of education for policy makers and teachers. Scrutiny of examples plays a vital role in communicating with such an audience. Starting points include "accommodations" for disabled students, allegedly gender-biased tests, and the recruitment procedures of "elitist" music conservatoires. A key intuition that fairness is associated with test validity turns out to be seriously flawed. Problems centre on the idea of a "construct", and the supposed divide between an underlying construct and its behavioural manifestations. Equality of opportunity notions underlie some accusations of unfairness but there are alternative approaches to a just society. Both the judgments about fairness, and the proposed remedies are open to serious philosophical criticisms. There are widespread conceptual difficulties, together with inconsistent and contestable value judgments.