* A school of thought: Abelard's ideas, particularly concerning logic, dialectic, and the nature of faith and reason, formed a distinct school of thought within scholasticism. Someone might refer to "the Abelard school" to denote his followers or those who adhered to his philosophical and theological positions.
* A hypothetical or imagined institution: Someone might create a fictional school or program and name it after Abelard to evoke a connection to rigorous intellectual inquiry and debate.
Without more context, it's impossible to say precisely what "The Abelard School" refers to. If you encountered this name in a specific context (a book, article, conversation), providing that context would allow for a more accurate interpretation.