Contributed Talks

Title: The Windrush Scandal and the Right to be a First Class Citizen

Abstract:  ‘The Windrush Scandal’ refers to the widespread wrongful treatment of Black Britons of Caribbean origin who fell victim to the UK government’s ‘hostile environment’ migration control policies. In 2018, the Home Office commissioned an independent review into the causes of the Windrush Scandal. The review concluded that the scandal was ‘foreseeable and avoidable’, and it described various immigration and nationality policies as clear contributing factors.

In this paper, I explore Michael Dummett’s arguments in On Immigration and Refugees (2001) and in his wider writings on racism to reflect on the history and politics behind the Windrush Scandal. As Ann Dummett highlighted, Michael Dummett’s long years of experience as an antiracism campaigner and advocate for migrants, combined with his philosophical expertise, make for a ‘unique’ contribution to the critical analysis of nationality policies and migration controls. 

Dummett’s research on the relationship between racism and migration control underscores how and why a largescale injustice along the lines of the Windrush Scandal was both ‘foreseeable’ and ‘avoidable’. I also draw on Dummett’s work to identify the distinctive nature of the injustice embodied in the scandal. In particular, I reconstruct and develop his defence of ‘the right to be a first-class citizen’. This serves to illustrate what has gone wrong in successive immigration and nationality policies, and offers a route towards addressing a core feature of the injustice.

Title: Indefinite Extensibility and Intensionality

Abstract:  Indefinite extensibility is one of Dummett’s most controversial ideas. He thought that the indefinite extensibility of certain mathematical concepts was the key to overthrowing the reign of classical logic, as well explaining the failure of platonist accounts of mathematics such as Frege’s (1991: 319–321). But the very notion of indefinite extensibility is very difficult to understand, to the point that various critics have claimed it to be hopelessly confused and useless (see, for example, Boolos (1993), Burgess (2004), and Oliver (1998)). Dummett’s own characterisation of it is as follows:  

A concept is indefinitely extensible if, for any definite characterisation of it, there is a natural extension of this characterisation, which yields a more inclusive concept; this extension will be made according to some general principle for generating such extensions, and, typically, the extended characterisation will be formulated by reference to the previous, unextended, characterisation. (1963: 195–196).

He thinks that some of the most important concepts in mathematics (natural number, real number, set (1994: 26–28) and arithmetical truth (1963: 195)) satisfy this description. But what does it really mean? Two issues stand out on which Dummett is unclear. What is a definite characterisation? And what is it for the process of extension to be indefinite?

There is an ambiguity in Dummett’s writings as to how we should answer both of these questions.  The goal of this talk is to expose and resolve this ambiguity. Consequently, I distinguish two different interpretations of indefinite extensibility, namely the extensional and the intensional interpretations. In the process, I argue that the intensional interpretation is the right one. According to the extensional interpretation, a definite characterisation is an extensional entity, such as a set or class, and whether or not it can be extended indefinitely depends only upon whether or not the process of iteratively extending it has a limit of a certain kind. Dummett’s example of the concept set seems to support this reading. For any set of sets, we can form its Russell set, which is not a member of our original set on pain of contradiction. Thus we have a more inclusive characterisation of the sets – all the old ones, plus their Russell set. This new characterisation can be extended the same way, ad infinitum. The thing that gets extended here is an extensional entity (a set), and the process of extension is indefinite simply because there is no limit to it in the ordinals.  

By contrast, according to the intensional interpretation, a definite characterisation is an intensional entity (such as a description of a set or class), and whether or not the process of extending it is indefinite depends on whether we can conceive (in the right sort of way) of this process as having a limit. Dummett’s example of the concept arithmetical truth seems to support this interpretation. He claims the concept is indefinitely extensible because, for any intuitively correct (and hence sound) computable theory of arithmetic, we can obtain a more inclusive such theory by adding the Gödel sentence of the old theory as a new axiom. As in the first case, the process of extending the theory in this way can be iterated ad infinitum. However, an arithmetical theory is an intensional entity, in that the Gödelian construction is sensitive to the description of the axioms, not just to what formulae are derivable from them. And the process of extension here cannot be indefinite in the same sense as the Russellian process, since there are only countably many arithmetical truths.

I argue that, despite Dummett’s equivocation on the issue, we should endorse the intensional interpretation, on both the question of what a definite characterisation is, and the question of what it means for the iterative process of extending such a characterisation to be indefinite. I also sketch the significance of this, namely that Dummett’s argument against platonism and classical logic is fatally undermined. However, there is some hope that indefinite extensibility, conceived of as an intensional phenomenon, can offer a satisfying resolution of the paradoxes of infinity.