Abstract
Science is increasingly becoming automated. Tasks yet to be fully automated include the conjecturing, modifying, extending and testing of hypotheses. At present scientists have an array of methods to help them carry out those tasks. These range from the well-articulated, formal and unexceptional rules to the semi-articulated and variously understood rules-of-thumb and intuitive hunches. If we are to hand over at least some of the aforementioned tasks to machines, we need to clarify, refine and make formal, not to mention computable, even the more obscure of the methods scientists successfully employ in their inquiries. The focus of this essay is one such less-than-transparent methodological rule. I am here referring to the rule that ad hoc hypotheses ought to be spurned. This essay begins with a brief examination of some notable conceptions of ad hoc-ness in the philosophical literature. It is pointed out that there is a general problem afflicting most such conceptions, namely the intuitive judgments that are supposed to motivate them are not universally shared. Instead of getting bogged down in what ad hoc-ness exactly means, I shift the focus of the analysis to one undesirable feature often present in alleged cases of ad hoc-ness. I call this feature the ‘monstrousness’ of a hypothesis. A fully articulated formal account of this feature is presented by specifying what it is about the internal constitution of a hypothesis that makes it monstrous. Using this account, a monstrousness measure is then proposed and somewhat sketchily compared with the minimum description length approach.
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- 1.
The same dictionary traces the Latin expression, which literally means ‘for this’, to the middle of the sixteenth century. See: http://www.oxforddictionaries.com/us/definition/american_english/ad-hoc?q=ad+hoc
- 2.
Simplicity, according to Forster and Sober, ought to be understood formally in terms of the Akaike information criterion. This criterion provides a method for selecting hypotheses by estimating their predictive accuracy. It does so by taking into account the trade-off between the simplicity of a hypothesis and its goodness-of-fit toward the data. For more details, see Akaike (1974).
- 3.
Grünbaum (1976, p. 343) notes Popper’s ambiguous behaviour towards the logical status of the condition of excess testable content, sometimes treating it as merely a sufficient condition and sometimes as both necessary and sufficient for non-ad hoc-ness.
- 4.
Here are the other two: “It is ad hoc2 if none of its novel predictions have been actually ‘verified’… [a] theory is said to be ad hoc3 if it is obtained from its predecessor through a modification of the auxiliary hypotheses which does not accord with the spirit of the heuristic of the programme” (1973, p. 101) [original emphasis]. Grünbaum (1976, p. 341) notes the similarities between Zahar’s notion ad hoc1 and his own notion ad hoc (c). For a more detailed discussion of Zahar’s notions, particularly ad hoc2, the reader may consult Redhead (1978).
- 5.
This example has been contested by Earman and Glymour (1978) who argue, convincingly, that the perihelion was in fact explanatorily targeted. Less controversial examples include all the cases involving temporally novel phenomena, i.e. phenomena which were not known at the time a hypothesis was constructed and hence could not have been explanatorily targeted by the constructors.
- 6.
How much divergence exists between judgments elicited from the two conceptions depends on a number of factors. For example, if Zahar permits the notion of novel consequences to also range over consequences that cannot be tested, then the divergence is significant.
- 7.
Strictly speaking, H′ is ad hoc for G but non-ad hoc for F. If Zahar were a subjectivist then he could perhaps get away with this reply by claiming that ad hoc-ness is a subjective matter. The trouble is he is not – see his comments (1973, pp. 103–104). What is more, if ad hoc-ness is to have any epistemic import it could not be something that varies from subject to subject. For more on this and related problems see Votsis (2014).
- 8.
One possible approach which is eschewed here, though it is legitimate, is to admit several distinct notions of ad hoc-ness.
- 9.
A version of this notion was first explored in Votsis (2014).
- 10.
- 11.
Elsewhere, see Votsis (2015), I call this notion ‘confirmational disconnectedness’. Either name is fine.
- 12.
There is also an analogous notion that applies to predicates – see Schurz (2014).
- 13.
An example can be garnered from discussions of causal modelling. Two causes may be probabilistically independent and yet their presence may be sufficient to yield a joint effect. The presence of the joint effect confirms the presence of both causes. Thus, the two causes are confirmationally related even though they and the propositions expressing their presence are probabilistically independent – the latter presumably all the way down. Another example may be sourced from the domain of mathematics. Axioms are probabilistically independent (presumably all the way down) but two or more of them may be necessary to derive a single theorem. This last example is only meant as a crutch to help understand condition (ii). The view I am proposing here is restricted to empirical, not mathematical, hypotheses.
- 14.
One reason for its inadequacy is that when a pair of propositions α, β are deemed jointed the strength of their jointedness, e.g. the degrees of their probabilistic dependence, is neglected. Arguably such information should have a role in any suitably sensitive measure of monstrousness.
- 15.
This function only makes sense if the total number of content distributions is finite. I am assuming this is the case. Arguments for this assumption can be given but require quite a bit of stage-setting. For now, it suffices to say that this assumption is guaranteed to hold if the hypotheses in question can be fully decomposed into a finite number of atomic propositions.
- 16.
There are also intimate connections between the minimum description length approach and Schurz’s idea of a content element, since the latter is understood in terms of the length of a formula after it has been transformed to its negation-normal form.
References
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
Earman, J., & Glymour, C. (1978). Einstein and Hilbert: Two months in the history of general relativity. Archive for History of Exact Sciences, 19, 291–308.
Forster, M., & Sober, E. (1994). How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions. British Journal for the Philosophy of Science, 45, 1–35.
Gemes, K. (1994). A new theory of content I: Basic content. Journal of Philosophical Logic, 23(6), 595–620.
Gemes, K. (1997). A new theory of content II: Model theory and some alternatives. Journal of Philosophical Logic, 26(4), 449–476.
Grünbaum, A. (1976). Ad hoc auxiliary hypotheses and falsificationism. British Journal for the Philosophy of Science, 27(4), 329–362.
Holton, G. (1969). Einstein, Michelson, and the “crucial” experiment. Isis, 60(2), 132–197.
Leplin, J. (1975). The concept of an ad hoc hypothesis. Studies in History and Philosophy of Science, 5(4), 309–345.
Popper, K. R. (1972). Objective knowledge: An evolutionary approach. Oxford: Clarendon Press.
Popper, K. R. (1974). Replies to my critics. In P. A. Schilpp (Ed.), The philosophy of Karl Popper (pp. 961–1197). La Salle: Open Court.
Redhead, M. (1978). Ad hocness and the appraisal of theories. British Journal for the Philosophy of Science, 29(4), 355–361.
Rissanen, J. (1983). Universal prior for integers and estimation by minimum description length. The Annals of Statistics, 11(2), 416–431.
Schurz, G. (1991). Relevant deduction: From solving paradoxes towards a general theory. Erkenntnis, 35, 391–437.
Schurz, G. (2014). Bayesian pseudo-confirmation, use-novelty, and genuine confirmation. Studies in History and Philosophy of Science, 45(1), 87–96.
Shavlik, J. W., & Dietterich, T. G. (Eds.). (1990). Readings in machine learning. San Mateo: Morgan Kaufmann Publishers.
Votsis, I. (2014). Objectivity in confirmation: Post hoc monsters and novel predictions. Studies in History and Philosophy of Science, 45(1), 70–78.
Votsis, I. (2015). Unification: Not just a thing of beauty. Theoria: An International Journal for Theory, History and Foundations of Science, 30(1), 97–114.
Zahar, E. (1973). Why did Einstein’s programme supersede Lorentz’s? (Part I). British Journal for the Philosophy of Science, 24, 95–123.
Acknowledgements
My sincerest thanks to three anonymous referees as well as to my colleagues, Gerhard Schurz and Paul Thorn, for valuable feedback on the material presented in this essay. I acknowledge the German Research Foundation (Deutsche Forschungsgemeinschaft) for funding my research under project B4 of Collaborative Research Centre 991: The Structure of Representations in Language, Cognition, and Science. Part of this essay has been written while working on the project ‘Aspects and Prospects of Realism in the Philosophy of Science and Mathematics’ (APRePoSMa) during a visiting fellowship at the University of Athens. The project and my visits are co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program ‘Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF)—Research Funding Program: THALIS—UOA.
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Votsis, I. (2016). Ad Hoc Hypotheses and the Monsters Within. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_18
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