The best evidence to support the statement "John Harvard did not anticipate that a university would be named after him" includes:
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"Little did young Harvard dream of the fame to be attached to his name for this modest act of charity." - This directly suggests that John Harvard did not foresee the significant recognition or fame that would come from his contributions.
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"And even less could he have dreamed that his little library of four hundred books would one day increase to more than eight million." - This indicates that not only did he not anticipate fame, but he also could not have imagined the vast growth and significance his initial contributions would lead to.
Both pieces of evidence imply that John Harvard did not foresee the legacy that would develop as a result of his actions, supporting the statement in question.