Sosa, Pritchard, and Vogel have all argued that there are cases in which one knows something inductively but does not believe it sensitively, and that sensitivity therefore cannot be necessary for knowledge. I defend sensitivity by showing that inductive knowledge is sensitive.

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.

In this article, I argue that arguments from the history of science against scientific realism, like the arguments advanced by P. Kyle Stanford and Peter Vickers, are fallacious. The so-called Old Induction, like Vickers's, and New Induction, like Stanford's, are both guilty of confirmation bias—specifically, of cherry-picking evidence that allegedly challenges scientific realism while ignoring evidence to the contrary. I also show that the historical episodes that Stanford adduces in support of his New Induction are indeterminate between (...) a pessimistic and an optimistic interpretation. For these reasons, these arguments are fallacious, and thus do not pose a serious challenge to scientific realism. (shrink)

Most social policies cannot be defended without making inductive inferences. For example, consider certain arguments for racial profiling and affirmative action, respectively. They begin with statistics about crime or socioeconomic indicators. Next, there is an inductive step in which the statistic is projected from the past to the future. Finally, there is a normative step in which a policy is proposed as a response in the service of some goal—for example, to reduce crime or to correct socioeconomic imbalances. In comparison (...) to the normative step, the inductive step of a policy defense may seem trivial. We argue that this is not so. Satisfying the demands of the inductive step is difficult, and doing so has important but underappreciated implications for the normative step. In this paper, we provide an account of induction in social contexts and explore its implications for policy. Our account helps to explain which normative principles we ought to accept, and as a result it can explain why it is acceptable to make inferences involving race in some contexts (e.g., in defense of affirmative action) but not in others (e.g., in defense of racial profiling). (shrink)

In my 2007 paper, “Is There a Problem of Induction for Mathematics?” I rejected the idea that enumerative induction has force for mathematical claims. My core argument was based on the fact that we are restricted to examining relatively small numbers, so our samples are always biased, and hence they carry no inductive weight. In recent years, I have come to believe that this argument is flawed. In particular, while arithmetical samples are indeed biased, my new view is (...) that this bias actually strengthens the inductive support that accrues from them. The reason is that small numbers typically provide a more severe test of general arithmetical claims due to the greater frequency of significant properties and boundary cases among such numbers. In this paper, I describe and defend this new view, which a call Positive Bias Pro-Inductivism. (shrink)

I review prominent historical arguments against scientific realism to indicate how they display a systematic overshooting in the conclusions drawn from the historical evidence. The root of the overshooting can be located in some critical, undue presuppositions regarding realism. I will highlight these presuppositions in connection with both Laudan’s ‘Old induction’ and Stanford’s New induction, and then delineate a minimal realist view that does without the problematic presuppositions.

Views which deny that there are necessary connections between distinct existences have often been criticized for leading to inductive skepticism. If there is no glue holding the world together then there seems to be no basis on which to infer from past to future. However, deniers of necessary connections have typically been unconcerned. After all, they say, everyone has a problem with induction. But, if we look at the connection between induction and explanation, we can develop the problem (...) of induction in a way that hits deniers of necessary connections, but not their opponents. The denier of necessary connections faces an `internal' problem with induction -- skepticism about important inductive inferences naturally flows from their position in a way that it doesn't for those who accept necessary connections. This is a major problem, perhaps a fatal one, for the denial of necessary connections. (shrink)

This paper formulates some paradoxes of inductive knowledge. Two responses in particular are explored: According to the first sort of theory, one is able to know in advance that certain observations will not be made unless a law exists. According to the other, this sort of knowledge is not available until after the observations have been made. Certain natural assumptions, such as the idea that the observations are just as informative as each other, the idea that they are independent, and (...) that they increase your knowledge monotonically (among others) are given precise formulations. Some surprising consequences of these assumptions are drawn, and their ramifications for the two theories examined. Finally, a simple model of inductive knowledge is offered, and independently derived from other principles concerning the interaction of knowledge and counterfactuals. (shrink)

Applying good inductive rules inside the scope of suppositions leads to implausible results. I argue it is a mistake to think that inductive rules of inference behave anything like 'inference rules' in natural deduction systems. And this implies that it isn't always true that good arguments can be run 'off-line' to gain a priori knowledge of conditional conclusions.

This article challenges the assumption that novel conceptual and theoretical work should be generated through induction from existing literature. While induction remains valuable in empirical inquiry, its role changes when the object of inquiry is not observed phenomena but inherited concepts, theories, and frameworks. In conceptual and metatheoretical work, premature induction from the literature can constrain originality by anchoring inquiry within the existing possibility-space of a field. The article develops a creativity-based critique of induction, distinct from (...) the classical philosophical critique associated with Hume. The problem is not that induction lacks logical justification, but that it may prematurely narrow the imagination. To support this claim, the article examines a representative set of influential theories in four fields — psychology, sociology, leadership studies, and cognitive science/philosophy of mind — finding that across all four, the large majority of major theories did not emerge through strict literature-first induction, but through abductive, interpretive, metaphorical, clinical, historical, normative, or architectonic moves later refined through evidence, literature, and application. Drawing on the phenomenological distinction between filling and emptying, the concept of beginner's mind, and the expert's internalized literature, the article argues that formal literature review at the generative stage is not merely unnecessary for expert theorists — it is phenomenologically counter-productive. An alternative seven-stage sequence is proposed, repositioning the literature review as a situating and novelty-confirming device that performs its best work after, not before, the generative act. Boundary conditions are discussed, with particular attention to the role of expertise: the critique applies most strongly to expert theorists and least to novice researchers for whom the literature review still serves a genuine capacity-building function. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth (...) century. Recent scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (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)

This paper defends a new argument in the spirit of Golemon and Graber’s Deductive No-Miracles Argument (DNMA) for scientific realism, recently criticized by Kok Yong Lee. While Lee argues that the DNMA is invalid or leads to a collapse in probability assignments, I develop an Inductive No-Miracles Argument (INMA) that preserves logical strength without relying on abductive inference or explanatory premises. By introducing an “approximately equal” probabilistic operator (≈), I show how probabilistic reasoning can license a strong inductive inference without (...) collapsing probability calculus. The resulting INMA satisfies the desiderata motivating the DNMA and clarifies how probabilistic reasoning can underwrite realist inference without appeal to explanatory virtue. Moreover, the structure argued for seems ripe for use in other contexts where avoiding abduction in lieu of less theory-laden probability is attractive, such as fine-tuning arguments and evolutionary debunking arguments. (shrink)

I attempt to refute Hume’s problem of induction. I raise the problem of counter-induction. I develop a template for generating philosophical problems. I develop and defend stage theory of scientific development for scientific realism. I develop and defend two new metaethical theories: cultural emotivism and moral functionalism. I argue that to compare morality to mathematics is to lose credibility. I develop the problem of moral induction against moral realism.

There is enormous excitement surrounding AI technology. This excitement is driven, at least in part, by hype: exaggerated claims about the capabilities of AI. Since AI is an inherently interesting and sensational topic, and since there has been a lot of hype claims made about it, discussions of AI in public discourse are suffused with hype. These hype conditions have significant potential consequences concerning distribution of resources and environmental damage. This paper argues that these hype conditions also pose a distinct (...) risk for researchers who work on AI. In short, the risk is that, in hype conditions, ordinary research activities and communication may unintentionally contribute to hype. Research is often exploratory or involves arguing for hypotheses that are not accepted as scientific consensus. Furthermore, there is always a chance that even excellent science will result in error; this is known as inductive risk. However, not all errors have the same consequences. Sometimes, accepting a false hypothesis can have worse consequences than rejecting a true one, or vice versa. A researcher might, quite reasonably, argue in a published article for a hypothesis about AI that turns out to be false. At the same time, because of the hype conditions surrounding AI, the article may be read by a much wider audience than they intend. Thus, when arguing for hypotheses, researchers run an inductive risk of contributing to AI hype. This risk needs to be considered by researchers when deciding how to conduct inquiry and communicate their results. (shrink)

In this paper, we analyse conceptions of induction and certainty in Wolff and Crusius, highlighting their competing conceptions of physics. We discuss (i) the perspective of Wolff, who assigned induction an important role in physics, but argued that physics should be an axiomatic science containing certain statements, and (ii) the perspective of Crusius, who adopted parts of the ideal of axiomatic physics but criticized the scope of Wolff’s ideal of certain science. Against interpretations that take Wolff’s proofs in (...) physics to be based on empirical statements that are probable, we show how inductively established statements, coupled with assumptions concerning the uniformity of nature, can be certain according to Wolff. We examine Crusius’ little known work on physics and show that he attacked Wolff, arguing that many statements of physics are probable. We provide a discussion of the reception of methodological rules similar to Newton’s Regulae Philosophandi, discussing different interpretations of such rules. We conclude by briefly hinting at how the debate between Wolff and Crusius provides historical context for understanding Kant’s philosophy of natural science. (shrink)

In the first part of this chapter, the role and embeddedness of Inductive Metaphysics (IM) in contemporary philosophy are discussed, in comparison to competing metaphysical programs, including the relation to conceptual a priori metaphysics as well as to other a posteriori programs in metaphysics. The basic methodological principles of IM are explained, consisting of (1) the employment of inductive and abductive methods and (2) making use of empirical sources. In the second part, important challenges for the methodology of IM are (...) investigated. These challenges arise from the fact that theories of IM have to be justified by abductive inferences that introduce new theoretical concepts. Two rationality criteria are proposed in order to distinguish scientifically meaningful metaphysical theories from pure speculations: (i) the unification of empirical facts or laws by metaphysical theories, and (ii) the independent testability of metaphysical theories by entailing use‑novel empirical consequences. (shrink)

Deduction tells us what follows from granted premises, but finite agents rarely possess indubitable premises about the world. The result is not skepticism by default. It is a need for a method that forms expectations under uncertainty, corrects itself through experience, and remains answerable to performance. This paper defends induction as the best available game for fallible agents who must act before certainty arrives. The defense is not a deductive proof that nature must remain uniform. Hume’s challenge remains instructive: (...) no purely deductive argument forces the future to resemble the past. The stronger and more honest claim is pragmatic. A rule that says “let methods inform expectations to the degree and for as long as they work” is rule-circular, but not viciously so. It does not assume the reliability of induction independently of performance. It exposes every method, including itself, to the same discipline of success, failure, revision, and abandonment. Drawing on Hume, Reichenbach, Goodman, Salmon, Norton, Bayesian confirmation, and no-regret learning, I distinguish deductive justification from methodological vindication. Induction is justified not by escaping all circularity but by being the only procedure that can learn which procedures deserve continued use. A compact formalization shows how a performance-tracking meta-rule selects induction when induction wins and abandons it if it stops winning. The result is a non-dogmatic defense of expectation: not certainty, but calibrated reliance. (shrink)

How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as (...) Lorenzo Valla and Rudolph Agricola, Paduan Aristotelians such as Agostino Nifo, Jacopo Zabarella, and members of the medical faculty, writers on philosophy of mind such as the Englishman John Case, writers of reasoning handbooks, and Francis Bacon. (shrink)

Inductive thinking is a universal human habit; we generalise from our experiences the best we can. The induction problem is to identify which observed regularities provide reasonable justification for inductive conclusions. In the natural sciences, we can often use strict laws in making successful inferences about unobserved states of affairs. In the social sciences, by contrast, we have no strict laws, only regularities which most often are conditioned on ceteris paribus clauses. This makes it much more difficult to make (...) reliable inferences in the social sciences. In particular, we want knowledge about general causal relations in order to be able to determine what to do in order to achieve a certain state of affairs. Knowledge about causal relations that are also valid in the future requires experiments or so called ‘natural experiments’. Only knowledge derived from such experiences enable us to draw reasonably reliable inferences about how to act in order to achieve our goals. (shrink)

Deduction is often introduced as the clean room of reason: once the premises and rules are fixed, necessity takes over. I keep that formal achievement intact while denying a stronger myth about it. Deduction is not self-authorizing for finite human knowers. Human confidence that a rule should be used, that a system applies to a domain, that premises have been correctly identified, and that symbolic operations have been reliably performed depends on inductive learning, empirical correction, social training, and practical success. (...) Deduction is therefore formally powerful but epistemically downstream in human cognition. The central formal distinction is between system-internal validity and agent-level warrant. A rule can be valid in a calculus without a human agent yet being warranted in applying it to the world. That warrant is earned by inductive validation, not by the rule syntax alone. (shrink)

In this paper, I outline a reductio against Stanford’s “New Induction” on the History of Science, which is an inductive argument against scientific realism that is based on what Stanford (2006) calls “the Problem of Unconceived Alternatives” (PUA). From the supposition that Stanford’s New Induction on the History of Science is cogent, and the parallel New Induction on the History of Philosophy (Mizrahi 2014), it follows that scientific antirealism is not worthy of belief. I also show that (...) denying a key premise in the reductio only forces antirealists who endorse Stanford’s New Induction on the History of Science into a dilemma: either antirealism falls under the axe of Stanford’s New Induction on the History of Science or it falls under the axe of the New Induction on the History of Philosophy. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

This paper provides an inductive interpretation of the sorites paradox. It is argued that the sorites paradox is an inductive meta-meta-inference that future modus ponens applications in a soritical series will be sound. The root of the paradox lies in the fact that inductive inferences rely on evidence and epistemic norms that are insensitive to incremental differences, since they are low probability events. This prevents an epistemicist solution given that cut-off points are incremental differences. This diagnosis is also adapted to (...) epistemic paradoxes such as the lottery paradox, the prediction paradox and the preface paradox. The other main idea of this paper is that the soritical nature of inductive inferences in addition to epistemicism motivates some arguments for inductive skepticism, such as that the evidentiary threshold of inductive inferences is unknowable, which can generate another soritical series that requires another unknowable cut-off point, and so on. The conclusion is that inductive inferences are unjustified. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an internal opacity (...) problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

In this three-part paper, my concern is to expound and defend a conception of science, close to Einstein's, which I call aim-oriented empiricism. I argue that aim-oriented empiricsim has the following virtues. (i) It solve the problem of induction; (ii) it provides decisive reasons for rejecting van Fraassen's brilliantly defended but intuitively implausible constructive empiricism; (iii) it solves the problem of verisimilitude, the problem of explicating what it can mean to speak of scientific progress given that science advances from (...) one false theory to another; (iv) it enables us to hold that appropriate scientific theories, even though false, can nevertheless legitimately be interpreted realistically, as providing us with genuine , even if only approximate, knowledge of unobservable physical entities; (v) it provies science with a rational, even though fallible and non-mechanical, method for the discovery of fundamental new theories in physics. In the third part of the paper I show that Einstein made essential use of aim-oriented empiricism in scientific practice in developing special and general relativity. I conclude by considering to what extent Einstein came explicitly to advocate aim-oriented empiricism in his later years. (shrink)

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on (...) the philosophical and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)

While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial standards for evaluating non-deductive inferences have been assumed separately in those areas, but can actually be justified by a unifying principle.

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument, (1) If H then E; (2) E; (3) Therefore, (probably) H (here referred to as ‘hypothetico-deductive confirmation argument’), (...) is inductively strong. Yet this argument looks nothing like an inductive generalization, i.e., it does not seem inductive in the term’s traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘induction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction. (shrink)

Inductive Logic is a ‘thematic compilation’ by Avi Sion. It collects in one volume many (though not all) of the essays, that he has written on this subject over a period of some 23 years, which all demonstrate the possibility and conditions of validity of human knowledge, the utility and reliability of human cognitive means when properly used, contrary to the skeptical assumptions that are nowadays fashionable. A new essay, The Logic of Analogy, was added in 2022.

From what norms does the ethics of belief derive its oughts, its attributions of virtues and vices, responsibilities and irresponsibilities, its permissioning and censuring? Since my inductive risk account is inspired by pragmatism, and this method understands epistemology as the theory of inquiry, the paper will try to explain what the aims and tasks are for an ethics of belief, or project of guidance, which best fits with this understanding of epistemology. More specifically, this chapter approaches the ethics of belief (...) from a focus on responsible risk management, where doxastic responsibility is understood in terms of the degree of riskiness of agents’ doxastic strategies, a riskiness which is in turn most objectively measured through accordance or violation of inductive norms. Doxastic responsibility is attributable to agents on the basis of how epistemically risky was the process or strategy of inquiry salient in the etiology of their belief or in their maintenance of what one believes or accepts. (shrink)

This paper develops a formal theory of inductive symmetry and applies it chiefly to theistic apologetics. The central claim is that relevantly similar inductive assessments must be governed by the same evidential calculus unless a relevant differentiator is explicitly identified and justified. The paper argues that many apologetic arguments violate this constraint by treating one inductive pattern as forceful when it supports theism while rejecting parallel inductive patterns when they count against the same conclusion. The defect is not unequal posterior (...) credence as such; the defect occurs when the asymmetry in evidential treatment exceeds the evidentially justified asymmetry between the cases. To make this claim precise, the paper models inductive assessment in terms of hypothesis, evidence, background information, scope, dependence structure, rival-hypothesis space, specificity burden, defeaters, and evidential quality. It then analyzes how invariant observations can be smuggled into deductive-looking or modalized premises, especially in causal apologetics. Theistic arguments from causation, design, consciousness, revelation, testimony, and miracle reports serve as the major application, while the general framework remains portable to other cases of selective evidential governance. The paper concludes by presenting the theory as the foundation for an Inductive Symmetry Audit, a diagnostic tool for exposing hidden bridge premises, scope drift, unsupported exceptions, specificity inflation, modal smuggling, and cherry-picked evidential standards. (shrink)

The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in ZFC, states that a predictive function M exists with the following property: whatever world we live in, M ncorrectly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On (...) the usual model of time a well-ordered subset is small relative to the set of all times. M’s existence therefore seems to provide a solution to the hard problem. My paper argues for two conclusions. First, the theorem does not solve the hard problem of induction. More positively though, it solves a version of the problem in which the structure of time is given modulo our choice of set theory. (shrink)

I present a new thermodynamic argument for the existence of God. Naturalistic physics provides evidence for the failure of induction, because it provides evidence that the past is not at all what you think it is, and your existence is just a momentary fluctuation. The fact that you are not a momentary fluctuation thus provides evidence for the existence of God – God would ensure that the past is roughly what we think it is, and you have been in (...) existence for roughly the amount of time you think you have. I don’t have a definitive way for the atheist to refute this argument, but I give one suggestion that relies on physics-based simplicity considerations. I close with an epistemological discussion of self-undermining arguments. (shrink)

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the (...) properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

I set up two axiomatic theories of inductive support within the framework of Kolmogorovian probability theory. I call these theories ‘Popperian theories of inductive support’ because I think that their specific axioms express the core meaning of the word ‘inductive support’ as used by Popper (and, presumably, by many others, including some inductivists). As is to be expected from Popperian theories of inductive support, the main theorem of each of them is an anti-induction theorem, the stronger one of them (...) saying, in fact, that the relation of inductive support is identical with the empty relation. It seems to me that an axiomatic treatment of the idea(s) of inductive support within orthodox probability theory could be worthwhile for at least three reasons. Firstly, an axiomatic treatment demands from the builder of a theory of inductive support to state clearly in the form of specific axioms what he means by ‘inductive support’. Perhaps the discussion of the new anti-induction proofs of Karl Popper and David Miller would have been more fruitful if they had given an explicit definition of what inductive support is or should be. Secondly, an axiomatic treatment of the idea(s) of inductive support within Kolmogorovian probability theory might be accommodating to those philosophers who do not completely trust Popperian probability theory for having theorems which orthodox Kolmogorovian probability theory lacks; a transparent derivation of anti-induction theorems within a Kolmogorovian frame might bring additional persuasive power to the original anti-induction proofs of Popper and Miller, developed within the framework of Popperian probability theory. Thirdly, one of the main advantages of the axiomatic method is that it facilitates criticism of its products: the axiomatic theories. On the one hand, it is much easier than usual to check whether those statements which have been distinguished as theorems really are theorems of the theory under examination. On the other hand, after we have convinced ourselves that these statements are indeed theorems, we can take a critical look at the axioms—especially if we have a negative attitude towards one of the theorems. Since anti-induction theorems are not popular at all, the adequacy of some of the axioms they are derived from will certainly be doubted. If doubt should lead to a search for alternative axioms, sheer negative attitudes might develop into constructive criticism and even lead to new discoveries. I proceed as follows. In section 1, I start with a small but sufficiently strong axiomatic theory of deductive dependence, closely following Popper and Miller (1987). In section 2, I extend that starting theory to an elementary Kolmogorovian theory of unconditional probability, which I extend, in section 3, to an elementary Kolmogorovian theory of conditional probability, which in its turn gets extended, in section 4, to a standard theory of probabilistic dependence, which also gets extended, in section 5, to a standard theory of probabilistic support, the main theorem of which will be a theorem about the incompatibility of probabilistic support and deductive independence. In section 6, I extend the theory of probabilistic support to a weak Popperian theory of inductive support, which I extend, in section 7, to a strong Popperian theory of inductive support. In section 8, I reconsider Popper's anti-inductivist theses in the light of the anti-induction theorems. I conclude the paper with a short discussion of possible objections to our anti-induction theorems, paying special attention to the topic of deductive relevance, which has so far been neglected in the discussion of the anti-induction proofs of Popper and Miller. (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)

Meta-induction, in its various forms, is an imitative prediction method, where the prediction methods and the predictions of other agents are imitated to the extent that those methods or agents have proven successful in the past. In past work, Schurz demonstrated the optimality of meta-induction as a method for predicting unknown events and quantities. However, much recent discussion, along with formal and empirical work, on the Wisdom of Crowds has extolled the virtue of diverse and independent judgment as (...) essential to maintenance of 'wise crowds'. This suggests that meta-inductive prediction methods could undermine the wisdom of the crowd inasmuch these methods recommend that agents imitate the predictions of other agents. In this article, we evaluate meta-inductive methods with a focus on the impact on a group's performance that may result from including meta-inductivists among its members. In addition to considering cases of global accessibility (i.e., cases where the judgments of all members of the group are available to all of the group's members), we consider cases where agents only have access to the judgments of other agents within their own local neighborhoods. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such (...) a metaphysics can help us make progress on the problem of induction. (shrink)

Kyle Stanford has recently claimed to offer a new challenge to scientific realism. Taking his inspiration from the familiar Pessimistic Induction (PI), Stanford proposes a New Induction (NI). Contra Anjan Chakravartty’s suggestion that the NI is a ‘red herring’, I argue that it reveals something deep and important about science. The Problem of Unconceived Alternatives, which lies at the heart of the NI, yields a richer anti-realism than the PI. It explains why science falls short when it falls (...) short, and so it might figure in the most coherent account of scientific practice. However, this best account will be antirealist in some respects and about some theories. It will not be a sweeping antirealism about all or most of science. (shrink)

The present research aims to examine the different accounts of induction given by Aristotle, Leibniz, Hume, Carnap and De Finetti, trying to support that probability calculus offers a sufficient grounding of inductive logic. The term induction had been contrasted to deduction, by Aristotle. The Neoplatonic philosopher Alcinous suggested that dialectic firstly investigates the substances and then the accidents. There are five kinds of dialectic reasoning: division, definition, analysis, induction and syllogistic. The first three concern with substances, the (...) last two with accidents. Although Leibniz regarded probability theory as a basis of inductive logic, Hume’s skepticism was seminal for the reappraisal of the role of induction in modern philosophy. Enhancing Hume’s criticism, Popper and Wittgenstein completely denied that scientists use induction. Hans Reichenbach, however, attempted to build a theory of justification for the use of induction, based on a factual basis of other successful predictive methods that make induction feasible (Earman & Salmon 1999). Moreover, Buchdall (1969) stressed that we must distinguish the inductive process of the scientist from the inductive conclusion, which comes after the completion of observation and experimentation. (shrink)

There are nine antirealist explanations of the success of science in the literature. I raise difficulties against all of them except the latest one, and then construct a pessimistic induction that the latest one will turn out to be problematic because its eight forerunners turned out to be problematic. This pessimistic induction is on a par with the traditional pessimistic induction that successful present scientific theories will be revealed to be false because successful past scientific theories were (...) revealed to be false. (shrink)

John Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally. He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory (...) but would highlight areas where Norton has not freed himself from the straightjacket of formal induction as much as he might think. This essay begins that recovery. (shrink)

Inductive conclusions rest upon the Uniformity Principle, that similar events lead to similar results. The principle derives from three fundamental axioms: Existence, that the observed object has an existence independent of the observer; Identity, that the objects observed, and the relationships between them, are what they are; and Continuity, that the objects observed, and the relationships between them, will continue unchanged absent a sufficient reason. Together, these axioms create a statement sufficiently precise to be falsified. Simple enumeration of successful observations (...) is ineffective to support an inductive conclusion. First, as its analytical device, induction uses the contrapositive form of the hypothesis; a successful observation merely represents the denial of the antecedent, from which nothing follows. Second, simple enumeration uses an invalid syllogism that fails to distribute its middle term. Instead, the inductive syllogism identifies its subject by excluding nonuniform results, using the contrapositive form of the hypotheses. The excluded data allows an estimate of the outer boundaries of the subject under examination. But an estimate of outer boundaries is as far as the inductive process may proceed; an affirmative identification of the content of the subject never becomes possible. (shrink)

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? The paper advances grounds for doubt. [A longer and more detailed sequel to this paper, 'Proving Induction', was published in the Australasian Journal of Logic in 2011.].

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

Large language models (LLMs) often appear to vindicate a radical empiricist picture: train on vast corpora of experience-like text, and capacities emerge without explicit symbolic rules. Yet contemporary machine learning research repeatedly emphasizes that what is learned, how quickly it is learned, and how well it generalizes depend crucially on prior constraints: architectural structure, training objectives, optimization dynamics, and representational bottlenecks. These constraints constitute inductive biases in a precise, technical sense. This paper develops a philosophical argument that uses LLMs as (...) a case study to reassess the classical tabula rasa thesis associated with Locke and its descendants. I defend two claims. First, even the most ``data-driven'' generative models are saturated with structural priors that make learning possible at scale; thus, their success cannot be straightforwardly read as a triumph of unstructured empiricism. Second, once this is appreciated, the rhetorical appeal of a ``blank slate'' conception of the infant mind weakens further: if artificial systems trained on orders of magnitude more linguistic input than any child still require rich inductive biases, it is implausible that human cognition begins wholly unstructured. I then show how contemporary debates about whether LLMs ``understand'' language recapitulate the older dispute about whether experience alone can generate semantics and conceptual structure. The upshot is a more balanced, non-caricatured empiricism: experience matters, but explanation must explicitly account for the learning system's prior structure. (shrink)

In contemporary philosophy of science, the no-miracles argument and the pessimistic induction are regarded as the strongest arguments for and against scientific realism, respectively. In this paper, I construct a new argument for scientific realism which I call the anti-induction for scientific realism. It holds that, since past theories were false, present theories are true. I provide an example from the history of science to show that anti-inductions sometimes work in science. The anti-induction for scientific realism has (...) several advantages over the no-miracles argument as a positive argument for scientific realism. (shrink)

After decades of intense debate over the old pessimistic induction (Laudan, 1977; Putnam, 1978), it has now become clear that it has at least the following four problems. First, it overlooks the fact that present theories are more successful than past theories. Second, it commits the fallacy of biased statistics. Third, it erroneously groups together past theories from different fields of science. Four, it misses the fact that some theoretical components of past theories were preserved. I argue that these (...) four problems entitle us to construct what I call the grand pessimistic induction that since the old pessimistic induction has infinitely many hidden problems, the new pessimistic induction (Stanford, 2006) also has infinitely many hidden problems. (shrink)

Some patients, following brain injury, do not outwardly respond to spoken commands, yet show patterns of brain activity that indicate responsiveness. This is 'cognitive-motor dissociation' (CMD). Recent research has used machine learning to diagnose CMD from electroencephalogram recordings. These techniques have high false discovery rates, raising a serious problem of inductive risk. It is no solution to communicate the false discovery rates directly to the patient's family, because this information may confuse, alarm and mislead. Instead, we need a procedure for (...) generating case-specific probabilistic assessments that can be communicated clearly. This article constructs a possible procedure with three key elements: (1) A shift from categorical 'responding or not' assessments to degrees of evidence; (2) The use of patient-centred priors to convert degrees of evidence to probabilistic assessments; and (3) The use of standardised probability yardsticks to convey those assessments as clearly as possible. (shrink)