One of the things that logicians study is how opposition is expressed in formal or informal languages. The most obvious type of opposition appears when we negate a simple sentence: (1) “the cat is black” becomes (2) “the cat is not black”. In this case, (1) and (2) are strongly opposed to each other: they are contradictories. This sense of binarity is even stronger in mathematics, where natural numbers can be either even or uneven, with no other options. But often, we find more sophisticated ways to express opposition. A good example is that if we have eight people in front of us, we can refer to all, some, or none of them. We could, for example, say that all the people at the party have grey hair. What oppositions exist when we have not two, but three basic terms? It turns out that there are three types.
Some Instances of the Hexagon of Opposition in Mathematics, Aesthetics, and Politics
A Triple Crisis of the Face: Justice in the Tradition of Zwarte Piet
Rietveld & Lot Madeleine (photo: Gwen Denswil) – Neither Black nor White
December 13th, 2011
Act I: A Strange Boat Arrives on the Shore!
The Dutch national event around “Sinterklaas en zijn Zwarte Pieten” is celebrated with great enthusiasm by the population, however, already for decades, with growing complaints by some about its racist meaning or connotation. This form of protest is spearheaded by activists from Dutch minority groups whose history is partly rooted in the colonial epoch of the Dutch. Recently this yearly form of protest has become more eventful when two activists were violently arrested for attempting to protest during the arrival of Sinterklaas in Dordrecht.1
At the same time, it seems very clear that any attempt to condemn the character of Zwarte Piet provokes a defensive reproach from a large part of the native Dutch population. The message seems clear: tradition is here to stay. For years, Sinterklaas has been the most popular Dutch national holiday around, and it encompasses not only commerce but also primary school education. Those who want to change the tradition ask: whom to face in this deadlock?
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