Excerpt from Induction and Deduction: A Historical Critical Sketch of Successive Philosophical Conceptions Respecting the Relations Between Inductive and Deductive Thought and Other Essays It is a painful and pathetic task for an intimate friend of Constance Naden to be called upon to write a memoir, however brief, of her short life, instead of looking forward to years of happy and elevating intercourse, sharing in works of benevolent usefulness, and gladly watching her rise to the distinction which her (...) intellectual gifts entitled her circle of friends to anticipate. The sorrow for her loss must be lifelong. As Mrs. Browning says, "the inevitable strikes us dead," but the expression of it is unavailing. All that remains for the most devoted of her friends is to keep her memory green, by striving to let the world know what it has lost, both in promise and in fulfilment. Miss Naden's earlier life was uneventful, and almost all the details for this portion of it have been drawn from accounts published in the Birmingham papers, at the time of her death, by those associated with her school and college career. Constance Caroline Woodhill Naden was born on the 24th January, 1858, at her father's house in Edgbaston, where he still resides, and is the President of the Birmingham Architectural Association. Her mother died on the 5th February, a few days after the birth of her child. Shortly afterwards the motherless infant was domesticated with her mother's parents, Mr. and Mrs. Woodhill, of Pakenham House, Edgbaston, and here Constance lived a retired, peaceful life, adored by her grandparents, till they died, Mr. Woodhill in 1881, and his widow in 1887. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Ever since Aristotle it has been accepted that there exists a combination of inductive and deductive reasoning and a sort of unified inductive-deductive methodology. If one analyzes the procedures and logic of scientific explanation and the methods of generating and justifying scientific knowledge, one recognizes the prototype of philosophy of science found in Aristotle’s inductive and deductive procedure that is described in his Posterior Analytics, Physics and Metaphysics, where heviewed scientific inquiry as a progression from observations to general principles and (...) back to observation. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premisses which include these principles. (shrink)

Ever since Aristotle it has been accepted that there exists a combination of inductive and deductive reasoning and a sort of unified inductive-deductive methodology. If one analyzes the procedures and logic of scientific explanation and the methods of generating and justifying scientific knowledge, one recognizes the prototype of philosophy of science found in Aristotle’s inductive and deductive procedure that is described in his Posterior Analytics, Physics and Metaphysics, where heviewed scientific inquiry as a progression from observations to general principles and (...) back to observation. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premisses which include these principles. (shrink)

We present a reference model for finding evidence of discrimination in datasets of historical decision records in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. We formalize the process of direct and indirect discrimination discovery in a rule-based framework, by modelling protected-by-law groups, such as minorities or disadvantaged segments, and contexts where discrimination occurs. Classification rules, extracted from the historical records, allow for unveiling contexts of unlawful discrimination, where the degree of burden over protected-by-law (...) groups is evaluated by formalizing existing norms and regulations in terms of quantitative measures. The measures are defined as functions of the contingency table of a classification rule, and their statistical significance is assessed, relying on a large body of statistical inference methods for proportions. Key legal concepts and reasonings are then used to drive the analysis on the set of classification rules, with the aim of discovering patterns of discrimination, either direct or indirect. Analyses of affirmative action, favoritism and argumentation against discrimination allegations are also modelled in the proposed framework. Finally, we present an implementation, called LP2DD, of the overall reference model that integrates induction, through data mining classification rule extraction, and deduction, through a computational logic implementation of the analytical tools. The LP2DD system is put at work on the analysis of a dataset of credit decision records. (shrink)

The articles in this volume deal with the main inferential methods that can be applied to different kinds of experimental evidence.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps, and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely (...) copy and distribute this work, as no entity has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The paper aims to expose the induction – deduction relation within W. Whewell’s treatise «Novum Organon Renovatum». Since Aristotle’s time. induction and deduction have been interpreted as independent and even «opposite» inferences (ways of connecting premises and conclusions), but this intuition is violated in W. Whewell’s works. Based on contemporary practice of some specific natural sciences W. Whewell quite reasonably concludes that “Aristotle overlooks a step which is of far more importance to our knowledge, namely, the (...) invention of the second extreme term” and that “induction moves upward, and deduction downwards the same stair”. Ultimately, assessing the contribution of W. Whewell to the development and consolidation of the classical image of science, it can be noted that his thesis that “deduction justifies induction” is much more in line with the instrumentalism of E. Mach and A. Poincaré than J. Mill’s inductivism. (shrink)

While inductive and deductive reasoning are considered distinct logical and psychological processes, little is known about their respective neural basis. To address this issue we scanned 16 subjects with fMRI, using an event-related design, while they engaged in inductive and deductive reasoning tasks. Both types of reasoning were characterized by activation of left lateral prefrontal and bilateral dorsal frontal, parietal, and occipital cortices. Neural responses unique to each type of reasoning determined from the Reasoning Type by Task interaction indicated greater (...) involvement of left inferior frontal gyrus in deduction than induction, while left dorsolateral prefrontal gyrus showed greater activity during induction than deduction. This pattern suggests a dissociation within prefrontal cortex for deductive and inductive reasoning. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended (...) as part of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

In the late 19th century great changes in theories of light and electricity were in direct conflict with certitude, the view that scientific knowledge is infallible. What is, then, the epistemic status of scientific theory? To resolve this issue Duhem and Poincaré proposed images of fallible knowledge, Instrumentalism and Conventionalism, respectively. Only in 1919–1922, after Einstein's relativity was published, he offered arguments to support Fallibilism, the view that certainty cannot be achieved in science. Though Einstein did not consider Duhem's Instrumentalism, (...) he argued against Poincaré's Conventionalism. Hitherto, Einstein's Fallibilism, as presented at first in a rarely known essay of 1919, was left in the dark. Recently, Howard obscured its meaning. Einstein's essay was never translated into English. In my paper I provide its translation and attempt to shed light on Einstein's view and its context; I also direct attention to Einstein's images of philosophical opportunism in scientific practice. (shrink)

The aim of this paper is twofold. First, I want to argue that the distinction between induction and deduction is less clear-cut than traditionally assumed, and that, moreover, most reasoning processes in the sciences involve an integration of inductive and deductive steps. Next, I want to show how so-called adaptive logics may lead to a better understanding of this integrated use of induction and deduction.

In the middle of a conference on the logic of science, an eminent biologist once said: “Does it not bother you guys that we scientists do not use any logic at all.” This statement was meant to be a friendly provocation, but there also was a serious message. Scientists often say that the logical analyses are exercises in formal logic and fail to illuminate what the scientists are doing, actual scientific practice. This recurring complaint, although not completely as I will (...) suggest, has not gone unnoticed in the philosophy of science. Indeed, the current trend in analytic philosophy of science as well as in teaching the method of science has been away from logic as a means of illuminating scientific inquiry. (shrink)

In the middle of a conference on the logic of science, an eminent biologist once said: “Does it not bother you guys that we scientists do not use any logic at all.” This statement was meant to be a friendly provocation, but there also was a serious message. Scientists often say that the logical analyses are exercises in formal logic and fail to illuminate what the scientists are doing, actual scientific practice. This recurring complaint, although not completely as I will (...) suggest, has not gone unnoticed in the philosophy of science. Indeed, the current trend in analytic philosophy of science as well as in teaching the method of science has been away from logic as a means of illuminating scientific inquiry. (shrink)

(1994). Inductive reasoning, deductive reasoning and mental models. International Studies in the Philosophy of Science: Vol. 8, No. 1, pp. 65-67. doi: 10.1080/02698599408573483.

Elementary results concerning the connections between deductive relations and probabilistic support are given. These are used to show that Popper-Miller's result is a special case of a more general result, and that their result is not very unexpected as claimed. According to Popper-Miller, a purely inductively supports b only if they are deductively independent — but this means that a b. Hence, it is argued that viewing induction as occurring only in the absence of deductive relations, as Popper-Miller sometimes (...) do, is untenable. Finally, it is shown that Popper-Miller's claim that deductive relations determine probabilistic support is untrue. In general, probabilistic support can vary greatly with fixed deductive relations as determined by the relevant Lindenbaum algebra. (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 (...) induction and deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The (...) argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position. (shrink)

In this paper I focus on two contrasting concepts of deduction and induction that have appeared in introductory (formal) logic texts over the past 75 years or so. According to the one, deductive and inductive arguments are defined solely by reference to what arguers claim about the relation between the premises and the conclusions. According to the other, they are defined solely by reference to that relation itself. Arguing that these definitions have defects that are due to their (...) simplicity, I develop definitions that remove these defects by assigning a combination of roles to both arguers’ claims concerning the premises/conclusion relation and the relation itself. Along the way I also present and briefly defend definitions of both deductive and inductive validity that are significantly different from the norm. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

We propose a French translation of the preface written by H. nov Helmholtz to the second part of volume one of the translation of the Treatise on Natural Philosophy due to Sir William Thompson and Tait. The numbers in square brackets refer to the page numbers of the original text.RésuméNous proposons une traduction française de la préface de H. von Helmholtz à la seconde partie du premier volume de la traduction du Treatise on Natural Philosophy de Sir William Thompson et (...) Tait. Les nombres entre crochets rappellent la pagination du texte original. (shrink)

In this paper I want to cast doubt on the claim that there is a legitimate process of reasoning to the best explanation which can serve as an alternative to either straightforward inductive reasoning or a combination of inductive and deductive reasoning. I shall argue a) that paradigmatic cases of acceptable arguments to the best explanation must be considered enthymemes and b) that when the suppressed premises are made explicit we have all of the premises we need to present either (...) a straightforward inductive argument or an argument employing both induction and deduction. (shrink)

The 20th century philosophy of science began on a positivistic note. Its focal point was scientific explanation and the hypothetico-deductive (HD) framework of explanation was proposed as the standard of what is meant by “science.” HD framework, its inductive and statistical variants, and other logic-based approaches to modeling scientific explanation were developed long before the dawn of the information age. Since that time, the volume of observational data and power of high performance computing have increased by several orders of magnitude (...) and reshaped the practice and concept of science, and indeed, the philosophy of science. A new observational-inductive (OI) framework for scientific research is emerging due to recent developments in sensors, data systems, computers, and knowledge discovery techniques. We examine the nature of these changes and their impact on the question of what is meant by “science” after discussing five examples of the OI framework, and conclude that the HD and OI frameworks are complementary and synergistic. (shrink)

Inference to the best explanation (IBE) is considered to be the main means of discovery and justification of scientific hypotheses and theories. The article investigates this inference and its relationship to the main kinds of inference: deduction, induction and abduction. IBE has an abductive inference mechanism, but, contrary to abduction, infers not a possible, but a true conclusion. IBE is an inductive inference, because it is underdetermined by the rules of deduction and by evidence. The article claims (...) that despite its abductive and inductive features which demonstrate that it is not and cannot be deductive inference, IBE nevertheless makes pretense to an absolute truth of its inference, i.e. claims for an almost deductive validity. (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)

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.