According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...) be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification. (shrink)

The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind raven is more natural than the kind black. (...) The solution applies to any generalization “All F’s are G” in which F is more natural than G. (shrink)

Many philosophers agree that Hume was not simply objecting to inductive inferences on the grounds of their logical invalidity and that his description of our inductive behaviour was inadequate, but none the less regard his argument against induction as irrefutable. I argue that this constellation of opinions contains a serious tension. In the light of the tension, I re-examine Hume’s actual sceptical argument and show that the argument as it stands is valid but unsound. I argue that it can only (...) be converted into a sound one if our inductive behaviour can be characterized as a process of rule-governed ampliation. Drawing on some Bayesian ideas, I argue that our inductive behaviour probably cannot be characterized in that way, so our immunity from Hume is secure. Finally, I compare my response to Hume’s argument with some other well known responses. (shrink)

Many philosophers have claimed that Bayesianism can provide a simple justification for hypothetico-deductive inference, long regarded as a cornerstone of the scientific method. Following up a remark of van Fraassen, we analyze a problem for the putative Bayesian justification of H-D inference in the case where what we learn from observation is logically stronger than what our theory implies. Firstly, we demonstrate that in such cases the simple Bayesian justification does not necessarily apply. Secondly, we identify a set of sufficient (...) conditions for the mismatch in logical strength to be justifiably ignored as a "harmless idealization''. Thirdly, we argue, based upon scientific examples, that the pattern of H-D inference of which there is a ready Bayesian justification is only rarely the pattern that one actually finds at work in science. Whatever the other virtues of Bayesianism, the idea that it yields a simple justification of a pervasive pattern of scientific inference appears to have been oversold. (shrink)

It is customary to distinguish experimental from purely observational sciences. The former include physics and molecular biology, the latter astronomy and palaeontology. Experiments involve actively intervening in the course of nature, as opposed to observing events that would have happened anyway. When a molecular biologist inserts viral DNA into a bacterium in his laboratory, this is an experiment; but when an astronomer points his telescope at the heavens, this is an observation. Without the biologist’s handiwork the bacterium would never have (...) contained foreign DNA; but the planets would have continued orbiting the sun whether or not the astronomer had directed his telescope skyward. The observational/experimental distinction would probably be difficult to make precise 1, as the notion of an ‘intervention’ is not easily defined, but it is intuitively fairly clear, and is frequently invoked by scientists and historians of science. Experimentation, or ‘putting questions to nature’, is often cited as a hallmark of the modern scientific method, something that permitted the enormous advances of the last 350 years. And it is sometimes said that the social sciences lag behind the natural because controlled experiments cannot be done so readily in the former. Moreover in certain sciences, e.g. epidemiology, students are explicitly taught that experimental data is preferable to observational data, particularly for doing causal inference. So the distinction between observational and experimental science has quite wide currency, and is often regarded as methodologically significant. Surprisingly, mainstream philosophy of science has had rather little to say about the observational/experimental distinction. 2 For example, discussions of confirmation usually invoke a notion of ‘evidence’, to be contrasted with ‘theory’ or ‘hypothesis’; the aim is to understand how the evidence bears on the hypothesis. But whether this ‘evidence’ comes from observation or experiment generally plays no role in the discussion; this is true …. (shrink)

Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a variety (...) of other responses and is shown to differ from all of them. (shrink)

R. C. Jeffrey has proposed probabilism as a solution to Hume's problem of justifying induction. This paper shows that the assumptions of his Estimation Theorem, used to justify induction, can be weakened to provide a more satisfactory interpretation. It is also questioned whether the use of probabilism adds significantly to our understanding (or even Hume's understanding) of the problem of induction.

Laudan famously argued that neither truth nor approximate truth can be part of an explanation of a scientific theory's predictive success because in the history of science there were theories that enjoyed some limited success but now are considered outright false. The power of his argument lay in the many historic examples he listed . Realists have disputed that all theories on Laudan's list can be regarded as predictively successful but let's suppose momentarily that at least some exist that support (...) his point. In this case, there are historic false theories that made some true predictions. We are aiming for a general explanation of a theory's predictive success and hence these false theories necessarily are on board. Now, Laudan also argues that historic false theories – the downright false ones and the ones we nowadays judge as strictly false, but approximately true – do not in any principled sense differ from the ones we presently accept. These theories seem to present a good basis for inductively inferring that any presently accepted scientific theory is actually false. Many presently accepted theories certainly are predictively successful to a great extent and certainly their success should be covered by an acceptable explanation. Since there seems to be inductive support for the conclusion that …. (shrink)