 How is this multiple interpretability achieved? At least in part by Bishop’s refusal to pin down his primitive notion of “algorithm” or, in his words, “finite routine”. This refusal has led to the criticism that his approach lacks the precision that a logician would normally expect of a foundational system. However, this criticism can be overcome by looking more closely at what practitioners of BISH actually do when they prove theorems: in practice, they are doing mathematics with intuitionistic logic. Experience shows that the restriction to intuitionistic logic always forces mathematicians to work in a manner that, at least informally, can be described as algorithmic; so algorithmic mathematics appears to be equivalent to mathematics that uses only intuitionistic logic. If that is the case, then we can practice constructive mathematics using intuitionistic logic on any reasonably defined mathematical objects, not just some class of “constructive objects”.