Where does paradox collide?

The liar paradox, attributed to Eubulides of Miletus in the 4th century BCE, is the oldest example: the single line 'this statement is false' cannot be consistently called true or false. Bertrand Russell gave the modern form in The Principles of Mathematics (1903), showing that the set of all sets that are not members of themselves both must and must not contain itself, a contradiction that broke naive set theory. Here a paradox is an argument whose steps each look acceptable yet whose conclusion is a flat contradiction, and the work is to find which step to give up. This referent is a defect in reasoning to be diagnosed and repaired, not a figure of style a writer chooses, and not a management condition to be sustained.[1]

Unit

One self-undermining argument: a contradiction derived from premises that each look true

Recovery means

Dissolved by rejecting a premise or restricting the rules, as Russell's type theory blocked the offending set

Measured by

Identified by deriving a contradiction from assumptions each of which seems separately acceptable

In rhetoric and literary theory a paradox is a figure in which a statement that appears to contradict itself turns out, on reflection, to state a truth, as in the line 'the child is father of the man'. The term is classical, from the Greek paradoxon ('contrary to expectation'), and the figure was long treated in rhetoric before Cleanth Brooks made it central to modern criticism in The Well Wrought Urn (1947), arguing that the language of poetry is the language of paradox. Here the apparent contradiction is deliberate and is meant to be kept, because flattening it into plain statement would lose the meaning. This referent is a chosen device of expression, unlike the argument a logician must repair or the competing demands a manager must hold in balance.[2]

Unit

One utterance whose surface contradiction resolves into a truth on reflection

Recovery means

Not applicable

Measured by

Read qualitatively by close analysis of how the contradiction works within a text

Poole and Van de Ven's Using paradox to build management and organization theories (1989) brought the term into organization studies, treating paradox as two contradictory yet interdependent propositions that both hold. Smith and Lewis then set out the modern account in Toward a theory of paradox (2011), defining a paradox as contradictory yet interrelated demands that persist over time, such as exploring new business while exploiting the current one, or granting autonomy while keeping control. Here the contradiction is not an error to fix or a phrase to admire but a lasting tension to be managed, since choosing one side alone degrades the other. This referent is an organizational condition held in dynamic balance, distinct from the logician's contradiction and the writer's figure of speech.[3][4]

Unit

One pair of opposed but interdependent demands that both persist in an organization

Recovery means

Not applicable

Measured by

Assessed through case studies and survey scales of how organizations hold competing demands together