Abstract

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, measures b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. Furthermore, it is still not easy to use b*, F, or another measure to clarify the Raven Paradox. For this reason, measure c* similar to the correct rate is derived. Measure c* supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the Raven Paradox. An example indicates that measures F and b* are helpful for diagnosing the infection of Novel Coronavirus, whereas most popular confirmation measures are not. Another example reveals that all popular confirmation measures cannot be used to explain that a black raven can confirm “Ravens are black” more strongly than a piece of chalk. Measures F, b*, and c* indicate that the existence of fewer counterexamples is more important than more positive examples’ existence, and hence, are compatible with Popper’s falsification thought.

Highlights

  • A universal judgment is equivalent to a hypothetical judgment or a rule, such as “All ravens are black” is equivalent to “For every x, if x is a raven, x is black”

  • Can we provide reasonable degrees of confirmation to help us choose a better result from NAT-negative and CT-positive? Can these degrees of confirmation reflect the probability of the infection?

  • Medical experts explain that sensitivity, of is so low

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Summary

Introduction

A universal judgment is equivalent to a hypothetical judgment or a rule, such as “All ravens are black” is equivalent to “For every x, if x is a raven, x is black”. The main contributions of this paper are: It clarifies that we cannot use one confirmation measure for two different tasks: (1) to assess (communication) channels, such as medical tests as testing means, and (2) to assess probability predictions, such as to assess “Ravens are black”. It provides measure c* that manifests the Nicod criterion and provides a new method to clarify the Raven Paradox. It provides many confirmation formulas for major premises with different antecedents and consequents.

Background
To Review Popular Confirmation Measures
To Distinguish a Major Premise’s Evidence and Its Consequent’s Evidence
Incremental Confirmation or Absolute Confirmation
The Semantic Channel and the Degree of Belief of Medical Tests
Semantic Information Formulas and the Nicod–Fisher Criterion
These conclusions accord with
Selecting Hypotheses and Confirming Rules
To Derive Channel Confirmation Measure b*
To Derive Prediction Confirmation Measure c*
Likelihood
Eight Confirmation Formulas for Different Antecedents and Consequents
Using Three Examples to Compare Various Confirmation Measures
To Clarify the Raven Paradox
About Incremental Confirmation and Absolute Confirmation
Is Hypothesis Symmetry or Consequent Symmetry desirable?
About Bayesian Confirmation and Likelihoodist Confirmation
About the Certainty Factor for Probabilistic Expert Systems
Conclusions
Full Text
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