 These biconditionals (or abstraction principles) appear to have a special semantic status. While they are not strictly speaking definitions of the functional expression that occurs on the left hand side, they would appear to hold in virtue of the meaning of that expression. To understand the term ‘direction’ is (in part) to know that the direction of \(a\) and the direction of \(b\) are the same entity if and only if the lines \(a\) and \(b\) are parallel. Moreover, the equivalence relation that appears on the right hand side of the biconditional would appear to be semantically and perhaps epistemologically prior to the functional expressions on the left (Noonan 1978). Mastery of the concept of a direction presupposes mastery of the concept of parallelism, but not vice versa.