The Cambridge Dictionary of Philosophy defines a paradox as:
a seemingly sound piece of reasoning based on seemingly true assumptions that leads to a contradiction (or other obviously false conclusion). A paradox reveals that either the principles of reasoning or the assumptions on which it is based are faulty. It is said to be solved when the mistaken principles or assumptions are clearly identified and rejected. The philosophical interest in paradoxes arises from the fact that they sometimes reveal fundamentally mistaken assumptions or erroneous reasoning techniques.
Perhaps the paradox is little more than an error in reasoning, which must be ferreted out and resolved. Nevertheless examining paradoxes might lead us to greater understanding of lateral issues related to the inception of the paradox. Perhaps the paradox is a useful flag pointing us in directions where we can examine unexpected cracks in reality. Perhaps resolving a paradox is not the end of its purpose.
Is it useful to intentionally create paradoxes as a tool to break open unintended paths of thinking? Can we explore this idea further in existing paradoxes?