Online research in philosophy

From a reliabilist point of view, our inferential practices make us into instruments for determining the truth value of hypotheses where, like all instruments, reliability is a central virtue. I apply this perspective to second-order inductions, the inductive assessments of inductive practices. Such assessments are extremely common, for example whenever we test the reliability of our instruments or our informants. Nevertheless, the inductive assessment of induction has had a bad name ever since David Hume maintained that any attempt to justify induction by means of an inductive argument must beg the question. I will consider how the inductive justification of induction fares from the reliabilist point of view. I will also consider two other wellknown arguments that can be construed as inductive assessments of induction. One is the miracle argument, according to which the truth of scientific theories should be inferred as the best explanation of their predictive success; the other is the disaster argument, according to which we should infer that all present and future theories are false on the grounds that all past theories have been found to be false.

From a reliabilist point of view, our inferential practices make us into instruments for determining the truth value of hypotheses where, like all instruments, reliability is a central virtue. I apply this perspective to second-order inductions, the inductive assessments of inductive practices. Such assessments are extremely common, for example whenever we test the reliability of our instruments or our informants. Nevertheless, the inductive assessment of induction has had a bad name ever since David Hume maintained that any attempt to justify induction by means of an inductive argument must beg the question. I will consider how the inductive justification of induction fares from the reliabilist point of view. I will also consider two other wellknown arguments that can be construed as inductive assessments of induction. One is the miracle argument, according to which the truth of scientific theories should be inferred as the best explanation of their predictive success; the other is the disaster argument, according to which we should infer that all present and future theories are false on the grounds that all past theories have been found to be false.

The problem of valid induction could be stated as follows: are we justified in accepting a given hypothesis on the basis of observations that frequently confirm it? The present paper argues that this question is relevant for the understanding of Machine Learning, but insufficient. Recent research in inductive reasoning has prompted another, more fundamental question: there is not just one given rule to be tested, there are a large number of possible rules, and many of these are somehow confirmed by the data — how are we to restrict the space of inductive hypotheses and choose effectively some rules that will probably perform well on future examples? We analyze if and how this problem is approached in standard accounts of induction and show the difficulties that are present. Finally, we suggest that the explanation-based learning approach and related methods of knowledge intensive induction could be, if not a solution, at least a tool for solving some of these problems.

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.

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive rules are formulated, does not go deep enough in representing the kind of information used in inductive inferences. As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction. In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are "quality dimensions". In relation to such a representation it is possible to define "natural" properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems.

For several years, through the “material theory of induction,” I have urged that inductive inferences are not licensed by universal schemas, but by material facts that hold only locally (Norton, 2003, 2005). My goal has been to defend inductive inference against inductive skeptics by demonstrating when and how inductive inferences are properly made. Since I have always admired Peter Achinstein as a staunch defender of induction, it was a surprise when Peter..

In this paper I want to cast doubt on the claim that there is a legitimate process of reasoning to the best explanation which can serve as an alternative to either straightforward inductive reasoning or a combination of inductive and deductive reasoning. I shall argue a) that paradigmatic cases of acceptable arguments to the best explanation must be considered enthymemes and b) that when the suppressed premises are made explicit we have all of the premises we need to present either a straightforward inductive argument or an argument employing both induction and deduction.

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that Hume’s celebrated “problem of induction” can no longer be set up and is thereby dissolved.

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction.