There are two ways to characterize symmetric relations. One is intensional: necessarily, Rxy iff Ryx. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent them from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations’ real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds.

有两种方法可以描述对称关系。一种是内涵式的：必然是Rxy iff Ryx。然而，在一些关于关系的讨论中，重要的是一个关系对于某些固定关系的每个可能应用是否会产生给定类型（事实、事态或命题）的相同完成。Kit Fine 称这种关系为“严格对称”。必要对称和严格对称的概念之间是否存在差异，导致它们在此类讨论中不能互换使用？我证明是有的。虽然这些概念在假设关系及其完成的内涵性说明的情况下是一致的，根据该概念，如果它们必然同时实例化/等价，则关系/完成是相同的，但它们在假设超内涵说明的情况下分开，该说明在关系的基础上更精细地个体化关系和完成' 真正的定义。我通过识别两个可定义的关系来建立这一点，每个关系都必然是对称的，但当它以相反的顺序应用于相同的对象时，仍然会产生不同的事实。在每种情况下，我认为这些事实都是不同的，因为它们有不同的理由。