Charles Peirce was one of those rare individuals, an expert logician who is at the same time an experienced practical scientist. His logical acumen was apparent even to his contemporaries; while an early training in chemistry, astronomy, geodesy and optics, left him, as he declares, “saturated through and through with the spirit of the physical sciences.“ One is therefore hardly surprised to discover that he was deeply interested in scientific methodology—particularly in the logic of induction. Indeed, it would not (...) be an exaggeration to say that some of his most significant contributions to philosophy were made in precisely this field. No apology is thus required for devoting attention to them. In the present paper I want to sketch his treatment of induction very briefly, and attempt a tentative estimate of its validity. (shrink)

This study is an inductive approach to investigating and acquiring knowledge of nature in African culture. It begins, without any assumption of foreknowledge, but without any overindulgence, with a brief exposition of the meaning of induction. It analyses, defuses and rejects the attempted arguments made recently by some scholars that induction is not a part of the African reasoning faculty, that it is western exclusive and that most traditional beliefs are irrational, superstitious and non-inferential. It continues with a brief (...) analysis of the African engagement with inductive reasoning, and thereafter, connects induction and the natural environment by concretely analysing some ways the African understands and acquires knowledge of the natural environment through inductive reasoning particularly in traditional African society. It made a demonstrative inquiry into these ways with medicine, agriculture, science, technology, time, and season, among others, and how such thought patterns and the resultant knowledge informs the African beliefs and practices. The study concurrently argues that the African inductive understanding of nature is a demonstration of the inductive creativity, skill and competence of traditional African people. It concludes by arguing that if it is established that the traditional Africans acquire knowledge of nature inductively and shows how this knowledge is acquired, it would concurrently have been established that Africans are capable of inductive logic, whose components includes inferences and rationality. The study adopts the conceptual and critical methods of philosophical analyses. (shrink)

In his The Poverty of Historicism 1 K.R. Popper and before him F. Kaufmann2 distinguish two broad classes of epistemological and methodological positions held in the social sciences: Antinaturalistic positions and pronaturalistic positions. These positions are distinguished with respect to their attitude regarding the applicability of the methods of the natural sciences, or rather what the representatives of the anti and pronaturalistic positions assume to be the method of the natural sciences. According to Popper and Kaufmann the representatives of antinaturalistic (...) positions hold that the methods of the natural sciences can not be applied in the social sciences, whereas the representatives of the pronaturalistic positions have the opposite view. This of course raises the question what views the representatives of the anti and pronaturalistic positions embrace with respect to the methods of the natural sciences. It is interesting to note, however, that Popper in his The Poverty of Historicism, indicates those views only briefly, the reasons presumably being the special tasks and aims he set himself in that analysis. These are primarily to show the disastrous political and social consequences of a false social science methodology and the invalidity of the ideas of historical necessity and that of laws of historical development. But it is well known that Popper analysed and discussed the methods and the philosophy of science with great rigour and acumen in his other books and articles and that he triggered a philosophical revolution in that field.3 Before Popper the prevailing. (shrink)

THE PHILOSOPHY OF THe INDUCTIVE SCIENCES. PART II. OF KNOWLEDGE. ' . VOL. II. ...

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...) degree of confirmation of the hypothesis h on the evidence e“; the evidence is usually a report on the results of our observations. On the other hand, probability2 is an empirical concept; it is the relative frequency in the long run of one property with respect to another. The controversy between the so-called logical conception of probability, as represented e.g. by Keynes, and Jeffreys, and others, and the frequency conception, maintained e.g. by v. Mises and Reichenbach, seems to me futile. These two theories deal with two different probability concepts which are both of great importance for science. Therefore, the theories are not incompatible, but rather supplement each other. (shrink)

3 in philosophy, and therefore in metaphilosophy, cannot be based on rules that avoid spending time on pseudo-problems. Of course, this implies that, if one succeeds in demonstrating convincingly the pseudo-character of a problem by giving its 'solution', the time spent on it need not be seen as wasted. We conclude this section with a brief statement of the criteria for concept explication as they have been formulated in several places by Carnap, Hempel and Stegmiiller. Hempel's account is still very (...) adequate for a detailed introduction. The process of explication starts with the identification of one or more vague and, perhaps, ambiguous concepts, the so-called explicanda. Next, one tries to disentangle the ambiguities. This, however, need not be possible at once. Ultimately the explicanda are to be replaced by certain counterparts, the so-called explicata, which have to conform to four requirements. They have to be as precise as possible and as simple as possible. In addition, they have to be useful in the sense that they give rise to the formulation of theories and the solution of problems. The three requirements of preciseness, simplicity and usefulness. have of course to be pursued in all concept formation. (shrink)

Then, in 1960, Carnap drew up a plan of articles for Studies in Inductive Logic and Probability — a surrogate for Volume II of the ...

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)

L. Jonathan Cohen has written a number of important books and articles in which he argues that mathematical probability provides a poor model of much of what paradigmatically passes for sound reasoning, whether this be in the sciences, in common discourse, or in the law. In his book, The Probable and the Provable, Cohen elaborates six paradoxes faced by advocates of mathematical probability (PM) when treating issues of evidence as they would arise in a court of law. He argues that (...) his system of inductive probability (PI) satisfactorily handles the issues that proved paradoxical for mathematical probability, and consequently PI deserves to be thought of as an important standard of rational thinking. I argue that a careful look at each of the alleged paradoxes shows that there is no conflict between mathematical probability and the law, except when for reasons of policy we opt for values in addition to accuracy maximization. Recognizing the role of such policies provides no basis for questioning the adequacy of PM. The significance of this critical treatment of Cohen's work is that those interested in revising the laws of evidence to allow for more explicitly mathematical approaches ought to feel that such revisions will not violate the spirit of forensic rationality. (shrink)

English summary: Bachelards fundamental 1929 text takes mathematics as the means for constructing and investigating physical reality, anticipating many of the great theories developed over the course of the next century. French description: Quatorze ans apres la theorie de la relativite generale (1915), Bachelard publie La Valeur inductive de la relativite (1929). Cet ouvrage qu'on reduit souvent a sa polemique avec Meyerson, auteur de La Deduction relativiste (1925), est en realite un eloge des mathematiques - et notamment du calcul (...) tensoriel - comme mode de construction et d'investigation du reel physique. Dans ce livre non reedite, qui minimise l'experience mais qui contient aussi en germe nombre de themes ulterieurement developpes par l'auteur, Bachelard apparait retrospectivement beaucoup plus prophetique qu'il ne pouvait le penser lui-meme. Les grandes theories physiques du XXe et du XXIe siecle ne cesseront de lui donner raison. (shrink)

One of the primary tools in the theist’s defense against “noseeum” arguments from evil is an epistemic principle concerning the Conditions Of ReasoNableEpistemic Access (CORNEA) which places an important restriction on what counts as evidence. However, CORNEA is false because it places too strong acondition on what counts as inductive evidence. If CORNEA is true, we lack evidence for a great many of our inductive beliefs. This is because CORNEA amounts to a sensitivity constraint on evidence, and (...) class='Hi'>inductive evidence is often insensitive. So unless a theist is also an inductive skeptic, she must abandon CORNEA in responding to this sort of argument from evil. (shrink)

The focus of this chapter will be on the epistemic and normative questions at issue in debates about cancer screening, with a special focus on mammography as a case study. Such questions include: How do we know who needs to be screened? What are the benefits and harms of cancer screening, and what is the quality of evidence for each? How ought we to measure and compare these benefits and harms? What are the sources of uncertainty about our estimates of (...) benefit and harm? Why are such issues so contested? What are the major drivers of dissent and consensus on the data and their interpretation? How, if at all, do values play a role in debates surrounding mammography screening? In sum: In what ways does inductive risk, broadly conceived, 1 come into play in the science behind cancer screening, and mammography screening in particular? (shrink)

The paper examines constraints and preferences employed by people in learning decision rules from preclassified examples. Results from four experiments with human subjects were analyzed and compared with artificial intelligence (AI) inductive learning programs. The results showed the people's rule inductions tended to emphasize category validity (probability of some property, given a category) more than cue validity (probability that an entity is a member of a category given that it has some property) to a greater extent than did the (...) AI programs. Although the relative proportions of different rule types (e.g., conjunctive vs. disjunctive) changed across experiments, a single process model provided a good account of the data from each study. These observations are used to argue for describing constraints in terms of processes embodied in models rather than in terms of products or outputs. Thus AI induction programs become candidate psychological process models and results from inductive learning experiments can suggest new algorithms. More generally, the results show that human inductive generalizations tend toward greater specificity than would be expected if conceptual simplicity were the key constraint on inductions. This bias toward specificity may be due to the fact that this criterion both maximizes inferences that may be drawn from category membership and protects rule induction systems from developing over‐generalizations. (shrink)

Proponents of the value ladenness of science rely primarily on arguments from underdetermination or inductive risk, which share the premise that we should only consider values where the evidence runs out or leaves uncertainty; they adopt a criterion of lexical priority of evidence over values. The motivation behind lexical priority is to avoid reaching conclusions on the basis of wishful thinking rather than good evidence. This is a real concern, however, that giving lexical priority to evidential considerations over values (...) is a mistake and unnecessary for avoiding the wishful thinking. Values have a deeper role to play in science. (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.

A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions—namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. In (...) two new experiments we established a double dissociation of deductive and inductive instructions when validity and plausibility of conditional problems were pitted against each other. This indicates that at least two processes contribute to conditional reasoning. We conclude that single-process theories of conditional reasoning cannot explain the observed results. Theories that postulate at least two processes are needed to account for our findings. (shrink)

Inductive reasoning is a fundamental and complex aspect of human intelligence. In particular, how do subjects, given a set of particular examples, generate general descriptions of the rules governing that set? We present a biologically plausible method for accomplishing this task and implement it in a spiking neuron model. We demonstrate the success of this model by applying it to the problem domain of Raven's Progressive Matrices, a widely used tool in the field of intelligence testing. The model is (...) able to generate the rules necessary to correctly solve Raven's items, as well as recreate many of the experimental effects observed in human subjects. (shrink)

Several current theories have essences as primary drivers of inductive potential: e.g., people infer dogs share properties because they share essences. We investigated the possibility that people take occupational roles as having robust inductive potential because of a different source: their position in stable social institutions. In Studies 1–4, participants learned a novel property about a target, and then decided whether two new individuals had the property (one with the same occupation, one without). Participants used occupational roles to (...) robustly generalize rights and obligations, functional behaviors, personality traits, and skills. In Studies 5–6, we contrasted occupational roles (via label) with race/gender (via visual face cues). Participants reliably favored occupational roles over race/gender for generalizing rights and obligations, functional behaviors, personality traits, and skills (they favored race/gender for inferring leisure behaviors and physiological properties). Occupational roles supported inferences to the same extent as animal categories (Studies 4 and 6). In Study 7, we examined why members of occupational roles share properties. Participants did not attribute the inductive potential of occupational roles to essences, they attributed it to social institutions. In combination, these seven studies demonstrate that any theory of inductive potential must pluralistically allow for both essences and social institutions to form the basis of inductive potential. (shrink)

Does the Bayesian theory of confirmation put real constraints on our inductive behavior? Or is it just a framework for systematizing whatever kind of inductive behavior we prefer? Colin Howson (Hume's Problem) has recently championed the second view. I argue that he is wrong, in that the Bayesian apparatus as it is usually deployed does constrain our judgments of inductive import, but also that he is right, in that the source of Bayesianism's inductive prescriptions is not (...) the Bayesian machinery itself, but rather what David Lewis calls the ``Principal Principle''. (shrink)

Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’.

According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of sentences of a first-order predicate language, however, it is by no means obvious how to determine these maximal entropy functions. This paper makes progress on the problem in the following ways. Firstly, we introduce the concept of a limit (...) in entropy and show that, if the set of probability functions satisfying the premisses contains a limit in entropy, then this limit point is unique and is the maximal entropy probability function. Next, we turn to the special case in which the premisses are categorical sentences of the logical language. We show that if the uniform probability function gives the premisses positive probability, then the maximal entropy function can be found by simply conditionalising this uniform prior on the premisses. We generalise our results to demonstrate agreement between the maximal entropy approach and Jeffrey conditionalisation in the case in which there is a single premiss that specifies the probability of a sentence of the language. We show that, after learning such a premiss, certain inferences are preserved, namely inferences to inductive tautologies. Finally, we consider potential pathologies of the approach: we explore the extent to which the maximal entropy approach is invariant under permutations of the constants of the language, and we discuss some cases in which there is no maximal entropy probability function. (shrink)

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)

This note makes a contribution to the issue raised in a paper by Popper and Miller (1983) in which it was claimed that probabilistic support is purely deductive. Developing R. C. Jeffrey's remarks, a new general approach to the crucial concept of "going beyond" is here proposed. By means of it a quantitative measure of the inductive component of a probabilistic inference is reached. This proposal leads to vindicating the view that typical predictive probabilistic inferences by enumeration and analogy (...) are purely inductive. (shrink)

Inductive reasoning is fundamental to human cognition, yet it remains unclear how we develop this ability and what might influence our inductive choices. We created novel categories in which crucial factors such as domain and category structure were manipulated orthogonally. We trained 403 4–9-year-old children to categorise well-matched natural kind and artefact stimuli with either featural or relational category structure, followed by induction tasks. This wide age range allowed for the first full exploration of the developmental trajectory of (...) inductive reasoning in both domains. We found a gradual transition from perceptual to categorical induction with age. This pattern was stable across domains, but interestingly, children showed a category bias one year later for relational categories. We hypothesise that the ability to use category information in inductive reasoning develops gradually, but is delayed when children need to process and apply more complex category structures. (shrink)

The ‘death of evidence’ issue in Canada raises the spectre of politicized science, and thus the question of what role social values may have in science and how this meshes with objectivity and evidence. I first criticize philosophical accounts that have to separate different steps of research to restrict the influence of social and other non-epistemic values. A prominent account that social values may play a role even in the context of theory acceptance is the argument from inductive risk. (...) It maintains that the more severe the social consequences of erroneously accepting a theory would be, the more evidence is needed before the theory may be accepted. However, an implication of this position is that increasing evidence makes the impact of social values converge to zero; and I argue for a stronger role for social values. On this position, social values may determine a theory’s conditions of adequacy, which among other things can include co.. (shrink)

Viewing moral scepticism as the rejection of objective desirabilities, inductive scepticism may be seen as the rejection of objective believabilities. Moral scepticism leads naturally to amoralism rather than subjectivism, and inductive scepticism undermines not our practices of induction but only a view about justification. The two scepticisms together amount to the adoption of a defensibly narrow, formal view of reason.

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work (...) constitutes essential reading for anyone seeking a full understanding of Mill's thought. Continuing the discussion of induction, Volume 2 concludes with Book VI, 'On the Logic of the Moral Sciences', in which Mill applies empirical reasoning to human behaviour. A crucial early formulation of his thinking regarding free will and necessity, this book establishes the centrality of 'the social science' to Mill's philosophy. (shrink)

It is a privilege to be invited to contribute to the Festschrift dedicated to Professor Johan Buitendag, Emeritus Dean, Faculty of Theology and Religion at the University of Pretoria, South Africa. While his own work often examined the relationship between theology and natural science, he was also passionate about ecumenism and, in that spirit, the present essay utilised what might be described as an inductive approach to an important ecumenical question, the unity between Methodists and Catholics. Ecumenical dialogue is (...) often undertaken from a theological and dogmatic perspective. This essay took a different approach in that it sought to inductively examine what might be described as the inner logic of two ecclesial systems (Methodist and Catholic). In doing so, it was premised upon an Aristotelian philosophical principle, epistemic fit, in that it presupposed that both these ecclesial bodies possess an intrinsic logic that can be brought to the surface in order to exhibit parallel contours in the wider ecclesial terrain.Contribution: This article fits well within the scope of HTS Teologiese Studies/Theological Studies in that it contributed to a new subdiscipline in epistemology, which explores the conceptual and epistemological dimensions of ecclesiology. Using the concept of epistemic fit, the article offered an inductive approach to some of the practical issues that emerge in ecumenical dialogue. (shrink)

In this paper Whewell’s concept of necessity is scrutinized and its historical development is outlined (ca. 1833-1860). Particular attention will be paid to how Whewell interpreted the laws of the inductive sciences as being necessary since the laws of nature are concretizations of the Fundamental Ideas which can be partially described by Axioms.

This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. Accordingly, (...) industry bias does not only threaten existing conventions but may impede their empirically warranted improvement if they align with industry preferences. My empiricist account of standards of inductive risk avoids such a problem by asserting that conventional justification can be pragmatically warranted but has, in principle, only a provisional status. Methodological conventions, therefore, should not only be defended from preference-based infringements on their coordinative function but ought to be subjected to empirical criticism. (shrink)