Abstract
It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, which, it is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases.
Similar content being viewed by others
References
Alexander, H. G. (Ed.) (1956) The Leibniz–Clarke correspondence. Manchester University, Manchester
Atkinson, D. (2009). Confirmation and justification. A commentary on Shogenji’s measure. Synthese. doi:10.1007/s11229-009-9696-4.
Ayer A. J. (1952) Language, truth and logic (2nd ed.). Dover, New York
Bergmann P. G. (1958) Conservation laws in general relativity as the generators of coordinate transformations. Physical Review 112: 287–289
Blumenfeld D. (1995) Perfection and happiness in the best possible world. In: Jolley N. (Ed.) The Cambridge Companion to Leibniz. Cambridge University Press, Cambridge, pp 382–410
Brush S. G. (1982) Finding the age of the Earth: By physics or by faith?. Journal of Geological Education 30: 34–58
Burks A. W. (1953) The presupposition theory of induction. Philosophy of Science 20: 177–197
Carnap R. (1962) Logical foundations of probability (2nd ed.). University of Chicago, Chicago
Child J. M. (1920) The early mathematical manuscripts of Leibniz. Open Court, Chicago
Churchill R. V., Brown J. W. (1990) Complex variables and applications (5th ed.). McGraw-Hill, New York
Crupi V., Tentori K. (2010) Irrelevant conjunction: Statement and solution of a new paradox. Philosophy of Science 77: 1–13
Cupillari A. (2004) Another look at the rules of differentiation. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 14: 193–200
Descartes, R. (1985). Principles of philosophy, part 3, number 45. In R. S. John Cottingham & D. Murdoch, The philosophical writings of Descartes (Vol. I). Cambridge: Cambridge University Press.
Dorling J. (1992) Bayesian conditionalization resolves positivist/realist disputes. Journal of Philosophy 89: 362–382
Earman J. (1992) Bayes or bust? A critical examination of Bayesian confirmation theory. Massachusetts Institute of Technology Press, Cambridge
Edwards A. W. F. (1972) Likelihood: An account of the statistical concept of likelihood and its application to scientific inference. Cambridge University Press, Cambridge
Eells E., Fitelson B. (2002) Symmetries and asymmetries in evidential support. Philosophical Studies 107: 129–142
Ellenberger F., Carozzi M. (1999) History of geology, volume 2: The great awakening and its first fruits—1660–1810. A. A. Balkema, Rotterdam
Festa R. (1999) Bayesian confirmation. In: Galavotti M. C., Pagnini A. (eds) Experience, reality, and scientific explanation: Essays in honor of Merrilee and Wesley Salmon. Kluwer Academic, Dordrecht, pp 55–87
Finch H. A. (1960) Confirming power of observations metricized for decisions among hypotheses, Part II. Philosophy of Science 27: 391–404
Fitelson B. (1999) The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science 66: S362–S378
Fitelson, B. (2001). Studies in Bayesian confirmation theory. Ph.D. thesis, Department of Philosophy, University of Wisconsin–Madison.
Fitelson B. (2002) Putting the irrelevance back into the problem of irrelevant conjunction. Philosophy of Science 69: 611–622
Fitelson, B. (2011). Contrastive Bayesianism. In M. Blaauw (Ed.), Contrastivism in philosophy. Routledge. http://fitelson.org/cb.pdf, 07/14/10 draft.
Gärdenfors P. (1984) Epistemic importance and minimal changes of belief. Australasian Journal of Philosophy 62: 136–157
Gillies D. (1986) In defense of the Popper–Miller argument. Philosophy of Science 53: 110–113
Glymour C. (1980) Theory and evidence. Princeton University Press, Princeton
Good I. J. (1968) Corroboration, explanation, evolving probability, simplicity and a sharpened razor. The British Journal for the Philosophy of Science 19: 123–143
Good I. J. (1984) A Bayesian approach in the philosophy of inference: Review of probability and evidence by Paul Horwich. The British Journal for the Philosophy of Science 35: 161–166
Gould, S. J. (1985). Adam’s navel. In The Flamingo’s smile: Reflections in natural history (pp. 99–113). New York: Norton.
Hawthorne J., Fitelson B. (2004) Re-solving irrelevant conjunction with probabilistic independence. Philosophy of Science 71: 505–514
Hempel C. G. (1959) The empiricist criterion of meaning. In: Ayer A. J. (Ed.) Logical positivism. Free Press, Glencoe, IL, pp 108–129
Hempel, C. G. (1965). Studies in the logic of confirmation. In Aspects of scientific explanation and other essays in the philosophy of science (pp. 3–51). New York: The Free Press.
Hoefer C., Rosenberg A. (1994) Empirical equivalence, underdetermination, and systems of the world. Philosophy of Science 61: 592–607
Horwich P. (1982) Probability and evidence. Cambridge University Press, Cambridge
Horwich P. (1983) Explanations of irrelevance: On the relative merits of Bayesianism, the hypothetico-deductive method, and Glymour’s “bootstrap” theory of confirmation. In: Earman J. (Ed.) Testing scientific theories. University of Minnesota Press, Minneapolis, pp 55–65
Horwich, P. (1993). Wittgensteinian Bayesianism. In P. A. French, T. E. Uehling, Jr., & H. K. Wettstein (Eds.), Midwest studies in philosophy of science (Vol. XVIII, pp. 62–77). Notre Dame, IN: University of Notre Dame Press.
Howson C. (1983) Statistical explanation and statistical support. Erkenntnis 20: 61–78
Howson C. (2000) Hume’s problem: Induction and the justification of belief. Clarendon Press, Oxford
Howson C., Urbach P. (1993) Scientific reasoning: The Bayesian approach (2nd ed.). Open Court, Chicago
Jeffrey, R. C. (Ed.). (1980). Studies in inductive logic and probability (Vol. II). Berkeley: University of California Press.
Kemeny J. G. (1959) A philosopher looks at science. D. Van Nostrand Company, Princeton
Kuipers T. A. F. (2000) From instrumentalism to constructive realism: On some relations between confirmation, empirical progress, and truth approximation. Kluwer, Dordrecht
Kukla A. (1998) Studies in scientific realism. Oxford University Press, New York
Kukla A. (2001) Theoreticity, underdetermination, and the disregard for bizarre scientific hypotheses. Philosophy of Science 68: 21–35
Laudan L., Leplin J. (1991) Empirical equivalence and underdetermination. Journal of Philosophy 88: 449–472
Mackie J. L. (1969) The relevance criterion of confirmation. The British Journal for the Philosophy of Science 20: 27–40
Maher P. (2004) Bayesianism and irrelevant conjunction. Philosophy of Science 71: 515–520
Milne P. (1995) A Bayesian defence of Popperian science?. Analysis 55: 213–215
Milne P. (1996) log[P(h/eb)/P(h/b)] is the one true measure of confirmation. Philosophy of Science 63: 21–26
Norton J. D. (2007) Probability disassembled. The British Journal for the Philosophy of Science 58: 141–171
Norton J. D. (2008) Must evidence underdetermine theory?. In: Carrier M., Howard D., Kourany J. (eds) The challenge of the social and the pressure of practice: Science and values revisited. University of Pittsburgh Press, Pittsburgh, pp 17–44
Peirce C. S. (1934) Eighth Lowell lecture of 1903, “How to theorize”. In: Hartshorne C., Weiss P. (eds) The collected papers of Charles Sanders Peirce, volume 5: Pragmatism and pragmaticism. Harvard University Press, Cambridge, pp 413–422
Pitts J.B. (2010) Gauge-invariant localization of infinitely many gravitational energies from all possible auxiliary structures. General Relativity and Gravitation 42: 601–622
Rappaport R. (1997) When geologists were historians, 1665–1750. Cornell University Press, Ithaca
Reichenbach H. (1938) Experience and prediction: An analysis of the foundations and the structure of knowledge. University of Chicago Press, Chicago
Rosenkrantz R. (1983) Why Glymour is a Bayesian. In: Earman J. (Ed.) Testing scientific theories. University of Minnesota Press, Minneapolis, pp 69–97
Rosenkrantz R. D. (1994) Bayesian confirmation: Paradise regained. The British Journal for the Philosophy of Science 45: 467–476
Royall R. M. (1997) Statistical evidence: A likelihood paradigm. Chapman and Hall, London
Russell B. (1948) Human knowledge: Its scope and limits. George Allen and Unwin, London
Salmon W. C. (1974) The pragmatic justification of induction. In: Swinburne R. (Ed.) The justification of induction. Oxford University Press, London, pp 85–97
Schlesinger G. N. (1995) Measuring degrees of confirmation. Analysis 55: 208–212
Schupbach J. (2011) New hope for Shogenji’s coherence measure. The British Journal for the Philosophy of Science 62: 125–142
Schurz G. (2008) The meta-inductivist’s winning strategy in the prediction game: A new approach to Hume’s problem. Philosophy of Science 75: 278–305
Shogenji T. (1999) Is coherence truth conducive?. Analysis 59: 338–345
Sloan P.R. (1985) From logical universals to historical individuals: Buffon’s idea of biological species. In: Atran S., Burkhardt R.W., Corsi P., Diara A., Fantini B., Fischer J.-L., Hodge M.J.S., Laurent G., La Vergata A., Leikola A., Louis P., Mayr E., Müller G.H., Rey R., Roger J., Sloan P.R. (eds) Histoire du Concept d’Espèce dans les Sciences de la Vie. Fondation Singer-Polignac, Paris, pp 101–140
Sober, E. (2002). Bayesianism—Its scope and limits. In R. Swinburne (Ed.), Bayes’s theorem: Proceedings of the British Academy (Vol. 113, pp. 21–38). Oxford: The British Academy and Oxford University Press.
Steel D. (2007) Bayesian confirmation theory and the likelihood principle. Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science 156: 53–77
Swain, M. (Ed.) (1970) Induction, acceptance, and rational belief. Reidel, Dordrecht
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pitts, J.B. Irrelevant conjunction and the ratio measure or historical skepticism. Synthese 190, 2117–2139 (2013). https://doi.org/10.1007/s11229-011-9961-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-011-9961-1