The branch of philosophy called formal epistemology has very similar interests to those of the Less Wrong community. Formal epistemologists mostly work on (1) mathematically formalizing concepts related to induction, belief, choice, and action, and (2) arguing about the foundations of probability, statistics, game theory, decision theory, and algorithmic learning theory.
Those who value the neglected virtue of scholarship may want to study for themselves the arguments that have lead scholars either toward or against the very particular positions on formalizing language, decision theory, explanation, and probability typically endorsed at Less Wrong. As such, here's a brief overview of the field by way of some helpful links:
- Wikipedia, "Formal Epistemology" (contains an excellent list of today's leading formal epistemologists)
- Hendricks, Mainstream and Formal Epistemology (perhaps the best "introduction" to the subject, especially for those familiar with mainstream epistemology)
- The Reasoner, a free monthly digest of short articles and interviews on formal epistemology
- Choice & Inference, a group blog
- Introduction to Formal Epistemology, a short Stanford course with lecture slides and some literature in PDF
- Hajek & Hartmann, "Bayesian Epistemology" and Talbott, "Bayesian Epistemology" and Bovens & Hartmann, Bayesian Epistemology (an important sub-field of formal epistemology)
- Jeffrey, Subjective Probability (free introductory book on a Less Wrong-ish approach to probability.