The essence of formal epistemology is in developing or formulating models of knowledge using formal tools, including probability, logic, decision theory, and computations. Thus, formal epistemology explains probabilistic models of knowledge and belief systems using theoretical logics. This book brings together contributions from 47 researchers in the form of research articles. It consists of 43 chapters spread over five parts: “Bayesian Epistemology,” “Belief Change,” “Decision Theory,” “Logics of Knowledge and Belief,” and “Interactive Epistemology.”
Chapter 1 introduces the agents: agency and interaction, probability, belief change, decision theory, knowledge and belief logic, and epistemology (interactive and formal). Part 1 covers Bayesian epistemology, with its introduction in chapter 2. Chapter 3 highlights theories such as frequency and Keynes, degrees of belief, and the logic of consistency and truth. Chapter 4 is a pragmatic analysis of belief, probabilistic acts and observations, attention and selection, finite memory, and concept formation. Chapter 5 deals with full belief, supposition, personal and two-place probabilities, the idea of the a priori, the logic of full belief revision, its identification, and in a lexicographic model, with an appendix on transfinite consistency, rejection of the Bayesian paradigm and infinitesimals.
Chapter 6 details simple and general higher order probabilities using axiom (VI) and its consequences and logic and stage dependent modalities, respectively. Chapter 7 discusses indeterminate probabilities using three problems: rational credence, rational choice, and revision. Chapter 8, “Why I Am Not a Bayesian,” covers theoretical proofs against the Bayesian scheme. Chapter 9 discusses the three sequential analyses: a mistake in the dynamic coherence argument, a mistake is a mistake, and what makes the Cunning Bettor tick. Chapter 10 explores problems for conditionalization and reflection, that is, two roads to Shangri-La, the prisoner’s dilemma, John Collins’ prisoner, Sleeping Beauty, duplication, and so on. Chapter 11 covers degrees of belief, temporal conditionalization, and reflection, and tends to solve problems illustrated in chapter 10, with their proof of results in an appendix.
Part 2 begins with an introduction to belief change in chapter 12. Chapter 13 describes partial meet contraction and revision functions, maxichoice contraction functions, and factoring conditions, and diagrammatically presents their implication results. Chapter 14 covers six axiomatic characterizations using symmetry, conservativity, finitude, strong conservativity, indecisiveness, regularity, hyper-regularity, weak intersection, and conjunction. Chapter 15 details changes in full belief, focusing on doxastic commitment and its inconsistent state, deliberate contraction, and not at the cost of loss of informational value. Chapter 16 discusses general selection functions and constraints, rational choice, Samuelson and base preferences, postulates, and representation theorems for contraction functions. Chapter 17 surveys formal and philosophical aspects to ranks and probabilities, as well as their comparison to more recent computer science literature.
Part 3 covers decision theory beginning with an introductory chapter 18. Chapter 19, an interesting read, illustrates the Allais paradox involving gambling decisions. Chapter 20 reviews a simple lottery utility, the Allais and Ellsberg paradoxes, dynamic feasibility, and Levi’s decision theory. Chapter 21 explores the need for probability, the historical background of decision theory, and alternatives such as the Anscombe-Aumann setup, the Choquet and maxmin expected utilities, unanimity, and smooth and variational preferences.
Chapter 22 demonstrates state independent probability using de Finetti’s gambling approach, Savage’s “small worlds” example, and an example of prizes comprising dollars and yen. Chapter 23 creates interest with examples of the prisoner’s dilemma, including details about dominance, expected utility, and conditionals. Chapter 24 explains the cumulative prospect theory and its applicability over finite and continuous distributions, source-dependent probabilistic and uncertain prospects, and possessing different decision weights, with an appendix on axiomatic analysis.
Part 4, “Logics of Knowledge and Belief,” starts with an introduction in chapter 25. Chapter 26 explores epistemology without both knowledge and belief, covering the acquisition of information through questioning procedures, interrogation, and justification, and describes interrogative models and the place of knowledge in inquiry. Chapter 27 introduces three epistemic operators: sentential, penetrating, and semipenetrating. Chapter 28 discusses fallibilism, the rule of resemblance, the rule of actuality, the rule of belief, the rule of reliability, the rule of attention, and epistemic possibilities contrasting elusive knowledge. Chapter 29 elaborates on knowledge, skepticism, skeptical possibilities and results, and the theory of knowledge.
Chapter 30 details logics of knowledge and belief using partition models, basic theory, minimal and maximal extensions, defeasibility analysis, and causal dimension. Chapter 31 covers inconsistent, animal, and defining and partial belief states. Chapter 32 is more technical in terms of providing the language and tools related to the logic of justification. Chapter 33 covers formal learning theory, computable learning, the language learnability paradigm, concept learning, and the probably approximately correct (PAC) paradigm. Chapter 34 presents computational constraints in epistemic logic using modal logic.
Part 5 covers interactive epistemology, with its introduction in chapter 35. Chapter 36 discusses two sample consideration problems, including their analyses and solutions through higher-order expectations. Chapter 37 details three views of common knowledge: the iterate approach, the fixed-point approach, and the shared environment approach. Chapter 38 technically explains four epistemic scenarios into six Kripke models and their representations using a logical language with epistemic actions. Chapter 39 looks at single- and multi-agent plausibility models, defeasibility theories of knowledge, and doxastic attitudes. Chapter 40 is a short chapter covering the definition of common knowledge based on the reconciliation of subjective knowledge. Chapter 41 explains the Nash equilibrium and interactive belief systems using properties and counterexamples. Chapter 42 describes the model theory for games in detail. Chapter 43 discusses the technicalities behind Aumann’s and Stalnaker’s theorems, covering in detail attributes like common knowledge, rationality, and substantive rationality.
The book serves its purpose. The editors include an introductory chapter for each part, which makes the book worth reading. It is an interesting read for philosophers, historians, academics, and researchers who are working in the area of formal epistemology and its related fields.