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We present a foundation for inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying finite lattices of logical statements in a way that satisfies general lattice symmetries. With other applications in mind, our derivations assume minimal symmetries, relying on neither complementarity nor continuity or differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of rules governing quantification of the lattice. These rules form the familiar probability calculus. We also derive a unique quantification of divergence and information. Taken together these results form a simple and clear foundation for the quantification of inference.
the difference between hard and soft science is a matter of method, in particular what he refers to as “strong inference.”
in list: Philosophy Notes
Reasoning is defeasible when the corresponding argument is rationally compelling but not deductively valid. The truth of the premises of a good defeasible argument provide support for the conclusion, even though it is possible for the premises to be true and the conclusion false. In other words, the relationship of support between premises and conclusion is a tentative one, potentially defeated by additional information.
in list: Philosophy Notes
Annotated link http://www.diigo.com/bookmark/http%3A%2F%2Fwww.overcomingbias.com%2F2008%2F08%2Fno-self-trust.html
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Coming to terms with metaethics, I am beginning to think, is all about distinguishing between levels. I first learned to do this rigorously back when I was getting to grips with mathematical logic, and discovering that you could prove complete absurdities, if you lost track even once of the distinction between "believe particular PA proofs", "believe PA is sound", and "believe you yourself are sound". If you believe any particular PA proof, that might sound pretty much the same as believing PA is sound in general; and if you use PA and only PA, then trusting PA (that is, being moved by arguments that follow it) sounds pretty much the same as believing that you yourself are sound. But after a bit of practice with the actual math - I did have to practice the actual math, not just read about it - my mind formed permanent distinct buckets and built walls around them to prevent the contents from slopping over.
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