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Turning Norton’s Dome Against Material Induction

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Abstract

John Norton has proposed a position of “material induction” that denies the existence of a universal inductive inference schema behind scientific reasoning. In this vein, Norton has recently presented a “dome scenario” based on Newtonian physics that, in his understanding, is at variance with Bayesianism. The present note points out that a closer analysis of the dome scenario reveals incompatibilities with material inductivism itself.

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Notes

  1. Arguments against the universal viability of this understanding have been presented recently by [1].

  2. For a full presentation of the dome scenario, see [10].

  3. There is a last point in time when the ball is at rest rather than a first point when it is moving [14].

  4. Intuitively, the situation can be grasped more easily by looking at the time-reversed system. The system then has solutions where a ball sliding upwards stops exactly at the apex after a finite period of time.

  5. By “rigid material induction” I mean the understanding that all viable instances of inductive inference are licensed by valid scientific theories and/or by other facts regarding the context of scientific research. The weaker idea than most such instances are licensed in that way is not affected by the presented discussion of the dome scenario but does not amount to a universal theory of scientific induction.

  6. This includes, as will be discussed below, knowledge about the context of scientific research.

  7. The experimenter does, of course, rely on scientific knowledge for framing the question, defining the class of relevant experiments, etc. There is no scientific knowledge, however, that can support or contradict the inductive inference itself.

  8. In terms of rationality, the argument is based on a historicist notion of rationality see [7].

  9. One might add that this expectation could lose strength if no adequate theoretical description was found for a long period of time and if other regularities without general natural laws were observed.

  10. In our 16.8 s Norton’s dome example, no measure on the space of alternatives is provided that could support any probabilistic analysis. In cases where a probabilistic evaluation is possible and carried out, such probabilistic analysis reaches out beyond raw induction and is not univocal even in cases where raw induction itself univocally suggests one conclusion. For example, getting 10 times ‘up’ and no ‘down’ in a binary experiment generates a prediction based on raw induction: the next result will be ‘up’. The scenario also does allow for straightforward frequentist data analysis, which leads to probability 1 for ‘up’. However, in order to avoid probability 1 for a specific outcome (and therefore be compatible with Bayesian data analysis) one might deviate from the simple frequentist scheme and rather adhere to Laplace’s rule of succession.

  11. The presented view is fully consistent with Norton’s understanding that the discovery of new theories is itself not an inductive process. On the proposed view, raw induction is deployed in the absence of a more elaborate theoretical understanding of a regularity pattern. It is not deployed for finding new theories.

  12. Of course, even the system with a ball at the dome’s apex is heavily constrained by physics. We know that the ball will not fly away, not stop on the way down, etc. The indeterminism of the dome scenario is confined to only two parameters: t, which is the last time the ball is at rest, and the radial direction in which the ball falls.

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Dawid, R. Turning Norton’s Dome Against Material Induction. Found Phys 45, 1101–1109 (2015). https://doi.org/10.1007/s10701-015-9943-0

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