Article ID: CBB001024148

Abduction, Tomography, and Other Inverse Problems (2011)

unapi

Charles S. Peirce introduced in the late 19th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon's theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.

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Authors & Contributors
Brady, Geraldine
Heijenoort, Jean van
George, Alexander
Velleman, Daniel J.
Shin, Sun-Joo
Bernays, Paul
Journals
History and Philosophy of Logic
Transactions of the Charles S. Peirce Society
Studies in History and Philosophy of Science
Journal Electronique d'Histoire des Probabilités et de la Statistique
Synthese
Logica Universalis
Publishers
Elsevier/North-Holland
Harvard University Press
Blackwell Publishers
MIT Press
J. Vrin
University of Chicago Press
Concepts
Logic
Philosophy of mathematics
Mathematics
Philosophy
Godel's theorem
Incompleteness theorems
People
Peirce, Charles Sanders
Gödel, Kurt
Frege, Gottlob
Löwenheim, Leopold
Skolem, Thoralf Albert
Spinoza, Baruch
Time Periods
20th century
19th century
21st century
18th century
20th century, early
Places
United States
Massachusetts (U.S.)
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