 For example, one does not find a clear statement   of what Boole meant by equivalent or interpretable.  For those familiar with partial algebras the latter word can easily  be taken to mean is defined—the domain of definition of an algebraic term has a recursive definition, just as   algebraic term has a recursive definition. After verifying examples like those in LT that show Boole’s algebraic methods  give correct results for propositions about classes, the challenge for those who want to make sense of Boole’s algebra of logic  is to make  enough of the foundations of Boole’s  algebra sufficiently precise so as to be able to justify the algebraic  procedures he used. 