Random Predicate Logic I: A Probabilistic Approach to Vagueness

by William A. Dembski

Abstract—This is an old paper, written twelve years ago, that's been in cold storage ever since. I had always intended to get back to it and apply the formalism it develops, but other projects kept getting in the way. I finally decided to clean it up and get it into circulation, not only because it provides a more powerful and ultimately, I believe, more fruitful formalism than fuzzy logic, but also because I am eager to apply it to confirmation theory, logical paradoxes, and, most importantly from my view, to design-theoretic concepts. I want in particular to treat predicates that attribute complexity, specified complexity, and design as random predicates and see what fruit this reformulation will bear. Since Bart Kosko has shown that fuzzy logic cannot be subsumed under Bayesian techniques, and since fuzzy logic is strictly subsumable under random predicate logic, I intend, as it were, to transcend Bayesian techniques by moving to a completely different formalism. All of this, of course, constitutes a promissory note and will have to await "Random Predicate Logic II: Applications and Interpretations." The paper here merely lays out the basic formalism.

The full paper is available below:
Random Predicate Logic I: A Probabilistic Approach to Vagueness

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