Disagreement and Meaning: The application of social choice theory to deference, self-designation and vagueness.

Student thesis: Doctoral ThesisDoctor of Philosophy


Burge (1979, 1986), Fodor (1994), Greenberg (2014) and others discuss the possibility that an individual’s understanding of concepts can develop through deference to the views of others who have greater expertise or experience in their use. This dissertation extends this possibility by examining the individual’s response when the influencers do not agree. Their disagreement might result from differences of opinion, from social interaction that involves different influences on the influencers, from different interpretations of evidence or from vagueness which leaves open several possible precisifications that differ in their implied definitions of the extensions of concepts.

In the terminology of Lewis (1969), a language is a convention to which people wish to conform. People can be said to speak the same language, and obey its conventions, even if they do not agree on all uses of concepts. A use of a concept that lies outside the eligibilities allowed by the language is a mistake: our standard example involves concepts that are not natural kinds - namely the use of genre concepts to classify music. There is scope within the language for disagreement about whether Gershwin’s Rhapsody in Blue [82] is in (the extension of) jazz or of classical, but locating it in opera or hip hop does not conform to the conventions of the language.

In studies of ethics, elections, welfare economics and committee decisions, disagreement is often analysed using the techniques of social choice theory. The approach here is to adapt some of these techniques to consider the impact of disagreement on language learning. The tradition of preference aggregation when individuals disagree was formalised by Arrow (1951) and more recently surveyed by Sen (2017). Arrow’s celebrated impossibility theorem rules out all but dictatorial forms of social choice. In turn, this led to the formulation of ‘domain restrictions’ that reduce disagreement to a sufficient extent that dictatorship is avoided, and allow that decisions can be made by following majority views.

A second strand of social choice theory has been developed by Mirkin (1975), Maniquet & Mongin (2016) and others, who examine the consequences of disagreement between individuals about the location of objects in equivalence classes or named categories. We extend this strand of analysis in contexts that involve disagreement about the allocation of objects to the extensions of concepts. We show in chapter 12 that the structure introduced by Maniquet & Mongin is a special case of our own structure.

Our main conclusion (theorems 1 and 2) distinguishes circumstances in which the language restricts the extent of disagreement to the extent that the learner can devise an effective compromise between disparate views (plausibly by following the majority) from circumstances in which the learner must either violate one of the described principles of deference or nominate and follow a single dominant influencer (a dictator).

An alternative route for a language learner to develop her understanding of concepts arises when she considers the properties of the objects under consideration. She might decide, without reference to the views of others, that two compositions are sufficiently similar that she wants to include them in the same genre. This consideration can also involve the need to reconcile diverse evidence. Some properties of Rhapsody in Blue support its inclusion in jazz, while others support its inclusion in classical. A ‘dictatorial’ conclusion would then entail that the learner allocates music to genre concepts by ignoring all but one of the properties. However, there is a significant difference between learning through the consideration of properties and learning through deference. The former involves an internal consideration by the learner, who might legitimately recognise that she feels much more strongly about the impact of some properties compared to others. It is much more difficult for the learner to establish and compare the relative intensity with which her several influencers express their views. So ‘disagreement’ between the implications of properties need not result in an outcome that reflects only one of them.

We examine two other structures within the framework of language. One involves a structure that is often used in discussions of vagueness in which the objects under consideration can be graded in one dimension (the number of hairs on a head, grains of sand ...). The focus then is on potential disagreement about the placement of boundaries between the extensions of concepts (bald and not- bald; bucketful, heap and sand-dune and ...). In one sense, vagueness is a possible source of disagreement about where the boundaries are placed. However, the language itself might be vague, allowing the possibility that each individual uses their own private version of the language or idiolect, and that these in turn might be used by the learner to devise a compromise or representative idiolect. At a second stage, the learner devises through deference her own use of the underlying concepts, and these two stages might give contradictory outcomes.

The final structure concerns contexts in which the learner responds to individuals’ designations of themselves and others into extensions of the concepts. This might arise with demographic concepts of different genders, races or religions, or in more prosaic examples in which musicians designate themselves or others into jazzmusicians, classical-musicians .... We generalise a result of Kasher & Rubinstein (1997) that applied originally to designations of eligibility for Israeli citizenship. This result does not lead to dictatorship, but still shows that there are circumstances in which there is no scope for compromise between different views because all opinions that conflict with an individual’s self-designation must be ignored.
Date of Award1 Jul 2023
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorEliot Michaelson (Supervisor)

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