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**Formal epistemology** uses formal methods from decision theory, logic, probability theory and computability theory to model and reason about issues of epistemological interest. Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics. The focus of formal epistemology has tended to differ somewhat from that of traditional epistemology, with topics like uncertainty, induction, and belief revision garnering more attention than the analysis of knowledge, skepticism, and issues with justification.

**Decision theory** is the study of the reasoning underlying an agent's choices against nature. Decision theory is where results depends on another and can be broken into two branches: normative decision theory, which gives advice on how to make the best decisions given a set of uncertain beliefs and a set of values, and descriptive decision theory which analyzes how existing, possibly irrational agents actually make decisions.

**Logic** is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as *therefore*, *hence*, *ergo*, and so on.

**Probability theory** is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.

Though formally oriented epistemologists have been laboring since the emergence of formal logic and probability theory (if not earlier), only recently have they been organized under a common disciplinary title. This gain in popularity may be attributed to the organization of yearly Formal Epistemology Workshops by Branden Fitelson and Sahotra Sarkar, starting in 2004, and the PHILOG-conferences starting in 2002 (The Network for Philosophical Logic and Its Applications) organized by Vincent F. Hendricks. Carnegie Mellon University's Philosophy Department hosts an annual summer school in logic and formal epistemology. In 2010, the department founded the Center for Formal Epistemology.

**Branden Fitelson** is an American philosopher and Distinguished Professor of Philosophy at Northeastern University. He is known for his expertise on formal epistemology and philosophy of science.

**Sahotra Sarkar** is a philosopher of science, at the University of Texas at Austin.

**Vincent Fella Rune Møller Hendricks**, is a Danish philosopher and logician. He holds two doctoral degrees in philosophy and is Professor of Formal Philosophy and Director of the Center for Information and Bubble Studies (CIBS) at University of Copenhagen, Denmark. He was previously Professor of Formal Philosophy at Roskilde University, Denmark. He is member of IIP, the Institut International de Philosophie.

Some of the topics that come under the heading of formal epistemology include:

- Ampliative inference (including inductive logic);
- Belief revision theory
- Game theory and decision theory;
- Algorithmic learning theory (computational epistemology);
- Formal approaches to paradoxes of belief and/or action;
- Formal models of epistemic states, like belief and uncertainty;
- Formal theories of coherentism and confirmation;
- Foundations of probability and statistics.

**Belief revision** is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.

**Game theory** is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

**Algorithmic learning theory** is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include **formal learning theory** and **algorithmic inductive inference**. Algorithmic learning theory is different from statistical learning theory in that it does not make use of statistical assumptions and analysis. Both algorithmic and statistical learning theory are concerned with machine learning and can thus be viewed as branches of computational learning theory.

- Horacio Arló-Costa, Carnegie Mellon, Philosophy (Bayesian epistemology, epistemic logic, belief revision, conditionals, rational choice, normative and behavioral decision theory)
- Alexandru Baltag (dynamic-epistemic logic, probabilistic logics, belief revision etc.)
- Luc Bovens (Bayesian epistemology, probability, etc.)
- Samir Chopra (belief revision, physics, etc.)
- Jake Chandler (Bayesian epistemology, belief revision, etc.)
- John Collins Columbia, Philosophy (belief revision, causal decision theory)
- Franz Dietrich (collective decision-making, etc.)
- Trent Dougherty (Jeffrey's radical probabilism, semantics for modals, theories of probability)
- Igor Douven (Bayesian epistemology, etc.)
- Ellery Eells (confirmation, probability)
- Adam Elga (probabilistic reasoning, laws, etc.)
- Branden Fitelson (confirmation, logic, etc.)
- Malcolm Forster (confirmation, simplicity, causation)
- Haim Gaifman Columbia, Philosophy (foundations of probability, mathematical logic)
- Anthony Gillies (belief revision, formal semantics)
- Mario Gómez-Torrente
- Alan Hájek (foundations of probability, decision theory, etc.)
- Joseph Halpern (reasoning about knowledge and uncertainty)
- Sven Ove Hansson (risk, decision theory, belief revision, deontic logic)
- Gilbert Harman (epistemology, statistical learning theory, mind and language)
- Stephan Hartmann (Bayesian epistemology, probability, collective decision-making, etc.)
- James Hawthorne (confirmation theory, inductive logic, belief revision, nonmonotonic logic)
- Jeff Helzner Columbia, Philosophy (decision theory, rational choice)
- Vincent F. Hendricks Copenhagen and Columbia, Philosophy (epistemic logic, formal learning theory, information processing and analysis of democracy)
- Franz Huber (formal epistemology, philosophy of science, philosophical logic)
- Richard Jeffrey (probabilistic reasoning)
- James Joyce (decision theory)
- Kevin T. Kelly, Carnegie Mellon, Philosophy (computational epistemology, belief revision, etc.)
- Matthew Kotzen (formal epistemology, philosophy of science)
- Marion Ledwig (Newcomb's problem)
- Hannes Leitgeb (belief revision, probability, Bayesianism, etc.)
- Isaac Levi Columbia, Philosophy (belief revision, decision theory, probability)
- Patrick Maher (confirmation, inductive logic)
- David Miller (probability, induction, logic, Popper)
- Luca Moretti (confirmation, coherence, transmission of warrant, epistemic truth)
- Daniel Osherson (inductive logic, reasoning, vagueness)
- Rohit Parikh CUNY, Computer Science (epistemic logic, common knowledge)
- Gabriella Pigozzi (belief revision, decision theory)
- John L. Pollock (decision theory, reasoning, AI)
- Hans Rott (belief revision, nonmonotonic logic, rational choice)
- Darrell Rowbottom (foundations of probability, confirmation, philosophy of science, etc.)
- Nick Rugai (computational epistemology)
- Miriam Schoenfield (epistemology, ethics)
- Teddy Seidenfeld Carnegie Mellon, Philosophy (statistical decision theory, probability theory, game theory)
- Wolfgang Spohn (reasoning, probability, causation, philosophy of science, etc.)
- Paul Thorn (direct inference, defeasible reasoning, induction, etc.)
- Bas Van Fraassen (imprecise credence, probability kinematics)
- Peter Vranas (confirmation, deontic logic, time travel, ethics, etc.)
- Gregory Wheeler (probability, logic)
- Roger White (confirmation, cosmology)
- Sonja Smets (Dynamic-epistemic Logic, belief revision etc.)
- Jon Williamson (Bayesianism, probability, causation)
- Timothy Williamson (knowledge, modality, logic, vagueness, etc.)
- David Wolpert (No Free Lunch theorems, i.e., Hume done rigorously; physics and inference, i.e., monotheism theorems, Chomsky hierarchy of inference devices, etc.)

**Luc Bovens** is a Belgian professor of philosophy at the University of North Carolina at Chapel Hill. Bovens is a former editor of *Economics and Philosophy*. His main areas of research are moral and political philosophy, philosophy of economics, philosophy of public policy, Bayesian epistemology, rational choice theory, and voting theory. He has also published work, of some controversy to the anti-abortion movement, on issues regarding abortion and natural family planning methods of contraception.

**Joseph Yehuda Halpern** is a professor of computer science at Cornell University. Most of his research is on reasoning about knowledge and uncertainty.

**Sven Ove Hansson** is a professor of philosophy and chair of the Department of Philosophy and History of Technology at the Royal Institute of Technology (KTH) in Stockholm, Sweden. He is an author and scientific skeptic, with a special interest in environmental risk assessment, as well as in decision theory and belief revision.

- Algorithmic learning theory
- Belief revision
- Computability theory
- Computational learning theory
- Game theory
- Inductive logic

**Computability theory**, also known as **recursion theory**, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory.

In computer science, **computational learning theory** is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.

**Bayesian probability** is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

**Bayesian inference** is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".

**Inferences** are steps in reasoning, moving from premises to logical consequences; etymologically, the word *infer* means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, distinguishing abduction from induction, where abduction is inference to the best explanation.

**Inductive reasoning** is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion, this is in contrast to *deductive* reasoning. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be *probable*, based upon the evidence given.

Ray Solomonoff's theory of universal **inductive inference** is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor and the Principle of Multiple Explanations.

**Computational epistemology** is a subdiscipline of formal epistemology that studies the intrinsic complexity of inductive problems for ideal and computationally bounded agents. In short, computational epistemology is to induction what recursion theory is to deduction.

In logic, **defeasible reasoning** is a kind of reasoning that is rationally compelling, though not deductively valid.

The aim of a **probabilistic logic** is to combine the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure of formal argument. The result is a richer and more expressive formalism with a broad range of possible application areas. Probabilistic logics attempt to find a natural extension of traditional logic truth tables: the results they define are derived through probabilistic expressions instead. A difficulty with probabilistic logics is that they tend to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as those of Dempster-Shafer theory in evidence-based subjective logic. The need to deal with a broad variety of contexts and issues has led to many different proposals.

**Logic** is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.

The following outline is provided as an overview of and topical guide to epistemology:

**Buddhist logico-epistemology** is a term used in Western scholarship for *pramāṇa-vāda* and *Hetu-vidya*. Pramāṇa-vāda is an epistemological study of the nature of knowledge; Hetu-vidya is a system of logic. These models developed in India during the 5th through 7th centuries.

**Epistemology** or **theory of knowledge** is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", and "Why do we know what we know?". Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims.

**Gregory Wheeler** is an American logician, philosopher, and computer scientist, who specializes in formal epistemology. Much of his work has focused on imprecise probability. He is currently Professor of Philosophy and Computer Science at the Frankfurt School of Finance and Management, and has held positions at LMU Munich, Carnegie Mellon University, the Max Planck Institute for Human Development in Berlin, and the New University of Lisbon. He is a member of the PROGIC steering committee, the editorial boards of *Synthese*, and *Minds and Machines*, and was the editor-in-chief of *Minds and Machines* from 2011 to 2016. He obtained a Ph.D. in philosophy and computer science from the University of Rochester under Henry Kyburg.

The **psychology of reasoning** is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory.

**John L. Pollock** (1940–2009) was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence.

**Clark N. Glymour** is the Alumni University Professor in the Department of Philosophy at Carnegie Mellon University. He is also a senior research scientist at the Florida Institute for Human and Machine Cognition.

**Wolfgang Konrad Spohn** is a German philosopher. He is professor of philosophy and philosophy of science at the University of Konstanz.

**Timothy Joel McGrew** is Professor of Philosophy, and Chair of the Department of Philosophy at Western Michigan University. His research interests include Epistemology, the History and Philosophy of Science, and Philosophy of Religion. He is a specialist in the philosophical applications of probability theory.

- Arlo-Costa, H, van Benthem, J. and Hendricks, V. F. (eds.) (2012). A Formal Epistemology Reader. Cambridge: Cambridge University Press.
- Bovens, L. and Hartmann, S. (2003). Bayesian Epistemology. Oxford: Oxford University Press.
- Brown, B. (2017). Thoughts and Ways of Thinking: Source Theory and Its Applications. London: Ubiquity Press. .
- Hendricks, V. F. (2001). The Convergence of Scientific Knowledge: A View from The Limit. Dordrect: Kluwer Academic Publishers.
- Hendricks, V. F. (2006). Mainstream and Formal Epistemology. New York: Cambridge University Press.
- Hendricks, V. F. (ed.) (2006). Special issue on “8 Bridges Between Mainstream and Formal Epistemology”, Philosophical Studies.
- Hendricks, V. F. (ed.) (2006). Special issue on “Ways of Worlds I-II”, Studia Logica.
- Hendricks, V.F. and Pritchard, D. (eds.) (2006). New Waves in Epistemology. Aldershot: Ashgate.
- Hendricks, V. F. and Symons, J. (eds.) (2005). Formal Philosophy. New York: Automatic Press / VIP.
- Hendricks, V. F. and Symons, J. (eds.) (2006). Masses of Formal Philosophy. New York: Automatic Press / VIP.
- Hendricks, V. F. and Hansen, P.G. (eds.) (2007). Game Theory: 5 Questions. New York: Automatic Press / VIP.
- Hendricks, V.F. and Symons, J. (2006). Epistemic Logic. The Stanford Encyclopedia of Philosophy, Stanford. CA: USA.
- Wolpert, D.H., (1996) The lack of a priori distinctions between learning algorithms, Neural Computation, pp. 1341–1390.
- Wolpert, D.H., (1996) The existence of a priori distinctions between learning algorithms, Neural Computation, pp. 1391–1420.
- Wolpert, D.H., (2001) Computational capabilities of physical systems. Physical Review E, 65(016128).
- Zhu, H.Y. and R. Rohwer, (1996) No free lunch for cross-validation, pp. 1421– 1426.

- Weisberg, Jonathan. "Formal Epistemology". In Zalta, Edward N.
*Stanford Encyclopedia of Philosophy*. - Formal epistemology at the Indiana Philosophy Ontology Project
- Formal epistemology at PhilPapers
- Formal Epistemology Workshop
- Formal Epistemology Meets Experimental Philosophy Workshop
- Formal Epistemology Archive
- Carnegie Mellon Summer School in Logic and Formal Epistemology
- Formal Philosophy
- Formal Epistemology, a free online journal.
- The Reasoner
- Formal Epistemology Project
- Carnegie Mellon Center for Formal Epistemology
- Formal Epistemology
- Formal epistemology & Logics

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