Induction

It is shown that as knowledge is structured, it comes in modules. This provides different " layers of reality ". Each layer of reality has its own distinctive inductive logic which may differ from that of the others. All this is woven together to form a " web of induction " in a multidimensional space. It is the overall resilience, firmness and consistent interconnectedness of the whole web which justifies induction globally and which allows science to continue to "read" nature (...) using the inductive logic. (shrink)

The focus of this paper is to examine the problem of induction as a methodology for science. It also evaluates Karl Popper’s deductive approach as the suitable methodology for scientific research. Popper calls his theory ‘hypothetico-deductive methodology’. However, this paper argues the thesis that Popper’s theory of hypothetico-deductive methodology, which he claims is the only appropriate methodology of science is fraught with some theoretical difficulties, which makes it unacceptable. Popper’s logical asymmetry between verification and falsification, we argue, is philosophically untenable. (...) We argue the thesis for the complementarity of both inductive and deductive methodology in scientific investigation. This study seeks to establish the resonance of accepting both deductive and inductive reasoning as the basic methodologies upon which scientific research and discoveries proceed. (shrink)

Analogies have been traditionally recognized as a proper part of inductive procedures, akin to generalizations. Seldom, however, have they been presented as superior to generalizations, in the attainability of a higher degree of certitude for their conclusions or in other respects. Though Bacon definitely preferred analogy to generalization1, the tradition seems to me to go the other way-until the recent publication of works by Mary B. Hesse ([2], pp.21-28 and passim) and, perhaps, R. Harr6 ([1], pp.23-28 and passim). The aim (...) of the present note is to argue the following two points. First, generalizations proper are preferable to predictions from past observations to a single future observation, since the latter are ad hoc. Second, analogies are either generalizations proper-perhaps higher-level ones-or ad hoc. In any case, they are not more certain than generalizations, but they are still equally legitimate. (shrink)

After delineating the distinguishing features of pragmatism, and noting the resources that pragmatists have available to respond effectively as pragmatists to the two major objections to pragmatism, I examine and critically evaluate the various proposals that pragmatists have offered as a solution to the problem of induction, followed by a discussion of the pragmatic positions on the status of theoretical entities. Thereafter I discuss the pragmatic posture toward the nature of explanation in science. I conclude that pragmatism has (a) a (...) generally compelling solution to Hume's problem of induction; (b) no specific position on the status of theoretical entities, although something like the non-realism of the sort developed by van Fraassen seems a defensible candidate for most pragmatists in general, even though there are non-trivial objections to van Fraassen's position; and (c) central to the pragmatic conception of scientific explanation is the abandonment of our common conception of truth as a necessary condition for sentences to provide adequate explanations, and a drift in the direction of a contextualist account of explanation. (shrink)

Gian Aldo Antonelli and Cristina Bicchieri. Forward Induction.

There are two basic approaches to the problem of induction:the empirical one, which deems that the possibility of induction depends on how theworld was made (and how it works) and the logical one, which considers the formation(and function) of language. The first is closer to being useful for induction, whilethe second is more rigorous and clearer. The purpose of this paper is to create an empiricalapproach to induction that contains the same formal exactitude as the logical approach.This requires: (a) that (...) the empirical conditions for the induction are enunciatedand (b) that the most important results already obtained from inductive logic are againdemonstrated to be valid. Here we will be dealing only with induction by elimination,namely the analysis of the experimental confutation of a theory. The result will bea rule of refutation that takes into consideration all of the empirical aspect of theexperiment and has each of the asymptotic properties which inductive logic has shown tobe characteristic of induction. (shrink)

In this article I take a loose, functional approach to defining induction: Inductive forms of reasoning include those prima facie reasonable inference patterns that one finds in science and elsewhere that are not clearly deductive. Inductive inference is often taken to be reasoning from the observed to the unobserved. But that is incorrect, since the premises of inductive inferences may themselves be the results of prior inductions. A broader conception of inductive inference regards any ampliative inference as inductive, where an (...) ampliative inference is one where the conclusion ‘goes beyond’ the premises. ‘Goes beyond’ may mean (i) ‘not deducible from’ or (ii) ‘not entailed by’. Both of these are problematic. Regarding (i), some forms of reasoning might have a claim to be called ‘inductive’ because of their role in science, yet turn out to be deductive after all—for example eliminative induction (see below) or Aristotle’s ‘perfect induction’ which is an inference to a generalization from knowledge of every one of its instances. Interpretation (ii) requires that the conclusions of scientific reasoning are always contingent propositions, since necessary propositions are entailed by any premises. But there are good reasons from metaphysics for thinking that many general propositions of scientific interest and known by inductive inference (e.g. “all water is H2O”) are necessarily true. Finally, both (i) and (ii) fail to take account of the fact that there are many ampliative forms of inference one would not want to call inductive, such as counter-induction (exemplified by the ‘gambler’s fallacy’ that the longer a roulette wheel has come up red the more likely it is to come up black on the next roll). Brian Skyrms (1999) provides a useful survey of the issues involved in defining what is meant by ‘inductive argument’. Inductive knowledge will be the outcome of a successful inductive inference. But much discussion of induction concerns the theory of confirmation, which seeks to answer the question, “when and to what degree does evidence support an hypothesis?” Usually, this is understood in an incremental sense and in a way that relates to the rational credibility of a hypothesis: “when and by how much does e add to the credibility of h?”, although ‘confirms’ is sometimes used in an absolute sense to indicate total support that exceeds some suitably high threshold.. (shrink)

Peter Lipton argues that inference to the best explanation involves the selection of a hypothesis on the basis of its loveliness. I argue that in optimal cases, a form of eliminative induction takes place, which I call ‘Holmesian inference’. I illustrate Holmesian inference by reference to examples from the history of medicine.

An original study of the philosophical problems associated with inductive reasoning. Like most of the main questions in epistemology, the classical problem of induction arises from doubts about a mode of inference used to justify some of our most familiar and pervasive beliefs. The experience of each individual is limited and fragmentary, yet the scope of our beliefs is much wider; and it is the relation between belief and experience, in particular the belief that the future will in some respects (...) resemble the past and the unobserved the observed, which forms the subject of this book. Dr Blackburn's first aim is to state the problem of induction properly, to show that there does exist a genuine problem immune to the solutions in vogue at present, yet no tin principle insoluble. He gives an extended and original account of the concept of a reason and goes on to discuss prediction. In the end Dr Blackburn produces a rationale for belief in certain short-term predictions based on his reinterpretation of the classical principle of indifference. He claims that a justification for induction can be found along the lines he has suggested and must indeed be found there if anywhere. (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This approach explains (...) why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)