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Formal epistemology uses formal methods from
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
,
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
,
probability theory 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 o ...
and
computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since e ...
to model and reason about issues of epistemological interest. Work in this area spans several academic fields, including
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
,
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
,
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
, and
statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
. 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.


History

Though formally oriented epistemologists have been laboring since the emergence of
formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...
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 Branden Fitelson (; born August 17, 1969) 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. Bibliography * Edward ...
and
Sahotra Sarkar Sahotra Sarkar (born 1962) is an Indian-American professor at the University of Texas at Austin, specializing in the philosophy of biology. Education and career Sarkar is originally from India where he lived in Darjeeling until 1975. He earned ...
, starting in 2004, and the PHILOG-conferences starting in 2002 (The Network for Philosophical Logic and Its Applications) organized by
Vincent F. Hendricks Vincent Fella Rune Møller Hendricks (born 6 March 1970) is a Danish philosopher and logician. He holds a doctoral degree (PhD) and a habilitation (dr.phil) in philosophy and is Professor of Formal Philosophy and Director of the Center for Informa ...
. 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.


Bayesian epistemology

Bayesian epistemology Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its concep ...
is an important theory in the field of formal epistemology. It has its roots in
Thomas Bayes Thomas Bayes ( ; 1701 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would become his ...
' work in the field of probability theory. It is based on the idea that beliefs are held gradually and that the strengths of the beliefs can be described as subjective probabilities. As such, they are subject to the laws of
probability theory 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 o ...
, which act as the norms of
rationality Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abil ...
. These norms can be divided into static constraints, governing the rationality of beliefs at any moment, and dynamic constraints, governing how rational agents should change their beliefs upon receiving new evidence. The most characteristic Bayesian expression of these principles is found in the form of
Dutch book In gambling, a Dutch book or lock is a set of odds and bets, established by the bookmaker, that ensures that the bookmaker will profit—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which ...
s, which illustrate irrationality in agents through a series of bets that lead to a loss for the agent no matter which of the probabilistic events occurs. Bayesians have applied these fundamental principles to various epistemological topics but Bayesianism does not cover all topics of traditional epistemology. The problem of confirmation in the
philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...
, for example, can be approached through the Bayesian ''principle of conditionalization'' by holding that a piece of evidence confirms a theory if it raises the likelihood that this theory is true. Various proposals have been made to define the concept of coherence in terms of probability, usually in the sense that two propositions cohere if the probability of their conjunction is higher than if they were neutrally related to each other. The Bayesian approach has also been fruitful in the field of
social epistemology Social epistemology refers to a broad set of approaches that can be taken in epistemology (the study of knowledge) that construes human knowledge as a collective achievement. Another way of characterizing social epistemology is as the evaluation o ...
, for example, concerning the problem of
testimony In law and in religion, testimony is a solemn attestation as to the truth of a matter. Etymology The words "testimony" and "testify" both derive from the Latin word ''testis'', referring to the notion of a disinterested third-party witness. La ...
or the problem of group belief. Bayesianism still faces various theoretical objections that have not been fully solved.


Topics

Some of the topics that come under the heading of formal epistemology include: *
Ampliative inference Ampliative (from Latin ''ampliare'', "to enlarge"), a term used mainly in logic, meaning "extending" or "adding to that which is already known". This terminology was often used by medieval logicians in the analyses of the temporal content of thei ...
(including
inductive logic Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' rea ...
); *
Belief revision 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 age ...
theory *
Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
and
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
; *
Algorithmic learning theory 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 statistica ...
(
computational epistemology 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 ...
); * Formal approaches to
paradoxes A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
of belief and/or action; * Formal models of epistemic states, like
belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take i ...
and
uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...
; * Formal theories of
coherentism In philosophical epistemology, there are two types of coherentism: the coherence theory of truth; and the coherence theory of justification (also known as epistemic coherentism). Coherent truth is divided between an anthropological approach, wh ...
and confirmation; * Foundations of probability and statistics.


List of contemporary formal epistemologists


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 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 ...
(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 Adam; el, Ἀδάμ, Adám; la, Adam is the name given in Book of Genesis, Genesis 1-5 to the first human. Beyond its use as the name of the first man, ''adam'' is also used in the Bible as a pronoun, individually as "a human" and in a coll ...
(probabilistic reasoning, laws, etc.)
Branden Fitelson
(confirmation, logic, etc.) *
Malcolm Forster Malcolm, Malcom, Máel Coluim, or Maol Choluim may refer to: People * Malcolm (given name), includes a list of people and fictional characters * Clan Malcolm * Maol Choluim de Innerpeffray, 14th-century bishop-elect of Dunkeld Nobility * Máe ...
(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 Joseph Yehuda Halpern (born 1953) is an Israeli-American professor of computer science at Cornell University. Most of his research is on reasoning about knowledge and uncertainty. Biography Halpern graduated in 1975 from University of Toronto wi ...
(reasoning about knowledge and uncertainty) * Sven Ove Hansson (risk, decision theory, belief revision, deontic logic) *
Gilbert Harman Gilbert Harman (May 26, 1938 – November 13, 2021) was an American philosopher, who taught at Princeton University from 1963 until his retirement in 2017. He has published widely in philosophy of language, cognitive science, philosophy of min ...
(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 Vincent Fella Rune Møller Hendricks (born 6 March 1970) is a Danish philosopher and logician. He holds a doctoral degree (PhD) and a habilitation (dr.phil) in philosophy and is Professor of Formal Philosophy and Director of the Center for Informa ...
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 Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher, logician, and probability theorist. He is best known for developing and championing the philosophy of radical probabilism and the associated heuristic of ...
(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)

(belief revision, probability, Bayesianism, etc.) *
Isaac Levi Isaac Levi (June 30, 1930 – December 25, 2018) was an American philosopher who served as the John Dewey Professor of Philosophy at Columbia University. He is noted for his work in epistemology and decision theory. Education and career Levi wa ...
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 Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applica ...
,
common knowledge Common knowledge is knowledge that is publicly known by everyone or nearly everyone, usually with reference to the community in which the knowledge is referenced. Common knowledge can be about a broad range of subjects, such as science, literat ...
) *
Gabriella Pigozzi Gabriella may refer to: * Gabriella (given name), a feminine given name * '' Gabriella di Vergy'', an opera seria by Gaetano Donizetti (1826, revised 1838), and an opera by Mercadante (1828), based on the tragedy ''Gabrielle de Vergy'' by Dormont ...
(belief revision, decision theory) *
John L. Pollock John L. Pollock (1940–2009) was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence. Life and career Born John Leslie Pollock in Atchison, Kansas, on Janu ...
(decision theory, reasoning, AI)
Hans Rott
(belief revision, nonmonotonic logic, rational choice)
Darrell Rowbottom
(foundations of probability, confirmation, philosophy of science, etc.) *
Nick Rugai Nick may refer to: * Nick (given name) * A Glossary of cricket terms#nick, cricket term for a slight deviation of the ball off the edge of the bat * British slang for being arrested * British slang for a police station * British slang for stealin ...
(
computational epistemology 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 ...
) * 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 Bastiaan Cornelis van Fraassen (; born 1941) is a Dutch-American philosopher noted for his contributions to philosophy of science, epistemology and formal logic. He is a Distinguished Professor of Philosophy at San Francisco State University an ...
(imprecise credence, probability kinematics) * Peter Vranas (confirmation, deontic logic, time travel, ethics, etc.) *
Gregory Wheeler Gregory Wheeler (born 1968) 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 Scie ...
(probability, logic) * Roger White (confirmation, cosmology) *
Sonja Smets Sonja Smets is a Belgian and Dutch logician and epistemology, epistemologist known for her work in belief revision and quantum logic. She is Professor of Logic and Epistemology at the University of Amsterdam, where she was the Director of the Ins ...
(Dynamic-epistemic Logic, belief revision etc.)
Jon Williamson
(Bayesianism, probability, causation) *
Timothy Williamson Timothy Williamson (born 1955) is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. He is the Wykeham Professor of Logic at the University of Oxford, and fe ...
(knowledge, modality, logic, vagueness, etc.) *
David Wolpert David Hilton Wolpert is an American mathematician, physicist and computer scientist. He is a professor at Santa Fe Institute. He is the author of three books, three patents, over one hundred refereed papers, and has received numerous awards. His ...
(
No Free Lunch theorem In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready appears in the 1997 "No Free Lunch Theorems for Optimization".Wolpert, D.H., Macready, W.G. (1997),No Free Lunch Theorems f ...
s, i.e., Hume done rigorously; physics and inference, i.e., monotheism theorems, Chomsky hierarchy of inference devices, etc.)


See also

*
Algorithmic learning theory 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 statistica ...
*
Belief revision 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 age ...
*
Computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since e ...
*
Computational learning theory In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms. Overview Theoretical results in machine learning m ...
*
Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
*
Inductive logic Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' rea ...


References


Bibliography

*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 Founded in 2008 by Brian Hole, Ubiquity Press is an academic publisher focusing on open access, peer-reviewed scholarship. Ubiquity Press is a part oUbiquity which also provides full publishing infrastructure and services to university presses, an ...


*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 Automatic Press / VIP is an independent publishing house founded in 2005. It published interview books featuring prominent scholars and philosophers. Among the notables who have published interviews in are Nobel Prize Laureates Robert Aumann and T ...


*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.


External links

* * *
Formal Epistemology WorkshopFormal Epistemology Meets Experimental Philosophy WorkshopCarnegie Mellon Summer School in Logic and Formal EpistemologyFormal PhilosophyFormal Epistemology
a free online journal.
The ReasonerFormal Epistemology Project

Carnegie Mellon Center for Formal Epistemology
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Formal EpistemologyFormal epistemology & Logics
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