Inductive Logic (eBook)

Dov M. Gabbay, John Woods, Stephan Hartmann (Herausgeber)

eBook Download: PDF | EPUB

2011 | 1. Auflage
800 Seiten
Elsevier Reference Monographs (Verlag)
978-0-08-093169-2 (ISBN)

Infos

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

Inhalt

Front Cover 
1 
Inductive Logic 
4 
Copyright Page 
5 
Contents 6
Introduction 8
Contributors 10
Induction Before Hume 14
1 The Ancient World 14
2 The Middle Ages 27
3 The Renaissance 33
4 The Seventeenth Century and Early Eighteenth Century 36
5 Conclusion 49
Bibliography 50
Hume and the Problem of Induction 56
1 Introduction 56
2 Two Problems of Induction 58
3 Hume's Fork: The First Option 60
4 Hume's Fork: The Second Option 68
5 Three Ways of Rejecting Hume's Problem 74
6 Hume's Conclusion 80
7 Bonjour's a Priori Justification of Induction 83
8 Reichenbach's Pragmatic Justification of Induction 87
9 Bayesian Approaches 93
10 Williams' Combinatorial Justification of Induction 96
11 The Inductive Leap as Mythical 99
12 Conclusion 101
Bibliography 101
The Debate between Whewell and Mill on the Nature of Scientific Induction 106
1 Why the Debate is not Merely Terminological 106
2 The Kepler Example and the Colligation of Facts 108
3 Whewell's Tests of Hypotheses 115
4 Disputes about Induction that have Ignored these Lessons 118
5 Implications for Probabilistic Theories of Evidence and Confirmation 122
Acknowledgements 127
Bibliography 127
An Explorer Upon Untrodden Ground: Peirce on Abduction 130
1 Introduction 130
2 Ideas from Kant and Aristotle 131
3 Peirce's Two-Dimensional Framework 133
4 Hypothesis vs Induction 137
5 The Road to Abduction 144
6 From the Instinctive to the Reasoned Marks of Truth 149
7 The Three Stages of Inquiry 156
8 Looking Ahead 160
Further Reading 163
Bibliography 163
The Modern Epistemic Interpretations of Probability: Logicism and Subjectivism 166
1 The Logical Interpretation of Probability 166
2 The Subjective Interpretation of Probability 190
Concluding Remarks 209
Bibliography 210
Popper and Hypothetico-Deductivism 218
Enthymemes and their Deductivist Reconstructions 219
'Automobile Logic' 220
Formal and Semantic Validity 221
Historical Interlude: Mill Versus Aristotle 223
Wittgensteinian Instrumentalism 228
'Logic of Discovery' — Deductive or Inductive? 231
'Logic of Justification' — Deductive or Inductive? 238
Getting Started — 'Foundational Beliefs' 245
Bibliography 246
Hempel and the Paradoxes of Confirmation 248
1 Towards a Logic of Confirmation 248
2 Adequacy Criteria 251
3 The Satisfaction Criterion 254
4 The Raven Paradox 259
5 The Bayesian's Raven Paradox 265
6 Summary 273
Acknowledgements 274
Bibliography 274
Carnap and the Logic of Inductive Inference 278
1 Introduction 278
2 Probability 278
3 Confirmation 282
4 Exchangeability 284
5 The Continuum of Inductive Methods 287
6 Confirmation of Universal Generalizations 291
7 Instantial Relevance 294
8 Finite Exchangeability 295
9 The First Induction Theorem 301
10 Analogy 301
11 The Sampling of Species Problem 307
12 A Budget of Paradoxes 309
13 Carnap Redux 312
14 Conclusion 318
Bibliography 318
The Development of the Hintikka Program 324
1 Inductive Logic as a Methodological Research Program 324
2 From Carnap to Hintikka's Two-Dimensional Continuum 328
3 Axiomatic Inductive Logic 335
4 Extensions of Hintikka's System 338
5 Semantic Information 342
6 Confirmation and Acceptance 345
7 Cognitive Decision Theory 347
8 Inductive Logic and Theories 350
9 Analogy and Observational Errors 353
10 Truthlikeness 356
11 Machine Learning 359
12 Evaluation of the Hintikka Program 362
Bibliography 365
Hans Reichenbach's Probability Logic 370
1 Introduction 370
2 Probability Logic: The Basic Set-Up 373
3 Probabilities as Limiting Frequencies 376
4 Probability Logic 382
5 Critics: Popper, Nagel and Russell 390
6 Reichenbach on the Attempts of others and on Standard Problems 395
7 Commentary 397
Bibliography 400
Goodman and the Demise of Syntactic and Semantic Models 404
1 Historical Background 404
2 Developments in the Twentieth Century 406
3 The New Riddle of Induction 408
4 Some Misunderstandings 410
5 Proposed Asymmetries 412
6 The Entrenchment Solution 414
7 Implications 416
8 Values, Virtues and Hypothesis Selection 419
Bibliography 424
The Development of Subjective Bayesianism 428
2 The Problem of the Priors 436
3 Inductive Inference as Updating Subjective Probability 460
4 Subjective Probability and Objective Chance 471
5 Conclusion 485
Bibliography 486
Varieties of Bayesianism 490
1 Introduction 490
2 Interpretations of Probability 498
3 The Subjective-Objective Continuum 506
4 Justifications 529
5 Decision Theory 540
6 Confirmation Theory 547
7 Theories of Belief (A.K.A. Acceptance) 553
8 Summary 558
Bibliography 559
Inductive Logic and Empirical Psychology 566
Introduction 566
1 The Bayesian Approach to Cognition 570
2 Language 577
3 Inductive Reasoning 584
4 Deductive Reasoning 590
5 Decision Making 606
6 Argumentation 614
7 Challenges and Future Directions 618
Conclusion 622
Acknowledgements 623
Bibliography 623
Inductive Logic and Statistics 638
1 From Inductive Logic to Statistics 638
2 Observational Data 639
3 Inductive Inference 641
4 Carnapian Logics 643
5 Bayesian Statistics 645
6 Inductive Logic with Hypotheses 648
7 Neyman-Pearson Testing 650
8 Neyman-Pearson Test as an Inference 653
9 Fisher's Parameter Estimation 656
10 Estimations in Inductive Logic 657
11 Fiducial Probability 659
12 In Conclusion 661
Acknowledgements 662
Bibliography 662
Statistical Learning Theory: Models, Concepts, and Results 664
1 Introduction 664
2 The Standard Framework of Statistical Learning Theory 664
3 Consistency and Generalization for the K-Nearest Neighbor Classifier 677
4 Empirical Risk Minimization 680
5 Capacity Concepts and Generalization Bounds 686
6 Incorporating Knowledge into the Bounds 696
7 The Approximation Error and Bayes Consistency 700
8 No Free Lunch Theorem 705
9 Model Based Approaches to Learning 708
10 The vc Dimension, Popper's Dimension, and the Number of Parameters 715
11 Conclusion 717
Acknowledgements 717
Bibliography 718
Formal Learning Theory in Context 720
Introduction 720
The Character of Formal Learning Theory 720
Confidence Intervals 725
Comparison 728
Conclusion 729
Bibliography 730
Mechanizing Induction 732
1 Machine Learning and Computational Learning Theory 732
2 Nonmonotonic Reasoning 751
Acknowledgements 779
Bibliography 779
Index 786

Textauszug

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...

Produkt-Details

• Erscheint lt. Verlag: 27.5.2011
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• ISBN-10: 0-08-093169-3 / 0080931693
• ISBN-13: 978-0-08-093169-2 / 9780080931692