I've just seen Dave Gray's post on the paradoxes of organisation. Oh, this is a wonderfully rich area and something I'm looking forward to reading.
Over the years (based upon evolution), I've noticed several patterns from conflicts (innovation vs efficiency, agile vs six sigma) to misunderstandings to paradoxes. From Ashby's to Jevons' paradox to the impacts of componentisation then there is lots of interesting material.
Four of my favourite paradoxes in business (with each argument described by a scale from 0 to 1) are :-
Predictability (of what) + Predictability (of when) ≈ 1 (i.e. we can often say what will happen but not when or when stuff will happen but not what)
Predictability (of what) + Predictability (of when) ≈ 1 (i.e. we can often say what will happen but not when or when stuff will happen but not what)
Potential for future value + Certainty of value ≈ 1 (i.e. the more something has potential, the less certain we are about it. If we're certain about it then so is everyone else and the value is correspondingly smaller)
Simplification of management + Effectiveness of management ≈ 1 (impact from Ashby's law of requisite variety i.e. the more we pretend management is simple, the less effective it becomes.)
Organisational focus on survival today + Probability of survival tomorrow ≈ 1 (impact from Salaman & Storey i.e. survival today requires coherence, co-ordination and stability whilst survival tomorrow requires 'innovation' and hence a replacement of those values)