 Next, let’s draw a preliminary three-fold distinction between binary relations in terms of their behaviour with respect to the things they relate. A binary relation \(R\) is symmetric iff whenever \(x\) bears \(R\) to \(y\), \(y\) bears \(R\) to \(x\). By contrast, \(R\) is non-symmetric iff \(R\) fails to be symmetric. Asymmetric relations are a special case of non-symmetric ones: R is asymmetric iff whenever \(x\) bears \(R\) to \(y\) then \(y\) does not bear \(R\) to \(x\). So whilst all asymmetric relations are non-symmetric, not all non-symmetric relations are asymmetric. Some examples. Whenever \(x\) is married to \(y\), \(y\) is married to \(x\). So the relation in which \(x\) stands to \(y\) when \(x\) is married to \(y\) is a symmetric relation. But if \(x\) loves \(y\), it isn’t guaranteed that \(y\) loves \(x\). Because, alas, sometimes love is unrequited. So the relation in which \(x\) stands to \(y\) when \(x\) loves \(y\) is a non-symmetric relation. But love doesn’t have to go unrequited otherwise far fewer people would get married, only cynics and gold diggers. So this relation isn’t asymmetric. By contrast, the relation in which \(x\) stands to \(y\) when \(x\) is taller than \(y\) is asymmetric because if \(x\) is taller than \(y\) then \(y\) isn’t taller than \(x\). This doesn’t exhaust the logical classification of relations. It’s easy to see that further distinctions will need be drawn. Consider, for example, the between relation. It’s a ternary relation that is symmetric in the sense that if \(x\) is between \(y\) and \(z\) then \(x\) is between \(z\) and \(y\). But the between relation isn’t completely or strictly symmetric because it’s not the case that if \(x\) is between \(y\) and \(z\) then \(y\) is between \(x\) and \(z\). So the distinction between symmetric and non-symmetric relations for \(n\)-ary relations, where \(n \gt 2\), will need to be qualified. (In what follows we restrict ourselves to the more straightforward cases discussed in the philosophical literature on relations. But see Russell 1919: 41–52 for a more wide-ranging discussion of the logical variety of relations.)