State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by the (...) grue predicate. (shrink)

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these (...) paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance with (...) Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make (...) the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (shrink)

This paper explores the options available to the anti-realist to defend a Quinean empirical under-determination thesis using examples of dualities. I first explicate a version of the empirical under-determination thesis that can be brought to bear on theories of contemporary physics. Then I identify a class of examples of dualities that lead to empirical under-determination. But I argue that the resulting under-determination is benign, and is not a threat to a cautious scientific realism. Thus dualities are not new ammunition for (...) the anti-realist. The paper also shows how the number of possible interpretative options about dualities that have been considered in the literature can be reduced, and suggests a general approach to scientific realism that one may take dualities to favour. (shrink)

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such absences ‘the frontiers of science', where background scientific (...) theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science. (shrink)