Truth, Possibility and Probability - New Logical Foundations of Probability and Statistical Inference

1991 ◽  
Keyword(s):  
Statistical Inference ◽  
Logical Foundations ◽  
Foundations Of Probability

Logical Foundations of Probability, Second Edition

1963 ◽  
Vol 58 (303) ◽  
pp. 869 ◽  
Author(s):  
Rudolf Carnap
Keyword(s):  
Logical Foundations ◽  
Foundations Of Probability

The Logical Foundations of Probability

1963 ◽  
Vol 60 (13) ◽  
pp. 362-364 ◽  
Author(s):  
Henry E. Kyburg, ◽  
Keyword(s):  
Logical Foundations ◽  
Foundations Of Probability

scholarly journals Logical Foundations of Probability

Econometrica ◽  
1952 ◽  
Vol 20 (4) ◽  
pp. 688
Author(s):  
Leonard J. Savage ◽  
Rudolph Carnap
Keyword(s):  
Logical Foundations ◽  
Foundations Of Probability

scholarly journals Mutual Influence between Different Views of Probability and Statistical Inference

PARADIGMA ◽  
2021 ◽  
pp. 221-256
Author(s):  
Manfred Borovcnik
Keyword(s):  
Mathematical Models ◽  
Statistical Inference ◽  
Mathematical Theory ◽  
Mutual Influence ◽  
Axiomatic Theory ◽  
Foundations Of Probability ◽  
Scientific Analysis ◽  
Learning Paths ◽  
Unsolvable Problems

In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the different problems of how probability can be measured in each of the approaches, and how each of them can be well justified by a mathematical theory. We analyse the foundations of probability, where the scientific analysis of the theory that allows for a frequentist interpretation leads to unsolvable problems. Kolmogorov’s axiomatic theory does not suffice to establish statistical inference without further definitions and principles. Finally, we show how statistical inference essentially determines the meaning of probability and a shift emerges from purely objectivist views to a complementary conception of probability with frequentist and subjectivist constituents. For didactical purpose, the result of the present analyses explains basic problems of teaching, originating from a biased focus on frequentist aspects of probability. It also indicates a high priority for the design of suitable learning paths to a complementary conception of probability. In the applications, modellers use information in a pragmatic way processing this information regardless of its connotation into formal mathematical models, which are always thought as essentially wrong but useful.

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