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Unifying statistically autonomous and mathematical explanations

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Abstract

A subarea of the debate over the nature of evolutionary theory addresses what the nature of the explanations yielded by evolutionary theory are. The statisticalist line is that the general principles of evolutionary theory are not only amenable to a mathematical interpretation but that they need not invoke causes to furnish explanations. Causalists object that construction of these general principles involves crucial causal assumptions. A recent view claims that some biological explanations are statistically autonomous explanations (SAEs) whereby phenomena are accounted for statistically and which prescind from micro-causal details. I raise three major problems for this account and then advance a view which unifies SAEs as mathematical explanations: the MSAE view. The MSAE view not only resolves the issues bedeviling the original SAE account but serves to importantly broaden the class of non-causal explanations in population biology.

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Fig. 1

(Adapted from Stigler 2010)

Fig. 2

Adapted from Galton 1889)

Fig. 3

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Notes

  1. What Hacking has in mind here is what might also be termed “epistemic irreducibility”: the macro-level theory or explanation cannot be derived from nor reduced to the micro-level theory in principle (Fletcher et al. 2019).

  2. Alternative accounts of statistical explanation include Marc Lange’s really statistical (RS) view (Lange 2013, 2017) and Batterman and Rice’s minimal models account (Batterman and Rice 2014). For Lange, regression cases are not statistically autonomous since the explanandum in these cases can be accounted for causally (Lange 2013). The fact that these explananda admit of pluralism undercuts their status as SAEs.

  3. The emphasis on approximation is apropos of the fact that a normal distribution involves infinite trials. Therefore, real-world populations can only at best approximate a normal distribution.

  4. Ariew et al.’s (2017) treatment of Galton’s methodology is contested by Witteveen (2019). Witteveen’s objections are mostly historical and concern the Galton case particularly. Since my ambit is to unpack the SAE as a general explanatory framework, these objections will not be addressed here.

  5. A further step in demonstrating that biological populations which involve heredity could be represented as stochastic ensembles are Galton’s experiments with sweet peas. These details are left out here since focus is trained mostly at the primary explanatory moves in the case. For these details, see Ariew et al. (2017), pp. 67–68.

  6. One may object that this list (D1-D3) is not exhaustive since it excludes possibilities such as D4: “The gas is not an SAE and it could be either causal/non-causal” or D5: “The gas is an SAE and it could be either causal/non-causal.” The point of O2 is to show that whichever way the causal/non-causal status of SAEs is filled out in a determinate fashion, the SAE account as presently constructed is problematic. Falling back on agnosticism fails to settle the issue since each of the determinate causal/non-causal possibilities imply difficulties for the SAE account.

  7. This inquiry parallels the debate in the philosophy of physics over the nature of continuum and infinite idealizations whereby the macro-level theory fails to reduce to the micro-level theory. This gives rise to a similar question about the status of these idealizations: are they explanatorily indispensable in principle or rather explanatorily dipsensable (Shech 2013; Fletcher et al. 2019).

  8. As may be apparent from these two criteria, the REDC condition is clearly influenced by Lewis’ “Best Systems Analysis” of lawhood (Lewis 1994).

  9. Further examples of topological mathematical explanations are Pincock’s “Bridges of Königsberg case (2007) and Lange’s double pendulum case (Lange 2013). Huneman (2010) includes a further catalogue of such cases.

  10. For a clearer exposition, I have avoided constructing these arguments as valid ones here.

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Acknowledgements

The author would like to thank Andre Ariew for helpful conversations pertaining to the draft.

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  1. University of Missouri-Columbia, 438 Strickland Hall, Columbia, MO, 65201, USA

    Travis L. Holmes

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Holmes, T.L. Unifying statistically autonomous and mathematical explanations. Biol Philos 36, 33 (2021). https://doi.org/10.1007/s10539-021-09808-z

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