Turning the tables on Hume

Certain prior credence distributions concerning the future lead to inductivism, and others lead to inductive skepticism. I argue that it is difficult to consider the latter to be reasonable. I do not prove that they are not, but at the end of the paper, the tables are turned: in line with pre-philosophical intuitions, inductivism has retaken its place as the most reasonable default position, while the skeptic is called on to supply a novel argument for his. The reason is as follows. There are certain possibilities concerning the functioning of the world that, if assigned positive credence, support inductivism. Prima facie, one might think that the alternatives to those possibilities, if assigned similar or more credence, cancel out that support. However, I argue that it is plausible that reasonable credence distributions are such that the alternatives at most cancel themselves out, and thus leave the support for inductivism intact.

1. This is in opposition to, e.g., de Finetti (1937), who denied that there is such a thing as objective probabilities in addition to subjective ones.

2. This is in opposition to, e.g., Norton (2021).

3. This is perhaps in opposition to Howson (2000), but his book’s finale makes that unclear.

4. Atkinson and Peijnenburg (2017) have proved that infinitely descending hierarchies of probabilities are—with the exception of a few limit cases—not only well-defined but surprisingly well-behaved. Atkinson, Peijnenburg, and I are members of a growing group of believers of infinitism as the correct solution to Agrippa’s trilemma. The group also includes Klein (1998), Fantl (2003), and Aikin (2011).

5. See Huemer ( 2017, Sect. 5) for a similar view.

6. “At least as much” applies to the simplest example where $P(A_i)=P({\overline{A}}_i)=\frac{1}{2}$. In the general case, it should instead be “at least $\frac{P(A_i{)}^9}{P(A_i{)}^5\cdot P({\overline{A}}_i{)}^4}$ times as much.”

7. Note that it is mathematically possible that for every such pair of a ${\pi }_1$ and a ${\pi }_2$, the ratio of credence stays constant or changes in favor of the latter, and yet inductivism fails to obtain. This can happen if the collective credence for one such pair, where the ratio is and stays in favor of ${\pi }_1$, increases sufficiently while the collective credence for another such pair, where the ratio is in favor of ${\pi }_2$, decreases sufficiently. However, after the discussion in chapter 4, Stefan is wise enough to refrain from attempting an objection based on this: there is no plausible way to argue that Ingrid is right, but that everything nevertheless balances out in a skeptical equilibrium.

8. Alternatively, “non-green” could replace “blue” in the definition of “grue”.

9. BonJour gives an argument for inductivism himself in the final chapter of the book. It is a bad one that involves the standard fallacy of assuming that, in connection with a hypothesis test, a low p-value by itself implies that the non-null hypothesis is likely true. Simply swap my argument for inductivism in instead of his in the book, and you will have a coherent position. The result will not exactly by my position—I do not agree with BonJour about everything else—but I will not detail how else I diverge from him here.

I first explored the basic idea of this paper in a bachelor’s thesis written in 2003. Back then, I received help from Finn Guldmann, Jens Ulrik Hansen, Andreas Johnsen, Martin Klitgaard, and Thomas Vass. I returned to the subject of induction and started work on this paper in 2019. Since then, I have benefited from feedback and other assistance from Robert Israel, Robert Smithson, Yan Chunling, David Storrs-Fox, Wu Tungying, Wang Yafeng, Naoyuki Kajimoto, David Colaco, the audiences for talks in Moscow and Munich, and the anonymous reviewers.

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1. Copenhagen, Denmark

   Casper Storm Hansen

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Correspondence to Casper Storm Hansen.

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