Abstract
The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated.
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Notes
This objection, like all we list here, is disputed, and we do not take a stand on its success. For instance, this objection explains why we keep successful theories, but not how theories can be predictively successful. See, e.g., Alai 2014b, § 7.
Much turns on how approximately true is cashed out; “partly true” coupled with selective realism explains successful predictions (cf. Musgrave, 2006–2007).
This is not entirely accurate as you can tack on a bunch of superfluous (false) premises to a valid argument form and end up with a valid argument. For now, nothing of any importance turns on making this formulation precise so, for the sake of your sanity and ours, we’ll leave it as is.
We have not yet provided a complete defense of scientific realism, as some constructivists may be happy to embrace our conclusions here. We believe this framework provides a starting point for an argument against the constructivists as well, but the wide range of constructivist views and the complex and nuanced nature of the argument we plan to advance forces us to pursue that project elsewhere.
Though the ultimate probabilistic outcome will depend greatly on the exact ratios of “large number” “novel” and “improbable”. A great many novel, nontautological, but nevertheless probable (“easy”) predictions can still count in favor of T, just as much as, e.g., relatively fewer but harder predictions.
The transformation from “prohibitively improbable” to “exceedingly likely” is due to the law of total probability: if the probability of one disjunct is prohibitively low, then the probability of the other disjunct(s) is exceedingly likely. Alternatively, affirming the premise “If Pr(P) = prohibitively low, then ~ P” and then drawing the implication “~P” turns the inference into straightforward disjunctive syllogism.
It may, however, appear that some versions of the TNMA do not involve a comparative element. The TNMA is often reconstructed as an Argument to the only Explanation (IoE), where realism is proffered as the only explanation of predictive success (Psillos, 1999; Alai, 2014a, § 1; 2014c, § 3–5). If realism is the only explanation of predictive success, then it may appear that the TNMA does not involve a comparative element after all. This appearance is, however, misleading. The inferential pattern in IoE is generally justified as an extension of IBE (Lipton, 1993, 2004; Douven, 2021, § 1.2). IoE should thus be understood as a limiting case of IBE where the explanation in question is trivially the best explanation in virtue of being the only available explanation. The comparative component of IBE remains in IoE, though this can be disguised by the fact that, in IoE, the comparative claim is trivially true.
Suppose we come up with a random formula for predicting the path of a thrown ball. To think such a formula has a 95% chance of even roughly predicting the path is, in a word, absurd. Even cases of binary prediction (particle is negatively charged or not) are hard to get above 50% without losing novelty.
Note that this might not be sufficient to trust that T is true, but this is not our claim. Much depends on the kind of claim as well—is it one of great precision, or just to such-and-such significant digits? Cf. § 6.4 and § 6.5 on this point.
Consider, to take just one example, the Standard Model of physics. The Standard Model is a set of theories that describes three of the four known fundamental forces (electromagnetic, weak, and strong interactions; it excludes gravity) and classifies all elementary particles (6 leptons, 6 quarks, 4 gauge bosons, and the Higgs boson). Just these entities’ theories alone that make up the Standard Model adds up to 20 different theories, all of which interact with each other, constantly, all of the time. 0.9520 = 0.358.
Ptolemy’s system was a vast improvement on, say, Hipparchus’s system, in which common errors could be as great as 30 degrees. Nevertheless, Ptolemy’s system still had common errors up to 10 degrees—that is to say, merely enormous, rather than catastrophic.
See (Baker, 2016) for a historical and contemporary review.
Hence our repeated emphasis on improbability and the distinction between “easy” and “hard” guesses, which would drive this number down. Nevertheless, hard guesses, once known, can be accommodated, and thus can also be p-hacked in this way, requiring—as we will conclude shortly—that we recover novelty.
This kind of account has, of course, been developed elsewhere. Of particular interest is the work of deployment realists previously cited.
Assuming falsely that they were truly predictive, rather than merely retrodictive, as was actually the case. Accurate retrodiction is no surprise!
That is, some kind of epicyclic geocentrism that orders the planets correctly. Indeed, Einstein and Infeld note that such a view could even account for the elliptical orbits of the various planets in their textbook on the history of physics. Relativity affirms that one can formulate physical laws such that they hold true and correctly predict the paths of celestial objects regardless of what is chosen as the “center” of the solar system. The planets move in ellipses relative to the Sun, but the planets do not move elliptically relative to the Earth (Infeld, 1966, 212).
Though not these authors’ endorsed position, structural realism also can provide an answer to this objection. Indeed, any adequately realist account of theory change should be satisfactory.
For an interesting series of hard cases for deployment realism or replies attempting accommodation, see Laudan (1981), Psillos (1994, 2022), Lyons (2002, 2003), Chang (2003), Doppelt (2005), Alai (2014d, 2017, 2018, 2021), Vickers (2017) Boge (2021), and Tulodziecki (2021). For more theoretical criticisms, see Stanford (2006), Lyons (2006), Peters (2014).
Whether this entails that the DNMA uses deployment realism or that the DNMA uses a parallel but different scope-restricting move does not matter to the authors. For an alternative scope-restricting move that is not deployment realism, see § 6.4. Structural realism, though not the authors’ view, may also provide an adequate solution.
Hard and easy predictions are just descriptors for how improbable a lucky guess would be. For binary questions, it would be easy to get a lucky guess, since the probably is 50/50. For Newton, predicting that an undiscovered planet existed somewhere in the universe would be easy, but predicting the position and mass of an undiscovered planet is quite hard. See Alai 2014d, 275–276.
For some instances of this, consider how it has made predictions about planetary bodies, bodies on earth, underwater, bodies on planes, and so on. There are also corroborative ways to get independence, such as when it interacts with other laws.
The view has gained significant support since it came into the mainstream. Cf. Cartwright 1999.
Statistical mechanics may be an example of integration between classical or quantum mechanics and more macro phenomena, such as Einstein’s (1905) aforementioned ability to account for Brownian motion with such tools.
One might not need to embrace isolationism in its entirety, or isolationism as such at all. Again, what is most important is that one find a way to make two moves: (i) confirm that there “is truth” (here, with isolationism, an instance of the law) to the successful theory, and (ii) denying that the realist is committed to the overgeneralization of that true instance. Musgrave (2006–2007), for instance, provides one such answer that parallels the moves we make here without explicitly committing to isolationism, though the views and moves appear to be kindred spirits.
So reasonably exact, in fact, that NASA uses Newtonian physics to calculate trajectories for their nearby space missions, sans Mercury due to the proximity of the Sun.
Some deployment realists have made exactly this move. See, e.g., Alai (2014d).
As anti-realists can be isolationists, it should be clear that the inverse is not true. The isolationist need not embrace deployment realism.
Kitcher’s (1982) actual example is too long to place in the text of this paper; it has to do with the tenrecs of Madagascar and four novel predictions on its proposed evolutionary history.
We thank an anonymous reviewer for very helpful comments in this section, some of which we have simply adopted wholesale.
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Acknowledgements
We would like to give special thanks to Evan Fales for his encouragement and feedback on the early stages of this project. We are also grateful for three anonymous reviewers for their helpful comments. Finally, we wanted to thank Robert Lazo, Sara Aronowitz, and Curtis Howd for multiple fruitful conversations on various parts of the manuscript and Anna Bella Sicilia, Lenin Vazquez-Toledo, and Max Kramer for their discussions, especially on § 5.
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Golemon, L., Graber, A. A deductive variation on the no miracles argument. Synthese 201, 81 (2023). https://doi.org/10.1007/s11229-023-04078-6
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DOI: https://doi.org/10.1007/s11229-023-04078-6