Towards a Bayesian theory of second-order uncertainty: Lessons from non- standard logics. Hosni, H. In David Makinson on Classical Methods for Non-Classical Problems, pages 195--221, 2014. Outstanding Contributions to Logic Volume 3, Springer.
Towards a Bayesian theory of second-order uncertainty: Lessons from non- standard logics [pdf]Paper  doi  abstract   bibtex   16 downloads  
Second-order uncertainty, also known as model uncertainty and Knightian uncertainty, arises when decision-makers can (partly) model the parameters of their decision problems. It is widely believed that subjective probability, and more generally Bayesian theory, are ill-suited to represent a number of interesting second-order uncertainty features, especially “ignorance” and “ambiguity”. This failure is sometimes taken as an argument for the rejection of the whole Bayesian approach, triggering a Bayes vs anti-Bayes debate which is in many ways analogous to what the classical vs non-classical debate used to be in logic. This pa- per attempts to unfold this analogy and suggests that the development of non-standard logics offers very useful lessons on the contextualisa- tion of justified norms of rationality. By putting those lessons to work I will flesh out an epistemological framework suitable for extending the expressive power of standard Bayesian norms of rationality to second- order uncertainty in a way which is both formally and foundationally conservative. Contents

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