Computational epistemology
Encyclopedia
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
.
On making inductive problems easier to solve:
On the divergence of computational epistemology from Bayesian confirmation theory and the like:
Computational epistemology in a nutshell:
On the proper role of methodology:
Formal epistemology
Formal epistemology uses formal methods from decision theory, logic, probability theory and computability theory to elucidate epistemic problems. Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics...
that studies the intrinsic complexity of inductive problems for ideal and computationally bounded agents. In short, computational epistemology is to induction
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
what recursion theory
Recursion theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
is to deduction
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
.
Themes
Some of the themes of computational epistemology include:- the essential likeness of inductionInductive reasoningInductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
and deductionDeductive reasoningDeductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
(as illustrated by systematic analogies between their respective complexity classes) - the treatment of discovery, prediction and assessment methods as effective proceduresEffective methodIn computability theory, an effective method is a procedure that reduces the solution of some class of problems to a series of rote steps which, if followed to the letter, and as far as may be necessary, is bound to:...
(algorithms) as originates in algorithmic learning theoryAlgorithmic learning theoryAlgorithmic learning theory is a framework for machine learning.The framework was introduced in E. Mark Gold's seminal paper "Language identification in the limit"...
. - the characterization of inductive inference problems as consisting of:
- a set of relevant possibilities (possible worldsPossible WorldsPossible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...
), each of which specifies some potentially infinite sequence of inputs to the scientist’s method, - a question whose potential answers partitionPartition of a setIn mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...
the relevant possibilities (in the set theoretic sense), - a convergent success criterion and
- a set of admissible methods
- the notion of logical reliability for inductive problems
Quotations
Computational epistemology definition:- "Computational epistemology is an interdisciplinary field that concerns itself with the relationships and constraints between reality, measure, data, information, knowledge, and wisdom" (Rugai, 2011)
On making inductive problems easier to solve:
- "Eliminating relevant possibilities, weakening the convergence criterion, coarsening the question, or augmenting the collection of potential strategies all tend to make a problem easier to solve" (Kelly, 2000a)
On the divergence of computational epistemology from Bayesian confirmation theory and the like:
- "Whenever you are inclined to explain a feature of science in terms of probability and confirmation, take a moment to see how the issue would look in terms of complexity and success"(Kelly, 2000a)
Computational epistemology in a nutshell:
-
- Formal learning theory is very simple in outline. An inductive problem specifies a range of epistemically possible worlds over which to succeed and determines what sort of output would be correct, where correctness may embody both content and truth (or some analogous virtue like empirical adequacy). Each possible world produces an input stream which the inductive method processes sequentially, generating its own output stream, which may terminate (ending with a mark indicating this fact) or go on forever. A notion of success specifies how the method should converge to a correct output in each possible world. A method solves the problem (in a given sense) just in case the method succeeds (in the appropriate sense) in each of the possible worlds specified by the problem. We say that such a method is reliable since it succeeds over all the epistemically possible worlds. Of two non-solutions, one is as reliable as the other just in case it succeeds in all the worlds the other one succeeds in. That's all there is to it! (Kelly et al. 1997)
On the proper role of methodology:
- "It is for empirical science to investigate the details of the mechanisms whereby we track, and for methodologists to devise and refine even better (inferential) mechanisms and methods" (Nozick, 1981)
External links
- Research Areas: Computational Epistemology, Kevin Kelly
- LearningEpistemology.com "teaches computational epistemology intuitively using narrated animation and interactive explanations." part of Seth Casana's Masters thesis for the Department of Philosophy at Carnegie Mellon University
See also
- Algorithmic learning theoryAlgorithmic learning theoryAlgorithmic learning theory is a framework for machine learning.The framework was introduced in E. Mark Gold's seminal paper "Language identification in the limit"...
- Bayesian confirmation theory
- Belief revisionBelief revisionBelief 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....
- Computational learning theoryComputational learning theoryIn theoretical computer science, computational learning theory is a mathematical field related to the analysis of machine learning algorithms.-Overview:Theoretical results in machine learning mainly deal with a type of...
- Epistemology
- Formal epistemologyFormal epistemologyFormal epistemology uses formal methods from decision theory, logic, probability theory and computability theory to elucidate epistemic problems. Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics...
- Inductive reasoningInductive reasoningInductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
- Language identification in the limitLanguage identification in the limitLanguage identification in the limit is a formal model for inductive inference. It was introduced by E. Mark Gold in his paper with the same title . In this model, a learner is provided with presentation of some language. The learning is seen as an infinite process. Each time an element of the...
- Machine learningMachine learningMachine learning, a branch of artificial intelligence, is a scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases...
- MethodologyMethodologyMethodology is generally a guideline for solving a problem, with specificcomponents such as phases, tasks, methods, techniques and tools . It can be defined also as follows:...
- Philosophy of sciencePhilosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
- Problem of inductionProblem of inductionThe problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:...
- Scientific methodScientific methodScientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...