 In an informal setting, the formulae \(\phi(x)\) could be allowed to be arbitrary predicates. In a more formal setting they would be formulae of e.g. a suitable first-order language. The unrestricted comprehension principle says that for any property (expressed by \(\phi)\) there is the set of those entities that satisfy the property. This sounds as a very reasonable principle, and it more or less captures the intuitive concept of a set. Indeed, it is the concept of set originally brought forward by the father of set theory, Georg Cantor (1895), himself. Unfortunately, the principle is not sound, as it gives rise to Russell’s paradox. Consider the property of non-self-membership. This can be expressed by the formula \(x \not\in x\). If we let \(\phi(x)\) be the formula \(x \not\in x\) then the set \(\{ x \mid  \phi(x) \}\) becomes the Russell set \(R\), and we obtain the following instance of the unrestricted comprehension principle: