Ebook: Truthlikeness for Multidimensional, Quantitative Cognitive Problems

Philosophers of science have produced a variety of definitions for the notion of one sentence, theory or hypothesis being closer to the truth, more verisimilar, or more truthlike than another one. The definitions put forward by philosophers presuppose at least implicitly that the subject matter with which the compared sentences, theories or hypotheses are concerned has been specified,! and the property of closeness to the truth, verisimilitude or truth likeness appearing in such definitions should be understood as closeness to informative truth about that subject matter. This monograph is concerned with a special case of the problem of defining verisimilitude, a case in which this subject matter is of a rather restricted kind. Below, I shall suppose that there is a finite number of interrelated quantities which are used for characterizing the state of some system. Scientists might arrive at different hypotheses concerning the values of such quantities in a variety of ways. There might be various theories that give different predictions (whose informativeness might differ , too) on which combinations of the values of these quantities are possible. Scientists might also have measured all or some of the quantities in question with some accuracy. Finally, they might also have combined these two methods of forming hypotheses on their values by first measuring some of the quantities and then deducing the values of some others from the combination of a theory and the measurement results.

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This book is concerned with the problem of applying the theory of verisimilitude to cognitive problems of a quantitative nature. Attention is mostly focused on hypotheses concerned with (physical or other) systems whose state can be represented with an element of a multidimensional state space, but hypotheses concerned with quantitative laws are also considered. The book provides a systematic introduction to the main contemporary forms of the theory of verisimilitude, including both proposed definitions of quantitative degrees of verisimilitude and proposed definitions of the relation `closer to the truth than'. It shows why the quantitative measures that have been proposed earlier produce unacceptable results in the multidimensional case and, using the tools of geometric measuretheory, works out alternatives for them in detail. In addition, the standard structuralist theory of science and the way in which the problems of approximation are dealt with in it are presented and evaluated critically.

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This book is concerned with the problem of applying the theory of verisimilitude to cognitive problems of a quantitative nature. Attention is mostly focused on hypotheses concerned with (physical or other) systems whose state can be represented with an element of a multidimensional state space, but hypotheses concerned with quantitative laws are also considered. The book provides a systematic introduction to the main contemporary forms of the theory of verisimilitude, including both proposed definitions of quantitative degrees of verisimilitude and proposed definitions of the relation `closer to the truth than'. It shows why the quantitative measures that have been proposed earlier produce unacceptable results in the multidimensional case and, using the tools of geometric measuretheory, works out alternatives for them in detail. In addition, the standard structuralist theory of science and the way in which the problems of approximation are dealt with in it are presented and evaluated critically.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-18
On Competing Theories of Verisimilitude and on Evaluating Them....Pages 19-51
The Problems of Arbitrariness and Vagueness....Pages 52-75
The Measures of Verisimilitude of the Similarity Approach....Pages 76-125
Verisimilitude and the Standard Structuralist Framework....Pages 126-154
The Structuralist Definitions of Verisimilitude....Pages 155-180
Galileo, Aristotle, and Some Difficulties with Quantitative Laws....Pages 181-192
Concluding Remarks....Pages 193-195
Back Matter....Pages 196-228

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This book is concerned with the problem of applying the theory of verisimilitude to cognitive problems of a quantitative nature. Attention is mostly focused on hypotheses concerned with (physical or other) systems whose state can be represented with an element of a multidimensional state space, but hypotheses concerned with quantitative laws are also considered. The book provides a systematic introduction to the main contemporary forms of the theory of verisimilitude, including both proposed definitions of quantitative degrees of verisimilitude and proposed definitions of the relation `closer to the truth than'. It shows why the quantitative measures that have been proposed earlier produce unacceptable results in the multidimensional case and, using the tools of geometric measuretheory, works out alternatives for them in detail. In addition, the standard structuralist theory of science and the way in which the problems of approximation are dealt with in it are presented and evaluated critically.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-18
On Competing Theories of Verisimilitude and on Evaluating Them....Pages 19-51
The Problems of Arbitrariness and Vagueness....Pages 52-75
The Measures of Verisimilitude of the Similarity Approach....Pages 76-125
Verisimilitude and the Standard Structuralist Framework....Pages 126-154
The Structuralist Definitions of Verisimilitude....Pages 155-180
Galileo, Aristotle, and Some Difficulties with Quantitative Laws....Pages 181-192
Concluding Remarks....Pages 193-195
Back Matter....Pages 196-228
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