 In type theory all properties are, we may say, typed. This approach has never gained unanimous consensus and its many problematic aspects are well-known (see, e.g., Fitch 1952: Appendix C; Bealer 1989). Just to mention a few, the type-theoretical hierarchy imposed on properties appears to be highly artificial and multiplies properties ad infinitum (e.g., since presumably properties are abstract, for any property \(P\) of type \(n\), there is an abstractness of type \(n+1\) that \(P\) exemplifies). Moreover, many cases of self-exemplification are innocuous and common. For example, the property of being a property is itself a property, so it exemplifies itself. Accordingly, many recent proposals are type-free (see  §6.1)  and thus view properties as untyped, capable of being self-predicated, sometimes veridically. An additional motivation to move in this direction is a new paradox proposed by Orilia and Landini (2019), which affects simple type theory. It is “contingent” in that it is derived from a contingent assumption, namely that someone, say John, is thinking just about the property of being a property \(P\) such that John is thinking of something that is not exemplified by \(P\).