In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical (...) reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (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)

Many solutions of the Goodman paradox have been proposed but so far no agreement has been reached about which is the correct solution. However, I will not contribute here to the discussion with a new solution. Rather, I will argue that a solution has been in front of us for more than two hundred years because a careful reading of Hume’s account of inductive inferences shows that, contrary to Goodman’s opinion, it embodies a correct solution of the paradox. Moreover, the (...) account even includes a correct answer to Mill’s question of why in some cases a single instance is sufficient for a complete induction, since Hume gives a well-supported explanation of this reliability phenomenon. The discussion also suggests that Bayesian theory by itself cannot explain this phenomenon. Finally, we will see that Hume’s explanation of the reliability phenomenon is surprisingly similar to the explanation given lately by a number of naturalistic philosophers in their discussion of the Goodman paradox. (shrink)

Many solutions of the Goodman paradox have been proposed but so far no agreement has been reached about which is the correct solution. However, I will not contribute here to the discussion with a new solution. Rather, I will argue that a solution has been in front of us for more than two hundred years because a careful reading of Hume's account of inductive inferences shows that, contrary to Goodman's opinion, it embodies a correct solution of the paradox. Moreover, the (...) account even includes a correct answer to Mill's question of why in some cases a single instance is sufficient for a complete induction, since Hume gives a well-supported explanation of this reliability phenomenon. The discussion also suggests that Bayesian theory by itself cannot explain this phenomenon. Finally, we will see that Hume's explanation of the reliability phenomenon is surprisingly similar to the explanation given lately by a number of naturalistic philosophers in their discussion of the Goodman paradox. (shrink)

This paper considers Norton’s Material Theory of Induction. The material theory aims inter alia to neutralize Hume’s Problem of Induction. The purpose of the paper is to evaluate the material theory's capacity to achieve this end. After pulling apart two versions of the theory, I argue that neither version satisfactorily neutralizes the problem.

Many epistemologists believe that the distinction between the genesis and the validity of a belief is a fundamental presupposition of adequate epistemological reflection. In this article it will be argued that the arguments for this majority conviction are not convincing. As an alternative it is suggested that the distin- ction between epistemic and non-epistemic procedures should be regarded as fundamental for epistemology.

Science seems to develop by inducing new knowledge from observation. However, it is hard to find a rational justification for induction. Popper offers one attempt to resolve this problem. Nursing theorists have tended to ignore or reject Popper, often on the false belief that he is a logical positivist (and hence hostile to qualitative research). Logical positivism claims that meaningful sentences containing any empirical content should ultimately be reducible to simple, observation statements. Popper refutes positivism by showing that there are (...) no such simple statements. He is not a positivist. For Popper, the scientist begins with problems and puts forward trial solutions. These are subjected to rigorous testing aimed at falsifying them. A new theoretical position is then reached in which the scientist knows either that the trial solutions are false or that they have not yet been falsified. Science is characterized by the fact that it tests its ideas through attempted falsification. Nonscience tests its ideas through attempted refutation. Nursing theory is a mixture of science and non-science. Popper’s method requires rigorous testing of theory in both realms. As such, some nursing theory should be discarded. Popper’s view faces at least two important criticisms. One is that a scientist can always reject an apparent falsification by instead altering some auxiliary hypothesis (e.g. denying the accuracy of the falsifying observation). Popper can deal with this argument by saying that defence of a theory in this way will eventually break down if the theory is false. The second criticism is that Popper’s method does ultimately draw upon induction. This criticism is true, but his method can be usefully adapted. An adapted from of Popper’s philosophy of science provides a good basis for nursing theory. (shrink)

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such absences ‘the frontiers of science', where background scientific (...) theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science. (shrink)

It is widely agreed that Hume's description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume's argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume's sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume committed a (...) quantifier-shift fallacy, i.e. inferred a statement of ?? form from one of ?? form. The implications of this diagnosis for the traditional problem of induction are briefly examined. (shrink)

It is widely agreed that Hume’s description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume’s argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume’s sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume committed a (...) quantifier-shift fallacy, i.e. inferred a statement of ∃∀ form from one of V∀∃ form. The implications of this diagnosis for the traditional problem of induction are briefly examined. The author suggests that, were his philosophy received, we must alter from the foundation the greatest part of the sciences. Hume 1740. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive inferences' with probability distributions (...) which assign probability to contingent propositions/events. (shrink)

In this paper, I consider the pessimistic induction construed as a deductive argument (specifically, reductio ad absurdum) and as an inductive argument (specifically, inductive generalization). I argue that both formulations of the pessimistic induction are fallacious. I also consider another possible interpretation of the pessimistic induction, namely, as pointing to counterexamples to the scientific realist’s thesis that success is a reliable mark of (approximate) truth. I argue that this interpretation of the pessimistic induction fails, too. If this is correct, then (...) the pessimistic induction is an utter failure that should be abandoned by scientific anti-realists. (shrink)

In a recent paper replying to the inductive sceptic, Samir Okasha says that the Humean argument for inductive scepticism depends on mistakenly construing inductive reasoning as based on a principle of the uniformity of nature. I dispute Okasha's argument that we are entitled to the background beliefs on which (he says) inductive reasoning depends. Furthermore, I argue that the sorts of theoretically impoverished contexts to which a uniformity-of-nature principle has traditionally been restricted are exactly the contexts relevant to the inductive (...) sceptic's argument, and (pace Okasha) are not at all remote from actual scientific practice. I discuss several scientific examples involving such contexts. (shrink)

With respect to inductive reasoning, there are at least two broad projects that have been of interest to philosophers. The first project is that of accurately describing paradigmatic instances of inductive reasoning in the sciences and in everyday life. Thus, we might ask, of some particular historical episode, how exactly Newton, or Darwin, or Einstein arrived at some conclusion on the basis of the evidence that was before him. The second project is one of justification. The task here is that (...) of showing why paradigmatic inductive reasoning is good reasoning, or why skeptical challenges which purport to undermine the legitimacy of such reasoning fail to do so. As I understand it, this second, justificatory project prominently includes, but is not limited to, the task of either solving or dissolving Hume’s skeptical critique of induction.[1] Neither of these projects is trivial. Indeed, many think that we are currently far from successfully completing either one. But in any case, it would seem that the descriptive project has a certain priority to the justification project. After all, how could one justify our inductive practices, or defend them against skeptical challenge, in the absence of some reasonably detailed and accurate description of those practices? Given this apparent priority, it is a striking fact that the justification project has often been pursued in the absence of any significant attention to the project of accurate description. In particular, a great deal of the traditional discussion of Hume’s problem of induction has proceeded against the background of hopelessly crude models of our actual inductive practice—a fact sometimes acknowledged by participants in such discussions themselves. Plausibly, the thought which underlies this procedure is the following: whatever force Hume’s critique ultimately possesses, that force is not tied to the specific content of the general rules or principles that we follow in reasoning inductively. Rather, the force of Hume’s critique depends on our following any general rules or principles at all.. (shrink)

This paper explains what’s wrong with a Hume-inspired argument for skepticism about induction. Hume’s argument takes as a premise that inductive reasoning presupposes that the future will resemble the past. I explain why that claim is not plausible. The most plausible premise in the vicinity is that inductive reasoning from E to H presupposes that if E then H. I formulate and then refute a skeptical argument based on that premise. Central to my response is a psychological explanation for how (...) people judge that if E then H without realizing that they thereby settled the matter rationally. (shrink)

‘Simplicity’ comes up in different senses in scientific methodology. The simplicity criterion at issue here is relied on in all inductive inference, it’s argued. Therefore, it cannot be inductively...

Although the inferring of explanations plays an important role in both our everyday lives and in the workings of science, I argue that inference to the best explanation as it is commonly conceived is often not the best way to capture this sort of reasoning. I suggest that a different form of reasoning – so-called immediate explanatory inference – is instead often much better suited to this task. This is a form of inference in which we are justified in believing (...) explanations for the evidence before us purely in virtue of this evidence, and not in virtue of the evidence plus some general principle or rule of non-deductive reasoning. I defend the idea of such a notion of inference, and argue that it plays a central role in both ordinary life and science. (shrink)

This paper discusses recent attempts to solve the problem of induction. Two broad strategies to escape Hume's fork can be distinguished. The first tries to localize the justification of specific inductions in uncontroversial empirical knowledge, e.g.mundane scientific knowledge (J. D. Norton) or perception (M. Lange). I argue that related attempts to (dis)solve the problem fail. The second strategy tries to put forward an argument in favor of induction. As a discussion of work by R. White shows, this argument can barely (...) prove that induction is reliable or at least not unreliable. But D. Steel, F. Huber and G. Schurz could show that enumerative induction is necessary and sufficient for a certain epistemic goal or optimal in a certain sense. These proofs, however, only solve the problem of induction if the goal or a certain standard has priority over the avoidance of error. This suggests that the difficulties to justify induction do not so much derive from Hume's fork, but rather from a plurality of sensible epistemic goals that can conflict with each other. (shrink)

The subject of this essay is the classical problem of induction, which is sometimes attributed to David Hume and called “the Humean Problem of Induction.” Here, I examine a certain sort of Neo-Aristotelian solution to the problem, which appeals to the concept of natural kinds in its response to the inductive skeptic. This position is most notably represented by Howard Sankey and Marc Lange. The purpose of this paper is partly destructive and partly constructive. I raise two questions. The first (...) is: Are the natural kind solutions to the problem successful? The first thesis of this paper is that they are not, and I will show how and why they fail. And the second question I raise here is: Is there nonetheless some alternative Neo-Aristotelian solution to the problem which is successful and can overcome the shortcomings endemic to the Sankey-Lange account? The second thesis is that there is, and I’ll attempt to sketch one. My stance here may be summarized by saying that, while I agree with Sankey and Lange that the problem of induction can be adequately resolved, and while I am on the whole sympathetic with the Aristotelian spirit of their account, I am, for all that, dissatisfied with the letter of them. Nothing short of a more thoroughgoing Aristotelianism about the epistemology of induction will do. (shrink)

En este artículo defiendo que el problema humeano de la justificación racional de la inducción no ha contribuido a la comprensión filosófica de este tipo de inferencias. La teoría material de la inducción propuesta por Norton (2003) permite analizar el razonamiento inductivo más allá del laberinto justificativo humeano, pero con un corte demasiado alto: asumir que las inducciones dependen intrínsecamente de cómo es localmente la realidad. En su lugar, propongo una teoría de la inducción en la que las inducciones dependen (...) no de tesis ontológicas, sino de las capacidades cognitivas para comprimir información de un modo epistémicamente efectivo. (shrink)

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly (...) inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

Summary In chapter one I reject the thesis that a relation of partial entailment holds between probability evidence and conclusion, as also the claim that the propositions of applied geometry are synthetic a priori. By way of balance, I suggest that there may be a sense in which necessary conditions of discourse transcend the distinction between a priori and empirical. In chapter two I reject the claim that logical relations in the form of intrinsic probability enter into the no-miracles argument, (...) which I suggest is frequency-connected in its more systematic applications, so that it belongs within a system. I begin chapter three with a critique of an attempted formal probability solution to Hume’s problem, and I now suggest that inductive inference has application only within a system in which its validity is pre-supposed in its premises, a concomitant of which is that the sceptic about induction cannot stop short of global scepticism. Since my aim is to show that global scepticism is self-refuting, given that intentionality may be analysed in terms of a system, I now develop that analysis by devoting chapter four to an examination of Wittgenstein on meaning and understanding. In chapter five I reject his thesis equating meaning and understanding with use, arguing instead that they are irreducible and subject to dispositionality conditions, and in furtherance of that argument I try to solve the problem of the authoritativeness of belief avowals by showing again that there are necessary conditions of discourse. These are such that selfascribing belief, crediting oneself with understanding and with being suitably disposed, are inherent in reasoning. In chapter six I weave the threads of the previous discussion into a solution by arguing that the sceptic about induction, who is committed to global scepticism, necessarily refutes himself. In chapter seven, on the problem of other minds, I attempt a solution by modifying the arguments used against inductive scepticism. (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by the (...) grue predicate. (shrink)

Douven (in press) observes that Schurz's meta-inductive justification of induction cannot explain the great empirical success of induction, and offers an explanation based on computer simulations of the social and evolutionary development of our inductive practices. In this paper, I argue that Douven's account does not address the explanatory question that Schurz's argument leaves open, and that the assumption of the environment's induction-friendliness that is inherent to Douven's simulations is not justified by Schurz's argument.

I begin by making some distinctions between kinds of response to a skeptical claim, the purpose of which is to explain what I mean by a "dissolution" of the problem of induction, and to focus on one of the ways it can be implemented. I then argue that previous attempts to dissolve the problem in this way fail, present mine, and defend it. Finally, I show that the dissolution of the problem doesn't improve our normative situation and may even worsen (...) it. (shrink)

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

The “demarcation problem,” the issue of how to separate science from pseu- doscience, has been around since fall 1919—at least according to Karl Pop- per’s (1957) recollection of when he first started thinking about it. In Popper’s mind, the demarcation problem was intimately linked with one of the most vexing issues in philosophy of science, David Hume’s problem of induction (Vickers 2010) and, in particular, Hume’s contention that induction cannot be logically justified by appealing to the fact that “it works,” (...) as that in itself is an inductive argument, thereby potentially plunging the philosopher straight into the abyss of a viciously circular argument. (shrink)

If we add as an extra premise that the agent does know H, then it is possible for her to know E — H, we get the conclusion that the agent does not really know H. But even without that closure premise, or something like it, the conclusion seems quite dramatic. One possible response to the argument, floated by both Descartes and Hume, is to accept the conclusion and embrace scepticism. We cannot know anything that goes beyond our evidence, so (...) we do not know very much at all. This is a remarkably sceptical conclusion, so we should resist it if at all possible. A more modern response, associated with externalists like John McDowell and Timothy Williamson, is to accept the conclusion but deny it is as sceptical as it first appears. The Humean argument, even if it works, only shows that our evidence and our knowledge are more closely linked than we might have thought. Perhaps that’s true because we have a lot of evidence, not because we have very little knowledge. There’s something right about this response I think. We have more evidence than Descartes or Hume thought we had. But I think we still need the idea of ampliative knowledge. It stretches the concept of evidence to breaking point to suggest that all of our knowledge, including knowledge about the future, is part of our evidence. So the conclusion really is unacceptable. Or, at least, I think we should try to see what an epistemology that rejects the conclusion looks like. (shrink)

To demarcate the limits of experimental knowledge, we probe the limits of what might be called an experiment. By appeal to examples of scientific practice from astrophysics and analogue gravity, we demonstrate that the reliability of knowledge regarding certain phenomena gained from an experiment is not circumscribed by the manipulability or accessibility of the target phenomena. Rather, the limits of experimental knowledge are set by the extent to which strategies for what we call ‘inductive triangulation’ are available: that is, the (...) validation of the mode of inductive reasoning involved in the source-target inference via appeal to one or more distinct and independent modes of inductive reasoning. When such strategies are able to partially mitigate reasonable doubt, we can take a theory regarding the phenomena to be well supported by experiment. When such strategies are able to fully mitigate reasonable doubt, we can take a theory regarding the phenomena to be established by experiment. There are good reasons to expect the next generation of analogue experiments to provide genuine knowledge of unmanipulable and inaccessible phenomena such that the relevant theories can be understood as well supported. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’. (shrink)