Abstract
The title of this paper refers to a controversy concerning the logical status of the so-called statistical procedures, such as verification of hypotheses and estimation of parameters. The conflicting views are perhaps best represented in the writing of Sir Ronald Fisher and Jerzy Neyman. The problem under discussion is do the statistical procedures deserve the status of inferences or not? Neyman’s opinion is that they are not inferences (or reasonings) at all and are better called inductive behaviour: according to him there is no such thing as inductive inference.1 Fisher asserts the contrary.
The view has, however, really been advanced (Neyman, 1938) that Inductive Reasoning does not exist, but only Inductive Behaviour. (R.A. Fisher, 1956)
It will appear that the term ‘inductive reasoning’ is a misnomer, contributing to the confusion regarding the nature of scientific research, and that a better term would be something like ‘inductive behaviour‘. (J. Neyman, 1957)
Notes
This paper has been read in May 1958, at a meeting of the Moral Sciences Club, Cambridge (England).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Notes
This view is shared by some logicians, notably K. Popper.
Actually, the assumption that disutility is measurable is not such a strong one as it might seem at a first glance. Within the limits defined by certain postulates (cf. J. von Neumann and O. Morgenstern: Theory of Games and Economic Behaviour, Princeton 1947, p. 26–29; R.D. Luce and H. Raiffa: Games and Decisions, New York 1957, p. 23-32) the choice of loss function does not matter. Thus, for instance, if for a given problem L(ω, a) is the loss function, then a · L + β, where a > 0 and β is any number, could do just as well.
The design of the experiment, e.g. its size (the number of trials), is a matter to be decided upon and it might be influenced by such factors as the cost of experimenting and the results obtained in successive phases. We shall, however, simplify the situation by assuming that the experiment to be performed is well defined in advance.
The problem of choice of decision function, given the risk function the value of which is to be minimized in some sense, is a special case of the so-called decision problem under uncertainty. It is assumed that no a priori information concerning the value of ω (such as, e.g., a probability distribution over Ω) is available. Cf. K. Szaniawski: “Some Remarks Concerning the Decision Problem under Uncertainty”, Studia Logica IX, 1960.
Of course, the family of sets ωa is not, in general a partition of ω: the sets ω need not be disjoint and their sum may be a proper subset of ω.
It should be noticed that the opponents of Neyman’s view make use of the same argument in order to show that the theory of decision functions is inadmissible. Thus R. Fisher writes: ‘It is important that the scientific worker introduces no cost functions for faulty decisions, as it is reasonable and often necessary to do with an Acceptance Procedure. To do so would imply that the purposes to which new knowledge was to be put were known and capable of evaluation. If, however, scientific findings are communicated for the enlightment of other free minds, they may be put sooner or later to the service of a number of purposes, of which we know nothing. As workers in Science we aim, in fact, at methods of inference which shall be equally convincing to all freely reasoning minds, entirely independently of any intentions that might be furthered by utilizing the knowledge inferred’ (Statistical Methods and Scientific Inference, Edinburgh 1956, p. 102–103).
For the sake of simplicity only point-estimation will be treated here.
Cf. K. Szaniawski, “On Some Basic Paterns of Statistical Inference”, Studia Logica XI, 1961, p. 83 [see this volume, pp. 70–79.].
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Szaniawski, K. (1998). Inference or Behaviour?. In: Chmielewski, A., Woleński, J. (eds) On Science, Inference, Information and Decision-Making. Synthese Library, vol 271. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5260-0_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-5260-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6213-8
Online ISBN: 978-94-011-5260-0
eBook Packages: Springer Book Archive