The Problem of Analogical Inference in Inductive Logic

We consider one problem that was largely left open by Rudolf Carnap in his work on inductive logic, the problem of analogical inference. After discussing some previous attempts to solve this problem, we propose a new solution that is based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain how our new inductive logic can be developed within the Carnapian paradigm of inductive logic-deriving an inductive rule from a set of simple postulates about the observational process-and discuss some of its properties.

[1]  T. Kuipers.  Two types of inductive analogy by similarity , 1984 .

[2]  Sandy L. Zabell,et al.  The rule of succession , 1989 .

[3]  Sandy L. Zabell,et al.  Carnap and the Logic of Inductive Inference , 2011, Inductive Logic.

[4]  S. Zabell.  Characterizing Markov exchangeable sequences , 1995 .

[5]  R. Carnap,et al.  Induktive Logik und Wahrscheinlichkeit , 1959 .

[6]  W. E. Johnson.  I.—PROBABILITY: THE DEDUCTIVE AND INDUCTIVE PROBLEMS , 1932 .

[7]  Domenico Costantani.  The relevance quotient , 1979 .

[8]  D. Freedman,et al.  De Finetti's Theorem for Markov Chains , 1980 .

[9]  P. Maher.  Probabilities For Two Properties , 2000 .

[10]  P. Achinstein.  Variety and Analogy in Confirmation Theory , 1963, Philosophia Scientiæ.

[11]  W. Spohn.  Analogy and inductive logic: A note on Niiniluoto , 1981 .

[12]  David Lindley,et al.  Logical foundations of probability , 1951 .

[13]  Jeff B. Paris,et al.  An Analogy Principle in Inductive Logic , 2013, Ann. Pure Appl. Log..

[14]  Domenico Costantini.  Analogy by similarity , 1983 .

[15]  D. Freedman.  Mixtures of Markov Processes , 1962 .

[16]  M. Hesse.  Analogy and Confirmation Theory , 1963, Philosophy of Science.

[17]  Ilkka Niiniluoto,et al.  Analogy and inductive logic , 1981 .

[18]  S. Zabell.  W. E. Johnson's "Sufficientness" Postulate , 1982 .

[19]  B. Finetti.  La probabilitaà e la statistica nei rapporti con l'Induzione, Secondo i diversi Punti di vista , 2011 .

[20]  J. Romeijn.  Analogical Predictions for Explicit Similarity , 2006 .

[21]  David A. Freedman,et al.  De Finetti's generalizations of exchangeability , 1980 .

[22]  P. Maher.  Probabilities For Multiple Properties: The Models Of Hesse And Carnap And Kemeny , 2001 .

[23]  W. E. Johnson.  Logic - Part III - The Logical Foundations of Science (1924) , 1927 .

[24]  B. Skyrms.  Carnapian inductive logic for Markov chains , 1991, Erkenntnis.

[25]  Theo A.F. Kuipers.  Inductive analogy by similarity and proximity , 1988 .

[26]  L. Ladelli,et al.  On mixtures of distributions of Markov chains , 2002 .

[27]  Maria Concetta Di Maio.  Predictive probability and analogy by similarity in inductive logic , 1995 .

[28]  Brian Skyrms.  Carnapian inductive logic for Markov chains , 1991 .

[29]  T. Kuipers.  Studies in inductive probability and rational expectation , 1978 .

[30]  Richard C. Jeffrey,et al.  Studies in inductive logic and probability , 1971 .

[31]  Rudolf Carnap,et al.  The continuum of inductive methods , 1952 .

[32]  Rudolf Carnap,et al.  Logical foundations of probability , 1951 .

[33]  B. D. Finetti.  La prévision : ses lois logiques, ses sources subjectives , 1937 .