As part of a current project to revisit the Personal Development aspect of the Henley DBA (Doctor of Business Administration) programme, I’ve been forced to start to think about the concept of paradox. Let me tell you – it’s painful, mind-twisting stuff. And I blame my mentor, Professor Jane McKenzie for everything!
So, what is a paradox, and why does it matter for the DBAs? Good question. Answers on a postcard please. In the meantime, here is what I think.
First of all, a paradox must be both self-contradictory and not self-contradictory and it must be (or appear to be) both at the same time. When it is, it isn’t. And when it’s not, it is. Commonly cited examples of this include the Liar Paradox. A logic paradox sets up a kind of warp-speed oscillation, whereby you have to jump instantly from one side to the other as soon as you have comprehended either.
It’s rather like in the diagram below (maybe you see a smaller box in the corner of a room, then you see one large cube with a cube-shaped chunk missing (or vice versa), but you cannot see both simultaneously):
The cube illusion doesn’t usually occur to us as a paradox, though, because there isn’t a pressing need for us to understand one way over the other. We can grasp that it’s both, and neither. The sky does not fall on our heads. In fact, without a conflictual aspect or consequence, most paradoxes – like sleeping dogs – should be let to lie. We’re often quite unaware of the paradoxical nature of much of our perception and sense-making. The sorting out and sifting of all the possible double and contrary meanings happens mostly at an unconscious or habitual level – leaving us free to get on with the business of whatever we think our business ought to be. Paradox matters only when we are involved in some kind of change or learning process.
In the pure sciences such as mathematics paradoxes have been seen as non-axiomatic and can exist only in theory (in other words, in the imagination) and not in reality. That doesn’t prevent paradox being talked about a lot by mathematicians. Paradoxes appear a lot in philosophy, too. The eye, our organ of sight, can never see itself. In fact, the one thing none of our senses can do is sense themselves. And a statement such as “today is the only day that is not different” is self-referentially impossible because if it’s true that today is the only day which is the same as the others, then it instantly becomes different, which instantly makes it like all the others, so not different, which…
Near the beginning of the 20th century Bertrand Russell infamously dealt with paradox in mathematics by means of a the deus ex machina of the hierarchy of logical typing. Is the set of things that are non-cats itself a member of the set of things that are non-cats (i.e. a member of itself)? No, was the answer, because a set is always of a higher logical type than its members. This is very useful, as it turns out that this is why it is logical not to eat the packaging of your pizza but the contents inside, even though the package says “pizza”.
And yet, psychologically, socially, zoologically and aesthetically there are some nice paradoxes of identity and we do seem able to bend, twist and break Russell’s rule when it comes to social interaction. In fact, it may be necessary for us to do so. One famous example is the Ship of Theseus, which is the ancient question of whether a wooden sailing ship which over time, piece by piece, has every bit of wood, every rope and every scrap of sail replaced is still the same ship? A more modern and terribly funny equivalent is “Trigger’s Broom” from the British sitcom “Only Fools and Horses”:
I suppose one of the tensions present in the identity paradox is that between permanence and change, and this seems one of the interesting aspects for the DBAs as they are there on the course precisely because they wish to attain both, and this is surely contradictory. There are others they will find – the dichotomy of perceived gaps between “research” and “practice”, or “rigour” and “relevance” (and so on… and on) which social identity via membership of practitioner or academic communities prizes and demands. These sorts of paradox are experienced as real mainly because the oscillation between one side and the other is made possible by the passage of time.
No doubt it’s a paradox that will resolve itself – sooner or later. In the short run, a person is free to enlighten themselves and shake off the need to resolve a paradox at all (better to dissolve it through awareness), while in the long run – as Keynes reminds us – we’re all dead. This last view I take to mean that we should relish living in the present, not that we should feel helpless or gloomy about it.
“If the fool would persist in his folly he would become wise.” William Blake
Chris Dalton's Personal Development Blog 