Abstract
We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson’s Sufficientness Principle, JSP, which is classically important because it leads to Carnap’s influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix–Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of ‘irrelevance’ is an indication that this notion is imperfectly understood at present.
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References
Carnap, R. (1952). The continuum of inductive methods. University of Chicago Press.
Carnap, R., & Jeffrey, R. C. (Eds.). (1971). Studies in inductive logic and probability. University of California Press.
Carnap, R. (1980). A basic system of inductive logic. In R. C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. II, pp. 7–155). University of California Press.
Gaifman, H. (1964). Concerning measures on first order calculi. Israel Journal of Mathematics, 2, 1–18.
Hill, M. J., Paris, J. B., & Wilmers, G. M. (2002). Some observations on induction in predicate probabilistic reasoning. Journal of Philosophical Logic, 31, 43–75.
Johnson, W. E. (1932). Probability: The deductive and inductive problems. Mind, 49, 409–423.
Landes, J., Paris, J. B., & Vencovská, A. A survey of some recent results on spectrum exchangeability in polyadic inductive logic. Knowledge, Rationality and Action (to appear).
Landes, J., Paris, J. B., & Vencovská, A. (2009). Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic. International Journal of Approximate Reasoning, 51, 35–55.
Maher, P. (2010). Explication of inductive probability. Journal of Philosophical Logic. doi:10.1007/s10992-010-9144-4.
Nix, C. J. (2005). Probabilistic induction in the predicate calculus. Ph.D. thesis, University of Manchester. Available at http://www.maths.manchester.ac.uk/∼jeff/.
Nix, C. J., & Paris, J. B. (2006). A continuum of inductive methods arising from a generalized principle of instantial relevance. Journal of Philosophical Logic, 35(1), 83–115.
Paris, J. B. (1999). Common sense and maximum entropy. Synthese, 117, 75–93.
Paris, J. B. (1994). The uncertain reasoner’s companion. Cambridge University Press.
Paris, J. B. (2007). Short course in inductive logic. JAIST. Available at http://www.maths.manchester.ac.uk/∼jeff/.
Paris, J. B., & Vencovská, A. (1990). A note on the inevitability of maximum entropy. International Journal of Approximate Reasoning, 4(3), 183–224.
Landes, J., Paris, J. B., & Vencovská, A. (2008). Some aspects of polyadic inductive logic. Studia Logica, 90, 3–16.
Paris, J. B. (2005). On filling-in missing conditional probabilities in causal networks. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(3), 263–280.
Paris, J. B., & Waterhouse, P. J. (2009). Atom exchangeability and instantial relevance. Journal of Philosophical Logic, 38(3), 313–332.
Waterhouse, P. J. (2007). Probabilistic relationships, relevance and irrelevance within the field of uncertain reasoning. Ph.D. thesis, University of Manchester. Available at http://www.maths.manchester.ac.uk/∼jeff/.
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Supported by a UK Engineering and Physical Sciences Research Council (EPSRC) Research Associateship.
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Paris, J.B., Vencovská, A. A Note on Irrelevance in Inductive Logic. J Philos Logic 40, 357–370 (2011). https://doi.org/10.1007/s10992-010-9154-2
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DOI: https://doi.org/10.1007/s10992-010-9154-2