Statistics in Science

1. Front Matter

   Pages i-ix

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2. Method, Theory, and Statistics: The Lesson of Physics

   • Lorenz Krüger

   Pages 1-13

3. The Theory of Natural Selection as a Null Theory

   • Abner Shimony

   Pages 15-26

4. Causality and Exogeneity in Econometric Models

   • Maria Carla Galavotti, Guido Gambetta

   Pages 27-40

5. Statistics in Expert Resolution: A Theory of Weights for Combining Expert Opinion

   • Roger M. Cooke

   Pages 41-72

6. Short and Long Term Survival Analysis in Oncological Research

   • Ettore Marubini

   Pages 73-87

7. A statistical Approach to the Study of Pollen Fitness

   • T. Caliński, E. Ottaviano, M. Sari Gorla

   Pages 89-101

8. Statistics in Genetics: Human Migrations Detected by Multivariate Techniques

   • Alberto Piazza

   Pages 103-118

9. Quantum Probability and The Foundations of Quantum Theory

   • Luigi Accardi

   Pages 119-147

10. Indistinguishability, Interchangeability, and Indeterminism

    • Alexander Bach

    Pages 149-166

11. The Non Frequency Approach to Elementary Particle Statistics

    • Domenico Costantini, Ubaldo Garibaldi

    Pages 167-181

12. Back Matter

    Pages 183-184

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An inference may be defined as a passage of thought according to some method. In the theory of knowledge it is customary to distinguish deductive and non-deductive inferences. Deductive inferences are truth preserving, that is, the truth of the premises is preserved in the con­ clusion. As a result, the conclusion of a deductive inference is already 'contained' in the premises, although we may not know this fact until the inference is performed. Standard examples of deductive inferences are taken from logic and mathematics. Non-deductive inferences need not preserve truth, that is, 'thought may pass' from true premises to false conclusions. Such inferences can be expansive, or, ampliative in the sense that the performances of such inferences actually increases our putative knowledge. Standard non-deductive inferences do not really exist, but one may think of elementary inductive inferences in which conclusions regarding the future are drawn from knowledge of the past. Since the body of scientific knowledge is increasing, it is obvious that the method of science must allow non-deductive as well as deductive inferences. Indeed, the explosive growth of science in recent times points to a prominent role for the former. Philosophers of science have long tried to isolate and study the non-deductive inferences in science. The inevitability of such inferences one the one hand, juxtaposed with the poverty of all efforts to identify them, constitutes one of the major cognitive embarrassments of our time.

• Survival analysis
• probability
• statistics

• Department of Mathematics, Delft University of Technology, The Netherlands

  Roger Cooke

• Institute of Statistics, University of Genoa, Italy

  Domenico Costantini

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