Paradox of Confirmation

The article presents the empirical confirmation to the black hole and white hole juxtapose theory. The author based the experiment on the multi- mission multi-spectral space telescope data conducted remotely with the NASA Data Challenge and Harvard- Smithsonian Micro-Observatory. Since the loss of the original manuscript, the author reformulated the mathematics during the research. The observation developed a resonance observation technique that observed the white hole to the moon’s direction with the sun. The data reduction of the white hole and (...) other observations provides an explanation for the undetected gravitons and some empirical physical features of the white hole. (shrink)

Simple random sampling resolutions of the raven paradox relevantly diverge from scientific practice. We develop a stratified random sampling model, yielding a better fit and apparently rehabilitating simple random sampling as a legitimate idealization. However, neither accommodates a second concern, the objection from potential bias. We develop a third model that crucially invokes causal considerations, yielding a novel resolution that handles both concerns. This approach resembles Inference to the Best Explanation (IBE) and relates the generalization’s confirmation to confirmation of an (...) associated law. We give it an objective Bayesian formalization and discuss the compatibility of Bayesianism and IBE. (shrink)

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. (shrink)

Confirmation and falsification are different strategies for testing theories and characterizing the outcomes of those tests. Roughly speaking, confirmation is the act of using evidence or reason to verify or certify that a statement is true, definite, or approximately true, whereas falsification is the act of classifying a statement as false in the light of observation reports. After expounding the intellectual history behind confirmation and falsificationism, reaching back to Plato and Aristotle, I survey some of the main controversial issues and (...) arguments that pertain to the choice between these strategies: the Raven Paradox, the Duhem/Quine problem and the Grue Paradox. Finally, I outline an evolutionary criticism of inductive Bayesian approaches based on my assumption of doxastic involuntarism. (shrink)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these (...) paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind raven is more natural than the kind black. (...) The solution applies to any generalization “All F’s are G” in which F is more natural than G. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...) consists in working out the claim that one can have Hempel's cake and eat it too - in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence β if and only if a is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap's positive relevance account, thereby shedding new light on Carnap's analysis as well as solving another problem of confirmation theory. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)