Justification of Induction

Nicholas Maxwell is not afraid of big ideas. As the title suggests, this book covers several sweeping topics: aside from those in the title, Maxwell discusses the methodology of social science, interdisciplinarity, quantum mechanics, and more besides. Given the 325-page word-length, this scope inevitably means that the ideas and arguments are frequently underdeveloped. However, despite this proportion of pages to topics, Maxwell's book is clear, accessible, and (most importantly) thought-provoking.

Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer ([2009]) offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the (...) opposite is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (shrink)

Hans Reichenbach’s pragmatic treatment of the problem of induction in his later works on inductive inference was, and still is, of great interest. However, it has been dismissed as a pseudo-solution and it has been regarded as problematically obscure. This is, in large part, due to the difficulty in understanding exactly what Reichenbach’s solution is supposed to amount to, especially as it appears to offer no response to the inductive skeptic. For entirely different reasons, the significance of Bertrand Russell’s classic (...) attempt to solve Hume’s problem is also both obscure and controversial. Russell accepted that Hume’s reasoning about induction was basically correct, but he argued that given the centrality of induction in our cognitive endeavors something must be wrong with Hume’s basic assumptions. What Russell effectively identified as Hume’s (and Reichenbach’s) failure was the commitment to a purely extensional empiricism. So, Russell’s solution to the problem of induction was to concede extensional empiricism and to accept that induction is grounded by accepting both a robust essentialism and a form of rationalism that allowed for a priori knowledge of universals. So, neither of those doctrines is without its critics. On the one hand, Reichenbach’s solution faces the charges of obscurity and of offering no response to the inductive skeptic. On the other hand, Russell’s solution looks to be objectionably ad hoc absent some non-controversial and independent argument that the universals that are necessary to ground the uniformity of nature actually exist and are knowable. This particular charge is especially likely to arise from those inclined towards purely extensional forms of empiricism. In this paper the significance of Reichenbach’s solution to the problem of induction will be made clearer via the comparison of these two historically important views about the problem of induction. The modest but important contention that will be made here is that the comparison of Reichenbach’s and Russell’s solutions calls attention to the opposition between extensional and intensional metaphysical presuppositions in the context of attempts to solve the problem of induction. It will be show that, in effect, what Reichenbach does is to establish an important epistemic limitation of extensional empiricism. So, it will be argued here that there is nothing really obscure about Reichenbach’s thoughts on induction at all. He was simply working out the limits of extensional empiricism with respect to inductive inference in opposition to the sort of metaphysics favored by Russell and like-minded thinkers. (shrink)

In a recent Philosophy of Science article Gerhard Schurz proposes meta-inductivistic prediction strategies as a new approach to Hume's. This comment examines the limitations of Schurz's approach. It can be proven that the meta-inductivist approach does not work any more if the meta-inductivists have to face an infinite number of alternative predictors. With his limitation it remains doubtful whether the meta-inductivist can provide a full solution to the problem of induction.

Goodman sustentou que o ajuste mútuo entre inferências indutivas particulares e princípios indutivos constitui a única justificação necessária para ambos. Porém, a sua caracterização desse ajuste, posteriormente denominado de “equilíbrio reflexivo”, foi superficial. Isso levantou dúvida sobre a sua adequação. Neste artigo, argumento que o equilíbrio reflexivo, corretamente caracterizado, fornece a única justificação necessária e a melhor que podemos dar para a prática indutiva.

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in (...) a situation where the VC theorem can be applied for the purpose we want it to. (shrink)

Scientific realism is the position that the aim of science is to advance on truth and increase knowledge about observable and unobservable aspects of the mind-independent world which we inhabit. This book articulates and defends that position. In presenting a clear formulation and addressing the major arguments for scientific realism Sankey appeals to philosophers beyond the community of, typically Anglo-American, analytic philosophers of science to appreciate and understand the doctrine. The book emphasizes the epistemological aspects of scientific realism and contains (...) an original solution to the problem of induction that rests on an appeal to the principle of uniformity of nature. (shrink)

I would like to assume that Reichenbach's distinction of Justification and Discovery lives on, and to seek arguments in his texts that would justify their relevance in this field. The persuasive force of these arguments transcends the contingent circumstances apart from which their genesis and local transmission cannot be made understandable. I shall begin by characterizing the context distinction as employed by Reichenbach in "Experience and Prediction" to differentiate between epistemology and science (1). Following Thomas Nickles and Kevin T. Kelly, (...) one can distinguish two meanings of the context distinction in Reichenbach's work. One meaning, which is primarily to be found in the earlier writings, conceives of scientific discoveries as potential objects of epistemological justification. The other meaning, typical for the later writings, removes scientific discoveries from the possible domain of epistemology. The genesis of both meanings, which demonstrates the complexity of the relationships obtaining between epistemology and science, can be made understandable by appealing to the historical context (2). Both meanings present Reichenbach with the task of establishing the autonomy of epistemology through the justification of induction. Finally, I shall expound this justification and address some of its elements of rationality characterizing philosophy of science(3). (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...) deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

The paper sketches an ontological solution to an epistemological problem in the philosophy of science. Taking the work of Hilary Kornblith and Brian Ellis as a point of departure, it presents a realist solution to the Humean problem of induction, which is based on a scientific essentialist interpretation of the principle of the uniformity of nature. More specifically, it is argued that use of inductive inference in science is rationally justified because of the existence of real, natural kinds of things, (...) which are characterized as such by the essential properties which all members of a kind necessarily possess in common. The proposed response to inductive scepticism combines the insights of epistemic naturalism with a metaphysical outlook that is due to s cientific realism. (shrink)

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is what grounds (...) reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves. (shrink)

Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the opposite (...) is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (shrink)

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-inductively to prefer the principle that corroboration is more successful over all human history than that, say, counter-corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-corroborationist alternative is beside the point. However, as whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we (...) are not required to act in the past, and his argument for rejecting the second presupposes induction. (shrink)

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

Claims to have solved the problem of induction are always stimulating, and especially so when the claim is put forward with the wit and sparkle of Professor Mellor's inaugural lecture The Warrant of Induction (Cambridge: Cambridge University Press, 1988). Unfortunately, however, Mellor's proposed solution is inadequate to its task.

I critically examine an evolutionary debunking argument against moral realism. The key premise of the argument is that there is no adequate explanation of our moral reliability. I search for the strongest version of the argument; this involves exploring how ‘adequate explanation’ could be understood such that the key premise comes out true. Finally, I give a reductio: in the sense in which there is no adequate explanation of our moral reliability, there is equally no adequate explanation of our inductive (...) reliability. Thus, the argument that would debunk our moral views would also, absurdly, debunk all inductive reasoning. (shrink)

Howson's critique of my essay on Hume's problem of induction levels two main charges. First, Howson claims that I have attributed to him an error that he never made, and in fact which he warned against in the very text that I cite. Secondly, Howson argues that my proposed solution to Hume's problem is flawed on technical and philosophical grounds. In response to the first charge, I explain how Howson's text justifies attributing to him the claim that the principle of (...) induction is shown to be inconsistent by Goodman's riddle. In regards to the second, I show that Howson's objections rest on misunderstandings of formal learning theory and on conflating the problem of induction with the problem of unconceived alternatives. (shrink)

A common criticism of Hume’s famous anti-induction argument is that it is vitiated because it fails to foreclose the possibility of an authentically probabilistic justification of induction. I argue that this claim is false, and that on the contrary, the probability calculus itself, in the form of an elementary consequence that I call Hume’s Theorem, fully endorses Hume’s argument. Various objections, including the often-made claim that Hume is defeated by de Finetti’s exchangeability results, are considered and rejected.

If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? I advance grounds for doubt.

In a recent article in this journal, Daniel Steel charges me with committing a fallacy in my discussion of inductive rules. I show that the charge is false, and that Steel's own attempt to validate enumerative induction in terms of formal learning theory is itself fallacious. I go on to argue that, contra Steel, formal learning theory is in principle incapable of answering Hume's famous claim that any attempt to justify induction will beg the question.

At the seventh international congress of Logic, Methodology, and Philosophy of Science, held at Salzburg in 1983, I was talking with John Searle when I glanced at my watch and exclaimed, I must run. I'm due to solve the problem of induction at 2.15. ‘Yes,’ he replied, I must go too; I'm due to solve the mind-body problem. I don't know how seriously he meant his remark, but I did actually believe that I had cracked this old problem in the (...) Epilogue of my Science and Scepticism,1 the manuscript of which was then with the publisher. In that book I drew a sharp distinction between the problem which faces a theoretical scientist trying to select, out of several competing theories, the one that best fulfils the aim of science, and the pragmatic problem which faces an applied scientist or practical decision-maker trying to select, out of several competing hypotheses, the one that offers the best guidance. I had what I still regard as a viable solution to the theoreticians problem. It aid that theoreticians should prefer that theory, if there is one, that is the best corroborated; for on a certain non-trivial but uncontroversial assumption about what kinds of test have been made, the best corroborated theory will best satisfy what I claimed to be the optimum aim for science: it will be deeper and wider than its rivals and, moreover, possibly true, given all the reported outcomes of tests in its field. For present purposes we can forget the explications I offered for ‘deeper’ and ‘wider’. As to ‘possibly true’: this reflects the abandonment of hopes that science can arrive at theories that are certainly true, or at least have a high probability of being true, or at the very least have had their probability raised by the experimental evidence. (shrink)

David Armstrong once argued that to solve the problem of induction with inference to the best explanation we need an anti-Humean conception of law. Some Humeans have argued that this argument begs the question against Humeanism. In this paper, I propose a new argument for the same conclusion which is not vulnerable to this criticism. In particular, I argue that explanationist approaches to the problem of induction that are combined with Humeanism is internally incoherent.

According to Hume, the paradigm type of inductive reasoning, or—to use his terminology 1—"the inference we draw from cause to effect", involves a constant conjunction. "We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them.... Thus we remember to have seen that species of object we call flame, and to have felt that species of sensation we call heat. We likewise (...) call to mind their constant conjunction in all past instances. Without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the. (shrink)

Nelson Goodman cast the ‘problem of induction’ as the task of articulating the principles and standards by which to distinguish valid from invalid inductive inferences. This paper explores some logical bounds on the ability of a rational reasoner to accomplish this task. By a simple argument, either an inductive inference method cannot admit its own fallibility, or there exists some non-inferable hypothesis whose non-inferability the method cannot infer (violating the principle of ‘negative introspection’). The paper discusses some implications of this (...) limited self-knowledge for the justifiability of inductive inferences, auto-epistemic logic, and the epistemic foundations of game theory. (shrink)

Hume's sceptical arguments regarding induction have not yet been successfully answered. However, I shall not in this paper discuss the important attempts to answer Hume since that would be too lengthy a task. On the supposition that Hume's sceptical arguments have not been met, the empirical world is a place where, as the popular metaphor goes, all the glue has been removed. For the Humean sceptic, the only empirical knowledge that we can have is given to us in immediate perception. (...) We have no reason to believe that the patterns of future events will in any way resemble patterns of events in the present or past. We have no reason to believe even that present events not observed resemble present events that are observed, or that knowledge of past and present can be any guide in making new discoveries about what took place in the past. What we have is an ideal setting for the calculation of a priori probabilities. We have a field of distinct events having no logical or evidential ties to one another. The attempt to justify induction that I wish to present is an appeal to a priori probability. (shrink)

The necessitarian solution to the problem of induction involves two claims: first, that necessary connections are justified by an inference to the best explanation; second, that the best theory of necessary connections entails the timeless uniformity of nature. In this paper, I defend the second claim. My arguments are based on considerations from the metaphysics of laws, properties, and fundamentality.

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

"Understanding Scientific Progress constitutes a potentially enormous and revolutionary advancement in philosophy of science. It deserves to be read and studied by everyone with any interest in or connection with physics or the theory of science. Maxwell cites the work of Hume, Kant, J.S. Mill, Ludwig Bolzmann, Pierre Duhem, Einstein, Henri Poincaré, C.S. Peirce, Whitehead, Russell, Carnap, A.J. Ayer, Karl Popper, Thomas Kuhn, Imre Lakatos, Paul Feyerabend, Nelson Goodman, Bas van Fraassen, and numerous others. He lauds Popper for advancing beyond (...) verificationism and Hume’s problem of induction, but faults both Kuhn and Popper for being unable to show that and how their work could lead nearer to the truth." —Dr. Lloyd Eby teaches philosophy at The George Washington University and The Catholic University of America, in Washington, DC. (shrink)

One version of the problem of induction is how to justify hypotheses in the face of data. Why advance hypothesis A rather than B — or in a probabilistic context, why attach greater probability to A than B? If the data arrive as a stream of observations (distributed through time) then the problem is to justify the associated stream of hypotheses. Several perspectives on this problem have been developed including Bayesianism (Howson and Urbach, 1993) and belief-updating (Hansson, 1999). These are (...) broad families of approaches; the citations are meant just as portals. (shrink)

The basic task of the essay is to exhibit science as a rational enterprise. I argue that in order to do this we need to change quite fundamentally our whole conception of science. Today it is rather generally taken for granted that a precondition for science to be rational is that in science we do not make substantial assumptions about the world, or about the phenomena we are investigating, which are held permanently immune from empirical appraisal. According to this standard (...) view, science is rational precisely because science does not make a priori metaphysical presuppositions about the world forever preserved from possible empirical refutation. It is of course accepted that an individual scientist, developing a new theory, may well be influenced by his own metaphysical presuppositions. In addition, it is acknowledged that a successful scientific theory, within the context of a particular research program, may be protected for a while from refutation, thus acquiring a kind of temporary metaphysical status, as long as the program continues to be empirically progressive. All such views unite, however, in maintaining that science cannot make permanent metaphysical presuppositions, held permanently immune from objective empirical evaluation. According to this standard view, the rationality of science arises, not from the way in which new theories are discovered, but rather from the way in which already formulated theories are appraised in the light of empirical considerations. And the fundamental problem of the rationality of science—the Humean problem of induction— concerns precisely the crucial issue of the rationality of accepting theories in the light of evidence. In this essay I argue that this widely accepted standard conception of science must be completely rejected if we are to see science as a rational enterprise. In order to assess the rationality of accepting a theory in the light of evidence it is essential to consider the ultimate aims of science. This is because adopting different aims for science will lead us, quite rationally, to accept different theories in the light of evidence. I argue that a basic aim of science is to explain. At the outset science simply presupposes, in a completely a priori fashion, that explanations can be found, that the world is ultimately intelligible or simple. In other words, science simply presupposes in an a priori way the metaphysical thesis that the world is intelligible, and then seeks to convert this presupposed metaphysical theory into a testable scientific theory. Scientific theories are only accepted insofar as they promise to help us realize this fundamental aim. At once a crucial problem arises. If scientific theories are only accepted insofar as they promise to lead us towards articulating a presupposed metaphysical theory, it is clearly essential that we can choose rationally, in an a priori way, between all the very different possible metaphysical theories that can be thought up, all the very different ways in which the universe might ultimately be intelligible. For holding different aims, accepting different metaphysical theories conceived of as blueprints for future scientific theories will, quite rationally, lead us to accept different scientific theories. Thus it is only if we can choose rationally between conflicting metaphysical blueprints for future scientific theories that we will be in a position to appraise rationally the acceptability of our present day scientific theories. We thus face the crucial problem: How can we choose rationally between conflicting possible aims for science, conflicting metaphysical blueprints for future scientific theories ? It is only if we can solve this fundamental problem concerning the aims of science that we can be in a position to appraise rationally the acceptability of existing scientific theories. There is a further point here. If we could choose rationally between rival aims, rival metaphysical blueprints for future scientific theories, then we would in effect have a rational method for the discovery of new scientific theories! Thus we reach the result: there is only a rational method for the appraisal of existing scientific theories if there is a rational method of discovery. I shall argue that the aim-oriented theory of scientific inquiry to be advocated here succeeds in exhibiting science as a rational enterprise in that it succeeds in providing a rational procedure for choosing between rival metaphysical blueprints: it thus provides a rational, if fallible, method of discovery, and a rational method for the appraisal of existing scientific theories—thus resolving the Humean problem. In Part I of the essay I argue that the orthodox conception of science fails to exhibit science as a rational enterprise because it fails to solve the Humean problem of induction. The presuppositional view advocated here does however succeed in resolving the Humean problem. In Part II of the essay I spell out the new aim-oriented theory of scientific method that becomes inevitable once we accept the basic presuppositional viewpoint. I argue that this new aim oriented conception of scientific method is essentially a rational method of scientific discovery, and that the theory has important implications for scientific practice. (shrink)

In this paper, I respond to the paper “The Validation of Induction” by Robert Pargetter and John Bigelow (Australasian Journal of Philosophy, 75:1, 1997), in which the authors propound the thesis that the arguments commonly thought of as good inductive arguments “properly construed, are deductively valid”. I maintain that they have not established this claim, and neither have they established a number of associated but logically independent claims that they make about inductive arguments and inductive inferences.