The Russel Paradox and Dutch Constitution

Unlike many other countries, the Netherlands lack constitutional review.¹ This is determined in article 120 of the Dutch constitution (“grondwet”, “GW” for short):

De rechter treedt niet in de beoordeling van de grondwettigheid van wetten en verdragen.

(Courts do not test the constitutionality of acts of parliament and treaties.)

The idea of this provision is that it is up to the legislative power (i.e. parliament) to test laws and treaties against the constitution themselves, not the judicial power. However, this creates a somewhat strange, even paradoxical, situation.

To fully understand this, we need to know a bit about judicial review. In case of a conflict between laws (or provisions therein), the applicable provision is determined based on three criteria: “higher” law prevails above “lower” law, newer law above older law,² and more specific provisions above more general provisions. The first, often referred to as the lex superior³ rule, is relevant for our discussion. Which law is “higher” for this rule is determined by a hierarchy. For example, the constitution is considered higher than acts of parliament, which themselves are higher than ordinances issued by regional authorities.⁴

Suppose now that a majority of parliament (that is suposedly not large enough to change the constitution) dislikes article 120 GW, and passes a bill (say law X) mandating courts to perform constitutional review (thereby directly contradicting article 120 GW), e.g. in Dutch

De rechter beoordeeld de grondwettigheid van wetten.

(Courts tests the constitutionality of acts of parliament.)

Let us now consider a suit in which the constitutionality of some act of parliament is disputed. Now the court faces the question whether constitutional review lies within its power. Suppose the court rules that it has to perform constitutional review, in accordance with law X. Then in particular it has to test the constitutionality of law X. Clearly, law X violates article 120 of the constitution. Since the constitution is a higher law than law X, article 120 GW prevails. Hence, the court is not allowed to perform constitutional review, contradicting the courts ruling. Clearly, this was the wrong ruling. Therefore, the court must rule that it doesn’t have the power to perform constitutional review. But then, by its own ruling, the court isn’t allowed to test the constitutionality of law X. Thus there is no foundation to declare law X as inapplicable. Then the court should abide by this law, which it didn’t. Again a self-contradicting ruling.

This problem bears significant resemblance to a paradox in mathematics known as Russell’s paradox, named after the mathematician and philosopher Bertrand Russell. This is a contradiction that arises in some, now called “naive”, foundations of mathematics, that are based around collections.⁵ Here a collection is just a “bag” of objects. Any object is either in the collection, in which case it is called an element of the collection, or it is not. Collections are themselves objects, an can potentially have infinitely many elements. For example, one could consider a collection containing all numbers.

Now the paradox is the following. Suppose we make a collection, call it X, of all collections (Y) that are not an element of themselves. In pseudo-mathematical notation

Y in X <-> Y not in Y .

Now we wonder whether X is an element of itself? Suppose it is, i.e. X in X. Then taking Y := X in the above, the left-to-right implication tells us that X not in X, contradicting our assumption that X is an element of itself. So it is not, i.e. X not in X. But then again taking Y := X, the right-to-left implication tells us that X in X. But this contradicts the fact that X not in X, which we had just established.

The crucial issue in both Russell’s paradox and our thought experiment in law is the unrestricted use of self-reference when “creating” new objects. Our hypothetical law X dictates the (in)applicability of laws, and thereby the (in)applicability of itself. The collection X dictates which Y are its elements, in terms of the elements of Y, and thereby whether X is an element of itself in terms of the elements of X.⁶ Many other paradoxes arise from self-reference, for example the liar’s paradox, concerning the statement “this statement is false”.