When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument, (1) If H then E; (2) E; (3) Therefore, (probably) H (here referred to as ‘hypothetico-deductive confirmation argument’), (...) is inductively strong. Yet this argument looks nothing like an inductive generalization, i.e., it does not seem inductive in the term’s traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘induction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction. (shrink)

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is (...) what grounds reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves. (shrink)

Wesley Salmon's account of induction in terms of Bayesian priors and account of Popper is criticized in terms of Joseph Agassi's account.

Arguably, Hume's greatest single contribution to contemporary philosophy of science has been the problem of induction (1739). Before attempting its statement, we need to spend a few words identifying the subject matter of this corner of epistemology. At a first pass, induction concerns ampliative inferences drawn on the basis of evidence (presumably, evidence acquired more or less directly from experience)—that is, inferences whose conclusions are not (validly) entailed by the premises. Philosophers have historically drawn further distinctions, often (...) appropriating the term “induction” to mark them; since we will not be concerned with the philosophical issues for which these distinctions are relevant, we will use the word “inductive” in a catch-all sense synonymous with “ampliative”. But we will follow the usual practice of choosing, as our paradigm example of inductive inferences, inferences about the future based on evidence drawn from the past and present. A further refinement is more important. Opinion typically comes in degrees, and this fact makes a great deal of difference to how we understand inductive inferences. For while it is often harmless to talk about the conclusions that can be rationally believed on the basis of some.. (shrink)

We argue that Cohen’s concept of inductive or ampliative probability facilitates proper explication of sufficient strength for non-demonstrative arguments conforming to the Toulmin model. The data and claims of such arguments are singular statements. We may epistemically classify the warrants of such arguments as empirical (either physical or personal), institutional, or evaluative. Backing evidence and rebutting considerations vary with the epistemic type of warrant, but in each case the notion of ampliative probability for arguments with warrants of that (...) type can be characterized. We may then use ampliative probability to define sufficient strength and related notions for Toulmin arguments. (shrink)

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively (...) or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive. (shrink)

The problem of induction is one of the oldest, and one of the most intractable, of philosophical problems. Possibly its clearest formulation occurs in a celebrated discussion by David Hume, where it is posed as the question of whether there is anything “in any object, considered in itself, which can afford us a reason for drawing a conclusion beyond it.” Hume's answer, famously, is that there is not: “we have no reason to draw any inference concerning any object beyond (...) those of which we have had experience,” even after the observation of their “frequent or constant conjunction” (1739, bk 1, pt III. sec. XII; italics original). However extensive the observational evidence, there is, according to Hume, no legitimate inference to the truth or even the probability of any hypothesis whose logical content transcends that evidence; what today we call ampliative, or inductive, inference is for Hume no species of reasoning at all, merely a psychological propensity (see hume). (shrink)

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These (...) two types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)

Our purpose in this paper is to contribute to a practice-based characterization of scientific inference. We want to explore whether Brandom’s pragmatist–inferentialist framework can suitably accommodate several types of ampliative inference common in scientific reasoning and explanation (probabilistic reasoning, abduction and idealisation). First, we argue that Brandom’s view of induction in terms of merely permissive inferences is inadequate; in order to overcome the shortcoming of Brandom’s proposal, we put forward an alternative conception of inductive, probabilistic reasoning by appeal (...) to the notion of degrees of commitment. Moreover, we examine the sorts of inferential commitments operative in other types of ampliative inferences, such as abduction or reasoning involving idealizations and assumptions. We suggest that agents engaging in these forms of reasoning often undertake restricted inferential commitments, whose scope and reach are more limited that in the case of the commitments associated with full beliefs. (shrink)

This paper considers how explanatory factors can play a role in our ampliative inferential practices. Van Fraassen has argued that there is no possible rational rule that governs ampliative inferences and includes weightings for explanatory beauty. In opposition to van Fraassen, Douven has argued that ampliative inferential rules that include weightings for explanatory factors can be rationally followed. There is, however, a crucial difficulty with Douven's approach: applying the ampliative rule that he suggests leads into irrational (...) belief states. A way to remove the difficulties with Douven's account is suggested. The implications of rationally including explanatory factors in ampliative inferences are then considered. Introduction The proposed interpretations Van Fraassen's justification of the Bayesian approach A rational non-Bayesian interpretation? Further restrictions on D(A,B) Conclusion. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:@ @ Notes and Dlscussaons A NOTE ON CHARLES PEIRCE'S THEORY OF INDUCTION By "Peirce's theory of induction," I refer to a system or collection of ideas which Peirce formulated about the nature and validity of inductive inference or inductive reasoning. This system or collection of ideas covers Peirce's writings from 1867 to 1905.1 During this period of his long philosophical career from 1857 to 1914, Peirce (...) wrote his most important papers on the logic of science and probability. ~ These papers, though only a minor portion of Peirce's philosophical works, constitute a self-explanatory unit of study, simply because they deal with one single subject: the validity of synthetic inference. In the year 1867, Peirce wrote his paper "On the Natural Classification of Arguments," which provides a natural introduction to his treatment of inference and its validity in syllogistic terms and to his trichotomy of inference into deduction, induction, and hypothesis. Through the year 1877 to 1878, Peirce wrote a series of papers on "Illustrations of the Logic of Science." Beside the well-known "The Fixation of Belief" and "How to Make our Ideas Clear," there are four other important but comparatively little discussed papers which are essentially concerned with the logic of science and probability. They are in the following order: "Doctrine of Chances" (with corrections, 1893 and notes, 1910), "The Probability of Induction" (with corrections, 1893), "Deduction, Induction, and Hypothesis" (with corrections, 1893), and "The Order of Nature." In these papers, Peirce laid out his rationale for the validity of ampliative or synthetic inference and indicated a justification of induction in terms of probability. He also made explicit his conception of probabilty in terms of empirical frequency. But very often his ideas concerning the validity of synthetic inference appear disconnected and do not fit into a consistent, not to say wellorganized, whole. It was not until 1883 that Peirce wrote a comparatively systematic treatise on his general theory concerning the validity of ampliative or synthetic inference. This is his "A Theory of Probable inference," in which we find Peirce's statement of what a probable inference is and his argument that inductive inference is valid on account of its being a probable inference. After the year 1883, Peirce's philosophical writings appear to bear little upon his earlier problems in logic of science and probubility. But here and there we find a variety of topics under which Peirce touched the problem of justifying kinds of inference. One significant feature among these is Peirce's recurrent distinction between kinds of induction, a distinction which he had never made in his earlier writings. The distinction is between a "crude induction" (or "pooh-pooh" argument ), a "quantitative induction," and a "qualitative induction." This distinc1See the "Chronological Listing of Peirce's Papers Directly Bearing upon Induction and Probability" in the appendix. 2The earfiest of his papers which we have is dated 1857,and his philosophical activity continued until his death in 1914. [361] 362 HISTORY OF PHILOSOPHY tion is found in the following three short papers: "Three Kinds of Induction" (from "The Logic of Drawing History from Ancient Documents," 1901), "Kinds of Induction" (1903), and "The Varieties and Validity of Induction," (c. 1905). What Peiree calls a "crude induction" is an inference which concludes a universal generalization from what has been found in common in a group of instances. It is induction by simple enumeration. A quantitative induction is an inference from our knowledge of a statistical proportion of individual things having a certain character in a given sample to a conclusion regarding that in the population, from which the sample is chosen. ~ A qualitative induction, on the other hand, is a method of ascertaining factual truths by postulating hypotheses and confirming them on the basis of relevant evidences. That all these three forms of inference are considered induction by Peirce is due to the fact that they do not usually have the form of deduction, and they usually give rise to generalizations which are not deductively warranted by their premises. They differ, nevertheless, because they have different bases for generalizations and their generalizations have different contents. 4 In the light of Peirce's distinction between these three forms... (shrink)

Attempts by 20th century philosophers of science to define inductive concepts and methods concerning the support provided to scientific theories by empirical data have been unsuccessful. Although 20th century philosophers of science largely ignored statistical methods for testing theories, when they did address them they argued against rather than for their use. In contrast, this study demonstrates that traditional statistical methods used for validating computer simulation models provide tests of the scientific theories that those models may embody. This study shows (...) that these statistical methods are applicable regardless of whether the scientific theory or model is deterministic, stochastic, or chaos-based in nature. Traditional statistical methods, such as hypothesis testing, test theories by providing measures of their goodness-of-fit with the portion of the world the theories describe. Nothing more is needed to portray the agreement between theory and the world. Furthermore, the statistical measures of goodness-of-fit are not ampliative inductive measures. Therefore, the ultimate value and direction of the 20 th century ampliative inductive program within philosophy of science is thrown into question. This study also suggests that advanced statistical, visualization, and hybrid quantitative qualitative methods hold promise for offering scientists additional methods for testing scientific theories through validating their computer model representations. As a prerequisite to the above discussions, this study proves that scientific theories, when applied to concrete physical systems, can indeed be represented by computer models. (shrink)

William James’ argument against William Clifford in The Will to Believe is often understood in terms of doxastic efficacy, the power of belief to influence an outcome. Although that is one strand of James’ argument, there is another which is driven by ampliative risk. The second strand of James’ argument, when applied to scientific cases, is tantamount to what is now called the Argument from Inductive Risk. Either strand of James’ argument is sufficient to rebut Clifford's strong evidentialism and (...) show that it is sometimes permissible to believe in the absence of compelling evidence. However, the two considerations have different scope and force. Doxastic efficacy applies in only some cases but allows any values to play a role in determining belief; risk applies in all cases but only allows particular conditional values to play a role. (shrink)

I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peireean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peireean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. (...) In particular, I claim that Peireean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton's thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. (shrink)

The usual, comparative, conception of inference to the best explanation (IBE) takes it to be ampliative. In this paper I propose a conception of IBE ('Holmesian inference') that takes it to be a species of eliminative induction and hence not ampliative. This avoids several problems for comparative IBE (for example, how could it be reliable enough to generate knowledge?). My account of Holmesian inference raises the suspicion that it could never be applied, on the grounds that scientific (...) hypotheses are inevitably underdetermined by the evidence (i.e. are inevitably ampliative). I argue that this concern may be resisted by acknowledging, as Timothy Williamson has shown, that all knowledge is evidence. The latter suggests an approach to resisting scepticism different from those (e.g. the reliabilist approach) that embrace fallibilism. (shrink)

I offer a meta-level analysis of realist arguments for the reliability of ampliative reasoning about the unobservable. We can distinguish form-driven and content-driven arguments for realism: form-driven arguments appeal to the form of inductive inferences, whilst content-driven arguments appeal to their specific content. After regimenting the realism debate in these terms, I will argue that the content-driven arguments are preferable. Along the way I will discuss how my analysis relates to John Norton’s recent, more general thesis that the grounds (...) for licit induction are always material. (shrink)

The paper begins by focusing the basic idea that Gestalt phenomena belong not only to the realm of perception but to the realm of inference. It is shown that Gestalt effects often occur both in counterfactual and in ampliative – i.e. inductive and abductive – reasoning. The main thesis of the paper is that the common feature of such forms of non-deductive reasoning is provided by a rational selection between incompatible conclusions, where rationality lies in the choice of the (...) alternative which preserves the maximum of background information. It is also stressed a distinction between a weak and a strong notion of incompatibility. Such distinction may help in giving account of some alleged Gestalt phenomena which have been recognized in theory construction and theory change. (shrink)

(i) Scientific realism is primarily a metaphysical doctrine about the existence and nature of the unobservables of science. (ii) There are good explanationist arguments for realism, most famously that from the success of science, provided abduction is allowed. Abduction seems to be on an equal footing, at least, with other ampliative methods of inference. (iii) We have no reason to believe a doctrine of empirical equivalence that would sustain the underdetermination argument against realism. (iv) The key to defending realism (...) from the pessimistic meta-induction is that we have greatly improved our capacity to understand the unobservable world over recent centuries. (shrink)

Carnap took the content of a particularsentence or set of sentences to consist in the set ofthe consequences of the sentence or set. This claimequates meaning with inferential role, but itrestricts the inferences to deductive or explicativeones. Here I reject a recent proposal by RobertBrandom, where inductive or ampliative inferences arealso meant to confer contents on expressions. I arguethat if Brandom's inferentialist picture is upheld, andboth explicative and ampliative inferences confermeaning, one consequence of this is that the contentof (...) a sentence is to be read off from our ways ofrationally altering our beliefs. Meaning and contentthen are largely concepts of pragmatics, with no cleartheoretical interest. My critique affects certainaspects of Dummett's meaning-theoretic picture too,and the discussion also links up with the developmentof `dynamic semantics'. (shrink)

For Peirce, logic is essentially illative, a relation of inferential growth. It follows that inference and argumentation are essentially ecstatic, an asymmetrical, ampliative movement from antecedent to consequent. It also follows that logic is inherently inductive. While deduction remains an essential and irreplaceable aspect of logic, it should be seen as a more abstract expression of the illative, semiological essence of inference as such.

This monograph attempts to clarify one significant but much neglected aspect of Peirce's contribution to the philosophy of science. It was written in 1963 as my M. A. thesis at the Uni versity of Illinois. Since the topic is still neglected it is hoped that its pUblication will be of use to Peirce scholars. I should like to acknowledge my indebtedness to Dr. Max Fisch who broached this topic to me and who advised me con tinuously through its development, assisting (...) generously with his own insights and unpublished Peirce manuscripts. TABLE OF CONTENTS INTRODUCTION 1. A Current Issue in the Philosophy of Science 1 2. Peirce and His Theory of Abduction 5 3. The General Character of Abduction 7 PART I: THE EARLY THEORY 1. Peirce's Earliest Conception of Inference 11 2. Three Kinds of Inference and Three Figures of Syllogism 13 3. Ampliative Inference and Cognition 17 4. Induction and Hypothesis 20 5. The Method of Methods 23 PART II: THE LATER THEORY 1. The Transitional Period 28 2. Three Stages of Inquiry 31 3. Abduction and Guessing Instinct 35 4. Logic as a Normative Science 38 5. Hypothesis Construction and Selection 41 6. Abduction and Pragmatism 44 7. Economy of Research 47 8. Justification of Abduction 51 CONCLUSION 55 61 BIBLIOGRAPHY INTRODUCTION 1. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 128-129 [Access article in PDF] Robert Crocker, editor. Religion, Reason and Nature in Early Modern Europe. Dordrecht: Kluwer, 2001. Pp. xix + 228. Cloth, $77.00. By describing the early modern period as such, we thereby avow a continuity with it that ill squares with the following, insufficiently appreciated fact. The early modern counterparts of the largely atheistic American Philosophical Association, let's (...) say, were to an even greater degree theistic, and, moreover, theism affected their description and explanation of the world in a profound way—certainly more so than it does their few theistic descendents. This is true even of authors, like Hobbes and Spinoza, who might be read as leading to later atheism. The fact of early modern theism and its centrality in early modern philosophy and science are amply demonstrated in one after another of the eleven essays of this book.An emblematic figure is Robert Boyle, who figures as a main player in three of the essays, and is at least mentioned in five of the others. Lotte Mulligan, for example, investigates the role of "right reason" in Boyle's argument that religion is illuminated and made [End Page 128] plausible by metaphorically expressed analogies with natural philosophy, and conversely. The upshot is that only the "Christian Virtuoso," endowed with right reason whereby he is inspired to notice and express these analogies, was in a position to interpret the codes expressed both in the book of revelation and in the book of nature, one being incomplete without the other.Luisa Simonutti treats Boyle's engagement with the theological and scientific work of Spinoza through Spinoza's correspondence with Oldenburg. And G. A. J. Rogers deploys the work of Boyle, as well as of Locke, Newton, and the Cambridge Platonists, against the once-standard view (vide Butterfield) that "a major feature of the seventeenth-century was a secularization of knowledge." (Given just the other papers in this volume, this may seem like shooting fish in a barrel. Even so, perhaps one or two of the shots appear to miss. Newton seems proleptically to answer Hume's skepticism about induction by invoking, not divine simplicity, but an argument to the best explanation.)These papers overlap with two others, forming the core of the book. Sarah Hutton and Robert Crocker take on Cambridge Platonism. The former deals with Ralph Cudworth's rejection of Cartesian voluntarism in favor of an intellectualism of goodness and wisdom that grounds both the providential governance of the world and its intelligibility to human inquiry. The latter deals with Henry More's doctrine of the soul's pre-existence, a prima facie unlikely doctrine, but one that is less problematic, according to More, than the orthodox alternatives (creationism and traducianism).Three other papers fall outside this core, but their topics are no less relevant. Perhaps the most undeniable connection between the natural and the supernatural is to be found in Grotius, here studied by Jacqueline Lagree. Likely the most unexpected player will be the eccentric esprit fort, Cyrano de Bergerac. His work of nearly pure fantasy, in the Rabelaisian tradition, might well have made later, more serious heterodoxies possible. James E. Force provides a nice case study in Newton's reliance on what he took to be providentially guided comets as sources for the replenishment of otherwise declining celestial motion and matter (a line which, ironically, was picked up by Hume as a premise of an argument designed to undo the argument from design). Richard H. Popkin outlines three views of Judaism in the period. There is little connection with nature, but an important one with reason via a problem that exercised Cudworth and Newton: most peoples are polytheistic despite the clear monotheism of revelation. One theory had it that Judaism was the original, pure religion, which degenerated into various forms of paganism. But this degeneracy was soon read by the English deists such that originally there was a natural religion, of which Judaism and all others were a degeneration. Transmitted to the Enlightenment by Spinoza... (shrink)

I defend the thesis that most or all perceptual experiences are infused with imaginative contributions. While the idea is not new, it has few supporters. I begin by developing a framework for the underlying debate. Central to that framework is the claim that a perceptual experience is infused with imagination if and only if there are self-generated contributions to that experience that have ampliative effect on its phenomenal and directed elements. Self-generated ingredients to experience are produced by the subject (...) as opposed to being received from the world. Some form of stored content is an obvious starting point. Ampliative effects are aspects of perceptual experience that outstrip the content the senses get from the world. This conceptual framework is applied to three case studies: object-sameness and object-kind recognition (section 2), memory colour (section 3), and perceptual constancy and amodal completion (section 4). If the three cases and my overall analysis are accepted (a substantive if), then we have a forceful inductive argument for perception being infused with imagination. (shrink)

This paper formulates what I think is the basic problem of any attempt to characterise the abstract structure of scientific method, viz., that it has to satisfy two conflicting desiderata: it should be ampliative (contentincreasing) and it should confer epistemic warrant on its outcomes. Then, after two extreme solutions to the problem of the method, viz., Enumerative Induction and the Method of Hypothesis, are examined, the paper argues that abduction, suitably understood as Inference to the Best Explanation, offers (...) the best description of scientific method and solves the foregoing problem in the best way: it strikes the best balance between ampliation and epistemic warrant. (shrink)

I examine Nagarjuna’s averting an opponent’s argument, Paul Sagal’s general interpretation of Nagarjuna and especially Sagal’s conception of "averting" an argument. Following Matilal, a distinction is drawn between locutionary negation and illocationary negation in order to avoid errant interpretations of verse 29 The argument is treated as representing an ampliative or inductive inference rather than a deductive one. As Nagarjuna says in verse 30: "That [denial] of mine [in verse 29] is a non-apprehension of non-things" and non-apprehension is the (...) averting of arguments or "the relinquishing of all views." "Not making a proposition P" would be not speaking P or silence with regard to P and, as Sagal argues, not meaning a global linguistic silence. Such an interpretation would lead to attributing wholesale irrationalism to Nagarjuna-something I wish to avoid. (shrink)

Descartes rejected syllogism and its associated formal account of deductive reasoning. One of his main reasons was his concern for truth, and the ability to recognize new truths and to distinguish truths from falsehoods. Formal logic is non‐ampliative; the conclusion of a deductively valid argument does not impose any constraints on the truths that we know are not already imposed by the premises. Instead of rejecting deduction in favour of induction, like Bacon, Descartes developed a new, ampliative (...) theory of deduction in the Regulae. This theory of inference was based on intuition, a forerunner of his later account of clear and distinct perception. One directly intuited that two ideas were related in a certain way. One deduced that one idea was related to another by forming a chain of ideas, the connection between each idea and its neighbour being perceived by intuition. (shrink)

Inference to the best explanation (IBE) is a pattern of everyday and scientific reasoning, where a hypothesis is accepted if it gives a better explanation of the known evidence than any alternative hypothesis. This term was introduced by Gilbert Harman in 1965, and ever since IBE has been a central theme in the agenda of logic, artificial intelligence, and philosophy of science. However, a similar idea of a special kind of ampliative reasoning (besides deduction and induction) had been (...) advocated by Charles S. Peirce already a century earlier: “hypothetical reasoning” proceeds backward from effects to causes, or “abduction” leads from surprising facts to explanatory theories. The key issues in the explication of IBE concern the definition of “the best explanation” and the possibility of analyzing the nature of explanatory reasoning by the Bayesian probabilistic approach or by the truthlikeness framework. -/- . (shrink)

Among the many issues that relate to the role of Reason in science, I will focus my attention on two. The first concerns the problem of the justification of scientific method—and of induction in particular, which is the most basic and indispensable ampliative method of science. The second is related to the problem of theory-change in science: how can it be that theory-change is rational? In addressing these two issues (highlighting both their conceptual development and their present status), (...) I will try to stress the need for a conception of method and rationality that leaves room for values. (shrink)

As it is standardly conceived, Inference to the Best Explanation (IBE) is a form of ampliative inference in which one infers a hypothesis because it provides a better potential explanation of one’s evidence than any other available, competing explanatory hypothesis. Bas van Fraassen famously objected to IBE thus formulated that we may have no reason to think that any of the available, competing explanatory hypotheses are true. While revisionary responses to the Bad Lot Objection concede that IBE needs to (...) be reformulated in light of this problem, reactionary responses argue that the Bad Lot Objection is fallacious, incoherent, or misguided. This paper shows that the most influential reactionary responses to the Bad Lot Objection do nothing to undermine the original objection. This strongly suggests that proponents of IBE should focus their efforts on revisionary responses, i.e. on finding a more sophisticated characterization of IBE for which the Bad Lot Objection loses its bite. (shrink)

I offer a meta-level analysis of realist arguments for the reliability of ampliative reasoning about the unobservable. We can distinguish form-driven and content-driven arguments for realism: form-driven arguments appeal to the form of inductive inferences, whilst content-driven arguments appeal to their specific content. After regimenting the realism debate in these terms, I will argue that the content-driven arguments are preferable. Along the way I will discuss how my analysis relates to John Norton’s recent, more general thesis that the grounds (...) for licit induction are always material. (shrink)

Abstract The opening section outlines probabilism in the 20th century philosophy and shortly discusses the major accomplishments of Polish probabilist thinkers. A concise characterization of Bayesianism as the major recent form of probabilism follows. It builds upon the core personalist version of Bayesianism towards more objectively oriented versions thereof. The problem of a priori probability is shortly discussed. A tentative characterization of Kazimierz Ajdukiewicz’s standpoint regarding the inductive inference is cast in Bayesian terms. His objections against it presented in Pragmatic (...) Logic are presented. His 1958 paper on justification of non-deductive inference, as amply demonstrated by K. Szaniawski and I. Niiniluoto, extends his earlier Baysian position from 1928 monograph. In the closing section Ajdukiewicz’s standpoint is presented as a characteristically pragmatist and empiricist version of Bayesianism, which remains an unexplored and stimulating position. (shrink)

I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defend an ‘inferential’ (...) approach to the heuristic power of representations by arguing that these representations draw on ampliative inferences such as analogies and inductions. In effect, in order to construct a representation, we have to ‘assimilate’ diverse things, and this requires identifying similarities between them. These similarities form the basis for ampliative inferences that gradually build hypotheses to solve a problem.To support my thesis, I analyse two examples. The first one is intra-field, that is, the construction of an algebraic representation of 3-manifolds; the second is inter-fields, that is, the construction of a topological representation of DNA supercoiling. (shrink)

This article calls into question the charge that frequentist testing is susceptible to the base-rate fallacy. It is argued that the apparent similarity between examples like the Harvard Medical School test and frequentist testing is highly misleading. A closer scrutiny reveals that such examples have none of the basic features of a proper frequentist test, such as legitimate data, hypotheses, test statistics, and sampling distributions. Indeed, the relevant error probabilities are replaced with the false positive/negative rates that constitute deductive calculations (...) based on known probabilities among events. As a result, the ampliative dimension of frequentist induction—learning from data about the underlying data-generating mechanism—is missing. *Received August 2009; revised January 2010. †To contact the author, please write to: Department of Economics, Virginia Tech, Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

Underdetermination is a relation between evidence and theory. More accurately, it is a relation between the propositions that express the (relevant) evidence and the propositions that constitute the theory. Evidence is said to underdetermine theory. This may mean two things. First, the evidence cannot prove the truth of the theory. Second, the evidence cannot render the theory probable. Let’s call the first deductive underdetermination, and the second inductive (or ampliative) underdetermination. Both kinds of claim are supposed to have a (...) certain epistemic implication, viz., that belief in theory is never warranted by the evidence. This is the underdetermination thesis. (shrink)

Most scientists would hold that science has not established that the cosmos is physically comprehensible – i.e. such that there is some as-yet undiscovered true physical theory of everything that is unified. This is an empirically untestable, or metaphysical thesis. It thus lies beyond the scope of science. Only when physics has formulated a testable unified theory of everything which has been amply corroborated empirically will science be in a position to declare that it has established that the cosmos is (...) physically comprehensible. But this argument presupposes a widely accepted but untenable conception of science which I shall call standard empiricism. According to standard empiricism, in science theories are accepted solely on the basis of evidence. Choice of theory may be influenced for a time by considerations of simplicity, unity, or explanatory capacity, but not in such a way that the universe itself is permanently assumed to be simple, unified or physically comprehensible. In science, no thesis about the universe can be accepted permanently as a part of scientific knowledge independently of evidence. Granted this view, it is clear that science cannot have established that the universe is physically comprehensible. Standard empiricism is, however, as I have indicated, untenable. Any fundamental physical theory, in order to be accepted as a part of theoretical scientific knowledge, must satisfy two criteria. It must be (1) sufficiently empirically successful, and (2) sufficiently unified. Given any accepted theory of physics, endlessly many empirically more successful disunified rivals can always be concocted – disunified because they assert that different dynamical laws govern the diverse phenomena to which the theory applies. These disunified rivals are not considered for a moment in physics, despite their greater empirical success. This persistent rejection of empirically more successful but disunified rival theories means, I argue, that a big, highly problematic, implicit assumption is made by science about the cosmos, to the effect, at least, that the cosmos is such that all seriously disunified theories are false. Once this point is recognized, it becomes clear, I argue, that we need a new conception of science which makes explicit, and so criticizable and improvable the big, influential, and problematic assumption that is at present implicit in physics in the persistent preference for unified theories. This conception of science, which I call aim-oriented empiricism, represents the assumption of physics in the form of a hierarchy of assumptions. As one goes up the hierarchy, the assumptions become less and less substantial, and more and more nearly such that their truth is required for science, or the pursuit of knowledge, to be possible at all. At each level, that assumption is accepted which (a) best accords with the next one up, and (b) has, associated with it the most empirically progressive research programme in physics, or holds out the greatest hope of leading to such an empirically progressive research programme. In this way a framework of relatively insubstantial, unproblematic, fixed assumptions and associated methods is created, high up in the hierarchy, within which much more substantial and problematic assumptions and associated methods, low down in the hierarchy, can be changed, and indeed improved, as scientific knowledge improves. One assumption in this hierarchy of assumptions, I argue, is that the cosmos is physically comprehensible – that is, such that some yet-to-be-discovered unified theory of everything is true. Hence the conclusion: improve our ideas about the nature of science and it becomes apparent that science has already established that the cosmos is physically comprehensible – in so far as science can ever establish anything theoretical. (shrink)

In this article I take a loose, functional approach to defining induction: Inductive forms of reasoning include those prima facie reasonable inference patterns that one finds in science and elsewhere that are not clearly deductive. Inductive inference is often taken to be reasoning from the observed to the unobserved. But that is incorrect, since the premises of inductive inferences may themselves be the results of prior inductions. A broader conception of inductive inference regards any ampliative inference as inductive, (...) where an ampliative inference is one where the conclusion ‘goes beyond’ the premises. ‘Goes beyond’ may mean (i) ‘not deducible from’ or (ii) ‘not entailed by’. Both of these are problematic. Regarding (i), some forms of reasoning might have a claim to be called ‘inductive’ because of their role in science, yet turn out to be deductive after all—for example eliminative induction (see below) or Aristotle’s ‘perfect induction’ which is an inference to a generalization from knowledge of every one of its instances. Interpretation (ii) requires that the conclusions of scientific reasoning are always contingent propositions, since necessary propositions are entailed by any premises. But there are good reasons from metaphysics for thinking that many general propositions of scientific interest and known by inductive inference (e.g. “all water is H2O”) are necessarily true. Finally, both (i) and (ii) fail to take account of the fact that there are many ampliative forms of inference one would not want to call inductive, such as counter-induction (exemplified by the ‘gambler’s fallacy’ that the longer a roulette wheel has come up red the more likely it is to come up black on the next roll). Brian Skyrms (1999) provides a useful survey of the issues involved in defining what is meant by ‘inductive argument’. Inductive knowledge will be the outcome of a successful inductive inference. But much discussion of induction concerns the theory of confirmation, which seeks to answer the question, “when and to what degree does evidence support an hypothesis?” Usually, this is understood in an incremental sense and in a way that relates to the rational credibility of a hypothesis: “when and by how much does e add to the credibility of h?”, although ‘confirms’ is sometimes used in an absolute sense to indicate total support that exceeds some suitably high threshold.. (shrink)

In this paper, I consider the pessimistic induction construed as a deductive argument (specifically, reductio ad absurdum) and as an inductive argument (specifically, inductive generalization). I argue that both formulations of the pessimistic induction are fallacious. I also consider another possible interpretation of the pessimistic induction, namely, as pointing to counterexamples to the scientific realist’s thesis that success is a reliable mark of (approximate) truth. I argue that this interpretation of the pessimistic induction fails, too. If (...) this is correct, then the pessimistic induction is an utter failure that should be abandoned by scientific anti-realists. (shrink)

We completely characterize the logical hierarchy of subsystems of open induction introduced by Boughattas [1].

This article poses a challenge to Schurz’s proposed metainductive justification of induction. It is argued that Schurz’s argument requires a notion of optimality that can deal with an expanding pool of prediction strategies.

The necessitarian solution to the problem of induction involves two claims: first, that necessary connections are justified by an inference to the best explanation; second, that the best theory of necessary connections entails the timeless uniformity of nature. In this paper, I defend the second claim. My arguments are based on considerations from the metaphysics of laws, properties, and fundamentality.

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that the celebrated “problem of induction” can no longer be set up and is thereby dissolved. Attempts to recreate the problem in the material theory of induction fail. They require relations of inductive support to conform to an (...) unsustainable, hierarchical empiricism. (shrink)