That past patterns may continue in many different ways has long been identified as a problem for accounts of induction. The novelty of Goodman’s ”new riddle of induction” lies in a meta-argument that purports to show that no account of induction can discriminate between incompatible continuations. That meta-argument depends on the perfect symmetry of the definitions of grue/bleen and green/blue, so that any evidence that favors the ordinary continuation must equally favor the grue-ified continuation. I argue that this very dependence (...) on the perfect symmetry defeats the novelty of the new riddle. The symmetry can be obtained in contrived circumstances, such as when we grue-ify our total science. However, in all such cases, we cannot preclude the possibility that the original and grue-ified descriptions are merely notationally variant descriptions of the same physical facts; or if there are facts that separate them, these facts are ineffable, so that no account of induction should be expected to pick between them. In ordinary circumstances, there are facts that distinguish the regular and grue-ified descriptions. Since accounts of induction can and do call upon these facts, Goodman’s meta-argument cannot provide principled grounds for the failure of all accounts of induction. It assures us only of the failure of accounts of induction, such as unaugmented enumerative induction, that cannot exploit these symmetry breaking facts. (shrink)

The principle of uniformity of nature has sometimes been invoked for the purpose of justifying induction. This principle cannot be established "a priori", And in the absence of a justification of induction, It cannot be established "a posteriori". There is no justification for assuming it as a postulate of science. Use of such a principle is, However, Neither sufficient nor necessary for a justification of induction. In any plausible form, It is too weak for that purpose, And hence, It is (...) insufficient. Since a justification which does not rely upon this principle can be given, It is not necessary. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

I discuss the philosophical significance of the statistical model selection criteria, in particular their relevance for philosophical of underdetermination. I present an easily comprehensible account of their simplest possible application and contrast it with their application to curve-fitting problems. I embed philosophers' earlier discussion concerning the situations in which the criteria yield implausible results into a more general framework. Among other things, I discuss a difficulty which is related to the so-called subfamily problem, and I show that it has analogies (...) in all legitimate applications of the model selection criteria, and that an analogy of Goodman's new riddle of induction can be formulated in only some of their applications. (shrink)

Scientists and decision makers rely on climate models for predictions concerning future climate change. Traditionally, physical processes that are key to predicting extreme events are either directly represented or indirectly represented. Scientists are now replacing physically based parameterizations with neural networks that do not represent physical processes directly or indirectly. I analyze the epistemic implications of this method and argue that it undermines the reliability of model predictions. I attribute the widespread failure in neural network generalizability to the lack of (...) process representation. The representation of climate processes adds significant and irreducible value to the reliability of climate model predictions. (shrink)

I discuss the philosophical significance of the statistical model selection criteria, in particular their relevance for philosophical problems of underdetermination. I present an easily comprehensible account of their simplest possible application and contrast it with their application to curve‐fitting problems. I embed philosophers' earlier discussion concerning the situations in which the criteria yield implausible results into a more general framework. Among other things, I discuss a difficulty which is related to the so‐called subfamily problem, and I show that it has (...) analogies in all legitimate applications of the model selection criteria, and that an analogy of Goodman's new riddle of induction can be formulated in only some of their applications. (shrink)

The model function for induction of Goodmans's composite predicate "Grue" was examined by analysis. Two subpredicates were found, each containing two further predicates which are mutually exclusive (green and blue, observed before and after t). The rules for the inductive processing of composite predicates were studied with the more familiar predicate "blellow" (blue and yellow) for violets and primroses. The following rules for induction were violated by processing "grue": From two subpredicates only one (blue after t) appears in the conclusion. (...) As a statement about a future and unobserved condition this subpredicate, however, is not projectible for induction whereas the only suitable predicate (green before t) does not show up in the conclusion. In a disjunction "a v b" where "a" is true and "b" false the disjunction is true. When, however, the only true component is dropped, what remains is necessarily false. An analogous mistake may be observed in the processing of "grue", where the only true component (green) was dropped in the conclusion. - As a potent criterion for correct inductions a check of the necessity of the conclusions is recommended. (shrink)

This is the first of two papers that use off-training set (OTS) error to investigate the assumption-free relationship between learning algorithms. This first paper discusses the senses in which there are no a priori distinctions between learning algorithms. (The second paper discusses the senses in which there are such distinctions.) In this first paper it is shown, loosely speaking, that for any two algorithms A and B, there are “as many” targets (or priors over targets) for which A has lower (...) expected OTS error than B as vice versa, for loss functions like zero-one loss. In particular, this is true if A is cross-validation and B is “anti-cross-validation” (choose the learning algorithm with largest cross-validation error). This paper ends with a discussion of the implications of these results for computational learning theory. It is shown that one cannot say: if empirical misclassification rate is low, the Vapnik-Chervonenkis dimension of your generalizer is small, and the training set is large, then with high probability your OTS error is small. Other implications for “membership queries” algorithms and “punting” algorithms are also discussed. (shrink)