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)

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)

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).

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

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)

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)

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.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

In his 1912 book _The Problems of Philosophy_, Bertrand Russell advocates an indirect realism with regard to physical objects. Only two years later, in his book _Our Knowledge of the External World_ and the paper “The Relation of Sense-Data to Physics”, he changes his method in philosophy. Instead of inferring the existence of physical objects, he now sets out to construct them out of sense-data. As I will argue in this article, the main argument from _The Problems of Philosophy_ can (...) be rationally reconstructed as an inference to the best explanation which infers to unobservable objects. The main motivation for the new approach in _Our Knowledge of the External World_, on the other hand, is to establish a more direct variant of realism, in particular because Russell became skeptical with regard to inferences to unobservable objects. As I will argue, the resulting theory of the physical world loses so much in simplicity that it becomes an unattractive alternative to his earlier position, and Russell’s reason for rejecting simplicity as a criterion of theory choice turns out to be inconsequential. (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.”.

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)

Resumen: El objetivo de este artículo es estudiar la inducción analítica como método científico de investigación, es decir, como modo válido de hacer ciencia. En 1934, su creador, el filósofo y sociólogo Florian Znaniecki, afirmó que este era el método que debía ser adoptado en toda investigación sociológica. Su relevancia radica en que se propone encontrar explicaciones globales de los fenómenos sociales a partir de la utilización de técnicas cualitativas de investigación. Aquí adopto una perspectiva histórica que permite inscribir su (...) emergencia y evolución en un contexto mayor del desarrollo de metodologías cualitativas en sociología, para luego reflexionar sobre sus presupuestos epistemológicos y las críticas de las que fue objeto. Por último, realizo un balance de los aportes de esta metodología a la disciplina.: The aim of this article is to study analytic induction as a scientific research method, that is, as a valid way of making science. In 1934, the philosopher and sociologist Florian Znaniecki, its creator, referred to this methodology as the method that should be adopted by any sociological research. Its relevance lies on the fact that its goal is to find global explanations to social phenomena by using qualitative research techniques. I adopt a historical perspective to inscribe this method’s emergency and evolution in a larger context of the development of qualitative methods in sociology, and then reflect upon its epistemological basis and the criticisms made in relation to it. Finally, I evaluate this method’s contributions to the discipline. (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 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)