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In this essay, I draw on the chapters by Fisher et al., Keller and Tian, and Zundel et al. that deal with the role of paradox in the context of jazz, linguistics, mathematics and poetry respectively to reflect on the nature of paradox, also considering examples from my own and other research. I argue specifically, that in everyday language, the notion of paradox is used mostly to refer not so much to persistent tensions between interdependent elements, but to describe an outcome as irony where action intended to achieve one goal actually results in its opposite or in something contrary to it. I suggest that while there may be a relation between the formal definition of paradox in the academic literature and the everyday understanding of paradox as irony, this has not been fully elucidated and would deserve further analysis and research. Doing so might perhaps bring back some of the feeling of discomfort and intractability that the notion of paradox naturally inspires, acting as a possible counterpoint to the optimism of both-and.