Rationality and Uncertainty:-

Our rationality, and our conceptualization and treatment of uncertainty, are sometimes viewed:

  • as habits,
  • as the result of the biology of our brains etc.,
  • as the result of our culture,
  • as having ‘objective’ benefits.

It is the last which is of interest here, although we should welcome challenges and insights from other areas. Mathematics links theorems to axioms via proofs that apply logics. The validity of the axioms and logics in a particular case, or to ‘the world in general’ is a matter for science. Mathematics can say what is possible or impossible, but can only say what actually is the case in its own abstract ‘world’. But we can say that no theory of rationality or uncertainty can be ‘mathematical’ in so far as it claims any domain over non-mathematical reality.

Mathematics, quite properly, has theories of decision-making based on utility maximization and a numeric conception of probability. But what is their relationship to real-world decision-making and uncertainty? Is it what most academics suppose? Are there any better mathematical theories?

The corpus is reviewed under the following headings:

  • Probability: A review of those works which many consider to  justify the notion that uncertainty is just a number. They don’t. They mostly provide good reasons for thinking the contrary.
  • Psychology: How people think, how psychologists think people should think, and hence the dangers of taking them literally.
  • Pragmatic Bayesianism: Bayesian reasoning, but with an awareness of it limitations
  • Broader uncertainties: Explicit consideration of uncertainty beyond numeric probabilities.
  • Logics: The underlying theories, and warnings.

Dave Marsay

PS:  I am also developing some puzzles, which may help motivate this blog.

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