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Link to PDF preprint.

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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.

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"Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole."

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"This is a familiar move in political argument (it is related to the tu quoque, or “so’s your old man” move). We saw it in spades a while ago when Democrats lamented the incivility of public discourse and blamed right-wingers for proclaiming over and over that President Obama was a foreign Islamic usurper working to undermine American values. The right replied by rehearsing the litany of things said by democrats about George Bush — he was a tool of corporate interests, a warmonger and an enemy of civil liberties. So what gives you the high moral ground, those on the right asked, when you were equally vile in your accusations?

I want to say that this is a bad move (and a cheap trick) because it deflects attention from the substantive claims being made and puts the spotlight instead on propositional consistency. The better move (by either party) would have been to insist that Obama or Bush was in fact those things and to back up the assertion with the marshaling of evidence. The better move, in short, would have been to take a stand on truth rather than shifting the focus to a calculation of reciprocal fairness. What gives someone the high moral ground is that he or she is right, not that he or she is fair."

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North America summer school in logic, language, and information.

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in list: Philosophy Notes

Professor Haack is the author of several well-known books, including Deviant Logic (Cambridge, 1974), Philosophy of Logics (Cambridge, 1978), Evidence and Inquiry: Towards Reconstruction in Epistemology (Blackwell, 1993), Deviant Logic, Fuzzy Logic: Beyond the Formalism (Chicago, 1996), Manifesto of a Passionate Moderate: Unfashionable Essays (Chicago, 1998), and Defending Science -- Within Reason: Between Scientism and Cynicism (Prometheus, 2003) as well as of numerous articles.

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profile of Timothy Williamson

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in list: Philosophy Notes

Paul Graham speculates about future of philosophy focused on usefulness.

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in list: Philosophy Notes

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"Retortion is the philosophical procedure whereby one seeks to establish a thesis by uncovering a performative inconsistency in anyone who attempts to deny it."

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in list: Philosophy Notes