Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)

Computer scientists have provided a distinct justification of Occam’s Razor. Using the probably approximately correct framework, they provide a theorem that they claim demonstrates that we should favor simpler hypotheses. The argument relies on a philosophical interpretation of the theorem. I argue that the standard interpretation of the result in the literature is misguided and that a better reading does not, in fact, support Occam’s Razor at all. To this end, I state and prove a very similar theorem that, if (...) interpreted the same way, would justify the contradictory Anti-Occam’s Razor—the principle that we should favor more complex hypotheses. (shrink)

Behavioural flexibility is often treated as the gold standard of evidence for more sophisticated or complex forms of animal cognition, such as planning, metacognition and mindreading. However, the evidential link between behavioural flexibility and complex cognition has not been explicitly or systematically defended. Such a defence is particularly pressing because observed flexible behaviours can frequently be explained by putatively simpler cognitive mechanisms. This leaves complex cognition hypotheses open to ‘deflationary’ challenges that are accorded greater evidential weight precisely because they offer (...) putatively simpler explanations of equal explanatory power. This paper challenges the blanket preference for simpler explanations, and shows that once this preference is dispensed with, and the full spectrum of evidence—including evolutionary, ecological and phylogenetic data—is accorded its proper weight, an argument in support of the prevailing assumption that behavioural flexibility can serve as evidence for complex cognitive mechanisms may begin to take shape. An adaptive model of cognitive-behavioural evolution is proposed, according to which the existence of convergent trait–environment clusters in phylogenetically disparate lineages may serve as evidence for the same trait–environment clusters in other lineages. This, in turn, could permit inferences of cognitive complexity in cases of experimental underdetermination, thereby placing the common view that behavioural flexibility can serve as evidence for complex cognition on firmer grounds. (shrink)

Statistical learning theory is often associated with the principle of Occam’s razor, which recommends a simplicity preference in inductive inference. This paper distills the core argument for simplicity obtainable from statistical learning theory, built on the theory’s central learning guarantee for the method of empirical risk minimization. This core “means-ends” argument is that a simpler hypothesis class or inductive model is better because it has better learning guarantees; however, these guarantees are model-relative and so the theoretical push towards simplicity is (...) checked by our prior knowledge. (shrink)

Putnam construed the aim of Carnap’s program of inductive logic as the specification of a “universal learning machine,” and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap’s program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff–Levin proposal is (...) successful in this respect. I expose the general strategy to evade Putnam’s argument, leading to a broader discussion of the outer limits of mechanized induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam’s impossibility claim. (shrink)