Assessing theories [Elektronische Ressource] : the problem of a quantitative theory of confirmation / by Franz Huber

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• Wissenschaft
• Philosophie
• Mathematics

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• Publié par: universitat_erfurt
• Publié le: 01 janvier 2002
• Nombre de lectures: 22
• Langue: English

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ASSESSING THEORIES
The Problem of a Quantitative Theory
of Confirmation
A DISSERTATION
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY (DR. PHIL.)
OF THE
PHILOSOPHICAL FACULTY OF THE
UNIVERSITY OF ERFURT, GERMANY
By
Franz Huber
Erfurt 2002First Reader: Prof. Dr. Gerhard Schurz
(Universities of Erfurt and Düsseldorf)
Second Reader: Prof. Dr. Alex Burri
(University of Erfurt)
Date: ...............c Copyright by Franz Huber 2002
All Rights Reserved
urn:nbn:de:gbv:547 200400640
http://nbn resolving.de/urn/resolver.pl?urn=nbn%3Ade%3Agbv%3A547
200400640. . .Acknowledgements
The list of people I would like to thank on this occasion is long, and I can
name only a few of them.
First of all, I thank Prof. Dr. Gerhard Schurz under whose supervision this
dissertation has been written, and to whom I have been assistant for two years at
the University of Erfurt.
Most of what I have learned during my studies in Salzburg and Erfurt is the
result of visiting his inspiring lectures and reading some of the numerous clearly
written and profound articles covering most, if not all topics of today’s analytic
philosophy, in particular, the philosophy of science of the day.
From the close and fruitful cooperation with him I have profited very much,
and his remarks showed me the direction in which to proceed. I am especially
indebted to him for his great involvement in my work and the many discussions
on the topic of confirmation and related issues which provided the basis for this
dissertation. The latter would not have come about in its present form without
his decisive suggestions, though he is, of course, not responsible for any of the
mistakes I have made here or elsewehere.
Furthermore I would like to thank Prof. Dr. Alex Burri, who has been
reader of this dissertation, and whose accomodating friendliness always ensured
that things could proceed in the way it was best.
Special thanks go to Prof. Luc Bovens for discussing in length many of
my ideas and relating them to probability theory, to Prof. Kenneth Gemes for his
readiness to help and cooperate, and to Prof. Donald Gillies for his interest in and
suggestions to some of my thoughts.
During my studies in Salzburg, I have also learned a lot from Prof.es Jo
hannes Czermak, Georg J.W. Dorn, and, most notably, Paul Weingartner.
Since September 2002 I have been research fellow in the working group
“Philosophy, Probability, and Modeling” led by Luc Bovens and Stephan Hart
mann. The group is part of the Center for Junior Research Fellows at the Univer-
sity of Konstanz, and is supported by the Alexander von Humboldt Foundation,
the Federal Ministry of Education and Research, and the Program for the Invest
ment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja
Award. I am grateful to the latter for a grant enabling me to finish this dissertation
– and to my colleagues in the group for providing such an inspiring atmosphere
(an impression of which one may get at: www.uni konstanz.de/ppm).My personal thanks are first, and foremost, due to Anna Hülsmann, who
knows more than anyone else how many hours it took me to write this dissertation,
and whose constant love provided the kind of support and encouragement I needed
for finishing it.
Among my friends and colleagues Karoline Krenn mostly deserves being
mentioned for her persistent friendship – and many hours on the telephone.
Last, but not least, I may thank my parents and my grandmother, who have
enabled my studies, and who have given me support throughout the years.Abstract
This dissertation deals with the problem of a quantitative theory of con
firmation. The latter can be sketched as follows: You are given a theory T , an
evidenceE, and a background knowledgeB. The question is how much doesE
confirmT relative toB. A solution consists in the definition of a functionC such
thatC (T,E,B) measures the degree to whichE confirmsT relative toB.
In chapter 1 I make precise what is meant by a theory, an evidence, and a
background knowledge. Next comes a chapter on formal conditions of adequacy
for any formal theory (not only of confirmation): A formal theory has to be non
arbitrary, comprehensible, and computable in the limit. Chapter 2 closes with a
critical remark on Bayesian confirmation theory.
In chapter 3 I list a set of material conditions of adequacy for any quantita
tive theory of confirmation: A measure of confirmation has to be sensitive to (and
only to) the confirmational virtues.
These give rise to two strategies of solving the problem under consideration:
The first is to argue that there is one distinguished property of theories in relation
to evidences and background knowledges that takes into account all (and only)
the confirmational virtues. The candidate here is coherence with respect to the
evidence, which is discussed in chapter 4 on foundationalist coherentism. This
approach is found to be unsuccessful.
The second strategy is first to define for every confirmational virtue V a
function f such that f (T,E,B) measures the extent to which V is exhibitedV V
by theory T , evidence E, and background knowledge B; and then to define the
measure of confirmationC as a function of (some of) the functionsf .V
In chapter 5 it is argued that this strategy is successful. In a nutshell, it
is observed that there are two conflicting concepts of confirmation, viz. loveli
ness and likeliness. I reason that it suffices to consider these two primary con
firmational virtues. The two main approaches to confirmation are Hypothetico
Deductivism and probabilistic theories of confirmation: The former is based on
loveliness, whereas the focus of the latter is on likeliness. The idea is simple:
Combine these two aspects, keep their merits, get rid of their drawbacks.
Chapter 6 is on evidential diversity, more generally: the goodness of the
evidence. A goodness measure is defined which together with the loveliness
∗ ∗likeliness measure gives rise to the refined measure of confirmation C . C cananswer the question why scientists (should) gather evidence, and it provides a
solution to the ravens paradox.Contents
1 Introduction 1
1.1 The Problem of a Quantitative Theory of Confirmation . . . . . . 1
1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Background Knowledge . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 A Quantitative Theory of Confirmation 21
2.1 Criteria for a Solution . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Formal Conditions of Adequacy . . . . . . . . . . . . . . . . . . 22
2.3 Why Be Formally Handy . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Down With Bayesianism? . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 The Less Reliable the Source of Information, the Higher
the Degree of Bayesian Confirmation . . . . . . . . . . . 36
2.4.1.1 Conditioning on the Entailment Relation . . . . 38
2.4.1.2 The Counterfactual Strategy . . . . . . . . . . . 40
2.4.1.2.1 Counterfactuals Degrees of Belief . . 41
2.4.1.2.2 Actual Degrees of Belief . . . . . . . 50
2.4.2 Steps Towards a Constructive Probabilism . . . . . . . . . 56
3 The Two Approaches 59
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 The Confirmational Virtues . . . . . . . . . . . . . . . . . . . . . 63
3.3 The Primary Confirmational Virtues . . . . . . . . . . . . . . . . 64
3.4 The Derived Virtues . . . . . . . . . . . . . . . . 67
4 Coherence with Respect to the Evidence 73
4.1 Coherence as Truth Indicator . . . . . . . . . . . . . . . . . . . . 73CONTENTS
4.2 Arbitrary Theories of Coherence . . . . . . . . . . . . . . . . . . 77
4.2.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . 77
4.2.2 TheTEC of Thagard (1989) . . . . . . . . . . . . . . . . 80
4.2.3 The FuzzyTEC of Schoch (2000) . . . . . . . . . . . . . 83
4.3 Foundationalist Coherentism . . . . . . . . . . . . . . . . . . . . 90
4.3.1 Why No Probabilistic Measure of Coherence? . . . . . . . 90
4.3.2 No Evidence Without Relevance . . . . . . . . . . . . . . 93
4.3.3 The Measure of Coherence w.r.t. the Evidence . . . . . . 96
4.3.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3.5 Properties ofCoh . . . . . . . . . . . . . . . . . . . . . . 101
5 Loveliness and Likeliness 107
5.1 Recapitulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 A Power Searcher and a Truth Indicator . . . . . . . . . . . . . . 108
5.3 The Measure of Confirmation . . . . . . . . . . . . . . . . . . . . 112
5.4 On Accounting . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.5 An Objection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.6 Properties ofC . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.7 A Shortcoming? . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Variety and Goodness of the Evidence 121
6.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 (Maximal) Classes of Facts . . . . . . . . . . . . . . . . . . . . . 123
6.3 Proper Classes of Facts . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 The Measure of the Goodness of the Ev