Confirming a predicted selection rule in inelastic neutron scattering spectroscopy: the quantum translator-rotator H2 entrapped inside C60

We report an inelastic neutron scattering (INS) study of H2 molecule encapsulated inside the fullerene C60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules

New Theory about Old Evidence:A framework for open-minded Bayesianism

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption-implicit in standard Bayesianism-that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes' rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, "keep[s] an open mind, but not so open that your brain falls out"

Gifting & The Absolute Priority Rule

(Excerpt) The absolute priority rule sets forth a hierarchical scheme for the distribution of proceeds obtained through liquidating the assets of a debtor. The scheme provides that property of an estate shall be distributed to secured creditors, then to administrative and priority unsecured creditors, then to unsecured creditors, and lastly to equity holders. Under Chapter 11, section 1129(b)(2)(B)(ii) for a dissenting class of impaired creditors, a plan is “fair and equitable” only if the allowed value of such creditors claims are paid in full, or the holder of any claim or equity that is junior to the dissenting creditors will not retain any property under the plan on account of such junior creditors claim. It must be noted that the absolute priority rule applies only to dissenting classes of creditors. If the class consents, the absolute priority rule does not apply, even with respect to the claims of a dissenting creditor in that class. In many cases, the strict application of the absolute priority rule will prevent the confirmation of an otherwise confirmable plan. This is particularly true in chapter 11 cases in which the continued participation of the credit and equity holders is vital to the reorganization. Other parties will try to use gifting as a method for confirming a plan that would otherwise violate the absolute priority rule over objecting classes of creditors. Such a plan may be essential to the debtor’s reorganization, especially if the junior creditors and equity holders are vital for the debtor’s reorganization. “Gifting,” in the context of bankruptcy, occurs when a senior creditor voluntarily relinquishes a portion of its distribution, provided for in a plan of reorganization, in favor of junior creditors or equity holders. The “gifting doctrine” is a concept that emerged as a result of attempts by creditors and equity holders to circumvent the absolute priority rule. Senior creditors agree to “gift” a portion of their distribution to junior creditors or equity holders in order to streamline the confirmation of reorganization plans and disregard the distribution scheme required by the Bankruptcy Code. While gifting sometimes violates the absolute priority rule, recent case law suggests that there ways to “gift” which are allowable by the courts

The lottery paradox, the preface paradox and rational belief

Traditionally rationality has been analysed in rather puristic terms; thus rational acceptance has been presented as unsullied by the demands of competing claims -- the only demand admitted generally being truth ('Do not have false beliefs'). Such a view leads us to the straightforward rejection of the thesis that a. rule of detachment forprobability statements is sufficient to explicate rational acceptance; since such a rule leads, apparently unavoidably, to the lottery paradox. (Lottery Paradox: Accept only those propositions whose probability is shown to be greater than N people enter a lottery, therefore the probability of an individual losing is this goes for each separately and so we may accept that each will lose, and so that all will lose. But we know that this is false.). The appeal of this rather contemptuous treatment diminishes in the face of the Preface Paradox. (Preface Paradox: A man writes the following, eminently reasonable, lines: Each of the propositions I assert in this book I believe to be true; but I am also sure that some will be proved false.). If we reason as before we have to accept the impossibility of rational belief. The two paradoxes are examined in detail and their consequences spelt out in Chapter One; giving us two alternatives:(1) To show, despite appearances, that neither set of beliefs is inconsistent, or (2) To show some difference between the two paradoxes that enables the traditional view of rationality to separate them. (1) is rejected, and (2) in the course of the same argument, in Chapters Two and Three, where we formulate a criterion for the consistency of sets of beliefs, defend it against apparent counter-examples, (versions of Moore's Paradox) and demonstrate that both sets of beliefs are inconsistent. This despite attempts by some, notably Kyburg, to show the opposite. If we are to avoid concluding rationality bankrupt, and yet maintain our original reaction to the rule of detachment must do two things: (a) reject the rule of detachment on grounds other than the Lottery paradox. (b) give an account of rationality that will accommodate the Preface paradox. In Chapter Four we justify (a) by considering the asymmetries that can be shown to exist between the syntax of the classical probability calculus and the syntax of confirmation in ordinary language, and by pointing to the difficulties encountered in giving an adequate semantics to such a calculus when cast in the role of s calculus of confirmation. Finally, in Chapter Five, we present a more complex account of rationality, capable of accommodating the Preface Paradox, one which takes seriously the diverse needs of human beings.<p

The Search for Invariance: Repeated Positive Testing Serves the Goals of Causal Learning

Positive testing is characteristic of exploratory behavior, yet it seems to be at odds with the aim of information seeking. After all, repeated demonstrations of one’s current hypothesis often produce the same evidence and fail to distinguish it from potential alternatives. Research on the development of scientific reasoning and adult rule learning have both documented and attempted to explain this behavior. The current chapter reviews this prior work and introduces a novel theoretical account—the Search for Invariance (SI) hypothesis—which suggests that producing multiple positive examples serves the goals of causal learning. This hypothesis draws on the interventionist framework of causal reasoning, which suggests that causal learners are concerned with the invariance of candidate hypotheses. In a probabilistic and interdependent causal world, our primary goal is to determine whether, and in what contexts, our causal hypotheses provide accurate foundations for inference and intervention—not to disconfirm their alternatives. By recognizing the central role of invariance in causal learning, the phenomenon of positive testing may be reinterpreted as a rational information-seeking strategy

Channels’ Confirmation and Predictions’ Confirmation: From the Medical Test to the Raven Paradox

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