Gabbay / Woods / Hartmann Inductive Logic

1. Auflage 2011
ISBN: 978-0-08-093169-2
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 10, 800 Seiten

Reihe: Handbook of the History of Logic

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic - as this handbook attests - is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. - Chapter on the Port Royal contributions to probability theory and decision theory - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights

Autoren/Hrsg.

Gabbay, Dov M.

Woods, John

Hartmann, Stephan

Inhaltsverzeichnis

1;Front Cover
;1
2;Inductive Logic
;4
3;Copyright Page
;5
4;Contents;6
5;Introduction;8
6;Contributors;10
7;Induction Before Hume;14
7.1;1 The Ancient World;14
7.2;2 The Middle Ages;27
7.3;3 The Renaissance;33
7.4;4 The Seventeenth Century and Early Eighteenth Century;36
7.5;5 Conclusion;49
7.6;Bibliography;50
8;Hume and the Problem of Induction;56
8.1;1 Introduction;56
8.2;2 Two Problems of Induction;58
8.3;3 Hume's Fork: The First Option;60
8.4;4 Hume's Fork: The Second Option;68
8.5;5 Three Ways of Rejecting Hume's Problem;74
8.6;6 Hume's Conclusion;80
8.7;7 Bonjour's a Priori Justification of Induction;83
8.8;8 Reichenbach's Pragmatic Justification of Induction;87
8.9;9 Bayesian Approaches;93
8.10;10 Williams' Combinatorial Justification of Induction;96
8.11;11 The Inductive Leap as Mythical;99
8.12;12 Conclusion;101
8.13;Bibliography;101
9;The Debate between Whewell and Mill on the Nature of Scientific Induction;106
9.1;1 Why the Debate is not Merely Terminological;106
9.2;2 The Kepler Example and the Colligation of Facts;108
9.3;3 Whewell's Tests of Hypotheses;115
9.4;4 Disputes about Induction that have Ignored these Lessons;118
9.5;5 Implications for Probabilistic Theories of Evidence and Confirmation;122
9.6;Acknowledgements;127
9.7;Bibliography;127
10;An Explorer Upon Untrodden Ground: Peirce on Abduction;130
10.1;1 Introduction;130
10.2;2 Ideas from Kant and Aristotle;131
10.3;3 Peirce's Two-Dimensional Framework;133
10.4;4 Hypothesis vs Induction;137
10.5;5 The Road to Abduction;144
10.6;6 From the Instinctive to the Reasoned Marks of Truth;149
10.7;7 The Three Stages of Inquiry;156
10.8;8 Looking Ahead;160
10.9;Further Reading;163
10.10;Bibliography;163
11;The Modern Epistemic Interpretations of Probability: Logicism and Subjectivism;166
11.1;1 The Logical Interpretation of Probability;166
11.2;2 The Subjective Interpretation of Probability;190
11.3;Concluding Remarks;209
11.4;Bibliography;210
12;Popper and Hypothetico-Deductivism;218
12.1;Enthymemes and their Deductivist Reconstructions;219
12.2;'Automobile Logic';220
12.3;Formal and Semantic Validity;221
12.4;Historical Interlude: Mill Versus Aristotle;223
12.5;Wittgensteinian Instrumentalism;228
12.6;'Logic of Discovery' — Deductive or Inductive?;231
12.7;'Logic of Justification' — Deductive or Inductive?;238
12.8;Getting Started — 'Foundational Beliefs';245
12.9;Bibliography;246
13;Hempel and the Paradoxes of Confirmation;248
13.1;1 Towards a Logic of Confirmation;248
13.2;2 Adequacy Criteria;251
13.3;3 The Satisfaction Criterion;254
13.4;4 The Raven Paradox;259
13.5;5 The Bayesian's Raven Paradox;265
13.6;6 Summary;273
13.7;Acknowledgements;274
13.8;Bibliography;274
14;Carnap and the Logic of Inductive Inference;278
14.1;1 Introduction;278
14.2;2 Probability;278
14.3;3 Confirmation;282
14.4;4 Exchangeability;284
14.5;5 The Continuum of Inductive Methods;287
14.6;6 Confirmation of Universal Generalizations;291
14.7;7 Instantial Relevance;294
14.8;8 Finite Exchangeability;295
14.9;9 The First Induction Theorem;301
14.10;10 Analogy;301
14.11;11 The Sampling of Species Problem;307
14.12;12 A Budget of Paradoxes;309
14.13;13 Carnap Redux;312
14.14;14 Conclusion;318
14.15;Bibliography;318
15;The Development of the Hintikka Program;324
15.1;1 Inductive Logic as a Methodological Research Program;324
15.2;2 From Carnap to Hintikka's Two-Dimensional Continuum;328
15.3;3 Axiomatic Inductive Logic;335
15.4;4 Extensions of Hintikka's System;338
15.5;5 Semantic Information;342
15.6;6 Confirmation and Acceptance;345
15.7;7 Cognitive Decision Theory;347
15.8;8 Inductive Logic and Theories;350
15.9;9 Analogy and Observational Errors;353
15.10;10 Truthlikeness;356
15.11;11 Machine Learning;359
15.12;12 Evaluation of the Hintikka Program;362
15.13;Bibliography;365
16;Hans Reichenbach's Probability Logic;370
16.1;1 Introduction;370
16.2;2 Probability Logic: The Basic Set-Up;373
16.3;3 Probabilities as Limiting Frequencies;376
16.4;4 Probability Logic;382
16.5;5 Critics: Popper, Nagel and Russell;390
16.6;6 Reichenbach on the Attempts of others and on Standard Problems;395
16.7;7 Commentary;397
16.8;Bibliography;400
17;Goodman and the Demise of Syntactic and Semantic Models;404
17.1;1 Historical Background;404
17.2;2 Developments in the Twentieth Century;406
17.3;3 The New Riddle of Induction;408
17.4;4 Some Misunderstandings;410
17.5;5 Proposed Asymmetries;412
17.6;6 The Entrenchment Solution;414
17.7;7 Implications;416
17.8;8 Values, Virtues and Hypothesis Selection;419
17.9;Bibliography;424
18;The Development of Subjective Bayesianism;428
18.1;2 The Problem of the Priors;436
18.2;3 Inductive Inference as Updating Subjective Probability;460
18.3;4 Subjective Probability and Objective Chance;471
18.4;5 Conclusion;485
18.5;Bibliography;486
19;Varieties of Bayesianism;490
19.1;1 Introduction;490
19.2;2 Interpretations of Probability;498
19.3;3 The Subjective-Objective Continuum;506
19.4;4 Justifications;529
19.5;5 Decision Theory;540
19.6;6 Confirmation Theory;547
19.7;7 Theories of Belief (A.K.A. Acceptance);553
19.8;8 Summary;558
19.9;Bibliography;559
20;Inductive Logic and Empirical Psychology;566
20.1;Introduction;566
20.2;1 The Bayesian Approach to Cognition;570
20.3;2 Language;577
20.4;3 Inductive Reasoning;584
20.5;4 Deductive Reasoning;590
20.6;5 Decision Making;606
20.7;6 Argumentation;614
20.8;7 Challenges and Future Directions;618
20.9;Conclusion;622
20.10;Acknowledgements;623
20.11;Bibliography;623
21;Inductive Logic and Statistics;638
21.1;1 From Inductive Logic to Statistics;638
21.2;2 Observational Data;639
21.3;3 Inductive Inference;641
21.4;4 Carnapian Logics;643
21.5;5 Bayesian Statistics;645
21.6;6 Inductive Logic with Hypotheses;648
21.7;7 Neyman-Pearson Testing;650
21.8;8 Neyman-Pearson Test as an Inference;653
21.9;9 Fisher's Parameter Estimation;656
21.10;10 Estimations in Inductive Logic;657
21.11;11 Fiducial Probability;659
21.12;12 In Conclusion;661
21.13;Acknowledgements;662
21.14;Bibliography;662
22;Statistical Learning Theory: Models, Concepts, and Results;664
22.1;1 Introduction;664
22.2;2 The Standard Framework of Statistical Learning Theory;664
22.3;3 Consistency and Generalization for the K-Nearest Neighbor Classifier;677
22.4;4 Empirical Risk Minimization;680
22.5;5 Capacity Concepts and Generalization Bounds;686
22.6;6 Incorporating Knowledge into the Bounds;696
22.7;7 The Approximation Error and Bayes Consistency;700
22.8;8 No Free Lunch Theorem;705
22.9;9 Model Based Approaches to Learning;708
22.10;10 The vc Dimension, Popper's Dimension, and the Number of Parameters;715
22.11;11 Conclusion;717
22.12;Acknowledgements;717
22.13;Bibliography;718
23;Formal Learning Theory in Context;720
23.1;Introduction;720
23.2;The Character of Formal Learning Theory;720
23.3;Confidence Intervals;725
23.4;Comparison;728
23.5;Conclusion;729
23.6;Bibliography;730
24;Mechanizing Induction;732
24.1;1 Machine Learning and Computational Learning Theory;732
24.2;2 Nonmonotonic Reasoning;751
24.3;Acknowledgements;779
24.4;Bibliography;779
25;Index;786

Leseproben

Handbook of the History of Logic, Vol. 10, Suppl (C), 2011 ISSN: 1874-5857 doi: 10.1016/B978-0-444-52936-7.50002-1 Hume and the Problem of Induction Marc Lange 1 Introduction
David Hume first posed what is now commonly called “the problem of induction” (or simply “Hume’s problem”) in 1739 — in Book 1, Part iii, section 6 (“Of the inference from the impression to the idea”) of A Treatise of Human Nature (hereafter T). In 1748, he gave a pithier formulation of the argument in Section iv (“Skeptical doubts concerning the operations of the understanding”) of An Enquiry Concerning Human Understanding (E).1 Today Hume’s simple but powerful argument has attained the status of a philosophical classic. It is a staple of introductory philosophy courses, annually persuading scores of students of either the enlightening or the corrosive effect of philosophical inquiry – since the argument appears to undermine the credentials of virtually everything that passes for knowledge in their other classes (mathematics notably excepted2). According to the standard interpretation, Hume’s argument purports to show that our opinions regarding what we have not observed have no justification. The obstacle is irremediable; no matter how many further observations we might make, we would still not be entitled to any opinions regarding what we have not observed. Hume’s point is not the relatively tame conclusion that we are not warranted in making any predictions with total certainty. Hume’s conclusion is more radical: that we are not entitled to any degree of confidence whatever, no matter how slight, in any predictions regarding what we have not observed. We are not justified in having 90% confidence that the sun will rise tomorrow, or in having 70% confidence, or even in being more confident that it will rise than that it will not. There is no opinion (i.e., no degree of confidence) that we are entitled to have regarding a claim concerning what we have not observed. This conclusion “leaves not the lowest degree of evidence in any proposition” that goes beyond our present observations and memory (T, p. 267). Our justified opinions must be “limited to the narrow sphere of our memory and senses” (E, p. 36). Hume’s problem has not gained its notoriety merely from Hume’s boldness in denying the epistemic credentials of all of the proudest products of science (and many of the humblest products of common-sense). It takes nothing for someone simply to declare himself unpersuaded by the evidence offered for some prediction. Hume’s problem derives its power from the strength of Hume’s argument that it is impossible to justify reposing even a modest degree of confidence in any of our predictions. Again, it would be relatively unimpressive to argue that since a variety of past attempts to justify inductive reasoning have failed, there is presumably no way to justify induction and hence, it seems, no warrant for the conclusions that we have called upon induction to support. But Hume’s argument is much more ambitious. Hume purports not merely to show that various, apparently promising routes to justifying induction all turn out to fail, but also to exclude every possible route to justifying induction. Naturally, many philosophers have tried to find a way around Hume’s argument — to show that science and common-sense are justified in making predictions inductively. Despite these massive efforts, no response to date has received widespread acceptance. Inductive reasoning remains (in C.D. Broad’s famous apothegm) “the glory of Science” and “the scandal of Philosophy” [Broad, 1952, p. 143]. Some philosophers have instead embraced Hume’s conclusion but tried to characterize science so that it does not involve our placing various degrees of confidence in various predictions. For example, Karl Popper has suggested that although science refutes general hypotheses by finding them to be logically inconsistent with our observations, science never confirms (even to the smallest degree) the predictive accuracy of a general hypothesis. Science has us make guesses regarding what we have not observed by using those general hypotheses that have survived the most potential refutations despite sticking their necks out furthest, and we make these guesses even though we have no good reason to repose any confidence in their truth: I think that we shall have to get accustomed to the idea that we must not look upon science as a ‘body of knowledge,’ but rather as a system of hypotheses; that is to say, a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests, and of which we are never justified in saying that we know that they are ‘true’ or ‘more or less certain’ or even ‘probable’. [Popper, 1959, p. 317; cf. Popper, 1972] However, if we are not justified in having any confidence in a prediction’s truth, then it is difficult to see how it could be rational for us to rely upon that prediction [Salmon, 1981]. Admittedly, “that we cannot give a justification … for our guesses does not mean that we may not have guessed the truth.” [Popper, 1972, p. 30] But if we have no good reason to be confident that we have guessed the truth, then we would seem no better justified in being guided by the predictions of theories that have passed their tests than in the predictions of theories that have failed their tests. There would seem to be no grounds for calling our guesswork “rational”, as Popper does. Furthermore, Popper’s interpretation of science seems inadequate. Some philosophers, such as van Fraassen [1981; 1989], have denied that science confirms the truth of theories about unobservable entities (such as electrons and electric fields), the truth of hypotheses about the laws of nature, or the truth of counterfactual conditionals (which concern what would have happened under circumstances that actually never came to pass — for example, “Had I struck the match, it would have lit”). But these philosophers have argued that these pursuits fall outside of science because we need none of them in order to confirm the empirical adequacy of various theories, a pursuit that is essential to science. So even these interpretations of science are not nearly as austere as Popper’s, according to which science fails to accumulate evidence for empirical predictions. In this essay, I will devote sections 2, 3, and 4 to explaining Hume’s argument and offering some criticism of it. In section 6, I will look at the conclusion that Hume himself draws from it. In sections 5 and 7-11, I will review critically a few of the philosophical responses to Hume that are most lively today.3 2 Two Problems of Induction
Although Hume never uses the term “induction” to characterize his topic, today Hume’s argument is generally presented as targeting inductive reasoning: any of the kinds of reasoning that we ordinarily take as justifying our opinions regarding what we have not observed. Since Hume’s argument exploits the differences between induction and deduction, let’s review them. For the premises of a good deductive argument to be true, but its conclusion to be false, would involve a contradiction. (In philosophical jargon, a good deductive argument is “valid”.) For example, a geometric proof is deductive since the truth of its premises ensures the truth of its conclusion by a maximally strong (i.e., “logical”) guarantee: on pain of contradiction! That deduction reflects the demands of non-contradiction (a semantic point) has a metaphysical consequence — in particular, a consequence having to do with necessity and possibility. A contradiction could not come to pass; it is impossible. So it is impossible for the premises of a good deductive argument to be true but its conclusion to be false. (That is why deduction’s “guarantee” is maximally strong.) It is impossible for a good deductive argument to take us from a truth to a falsehood (i.e., to fail to be “truth-preserving”) because such failure would involve a contradiction and contradictions are impossible. A good deductive argument is necessarily truthpreserving. In contrast, no contradiction is involved in the premises of a good inductive argument being true and its conclusion being false. (Indeed, as we all know, this sort of thing is a familiar fact of life; our expectations, though justly arrived at by reasoning inductively from our observations, sometimes fail to be met.) For example, no matter how many human cells we have examined and found to contain proteins, there would be no contradiction between our evidence and a given as yet unobserved human cell containing no proteins. No contradiction is involved in a good inductive argument’s failure to be truth-preserving. Once again, this semantic point has a metaphysical consequence if every necessary truth is such that its falsehood involves a...