Inductive methods can be used to estimate the accuracies of inductive methods. Call a method immodest if it estimates that it is at least as accurate as any of its rivals. It would be unreasonable to adopt any but an immodest method. Under certain assumptions, exactly one of Carnap's lambda-methods is immodest. This may seem to solve the problem of choosing among the lambda-methods; but sometimes the immodest lambda-method is λ =0, which it would not (...) be reasonable to adopt. We should therefore reconsider the assumptions that led to this conclusion: for instance, the measure of accuracy. (shrink)

According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important problems arising within the Bayesian approach to scientific methodology is the choice of prior probabilities. Here this problem is considered in detail w.r.t. two applications of the Bayesian approach: (1) the theory of inductive probabilities (TIP) developed by (...) Rudolf Carnap and other epistomologists and (2) the analysis of the multinational inferences provided by Bayesian statstics (BS). ... Zie: Summary. (shrink)

It is well known that Kant used inductive arguments in his pre-critical philosophy, for example, in his 1764 Prize essay according to which metaphysics should follow Newton’s “analytic method” of natural science. However, his critical metaphysics of nature also uses several inductive tools, contrary to the widespread belief that his apriorism is only compatible with deductive reasoning. In this chapter, we pre- sent three cases of inductive reasoning found in his critical metaphys- ics of nature. First, (...) Kant carries out an “experiment of pure reason” in Preface B of the Critique of Pure Reason to rule out transcendental realism via the cosmological antinomy. Second, he argues in the Ap- pendix to the Transcendental Dialectic that the transcendental ideas of traditional metaphysics can only serve as regulative principles for expanding our knowledge of nature, and he uses an inference to the best explanation (IBE) in the Metaphysical Foundations of Natural Science. Third, at the end of the Critique, he claims that these prin- ciples support doctrinal belief. The chapter shows how each of these cases of inductive reasoning can be understood as a kind of IBE and discusses the significance of Kant’s arguments. (shrink)

In this chapter, we will discuss John Stuart Mill’s (1806–1873) arguments on scientific induction and also types of scientific inductive method: for that J. S. Mill’s manuscript, A System of Logic (1872) of its eighth revised edition is considered. This edition is treated as a comprehensive work of J. S. Mill that assists in understanding his contributions to scientific induction.

베이컨은 타당한 철학 방법론으로 귀납법만을 인정한 경험론자로 평가받는다. 그런 평가는 귀납법이 학문의 정초를 위한 방법으로는 매우 불충분하다는 인식과 더불어 그의 철학 방법론이 근대철학의 형성에 공헌하지 못했다는 평가로 이어진다. 본 논문은 그의 귀납법에 대한 비판이 정당한가를 세밀히 검토해서, 그의 귀납법 내에 부재한다고 비판받는 점들이 오히려 그의 귀납법을 구성하는 핵심 특징임을 밝히려 한다. 그리고 지금까지 베이컨 철학 방법론의 현대적 의의를 드러내려 했던 연구자들조차 그의 귀납법 본질을 밝혀내지 못했는데, 그 주원인은 그들이 상호 모순되는 것처럼 보이는 그의 귀납법 특징들의 연관성 규명에 실패했기 때문이다. 본 (...) 논문은 그것을 밝혀줄 열쇠는 그의 우상론 재해석에 있음과 또한 다양한 그의 귀납법 특징들이 어떤 맥락에서 이해되어야만 하는가를 밝히려 한다. 마지막으로 그의 귀납법이 근대자연과학혁명에서 획기적 공헌을 했으며, 이미 지나간 과거의 철학사적 문제가 아니라, 모든 자연 탐구자들이 반드시 명심해야만 할 중요한 교훈을 주고 있음을 보여주려 한다. (shrink)

This paper contends that Bacon’s inductive method depends crucially on his general account of matter. I argue that Bacon develops a dynamic form of corpuscularianism, according to which aggregates of corpuscles undergo patterns of change that derive from active inclinations and appetites. The paper claims that Bacon’s corpuscularianism provides him with a theory of material form that enables him to theorize bodily change and possible material transformations. The point of natural histories and experiments is then to find the (...) processes of corpuscular change that correlate with making present or making absent simple natures. (shrink)

La formación ética de las fuerzas militares es esencial para la democracia, pues orienta el respeto por los derechos humanos, la observancia de las leyes de la guerra y la protección de lalegitimidad institucional. Por tal motivo, la ética militar se convierte en una herramienta crucialpara guiar el comportamiento de los militares en entornos complejos y garantizar la toma de decisiones responsables. En ese contexto, este artículo evalúa el impacto del curso Conceptos Básicos en Ética Militar y su enfoque inductivo (...) en las actitudes y comportamientos del personal militar colombiano. A través de una metodología con un enfoque cuantitativo, se realizó un estudiocon 230 participantes del curso en la Escuela Superior de Guerra General Rafael Reyes Prieto(ESDEG) de Colombia, para medir las actitudes sobre la ética militar, las reglas de enfrentamiento (RE) y la efectividad operacional. Dentro de los principales resultados se identificó que el curso tuvo un impacto positivo en las actitudes de los participantes sobre la importancia de la ética militar, su contribución a la cohesión de las unidades y su influencia en la toma de decisiones responsables.Se concluye que la formación en ética militar, a través de métodos innovadores como el inductivo, prepara a los militares para enfrentar los desafíos del mundo actual y garantizar el cumplimiento de su misión de manera responsable. (shrink)

Este estudio aborda la problemática en torno a la relación de las teorías y modelos pedagógicos,centrándose en su vínculo con la investigación educativa y la práctica en el aula. En este sentido, elobjetivo principal es analizar el rol del método inductivo en la relación entre las teorías y modelospedagógicos desde la praxis en el aula, utilizando la metainvestigación y la crítica reflexiva basada enla teoría fundamentada. De este modo, se exploran las definiciones de teorías y modelos pedagógicos,el rol histórico del (...) método inductivo en la investigación educativa, la relación entre el razonamientoinductivo, las principales teorías y modelos pedagógicos, y las implicaciones prácticas de estos enfoques en la enseñanza y el aprendizaje. Los resultados revelan que el método inductivo es esencial para formular hipótesis, teorías y modelos a partir de observaciones empíricas, proporcionando unabase sólida para la investigación educativa. Además, ha influido significativamente en el desarrollo dediversos modelos pedagógicos, facilitando la integración de teoría y práctica, lo cual es vital para una enseñanza efectiva. En conclusión, el estudio destaca la relevancia continua del método inductivoen la investigación educativa y su potencial para mejorar las prácticas pedagógicas, especialmentecon el avance de la tecnología, que ofrece nuevas oportunidades para mejorar la recopilación y elanálisis de datos. (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.

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on a (...) case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

In this study, information about inductive and deductive methods and the differences between these methods was given. Afterwards, grammar teaching in Turkey was evaluated in terms of method. Then, the grammar teaching methods of the Arabic grammar books called al-Naḥwu'l-Wâḍıḥ and al-Qawâʻid al-ʻArabiyya al-Muyassara, which were prepared by following the inductive method, were examined under the headings of preface, handling of the subjects and exercises. In the continuation of the study a qualitative research was conducted using (...) the semi-structured interview technique with 16 randomly selected students, 8 of whom who have been studying Arabic for a long time and 8 of whom have started their Arabic education at university in order to learn the approaches of the students to the grammar teaching methods who took the course which the work called al-Qavâʻid al-ʻArabiyya al-Muyassara was used as a source book in the 2020-2021 academic year, in the first year of the Department of Arabic Language and Literature at Selcuk University in addition to a lesson which the grammar book prepared with the deductive method. While it was seen that the majority of the students in both groups participated in the interview preferred the deductive method, it was understood that the students had different approaches with their method preferences in terms of explaining the grammar issue in detail and giving more space to terms. In the study, it was concluded that it would be more beneficial to follow a mixed method in which the the positive aspects are considered, since it was seen that there were aspects that both educators and students found positive and negative in both methods. (shrink)

The method of mathematical induction: The method of mathematical induction -- Examples and exercises -- The proof of induction of some theorems of elemetary algebra -- Solutions.

We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties.

This paper presents a reading of Bacon’s Novum Organum and the inductive method he offers therein. According to this reading, Bacon’s induction is the search for forms that are necessary and sufficient for making simple natures present. Simple natures are observable qualities. However, in the paper we argue that forms can best be understood via Bacon’s appetitive physics, according to which particles and bodies are endowed with appetites or inclinations that lead to bodily transformations. We argue that this (...) conceptual elaboration of the notion of form changes our understanding of Bacon’s inductive method. In fact, his inductive method is a reductive program designed to find, for each observable quality (or simple nature), the transformation or combination of transformations associated with its coming to being. The paper considers the textual evidence for this reading and argues for the benefits of this reading in relation to other, traditional interpretations. (shrink)

The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent;.... It would be interesting and valuable to compare this method with the method of mathematical induction.”.

This paper studies the use of hypotheses schemes in generatinginductive predictions. After discussing Carnap–Hintikka inductive logic,hypotheses schemes are defined and illustrated with two partitions. Onepartition results in the Carnapian continuum of inductive methods, the otherresults in predictions typical for hasty generalization. Following theseexamples I argue that choosing a partition comes down to making inductiveassumptions on patterns in the data, and that by choosing appropriately anyinductive assumption can be made. Further considerations on partitions makeclear that they do not suggest (...) any solution to the problem of induction.Hypotheses schemes provide the tools for making inductive assumptions, but theyalso reveal the need for such assumptions. (shrink)

By focusing on the nineteenth-century debate between William Whewell and Augustus De Morgan on the nature and scope of scientific method and induction, this article captures an important episode in the history of Baconianism. More specifically, it sheds new light on the social and intellectual construction of Francis Bacon as an emblem of modern science and on British Baconianism as part of the creation of a vision of the modern enterprise. A critic of Whewell’s renovated Baconianism and an advocate (...) of an alternative anti-Baconian (or pro-Newtonian) view of science, De Morgan is presented for the first time as a philosopher of science (or metascientist), one who pioneered the application of probability theory to scientific reasoning. (shrink)

John Stuart Mill’s System of Logic (1843) is often considered to be a work that defends an inductivist epistemology. In this article, I propose to question this status by examining the definition of induction set out in Mill’s book, and the consequences that can be deduced from it. I show that Mill’s inductivism implies a methodology of scientific research in which deductive reasoning is just as important, if not more important, than inductive methods, so that the classical opposition between (...) induction and deduction is transformed into a complementarity. I then show how the concepts of natural law and causality emerge from these discussions, and examine how well the methods proposed by Mill are able to account for subsequent scientific discoveries. (shrink)

An inductive method Cλ in the λ-system of Carnap [1] is immodest, on evidence e, iff its estimate, on e, of its own accuracy is higher than its estimate, on e, of the accuracy of any rival method Cλ′. Immodesty seems to be a condition of stable trust: if you trusted a modest Cλ, you should start by trusting its advice to replace it by a rival that it estimates to be more accurate. One might guess that (...) any Cλ would be immodest on any evidence. But in [2] I proved that, under a certain accuracy measure taken from Carnap [1], §§ 20–21, there would be exactly one immodest Cλ. Unfortunately, that one sometimes turns out to be C0 ; and since nobody in his right mind would trust C0 we are then left with no acceptable Cλ. Stephen Spielman [3] has proposed a remedy: an estimate of accuracy, on evidence e, should disregard accuracy under circumstances that are ruled out by e. Spielman proves that if this change is made, any Cλ is immodest on any evidence. (shrink)

In lucid dreams the dreamer is aware of dreaming and often able to influence the ongoing dream content. Lucid dreaming is a learnable skill and a variety of techniques is suggested for lucid dreaming induction. This systematic review evaluated the evidence for the effectiveness of induction techniques. A comprehensive literature search was carried out in biomedical databases and specific resources. Thirty-five studies were included in the analysis , of which 26 employed cognitive techniques, 11 external stimulation and one drug application. (...) The methodological quality of the included studies was relatively low. None of the induction techniques were verified to induce lucid dreams reliably and consistently, although some of them look promising. On the basis of the reviewed studies, a taxonomy of lucid dream induction methods is presented. Several methodological issues are discussed and further directions for future studies are proposed. (shrink)

This chapter traces the history of the notions of analysis and induction in German-language accounts of scientific inquiry between the mid-eighteenth and mid-nineteenth centuries. Many eighteenth-century scholars perceived analysis and induction as intertwined and tied to methods of empirical inquiry and discovery, as they had been perceived in the early modern period. Until well into the nineteenth century, the terms “(scientific) induction” or “inductive science” referred to any experience-based science (as opposed to a science based on first principles). (...) class='Hi'>Inductive science, thus understood, encompassed the making, evaluation, and testing of hypotheses—even of hypotheses about unobservable things—and “reduction” rather than “deduction” was its opposite. While the Kantian understanding of analysis influenced the notions of induction and scientific method, it did not wholly alter their interpretation. After Kant, formal logic and philosophy gradually became independent, but a more applied philosophy of empirical inquiry also persisted, linked to scientific practice while rooted in older ideas about analytic and inductive methods. Several authors recommended evaluating and testing hypotheses by deriving testable consequences but did not consider hypothesis testing to be a strictly deductive process opposed to, or more powerful than, induction. Inductive inquiry and the hypothetico-deductive (H-D) method are both integral to the inductive sciences, according to these pragmatic theories of empirical inquiry. (shrink)

The implementation of an artificial neural network for predicting induction heating region locations is proposed in this research. Steel plate deformations during the induction heating process are produced using an analytical solution derived from electromagnetic and plate theory. The plate transform following vertical displacements in each divided area was used as input of neural following desired shape of the steel plate and the specified heating areas for induction treatment as output parameters to predict and evaluate the model. A dataset used (...) 90% for training and remaining 10% for testing to implement on the efficient models when changing hidden layer and its neurons relatively. The trial and error for analyzing and predicting heating-affected regions with the ANNs model reached the high average accuracy and lowest mean square error at 98.08% and 0.00913, respectively. Consequently, the feasibility test indicates that the developed approach may be well utilized to identify the heating positions by grid area in order to achieve the desired plate deformation. Moreover, the analysis of vertical displacement during induction heating and its response behaviour of steel plate based on thermo-mechanical are also addressed. (shrink)

What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit (...) about what this tacit understanding of method is, rather than leave it as some unfathomable mystery. They robustly defend the idea that there is such a thing as scientific method and show how this might be legitimated. This book begins with the question of what methodology might mean and explores the notions of values, rules and principles, before investigating how methodologists have sought to show that our scientific methods are rational. Part 2 of this book sets out some principles of inductive method and examines its alternatives including abduction, IBE, and hypothetico-deductivism. Part 3 introduces probabilistic modes of reasoning, particularly Bayesianism in its various guises, and shows how it is able to give an account of many of the values and rules of method. Part 4 considers the ideas of philosophers who have proposed distinctive theories of method such as Popper, Lakatos, Kuhn and Feyerabend and Part 5 continues this theme by considering philosophers who have proposed naturalised theories of method such as Quine, Laudan and Rescher. This book offers readers a comprehensive introduction to the idea of scientific method and a wide-ranging discussion of how historians of science, philosophers of science and scientists have grappled with the question over the last fifty years. (shrink)

In this paper we will show Peirce’s distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce’s originality on this, we show Peirce’s distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, passing then to (...) the distinction between mathematics and logic. In the end, we propose a sketch of a comparison between Peirce and Whitehead concerning the two thinkers’ view of mathematics, hoping that this could point to further inquiries. (shrink)

In many areas of scientific inquiry, the phenomena under investigation are viewed as functions on the real numbers. Since observational precision is limited, it makes sense to view these phenomena as bounded functions on the rationals. One may translate the basic notions of recursion theory into this framework by first interpreting a partial recursive function as a function on Q. The standard notions of inductive inference carry over as well, with no change in the theory. When considering the class (...) of computable functions on Q, there are a number of natural ways in which to define the distance between two functions. We utilize standard metrics to explore notions of approximate inference — our inference machines will attempt to guess values which converge to the correct answer in these metrics. We show that the new inference notions, NV∞, EX∞, and BC∞, infer more classes of functions than their standard counterparts, NV, EX, and BC. Furthermore, we give precise inclusions between the new inference notions and those in the standard inference hierarchy. We also explore weaker notions of approximate inference, leading to inference hierarchies analogous to the EXn and BCn hierarchies. Oracle inductive inference is also considered, and we give sufficient conditions under which approximate inference from a generic oracle G is equivalent to approximate inference with only finitely many queries to G. (shrink)

In their paper on the influence of meta-induction to the wisdom of the crowd, Paul Thorn and Gerhard Schurz argue that adding meta-inductive methods to a group influences the group positively, whereas replacing independend methods of a group with meta-inductive ones may have a negative impact. The first fact is due to an improvement of average ability of a group, the second fact is due to an impairment of average diversity within a group by meta-induction. In this paper (...) some critical remarks to meta-inductive group expansion and replacement are made. In particular it is stressed that both ability and diversity are of equal importance to a group’s performance. (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)

The λ-continuum of inductive methods was derived from an assumption, called λ-condition, which says that the probability of finding an individual having property $x_{j}$ depends only on the number of observed individuals having property $x_{j}$ and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different from $x_{j}$ have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some property (...) similar to $x_{j}$ (the most complete proof of this result is presented in Carnap, 1980). The problem thus remained open to find some general condition, weaker than the λ-condition, which would allow for the derivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the λ-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived. In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed. (shrink)