 The notion of apparently possible refers to a procedure for determining inconsistency, which is a form of bounded procedural rationality  (section 2).  The challenges of avoiding paradox, which Savage alludes to, are formidable. However, work on bounded fragments of Peano arithmetic (Parikh 1971) provide coherent foundations for exploring these ideas, which have been taken up specifically to formulate bounded-extensions of default logic for apparent possibility (Wheeler 2004) and more generally in models of computational rationality (Lewis, Howes, &amp; Singh 2014).