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Common Knowledge, Sailboats, and Publicity

Sena Bozdag, Olivier Roy

TL;DR

The paper addresses how to reconcile the pre-theoretical notion of publicity with formal notions of common knowledge in the Sailboat case. It argues that Lewisian common knowledge—grounded in a reflexive basis A and shared reasoning standards—can capture publicity even when iterative common knowledge fails, and it formalizes this with an epistemic-plausibility model using conditional reasons to believe and a selection function. The authors construct a detailed butterfly-flutter model to realize a state in which $[>100]$ is Lewisian common knowledge and $r^n([>100])$ holds for all finite $n$, while iterative common knowledge about the same proposition can fail. The work contributes a concrete formalization and a principled philosophical argument for using Lewisian common knowledge to analyze publicity, offering a toolset that could illuminate other classic puzzles in epistemic logic and collective action.

Abstract

We revisit a recent puzzle about common knowledge, the ``sailboat" case (Lederman, 2018), and argue that Lewisian common knowledge allows us to reconcile the pre-theoretical intuition that certain facts are ``public" in such situations, while these facts cannot be common knowledge in the classical, iterative sense. The crux of the argument is to understand Lewisian common knowledge as an account of what it means for an event to be public. We first formulate this argument informally to clarify its philosophical commitment and then propose one way to capture it formally in epistemic-plausibility models. Taken together, we take the philosophical and the formal arguments as providing evidence that Lewisian common knowledge is a plausible account of what it means for an event to be public.

Common Knowledge, Sailboats, and Publicity

TL;DR

The paper addresses how to reconcile the pre-theoretical notion of publicity with formal notions of common knowledge in the Sailboat case. It argues that Lewisian common knowledge—grounded in a reflexive basis A and shared reasoning standards—can capture publicity even when iterative common knowledge fails, and it formalizes this with an epistemic-plausibility model using conditional reasons to believe and a selection function. The authors construct a detailed butterfly-flutter model to realize a state in which is Lewisian common knowledge and holds for all finite , while iterative common knowledge about the same proposition can fail. The work contributes a concrete formalization and a principled philosophical argument for using Lewisian common knowledge to analyze publicity, offering a toolset that could illuminate other classic puzzles in epistemic logic and collective action.

Abstract

We revisit a recent puzzle about common knowledge, the ``sailboat" case (Lederman, 2018), and argue that Lewisian common knowledge allows us to reconcile the pre-theoretical intuition that certain facts are ``public" in such situations, while these facts cannot be common knowledge in the classical, iterative sense. The crux of the argument is to understand Lewisian common knowledge as an account of what it means for an event to be public. We first formulate this argument informally to clarify its philosophical commitment and then propose one way to capture it formally in epistemic-plausibility models. Taken together, we take the philosophical and the formal arguments as providing evidence that Lewisian common knowledge is a plausible account of what it means for an event to be public.

Paper Structure

This paper contains 15 sections, 10 equations, 1 figure.

Table of Contents

  1. Iterated and Lewisian Common Knowledge
  2. The Sailboat Case
  3. Philosophical Argument
  4. Assumption: existence of a reflexive common indicator $A$:
  5. Assumption: shared standards of reasoning:
  6. Publicity of the margins:
  7. Publicity of $[>100]$:
  8. Consistency of publicity with failure of iterative common knowledge:
  9. An epistemic-plausibility model to flesh out the philosophical argument
  10. Language:
  11. Epistemic-Plausibility Frames, Models, and Selection Functions:
  12. Truth conditions:
  13. Remarks:
  14. Butterflies and the butterfly flutter:
  15. Conclusion

Figures (1)

  • Figure 1: A $k$-centered butterfly (Right), and its body (Left). The red and blue arrows represent Roman's and Columba's plausibility orderings, respectively.