Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free (...) information. Although dilation and non-conglomerability share some similarities, some authors maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation and non-conglomerability. This article reassesses the grounds for treating dilation and non-conglomerability differently. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability. (shrink)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E (...) is stochastically independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified.

Roger White objects to interval-valued credence theories because they produce a counterintuitive “dilation” effect in a story he calls the Coin Game. We respond that results in the Coin Game were bound to be counterintuitive anyway, because the story involves an agent who learns a biconditional. Biconditional updates produce surprising results whether the credences involved are ranged or precise, so White's story is no counterexample to ranged credence theories.

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a (...) precise state arbitrarily. (shrink)

I argue that truth is relative (in the sense recently defended by some prominent analytical philosophers) by focusing on some semantic issues raised by Einstein's theory of relativity together with our ordinary attributions of truth.

Architecture is the key mediator between time or duration and production. Creating architecture consists of spacing, leaving intervals, dilating. Space contributes to the construction of time, just as time contributes to the construction of space. This mutual construction of space and time by the means of architecture offers a new approach of the transcendental aesthetic, a transcendental aesthetic which determines the conditions of the productive system to promote the sustainable development.

A number of recent articles attribute the origin of the use of cervical balloon dilation in the induction of labor to either Barnes in the 1860s or Embrey and Mollison in the 1960s. This review examines the historical record and reveals that, based on current practice attribution should rather be made to two contemporaries of Barnes: the Storer and Mattei. More importantly, Storer’s warning about the rubber used in dilators was ignored, leading to decades of possibly unnecessary deaths following (...) childbirth. To conduct this study key search terms for PubMed, Google Scholar and the website of the University of Ryerson were utilized as “Barnes”, “Woodman”, “balloon dilation”, “balloon catheter”, “foley”, “colpeurynter”, “cervix uteri” and “induction.” Subsequent analysis was done on downloaded articles using BibDesk. (shrink)

Sensitivity to others’ emotional signals is an important factor for social interaction. While many studies of emotional reactivity focus on facial emotional expressions, signals such as pupil dilation which can indicate arousal, may also affect observers. For example, observers’ pupils dilate when viewing someone with dilated pupils, so-called pupillary contagion. Yet it is unclear how pupil size and emotional expression interact as signals. Further, examining individual differences in emotional reactivity to others can shed light on its mechanisms and potential (...) outcomes. In the current study, adults’ (N = 453) pupil size was assessed while they viewed images of the eye region of individuals varying in emotional expression (neutral, happy, sad, fearful, angry) and pupil size (large, medium, small). Participants showed pupillary contagion regardless of the emotional expression. Individual differences in demographics (gender, age, socioeconomic status) and psychosocial factors (anxiety, depression, sleep problems) were also examined, yet the only factor related to pupillary contagion was socioeconomic status, with higher socioeconomic status predicting less pupillary contagion for emotionally-neutral stimuli. The results suggest that while pupillary contagion is a robust phenomenon, it can vary meaningfully across individuals. (shrink)

We consider Geanakoplos and Polemarchakis’s generalization of Aumman’s famous result on “agreeing to disagree", in the context of imprecise probability. The main purpose is to reveal a connection between the possibility of agreeing to disagree and the interesting and anomalous phenomenon known as dilation. We show that for two agents who share the same set of priors and update by conditioning on every prior, it is impossible to agree to disagree on the lower or upper probability of a hypothesis (...) unless a certain dilation occurs. With some common topological assumptions, the result entails that it is impossible to agree not to have the same set of posterior probabilities unless dilation is present. This result may be used to generate sufficient conditions for guaranteed full agreement in the generalized Aumman-setting for some important models of imprecise priors, and we illustrate the potential with an agreement result involving the density ratio classes. We also provide a formulation of our results in terms of “dilation-averse” agents who ignore information about the value of a dilating partition but otherwise update by full Bayesian conditioning. (shrink)

We report two issues concerning diverging sets of Bayesian (conditional) probabilities-divergence of "posteriors"-that can result with increasing evidence. Consider a set P of probabilities typically, but not always, based on a set of Bayesian "priors." Fix E, an event of interest, and X, a random variable to be observed. With respect to P, when the set of conditional probabilities for E, given X, strictly contains the set of unconditional probabilities for E, for each possible outcome X = x, call this (...) phenomenon dilation of the set of probabilities (Seidenfeld and Wasserman 1993). Thus, dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962). (1) In a wide variety of models for Robust Bayesian inference the extent to which X dilates E is related to a model specific index of how far key elements of P are from a distribution that makes X and E independent. (2) At a fixed confidence level, (1-α), Classical interval estimates A n for, e.g., a Normal mean θ have length O(n -1/2 ) (for sample size n). Of course, the confidence level correctly reports the (prior) probability that θ ∈ A n ,P(A n )=1-α , independent of the prior for θ . However, as shown by Pericchi and Walley (1991), if an ε -contamination class is used for the prior on the parameter θ , there is asymptotic (posterior) dilation for the A n , given the data. If, however, the intervals A ′ n are chosen with length $O(\sqrt{\log (\text{n})/\text{n})}$ , then there is no asymptotic dilation. We discuss the asymptotic rates of dilation for ClassClassical and Bayesian interval estimates and relate these to Bayesian hypothesis testing. (shrink)

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our “burst” model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal “arms,” i.e., that at any space point the (...) light velocity (in moving frames the “there-and-back” velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon. (shrink)

We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell’s position and momentum. A Hamiltonian reduction is performed on the system, (...) and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed “universal” decoherence mechanism attributed to gravitational time dilation. We note that the proposed decoherence remains present in the limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect. (shrink)

A controversial claim in recent dual process accounts of reasoning is that intuitive processes not only lead to bias but are also sensitive to the logical status of an argument. The intuitive logic hypothesis draws upon evidence that reasoners take longer and are less confident on belief–logic conflict problems, irrespective of whether they give the correct logical response. In this paper, we examine conflict detection under conditions in which participants are asked to either judge the logical validity or believability of (...) a presented conclusion, accompanied by measures of eye movement and pupil dilation. The findings show an effect of conflict, under both types of instruction, on accuracy, latency, gaze shifts, and pupil dilation. Importantly, these effects extend to conflict trials in which participants give a belief‐based response (incorrectly under logic instructions or correctly under belief instructions) demonstrating both behavioral and physiological evidence in support of the logical intuition hypothesis. (shrink)

We provide counterexamples to some purported characterizations of dilation due to Pedersen and Wheeler :1305–1342, 2014, ISIPTA ’15: Proceedings of the 9th international symposium on imprecise probability: theories and applications, 2015).

The temporal widths of a light pulse as measured in different inertial frames are shown to have a relation more complicated than that of a simple time dilatation. The result is compared with the dilatation in the twin paradoxGedanken experiment. The light pulse measurement requires two observers in two different frames. The measurements of the observers are compared. For the twin experiment a comparison is made between two clocks which have undergone different histories between the two points at which their (...) world lines intersect. (shrink)

General relativity is the exact theory of gravity which has been experimentally found to be correct with extremely high accuracy. One of the most surprising predictions of the general theory is that time runs slow in a gravitational field. Its proof formally comes from Schwarzschild metric which is a solution of Einstein field equation for a spherically symmetric mass. However, as Einstein field equation is too complex, attempts have been made earlier to derive gravitational time dilation by direct use (...) of principle of equivalence and special theory of relativity. But, this objective has been accomplished partially till date as the resulting expression agrees with the exact expression only upto first order. In this paper, by using principle of equivalence and special relativity, we present a thought experiment which helps us to derive an expression that exactly matches with the expression for gravitational time delay. (shrink)

nur intern: darf nicht in RS, Preisverzeichnis und Kataloge aufgenommen werden.

We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...) F the point where the increasing F-sequence terminates. We apply these results to inverse Goodstein sequences, i.e. increasing (1 + Id) (ω) -sequences. We show that the theorem every inverse Goodstein sequence terminates (a combinatorial theorem about ordinal numbers) is not provable in ID 1 . For a general presentation of the results stated in this paper, see [1]. We use notions and results concerning the category ON (ordinal numbers), dilators and bilators, summarized in [2, pp. 25-31]. (shrink)

The circular arc swept out by the angular displacement of a clock indicator (or its equivalent representation) measuring time is shown to be a Lorentz invariant, representing “universal” time. The concepts of time dilation and transverse Doppler effect are accordingly not physically observable. The experiments on these effects when examined critically are found to be inconclusive. Length contraction, also experimentally unconfirmed, and kinematic temporal phase, both consequences of the Lorentz transformations, are as a matter of logical consistency also physically (...) unobservable. (shrink)

Applying Woodin's non-stationary tower notion of forcing, I prove that the existence of a supercompact cardinal κ in V and a Ramsey dilator in some small forcing extension V[G] implies the existence in V of a measurable dilator of size κ, measurable by κ-complete measures.

The main theorem of this paper is: If ƒ is a partial function from ℵ 1 to ℵ 1 which is ∑ 1 1 -bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite αϵdom , ƒ ⩽ D . The proof involves only elementary combinatorial constructions of trees. A generalization to ptykes is also given.