Peirce proposed the concept of abductive inference to inquire into the generation of new hypotheses and defined it as another term for pragmatism, no less (Admitting, then, that the question of Pragmatism is the question of Abduction, let us consider it under that form. What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? The question of the goodness of anything is whether that thing fulfills its end. What, then, is the end of an explanatory hypothesis? Its end is, through subjection to the test of experiment, to lead to the avoidance of all surprise and to the establishment of a habit of positive expectation that shall not be disappointed (Peirce. 1931–1966. The collected papers of Charles S. Peirce , 8 vols., C. Hartshorne, P. Weiss & A. W. Burks (eds.). Cambridge: Harvard University Press. 5.197)). Apart from being linked to the vague idea of the play of musement as an almost dreamlike process of epiphany or inspiration or as an inverted minor premise from a syllogism, we are far from understanding the dynamics and specificity of this kind of inference. Among authors dealing with this problem I could trace three factors at work in processes of abduction, i.e. combination, resemblance, and dialetics or questioning. In this paper I attempt to look a bit further into this enigma by a category of play I defined as “peripatos” or games of invention, riddles, and puzzles, hoping it could shed some light on the process of creativity in several social activities such as science, art, war, and religion. The approach will take on Huizinga’s idea of the play of culture, Lakoff and Johnson’s conception of cross-domain correlations, Kant’s view of “aesthetic ideas,” and my proposal of the play of peripatos through a “what if-as if” coupling into this very common yet little understood, and thus mystified, process of the generation of innovative ideas.