Thomas L Muinzer: Russell’s Paradox and the Principle of Parliamentary Sovereignty

The Brexit process has served to draw significant attention to a rich variety of questions engaging the character and scope of the doctrine of Parliamentary Sovereignty.  This includes on this blog, where various significant issues have been ably examined by, amongst others: Professor Mike Gordon, with reference to the European Union (Withdrawal Agreement) Bill and the implementation of the EU Withdrawal Agreement (part 1 and part 2); Professor David Feldman, with reference to R. (Miller) v. Secretary of State [2016] and issues arising therein.

In this brief discussion, I do not propose to re-tread this sort of erudite and valuable ground.  Rather, I seek to disconnect the doctrine of Parliamentary Sovereignty from typical legalistic discussion and consideration, situating it instead in the context of a particular philosophical method arising in the history and discipline of philosophical logic, prominently embodied by “Russell’s Paradox”.  It will be seen that this approach provides a novel perspective, and that it underscores a degree of logical inconsistency underlying the classic Diceyan conception of Parliamentary Sovereignty.

It is notable that issues arising in the discussion below share some affinity with extant legal discourse on the omnipotence conundrum.  At its core, this conundrum recognises and endeavours to unpack problems that appear to arise where the following question is recognised: if, by virtue of Parliamentary Sovereignty, Parliament may pass any law it likes, can it therefore create a law that limits its own powers?  Space precludes exploration of the point, but suffice it to say that one appears to encounter difficulty regardless of whether one answers “yes” or “no” to this question.  In philosophical discourse, the type of problem arising here – engaging a clash between omnipotence and power limitation – is echoed in consideration of the concept of an omnipotent God, where one may reply to the proposition that an omnipotent God exists as follows: God cannot be omnipotent because he cannot create a stone he cannot lift

The present discussion operates in the spirit of these considerations, but its approach differs in that it applies set theory to a key Diceyan statement on Parliamentary Sovereignty in order to point to underlying logical problems and open a particular channel for improvement within that context.

Dicey and Parliamentary Sovereignty

The principle of Parliamentary Sovereignty is typically considered to be a foundational component of the UK’s uncodified constitution.  The most influential statement on Parliamentary Sovereignty as an abstract concept is provided by AV Dicey in The Law of the Constitution (1885).  Endeavouring to reduce things to their essentials, Dicey summarises as follows:

The principle of Parliamentary sovereignty means neither more nor less than this, namely, that Parliament… has, under the English constitution, the right to make or unmake any law whatever; and, further, that no person or body is recognised by the law of England as having a right to override or set aside the legislation of Parliament.

If this influential definition is disconnected from traditional legal debates and commentary, and is situated instead in isolation within the context of the Russellian intellectual tradition alluded to above, an interesting perspective arises.  Indeed, in my view, this type of “thought experiment” goes so far as to offer a logical proof in its own right that the conception fails to hold. 

For present purposes, it is sufficient to isolate the following component of Dicey’s conception: UK Parliament has “the right to make or unmake any law whatever”.  Before proceeding, I must say a little about Russell’s Paradox and so-called “set theory”.

Russell’s Paradox

In the early 20th Century, distinguished British philosopher Bertrand Russell (1872–1970) wrote to German logician and philosopher Gottlob Frege (1848–1925), pointing out that certain hitherto undetected paradoxes arose in work Frege was doing in the area of logic.  Russell’s observations became known in philosophy as “Russell’s Paradox”.  Russell’s Paradox involves sets.  Sets are a collection of things that share some sort of common property.  For example, the set of all even whole numbers under 10 is: {2, 4, 6, 8}.  The set of all odd whole numbers under 10 is: {1, 3, 5, 7, 9}.  It is also possible to construct “sets of sets”.  For example, if a set that we call, say, X, is a set that contains the sets of all odd and even whole numbers under 10, we can assume with confidence that X will include amongst its contents both the set of all even whole numbers under 10 just noted, and the set of all odd whole numbers under 10 just noted.  Russell pointed out to Frege that certain logical problems can be seen to arise when we consider “sets of sets” from a certain perspective, and sketched out a particular paradox – Russell’s Paradox.

Explication of the technical minutiae of Russell’s Paradox, which is complex, is less helpful in the present setting than an illustration of the general type of problem it identifies.  This can be demonstrated usefully by way of example.  Take a village barber.  Let us say that he works in a village where all the men shave, and where the barber shaves all the men in the village that do not shave themselves.  Let us further stipulate that these are the only men that the barber shaves.  As Russell summarises it in The Philosophy of Logical Atomism, “You can define the barber as ‘one who shaves all those, and those only, who do not shave themselves’” (p.101 of the 2010 Routledge Classics edition). But problems arise if we then pose this question: does the barber shave himself?  If we conclude that the barber shaves himself, we seem compelled to place him in the category (i.e., the set) of those who do not shave themselves, because we know that the barber shaves only those who do not shave themselves.  If he does not shave himself, we seem compelled to place him in the category of those who are shaved by the barber, because those who do not shave themselves are shaved by the barber, i.e., himself.  As Quine puts it, therefore, “We are in trouble if we say the barber shaves himself and we are in trouble if we say he does not.”  A paradox has arisen.

Making and Unmaking any Law Whatever

Returning now to Dicey, and the proposition that Parliament can make and unmake any law whatever, this statement suggests on logical grounds that a set may be said to exist that represents the laws that Parliament can make and unmake.  I will call this set L (for “Law”).  Contained within this set is “any law whatever”.  Thus, the set L embodies the totality of laws that national Parliament has the capacity to make and unmake.  In summary: 

  • Parliament can make and unmake any law whatever
  • L = the laws that Parliament can make and unmake
  • Thus the following set can be expressed: L { any law whatever }

But there is a problem here.  Initially, one runs into no difficulty where one considers a conventional sort of Parliamentary law and seeks to situate it within set L.  For example, national Parliament can pass a Barber Shaving Act that asserts that all barbers must undertake a specified degree of formal training and achieve a practice certificate in order to be permitted to shave men in the UK.   Similarly, a Barber Shaving Restriction Act can be passed, asserting that no barbers are permitted to shave men in the UK.  These examples fall squarely within the set L.

It is possible, however, to conceive of a decidedly more problematic sort of Parliamentary law.  For example, let us take the hypothetical Perpetual and Permanent Barber Shaving Restriction Act.  Let us assume that this Act contains only one section, which reads as follows: 

All barbers in the UK are perpetually forbidden from shaving men, and national Parliament can never repeal or otherwise unmake this permanent law.

Parliament can make any law, and thus it can make the Permanent and Perpetual Barber Shaving Restriction Act, such that this Act falls within the set L.  However, the Act is a law that constrains Parliament from unmaking it.  Thus, simultaneously, the Act cannot be placed within the set L, because L is also the set of all laws that Parliament can unmake, and Parliament is precluded from unmaking this law.  The Act thus sits outwith the purview of L on these grounds.

Here, to borrow Quine’s words from above, we are in trouble again.  The conclusion on grounds of logic is that the dictate contained within the Diceyan statement of Parliamentary Sovereignty that we have isolated, which asserts that Parliament can make and unmake any law whatever, is in fact a paradox that is not logically sustainable.  The assertion is therefore logically inconsistent, and thus fallacious.

Further Thoughts

This isolated thought experiment indicates that the classic Diceyean conception of Parliamentary Sovereignty, at least as expressed in the reductive summative quotation considered above, is inconsistent and thus fallacious.  This suggests that it requires to be reframed in a logically coherent manner. 

Helpful reframing for the legal mind of the logically inconsistent Diceyan L category can be achieved, it appears, by framing it as two sets, as follows.  Firstly: the set of laws that national Parliament can make and unmake, which I will call set L1.  Secondly: the set of laws that national Parliament cannot make and unmake, which I will call set L2

In the isolated philosophic context of this thought experiment, a logically coherent contribution to knowledge can be achieved by taking the general rule that “Parliament can make and unmake any law whatever”, and calculating the latent categories of exceptions to the rule that exist.  These categories of exceptions can be inputted into set L2, in addition to the category that I have already inputted, which has been generated by the discussion above.

I am grateful to Prof Michael Beaney (Regius Chair of Logic, University of Aberdeen), Prof Gavin McLeod Little (University of Stirling), and students on Aberdeen Law School’s UK Constitutional Law module for contributing to the development of my thinking in this Blog through our various interactions.

Thomas L Muinzer, Senior Lecturer in Law, University of Aberdeen

(Suggested citation: T. L. Muinzer, ‘Russell’s Paradox and the Principle of Parliamentary Sovereignty’, U.K. Const. L. Blog (23rd April 2021) (available at