The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford (...) 2001, p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

In this paper, I respond to Sterpetti’s attempt to defend Kyle P. Stanford’s Problem of Unconceived Alternatives and his New Induction over the History of Science from my reductio argument outlined in Mizrahi :59–68, 2016a). I discuss what I take to be the ways in which Sterpetti has misconstrued my argument against Stanford’s NIS, in particular, that it is a reductio, not a dilemma, as Sterpetti erroneously thinks. I argue that antirealists who endorse Stanford’s NIS still face an absurd (...) consequence of this argument, namely, that they should not believe their own brand of scientific antirealism. (shrink)

The problem of unconceived alternatives (or the New Induction) states that, since scientists have recurrently failed to conceive relevant theoretical alternatives for some domains of science, current scientists are probably also failing to do so. Therefore, there may be theories which still exceed the grasp of scientists’ imagination, and one should not endorse a realist stance towards current science. In this paper, I raise a conceptual worry for the formulation of this problem: what does it mean to say that (...) scientists failed to conceive a relevant theory? What aggravates the problem is that no simple notion of relevance makes the New Induction as strong as it initially seems. I consider the three more obvious interpretations of relevance: relevance as objective probability; relevance as epistemic probability assessed by current scientists; and relevance as epistemic probability assessed by past scientists. I argue that assuming any of these three notions implies difficulties for the New Induction, hence their proponents shouldn’t take the notion of relevance for granted. A more precise definition of relevance is essential to understand what are the difficulties surrounding the problem of unconceived alternatives as an epistemic worry. Until now, such notion is missing. KeyWords: Scientific realism, unconceived alternatives, Kyle Stanford, New Induction, Pessimistic Induction. (shrink)

In the Introduction section, 6th point under the paragraph “Given the parallels between Stanford’s PUA and the PUO, and those between Stanford’s NIS and the NIP, I have sketched the following reductio against Stanford’s NIS (Mizrahi 2016a, pp. 63–64):….. should read as -/- (6) Scientific antirealism is a philosophical theory.

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)

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.

The idea that reason can justify induction was famously criticized by David Hume. Hume concluded that there is no rational justification for inductive inferences and hence, no rational justification for most of our daily beliefs. Many philosophers attempted to solve Hume's problem with no success. Bertrand Russell commented regarding Hume's problem: "[if we cannot justify induction] we have no reason to expect the sun to rise tomorrow, to expect bread to be more nourishing than a stone, or to (...) expect that if we throw ourselves off the roof we shall fall." The New Riddle of Induction was introduced by Nelson Goodman in his book Fact, Fiction and Forecast, published in 1954. Goodman's problem raised some serious doubts about our ability even to describe inductive principles. In this Book Rami Israel is attempting to solve Both Hume's and Goodman's philosophical problems by introducing a new approach to the subject and by drawing a new picture of our inductive practices. (shrink)

필자는 본 논문에서 귀납의 문제와 관련하여 흄이 『인성론』 1권에서 이성을 통하여서는 이를 정당화 할 수 없다고 주장한 것으로 해석하는 기존의 회의주의적 해석을 비판적으로 검토한다. 필자의 견해에 따르면, 흄이 『인성론』 1권에서 비판의 대상으로 삼고 있는 것은 인과 추론의 정당성 문제 그 자체가 아니라, 무비판적으로 받아들여져 온 무오류적 이성 개념이다. 흄은 이 무오류적 이성 개념을 부정하고, 이성을 넓은 의미에서의 상상력 아래로 포섭 시킨 후, 그 안에서 무작위로 작동하는 좁은 의미에서의 상상력과 개연성의 논리에 따라 작동하는 이성을 구분함으로써, 인과 추론을 정당화하는 새로운 길을 열고 (...) 있다. 따라서, 흄은 『인성론』 1권에서 인과 추론의 정당성을 부정하고 더 나아가 총체적 회의주의로 빠져드는 것이 아니라, 이성 개념을 새롭게 정립함으로써 오히려 총체적 회의 주의로 빠지지 않고 새로운 방식으로 인과 추론의 정당성을 확보하는 시도를 하고 있는 것이다. 이와 같은 필자의 해석은 『인성론』 1권과 『인성론』 2권, 3권을 단절적으로 해석하지 않고, 오히려 『인성론』 1권에서의 논의가 『인성론』 2권과 3권의 초석이 되어줌을 잘 드러내 보여준다. 다시 말해, 흄이 『인성론』 1권에서 주장하는 바, “우리의 감각들을 넘어서서 추적될 수 있고, 우리가 볼 수 없고 느낄 수 없는 존재들과 대상들을 우리들에게 알려주는 유일한 것은 인과이다”라고 하는 흄의 언명이 『인성론』 2권과 3권에서의 대상 세계에 대한 논의의 출발점이 되어주는 것이다. -/- This paper argues against the common interpretation that, in Book I of the Treatise, Hume attempts to show that inductive arguments concerning matters of fact cannot be justified by reason. It is true that he argues that inductive arguments cannot be justified by the traditional concept of infallible reason. However, it is important to note that contra to the traditional understanding of reason as infallible, he takes it to be open to errors by classifying it under the category of imagination in a broad sense. He then makes a distinction between reason as “the general and more establish’d properties of the imagination” and imagination as a narrow sense. From this, the paper concludes he attempts to justify inductive arguments concerning matters of fact by redefining reason as open to errors. That is, although inductive arguments cannot be justified by probable reasoning in terms of the traditional concept of infallible reason, the former can be justified by the logic of probability, which he calls “general rules” in terms of Hume’s concept of error-prone reason. (shrink)

I explain the New Riddle of Induction (Goodman 1946, 1955) in very brief words.

The paper deals with the New Riddle of Induction set forth by N. Goodman in his Fact, Fiction, and Forecast. The problem is introduced through the definition of grue-predicate. The relation between the grue-hypothesis and empirical evidence is examined. Goodman’s underlying thesis about the neutrality of empirical evidence is undermined. The intelligibility of the idea that disjunctive properties such as Grue can be observed and seen is questioned. A solution of Goodman’s riddle is outlined by means of the definition (...) of the identity of empirical properties and further deve- loped through postulating of the necessary condition of induction executability which prohibits the inference from “Some a, b, c, d emeralds are green” to the hypothesis “All emeralds are grue”. (shrink)

Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy between (...) class='Hi'>induction and deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)

Drawing on past work, we introduce a new approach to the New Riddle of Induction, showing that the inductive projection of gruesome properties is unreliable under particular ideal conditions that are sufficient for the reliable inductive projection of non-gruesome properties. As an auxiliary to our account, we introduce rules for resolving conflicts between background information and the conclusions of otherwise reliable inductive inferences. Our approach to the New Riddle of Induction is quite permissive in the range of properties (...) it recognizes as suitable for inductive projection, allowing for the inductive projection of highly gerrymandered non-natural properties. However, as an addendum to our discussion of the New Riddle, we show that natural properties do form a more reliable basis for inductive projection in cases where one’s sample is small. (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)

This paper analyzes and explores varying discourses within the talk of new practitioner direct entry (DE) midwives in Aotearoa/New Zealand. In Aotearoa/New Zealand, midwifery is theorized as a feminist profession undertaken in partnership with women. Direct entry midwifery education is similarly based on partnerships between educators and students in the form of liberatory pedagogies. The context for the analysis is a large ethnographic study undertaken with a variety of differently positioned midwives based mainly in one city in New Zealand. I (...) interviewed and observed over 40 midwives in their different practice settings in 2003. Complex and contesting forms of knowledge production are analyzed in this paper drawing on methodological insights from Foucauldian discourse analysis. New practitioners engage in techniques of self‐monitoring and surveillance as they move towards becoming established practitioners. New midwifery subjectivities and forms of knowledge production which contest authoritative forms of knowledge are produced. Midwives in New Zealand are seen to inhabit a complex and liminal space of midwifery praxis. Paradoxically, they are exhorted to remain the ‘guardians of normal birth’ in a time of increasing interventions into birth both locally and internationally. Paradoxes encountered by new midwifery practitioners in New Zealand as they struggle to maintain ideals of ‘normal’ birth may be paralleled by the constraints inadvertently produced through governing discourses of emancipatory or liberatory pedagogies. The relevance of this is also highly critical for midwifery and birth practices internationally. (shrink)

Some new double analogues of induction and transfinite recursion are given which yields a relatively simple proof of a result of Robert Cowen, [2] which in turn is a strengthening of an earlier result of Smullyan [1], which in turn gives a unified approach to Zorn's Lemma, the transfinite recursion theorem and certain results about ordinal numbers.

Hume’s familiar sceptical argument against induction brands as irrational our practice of generalising from observed regularities because of its reliance on the assumption that nature is uniform, an assumption which is unjustifiable. The argument which I wish to consider focuses instead on the observed regularities that are required if we are legitimately to extrapolate from experience. According to Hume, the paradigm type of inductive reasoning involves a constant conjunction. But in fact we do not encounter such invariable uniformities: our (...) experience is, almost invariably, irregular. So setting aside Hume’s sceptical qualms about the very attempt to form expectations about the hitherto unobserved, how can we justify our ignoring such irregularities? My conclusion is that, even if the principle of uniformity can be justified, our practice is irrational by Hume’s lights. This is a new Humean critique of our “causal reasoning,” for, although Hume does not present it, the ingredients are all his. (shrink)

Some 20 years ago Todd and colleagues proposed that rhythm perception is mediated by the conjunction of a sensory representation of the auditory input and a motor representation of the body (Todd, 1994a, 1995 ), and that a sense of motion from sound is mediated by the vestibular system (Todd, 1992a, 1993b ). These ideas were developed into a sensory-motor theory of rhythm and beat induction (Todd et al., 1999 ). A neurological substrate was proposed which might form the (...) biological basis of the theory (Todd et al., 2002 ). The theory was implemented as a computational model and a number of experiments conducted to test it. In the following time there have been several key developments. One is the demonstration that the vestibular system is primal to rhythm perception, and in related work several experiments have provided further evidence that rhythm perception is body dependent. Another is independent advances in imaging, which have revealed the brain areas associated with both vestibular processing and rhythm perception. A third is the finding that vestibular receptors contribute to auditory evoked potentials (Todd et al., 2014a, b ). These behavioral and neurobiological developments demand a theoretical overview which could provide a new synthesis over the domain of rhythm perception. In this paper we suggest four propositions as the basis for such a synthesis. (1) Rhythm perception is a form of vestibular perception; (2) Rhythm perception evokes both external and internal guidance of somatotopic representations; (3) A link from the limbic system to the internal guidance pathway mediates the “dance habit”; (4) The vestibular reward mechanism is innate. The new synthesis provides an explanation for a number of phenomena not often considered by rhythm researchers. We discuss these along with possible computational implementations and alternative models and propose a number of new directions for future research. (shrink)

In a recent paper in this journal, Schramm presents what he takes to be an answer to Goodman’s New Riddle of Induction. His solution relies on the technical notion of evidential significance, which is meant to distinguish two ways that evidence may bear on a hypothesis: either via support or confirmation. As he puts his view in slogan form: “confirmation is support by significant evidence”. Once we make this distinction, Schramm claims, we see that Goodman’s famous riddle is dissolved, (...) and we are no longer forced into the “intolerable result” that anything confirms anything. Schramm makes a number of incisive observations in his paper, but I do not think he has solved the New Riddle. There are two reasons for this. First, Schramm has an overly narrow conception of what the Riddle amounts to; I would venture to guess that it is narrower than that of most contemporary philosophers. Thus his proposal does not address the primary concern. Second, Schramm’s notion of significant evidence relies on a counterfactual condition that bears more than a passing resemblance to that made famous by Jackson in his paper on the topic. However, Jackson’s proposal faces several well-known counterexamples, some of which can be adapted into Schramm’s framework. Schramm’s solution thus inherits a number of outstanding problems from Jackson’s proposal, which he has not shown us how to handle. (shrink)

Maxwell claimed that the electrostatic inverse square law could be deduced from Cavendish's spherical condenser experiment. This is true only if the accuracy claims made by Cavendish and Maxwell are ignored, for both used the inverse square law as a premise in their analyses of experimental accuracy. By so doing, they assumed the very law the accuracy of which the Cavendish experiment was supposed to test. This paper attempts to make rational sense of this apparently circular procedure and to relate (...) it to some variants of traditional problems concerning old and new evidence. (shrink)

In section I the notions of logical and inductive probability will be discussed as well as two explicanda, viz. degree of confirmation, the base for inductive probability, and degree of evidential support, Popper's favourite explicandum. In section II it will be argued that Popper's paradox of ideal evidence is no paradox at all; however, it will also be shown that Popper's way out has its own merits.

The problem of induction is formulated as a set of three questions, namely: ‘What is the nature of the attitude of acceptance that we adopt in relation to certain theories?’ ‘What are the rules according to which we select those theories which we accept?’ and, ‘What is the justification for the adoption of those rules?’. An original answer is proposed for each question in turn, with the help of the new concepts of sub-theory, established sub-theory, aberrant, arbitrary and degenerate (...) theories. The answer to the third question follows the lines of Reichenbach's pragmatic strategy. (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 most innovative and important parts of Bertrand Russell's Human Knowledge were the result of his first attempt in three decades to come to grips with the problem of induction, or, more generally, ‘non-demonstrative inference’. My purpose here is to argue that that work constituted giant progress on the problem; if I succeed, something will have been done to restore this work to its proper place in the history of philosophy and, correlatively, to rearrange that history.

Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is linked (...) to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example. (shrink)

This chapter contains sections titled: Good Old‐Fashioned Inductive Logic (GOFIL): Carnap's Program Subjectivized Inductive Logic (SIL): De Finetti Regnant New‐Fangled Inductive Logic (NFIL).

The local justification of beliefs and hypotheses has recently become a major concern for epistemologists and philosophers of induction. As such, the problem of local justification is not entirely new. Most pragmatists had addressed themselves to it, and so did, to some extent, many classical inductivists in the Bacon-Whewell-Mill tradition. In the last few decades, however, the use of logic and semantics, probability calculus, statistical methods, and decision-theoretic concepts in the reconstruction of in ductive inference has revealed some important (...) technical respects in which inductive justification can be local: the choice of a language, with its syntactic and semantic features, the relativity of probabilistic evalua tions to an initial body of evidence or background knowledge and to an agent's utilities and preferences, etc. Some paradoxes and difficulties encountered by purely formal accounts of inductive justification, the erosion of the once dominant empiricist position, which most approaches to induction took for granted, and the increasing challenge of noninduc tivist epistemolgies have underscored the need of accounting for the methodological problems of applying inductive logic to real life contexts, particularly in science. As a result, in the late fifties and sixties, several related developments pointed to a new, local approach to inductive justification. (shrink)

In a recent work, Popper claims to have solved the problem of induction. In this paper I argue that Popper fails both to solve the problem, and to formulate the problem properly. I argue, however, that there are aspects of Popper's approach which, when strengthened and developed, do provide a solution to at least an important part of the problem of induction, along somewhat Popperian lines. This proposed solution requires, and leads to, a new theory of the role (...) of simplicity in science, which may have helpful implications for science itself, thus actually stimulating scientific progress. (shrink)

Traditional attempts to understanding inductive reasoning in science have typically involved analyzing language, focusing on statements or propositions. However, recent arguments suggest that this approach misconceives induction, prompting the need for a new perspective. This study offers a fresh view on induction by integrating William Whewell's theory of induction, which distinguishes two forms of reasoning: interpretation and representation. This perspective suggests that induction can be seen as a reasoning process based on semantic and pragmatic models rather (...) than statements or propositions. (shrink)

A challenger of traditions and boundaries A pivotal figure in 20th-century philosophy, Nelson Goodman has made seminal contributions to metaphysics, epistemology, aesthetics, and the philosophy of language, with surprising connections that cut across traditional boundaries. In the early 1950s, Goodman, Quine, and White published a series of papers that threatened to torpedo fundamental assumptions of traditional philosophy. They advocated repudiating analyticity, necessity, and prior assumptions. Some philosophers, realizing the seismic effects repudiation would cause, argued that philosophy should retain the familiar (...) framework. Others considered the arguments compelling, but despaired of doing philosophy without the framework. Goodman disagreed with both factions. Rather than regretting the loss of structure, he capitalized on the opportunities that arise when the strictures of tradition are loosened. (shrink)

Although the relevance and importance of his work has been recognized only belatedly, Charles Sanders Peirce was, throughout his life, a careful student and significant contributor to the development of logic, scientific theory, and philosophy generally. Occasionally, complete appreciation of Peirce's efforts has been hampered because his work is often unique and, at times, highly idiosyncratic. Yet, we hope to show in this paper that for one aspect of his work in logic Peirce did not abandon the ordinary without purpose. (...) Only relatively recently have philosophers of science become interested in the logic of discovery - that is, in the logic of the selection of hypotheses to be tested rather than simply in the ways of testing hypotheses which have already been selected. (shrink)

In this paper, I consider Goodman’s new riddle of induction and how we should best respond to it. Noticing that all the emeralds so far observed are green, we infer that all emeralds are green. However, all emeralds so far observed are also grue, so we could also infer that they are grue. Only one of these inductive inferences or projections could, however, be valid. For the hypothesis that all emeralds are green predicts that the next observed emerald will (...) be green; whereas the hypothesis that they are grue predicts that it will blue. Goodman’s new riddle is the problem of saying why the inductive inference involving “green” is the valid one. Goodman’s own solution appeals to the idea of entrenchment. His idea is that “green” is a more entrenched predicate than “grue” in the sense that it has figured many more times in our past projections than has “grue”. In his view, this explains why “green” is projectible whereas “grue” isn’t. I argue that this response doesn’t go far enough and that we additionally need an explanation of why “green” is more entrenched than “grue”—that we are otherwise left with the unsatisfactory view that its superior entrenchment is a mere linguistic accident. I try to supplement Goodman’s solution with an explanation of this kind. I argue that “grue” is not entrenched be- cause past successful inductions involving “green” show that past projections that could have been made using what I call “grue-like” predicates—predicates which are like “grue” except that the times featuring in their definitions are past—would have been unsuccessful. (shrink)

I propose a novel solution to Goodman's new riddle of induction, one on which aspects of scientific methodology preclude significant confirmation of the Grue Hypothesis. The solution appeals to intuitive constraints on the confirmation of explanatory hypotheses, and can be construed as a fragment of a theory of Inference to the Best Explanation. I give it an objective Bayesian formalisation, and contrast it with Goodman's and Sober's solutions, which make appeal to both methodological and non-methodological considerations, and those of (...) Jackson, Godfrey-Smith, and White, on which explanatory considerations play a very different role. (shrink)

In this paper, the contributions to the account of meta-induction (Schurz 2019) collected in this volume are critically discussed and thereby, new insights are developed. How broad and expandable the program of meta-induction is can be learned from Ortner’s contribution. New insights about the transition from the a priori justification of meta-induction to the a posteriori justification of object-induction emerge from the reflection of Shogenji’s paper. How meta-induction may be applied also to religious prophecies and (...) that their meta-inductive justification does not fail for a priori reasons but because of missing evidence for predictive success is learned from the discussion of Pitts’ contribution. That meta-induction does not rely on a particular prior distribution, while the no free lunch theorem depends implicitly on a uniform prior, is the major conclusion drawn from the discussion of Wolpert’s article. How the problem of induction is treated in different versions of the Bayesian account is learned from the discussion of Willliamson’s paper. That meta-induction can also be employed for abduction, and that abductive theory-revision can offer meta-inductive aggregation methods is a new insight emerging from the reflection of Aliseda’s contribution. (shrink)

Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic languages. We (...) extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science. (shrink)

In 1955, Goodman set out to 'dissolve' the problem of induction, that is, to argue that the old problem of induction is a mere pseudoproblem not worthy of serious philosophical attention. I will argue that, under naturalistic views of the reflective equilibrium method, it cannot provide a basis for a dissolution of the problem of induction. This is because naturalized reflective equilibrium is -- in a way to be explained -- itself an inductive method, and thus renders (...) Goodman's dissolution viciously circular. This paper, then, examines how the old problem of induction crept back in while nobody was looking. (shrink)

This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion of degrees (...) of testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)

Although the relevance and importance of his work has been recognized only belatedly, Charles Sanders Peirce was, throughout his life, a careful student and significant contributor to the development of logic, scientific theory, and philosophy generally. Occasionally, complete appreciation of Peirce's efforts has been hampered because his work is often unique and, at times, highly idiosyncratic. Yet, we hope to show in this paper that for one aspect of his work in logic Peirce did not abandon the ordinary without purpose. (...) Only relatively recently have philosophers of science become interested in the logic of discovery - that is, in the logic of the selection of hypotheses to be tested rather than simply in the ways of testing hypotheses which have already been selected. (shrink)

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.

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)

Formal topology aims at developing general topology in intuitionistic and predicative mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which allows distinction which are not expressible in classical topology. Here we give a systematic exposition of one of the main tools in formal topology: inductive generation. In fact, many formal topologies can be presented in (...) a predicative way by an inductive generation and thus their properties can be proved inductively. We show however that some natural complete Heyting algebra cannot be inductively defined. (shrink)