Let's assume (in practice quite realistic assuption) that tested object during eg Rorschach's test has several, for the simplicity purposes say two, associations with one card (at same time of being tested). So we have: I(Ri) → C1, I(Ri) → C2 where Ci are associations, I means process of association/interpretation , so it could be also written I1, I2 for two different connotations. What about situation which fulfils C1 ⊕ C2, that is: (C1 ˄ ¬C2) ˅ (¬C1 ˄ C2) and at the sime the object being tested replies C1 ˄ C2? Such contradiction is possible, so it can mean that eg C1 = psychopath and C2 = empathic individual or any kind of personality being the negation of a psychopath. What then? In pracice the tested object may select one of them and say it to psychologist loosing important part of knowledge or say both of them creating contradiction. It is obvoius that this contradiction appears in Rorschach "beliver's" mind who interprets those associations, not in tested object's mind. Possible? Yes it is possible, because people have very different associations with stains, worse at the same time!
P.S.: I applied for clarity reasons shorthand of course, because C (C stands for class/type of personality) is in practice psychologists's interpretation of tested object's association, so the whole chain of associations/interpretations looks like that:
Io(Ri) → Ai Ip(Ai) → Ci,
where Io - association of tested object process giving Ai , Ip - interpretation/classification by psychologist giving Ci .