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A note on “The no alternatives argument” by Richard Dawid, Stephan Hartmann and Jan Sprenger

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Abstract

The defence of The No Alternatives Argument in a recent paper by R. Dawid, S. Hartmann and J. Sprenger (forthcoming in the British Journal for the Philosophy of Science; latest version: February 2013) rests on the assumption (among others) that the number of acceptable alternatives to a scientific hypothesis is independent of the complexity of the scientific problem. This note proves a generalisation of the main theorem by Dawid, Hartmann and Sprenger, where this independence assumption is no longer necessary. Some of the other assumptions are also discussed, and the limitations of (this formalisation of) the no-alternatives argument are explored.

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Notes

  1. 1 In this context, we mean by a ‘knife-edge situation’ a combination of (in)equalities among the parameters y i ,t i ,f i k (i,k∈N) which will cease to hold if the slightest change in one of the parameters occurs. Formally, a combination of (in)equalities among y i ,t i ,f i k (i,k∈N) describes a knife-edge situation if the set of all sequences 〈y i ,t i ,f i k 〉 i,k∈N satisfying these (in)equalities has product Lebesgue measure zero in [0,1]N×[0,1]N×[0,1]N×N.

  2. 2 For example, theories that are heavily reliant on numerical models become increasingly acceptable when analytic models appear intractable; moreover, the range of acceptable models will depend on the computational facilities available.

References

  • Bovens, L, & Hartmann, S. (2003). Bayesian epistemology. Oxford: Oxford University Press.

  • Dawid, R, Hartmann, S, Sprenger, J (2012). The no alternatives argument, Preprint. http://philsci-archive.pitt.edu/9038/.

  • Dawid, R, Hartmann, S, Sprenger, J (2013). The no alternatives argument. Br J Philos Sci, forthcoming. http://laeuferpaar.de.

  • Königsberger, K. (2001). Analysis 1 (5., neu bearbeitete Auflage). Berlin: Springer.

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Authors and Affiliations

  1. Center for Mathematical Economics, Bielefeld University, Universitätsstraße 25, 33615, Bielefeld, Germany

    Frederik Herzberg

  2. Munich Center for Mathematical Economics, Ludwig Maximilian University of Munich, Geschwister-Scholl-Platz 1, 80539, Munich, Germany

    Frederik Herzberg

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  1. Frederik Herzberg
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Correspondence to Frederik Herzberg.

Additional information

I would like to thank Professors Richard Dawid, Stephan Hartmann, Hannes Leitgeb, David Miller and (in particular) Jan Sprenger as well as two anonymous referees and the Associate Editor for very helpful comments on an earlier version of this paper. A Visiting Fellowship of the Munich Center for Mathematical Philosophy funded by the Alexander von Humboldt Foundation is gratefully acknowledged.

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Herzberg, F. A note on “The no alternatives argument” by Richard Dawid, Stephan Hartmann and Jan Sprenger. Euro Jnl Phil Sci 4, 375–384 (2014). https://doi.org/10.1007/s13194-014-0092-7

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  • DOI: https://doi.org/10.1007/s13194-014-0092-7

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