We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the (...) entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system. (shrink)

The Bohm-Bub hidden-variable theory is able to predict the results of measuring a quantum system only in the special case where the set of commuting observables being measured is complete. To handle the much more common case where the set is incomplete, Tutsch has proposed a generalization of the Bohm-Bub model. Unfortunately, as we show here, Tutsch's original method does not yield the correct quantum mechanical transition probabilities. On the other hand, Belinfante's modification of Tutsch's method does yield the correct (...) probabilities, and it gives a satisfactory hidden-variable theory of partial measurement for the case where one or more commuting variable(s) are measured at a single space-time point. In the case where the variables are measured at different space-time points, the theory is inadequate, due to the fact that it is not relativistically covariant, and does not take relaxation of the hidden variables into account. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, and (...) (iii) its capacity to handle common instances of irrationality. (shrink)

The current literature standardly conceives of voting power in terms of decisiveness: the ability to change the voting outcome by unilaterally changing one’s vote. I argue that this classic conception of voting power, which fails to account for partial decisiveness or efficacy, produces erroneous results because it saddles the concept of voting power with implausible microfoundations. This failure in the measure of voting power in turn reflects a philosophical mistake about the concept of social power in general: a failure (...) to recognize that an agent can exercise individual social power with others’ assistance, in virtue of the group’s collective power, sometimes even when she could not unilaterally scuttle the group’s collective power. I therefore develop a conception of efficacy that admits of degrees and defend a Recursive Measure of voting power that takes partial efficacy into account. (shrink)

In their comment on Sandberg, Timmermans, Overgaard, and Cleeremans , Dienes and Seth argue that increased sensitivity of the Perceptual Awareness Scale is a consequence of the scale being less exclusive rather than more exhaustive. According to Dienes and Seth, this is because PAS may measure some conscious content, though not necessarily relevant conscious content, “If one saw a square but was only aware of seeing a flash of something, then one has not consciously seen a square.” In this reply, (...) we claim that there is a difference between conscious visual experience, which may be partial, and the resulting conscious content, which is conceptual. Whereas PAS measures the first, confidence judgments and post-decision wagering measure the second. (shrink)

Partially automated vehicle technology is increasingly common on-road. While this technology can provide safety benefits to drivers, it also introduces new concerns about driver attention. In particular, during partially automated driving, drivers are expected to stay vigilant so they can readily respond to important events in their environment. However, using partially automated vehicles on the highway places drivers in monotonous situations and requires them to do very little. This can place the driver in a state of cognitive underload in which (...) they experience a very small amount of cognitive demand. In this situation, drivers can exhibit vigilance decrements which impact their ability to respond to on-road threats. This is of particular concern in situations when the partially automated vehicle fails to respond to a potentially critical situation and leaves all responsibility to safely navigate to the driver. This paper reviews situations that lead to vigilance decrements and characterizes the different methodologies of measuring driver vigilance during PAD, highlighting their advantages and limitations. Based on our reading of the literature, we summarize several factors future research on vigilance decrements in PAD should consider. (shrink)

We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit (...) experiment in quantum mechanics. (shrink)

A correction to this paper has been published.

Philosophers and scientists have maintained that causation, correlation, and partial correlation are essentially related. These views give rise to various rules of causal inference. This essay considers the claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception (...) of causation being used and upon certain background assumptions. In section 4 five major kinds of partial correlation are explicated, and some of the important relations are established among two conceptions of partial correlation, the conception of screening off, the conception of partitioning, and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of partial correlation can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions.The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified. (shrink)

The Gratitude Questionnaire-Six Item Form (GQ-6; McCullough et al., 2002) is a well-established instrument for measuring gratitude. Recently, the Multi-Component Gratitude Measure (MCGM) was developed as a more holistic approach (Morgan et al., 2017). While the GQ-6 mainly focuses on the emotional component of gratitude, the MCGM encompasses conceptual, attitudinal and behavioral aspects. As of today, there is no validated German measure for gratitude. In order to close that research gap, the present study focused on validating the German versions of (...) the GQ-6 (GQ-6-G) and of the MCGM (MCGM-G). In addition, multi-group comparisons were conducted to test for cultural measurement invariance. Construct validity was tested similar to original validation studies of the two scales focusing on affect, well-being, empathy, anxiety and depression. The online survey was completed in random order by 508 participants. The one-factor model of the GQ-6-G and the hierarchical structure of the MCGM-G could be replicated. However, model fit of the Gratitude Questionnaire was significantly better after eliminating one item (GQ-5-G). Multi-group comparisons revealed cultural measurement invariance was established for the GQ-5-G and partial measurement invariance for five of six factors of the MCGM-G, respectively. Reliability analyses revealed good internal consistency for both instruments and measures for criterion-related and discriminant validity have shown hypothesized relationships. Thus, the GQ-5-G and the MCGM-G are two instruments with good reliability and validity for measuring gratitude in Germany. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in (...) defining a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

The unique problem of lost territory poses one of the most important and complex challenges of compensating for loss and damage due to anthropogenic climate change. Anthropogenic climate change will cause a significant increase in the sea level for centuries to come. A rising sea level endangers many low‐lying coastal areas but also entire states. However, the inundation of an entire state will remain a rare event. Partial loss of territory will be far more pervasive. As measured by the (...) number of states, the area of land, and, in particular, the number of people affected, the phenomenon of partial territorial loss is much more significant. I address this from the perspective of compensatory justice. In particular, I offer (i) background on basic concepts, (ii) an overview and critique of existing accounts, and propose (iii) a novel interpretation of territory as well as (iv) a corresponding criterion of a duty to compensate before (v) I flesh out the overall theory, (vi) take into consideration implications and details of application, and (vii) respond to potential objections. (shrink)

In this essay I discuss a person’s freedom to choose whatever that person may reasonably prefer to choose. This type of freedom of choice may be regarded as a candidate for a social good, being a hybrid between freedom of choice and preference satisfaction utility. To separate this preference dependent freedom of choice from other types, we may call it opportunity. The essay is concerned with the question of how opportunity should be identified and measured. I discuss what conditions an (...) opportunity measure should satisfy and propose that an opportunity measure should satisfy at least four specific conditions. I then present a new class of measures which satisfy the four conditions (the Root measures). Last I prove that these measures are the only ones that satisfy the conditions, given the extra assumption that the measures are analytic functions with non-zero partial derivatives. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in (...) defining a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based (...) on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability. (shrink)

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the (...) allocation outcomes? If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example (...) of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled. (shrink)

If is a random sequence, then the sequence is clearly not random; however, seems to be “about half random”. L. Staiger [Kolmogorov complexity and Hausdorff dimension, Inform. and Comput. 103 159–194 and A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 215–229] and K. Tadaki [A generalisation of Chaitin’s halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 219–253] have studied the degree of randomness of sequences or reals by measuring their “degree (...) of compression”. This line of study leads to various definitions of partial randomness. In this paper we explore some relations between these definitions. Among other results we obtain a characterisation of Σ1-dimension in terms of strong Martin-Löf ε-tests , and we show that ε-randomness for ε is different than the classical 1-randomness. (shrink)

This paper explores the scientific viability of the concept of causality—by questioning a central element of the distinction between “fundamental” and non-fundamental physics. It will be argued that the prevalent emphasis on fundamental physics involves formalistic and idealized partial models of physical regularities abstracting from and idealizing the causal evolution of physical systems. The accepted roles of partial models and of the special sciences in the growth of knowledge help demonstrate proper limitations of the concept of fundamental physics. (...) We expect that a cause precedes its effect. But in some tension with this point, fundamental physical law is often held to be symmetrical and all-encompassing. Physical time, however, has not only measurable extension, as with spatial dimensions, it also has a direction—from the past through the present into the future. This preferred direction is time’s arrow. In spite of this standard contrast of time with space, if all the fundamental laws of physics are symmetrical, they are indifferent to time’s arrow. In consequence, excessive emphasis on the ideal of symmetrical, fundamental laws of physics generates skepticism regarding the common-sense and scientific uses of the concept of causality. The expectation has been that all physical phenomena are capable of explanation and prediction by reference to fundamental physicals laws—so that the laws and phenomena of statistical thermodynam- ics —and of the special sciences—must be derivative and/or secondary. The most important and oft repeated explanation of time’s arrow, however, is provided by the second law of thermodynamics. This paper explores the prospects for time’s arrow based on the second law. The concept of causality employed here is empirically based, though acknowledging practical scientific interests, and is linked to time’s arrow and to the thesis that there can be no causal change, in any domain of inquiry, without physical interaction. (shrink)

This paper examines human planning abilities, using as its inspiration planning techniques developed in artificial intelligence. AI research has shown that in certain problems partial‐order planners, which manipulate partial plans while not committing to a particular ordering of those partial plans, are more efficient than total‐order planners, which represent all partial plans as totally ordered. This research asks whether total‐order planning and/or partial‐order planning are accurate descriptions of human planning, and if different populations use different (...) planning techniques. Using a simple planning task modeled after tasks designed in artificial intelligence we tested 7–8 year‐old children, 11–13 year‐old children, adult controls, and adults with damage to the prefrontal cortex. We found that adults and older children exhibited performance on planning tasks of varying complexity which matched that of artificial partial‐order planners, and that this pattern of performance did not vary with multiple presentations of the planning task. In contrast, young children and adults with damage to the prefrontal cortex exhibited performance matching that of artificial total‐order planners. This pattern of performance did vary, however, with multiple presentations of the planning task, with the young children and adults with cortical damage displaying aspects of total‐order planning. In a further study we found that adolescents who had sustained damage to the prefrontal cortex as children displayed two different patterns of performance; when measures of reaction time were analyzed they revealed a pattern of performance suggestive of partial‐order plan representations. However, analyses of the adolescents' protocols revealed a pattern of performance suggestive of total‐order plan representations. The significance of these results to psychology, neuroscience, and artificial intelligence are discussed. (shrink)

We introduce two new belief revision axioms: partial monotonicity and consequence correctness. We show that partial monotonicity is consistent with but independent of the full set of axioms for a Gärdenfors belief revision sytem. In contrast to the Gärdenfors inconsistency results for certain monotonicity principles, we use partial monotonicity to inform a consistent formalization of the Ramsey test within a belief revision system extended by a conditional operator. We take this to be a technical dissolution of the (...) well-known Gärdenfors dilemma.In addition, we present the consequential correctness axiom as a new measure of minimal revision in terms of the deductive core of a proposition whose support we wish to excise. We survey several syntactic and semantic belief revision systems and evaluate them according to both the Gärdenfors axioms and our new axioms. Furthermore, our algebraic characterization of semantic revision systems provides a useful technical device for analysis and comparison, which we illustrate with several new proofs. (shrink)

In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way (...) of formalizing Keynes' theory of economic action. (shrink)

Recent defenders of nationalism have pointed to the fact that most people feel that their obligations towards their compatriots are either more numerous or more stringent than those which bind them to people from other countries. They point to this fact as evidence that something is seriously amiss with the universalism which allegedly underpins liberal theory. That people believe quite strongly that they have such special obligations is taken as a datum for which different theories of justice must somehow offer (...) an account. It is taken to be a measure of the theoretical success of a theory of justice that what we might call the "special-obligations thesis" can be derived from it. (shrink)

This Article considers the conditions under which administrative agencies - particularly those with public health-related missions - may obtain partial autonomy from external interests or politicians. In the process, it critiques the proposition that administrative agencies in advanced industrialized countries such as the United States are routinely “captured” by external economic interests. Through case studies and the application of relevant theory from law and the study of political organization, the Article describes how agencies can produce a measure of autonomy (...) by forging coalitions of stakeholders both internal and external to the agency, and considers how partial autonomy may be modeled as a strategic process involving decisions under uncertainty. The Article then investigates how American publichealth agencies such as the Food and Drug Administration, the Food Safety Inspection Service, and the Centers for Disease Control have been able to use their partial autonomy to develop significant health policy innovations. Although agencies are by no means guaranteed even a partial degree of autonomy, they are nonetheless capable of affecting their political and legal environment, with consequences not only for public-health policy but also for the legitimacy of the nation-state. (shrink)

Recent defenders of nationalism have pointed to the fact that most people feel that their obligations towards their compatriots are either more numerous or more stringent than those which bind them to people from other countries. They point to this fact as evidence that something is seriously amiss with the universalism which allegedly underpins liberal theory. That people believe quite strongly that they have such special obligations is taken as a datum for which different theories of justice must somehow offer (...) an account. It is taken to be a measure of the theoretical success of a theory of justice that what we might call the "special-obligations thesis" can be derived from it. (shrink)

The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. (...) The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach-Kirchhoff program. (shrink)

A cardinal κ is nearly θ-supercompact if for every A⊆θ, there exists a transitive M⊨ZFC− closed under θ and j″θ∈N.2 This concept strictly refines the θ-supercompactness hierarchy as every θ-supercompact cardinal is nearly θ-supercompact, and every nearly 2θ<κ-supercompact cardinal κ is θ-supercompact. Moreover, if κ is a θ-supercompact cardinal for some θ such that θ<κ=θ, we can move to a forcing extension preserving all cardinals below θ++ where κ remains θ-supercompact but is not nearly θ+-supercompact. We will also show that (...) if κ is nearly θ-supercompact for some θ⩾2κ such that θ<θ=θ, then there exists a forcing extension preserving all cardinals at or above κ where κ is nearly θ-supercompact but not measurable. These types of large cardinals also come equipped with a nontrivial indestructibility result. A forcing poset is <κ-directed closed if it is γ-directed closed for all γ<κ in the sense of Jech [13, Def. 21.6]. We will prove that if κ is nearly θ-supercompact for some θ⩾κ such that θ<θ=θ, then there is a forcing extension where its near θ-supercompactness is preserved and indestructible by any further <κ-directed closed θ-c.c. forcing of size at most θ. Finally, these cardinals have high consistency strength. Specifically, we will show that if κ is nearly θ-supercompact for some θ⩾κ+ for which θ<θ=θ, then AD holds in L. In particular, if κ is nearly κ+-supercompact and 2κ=κ+, then AD holds in L. (shrink)

Philosophers and scientists have maintained that causation, correlation, and "partial correlation" are essentially related. These views give rise to various rules of causal inference. This essay considers the "claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception (...) of causation being used and upon certain background assumptions. In section 4 five major kinds of "partial correlation" are explicated, and some of the important relations are established among two conceptions of "partial correlation", the conception of "screening off", the conception of "partitioning", and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of "partial correlation" can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions. The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified. (shrink)

In reliability engineering and lifetime analysis, many units of the product fail with different causes of failure, and some tests require stress higher than normal stress. Also, we need to design the life experiments which present methodology for formulating scientific and engineering problems using statistical models. So, in this paper, we adopted a partially constant stress accelerated life test model to present times to failure in a small period of time for Gompertz life products. Also, considering that, units are failing (...) with the only two independent causes of failure and tested under type-I generalized hybrid censoring scheme the data built. Obtained data are analyzed with two methods of estimations, maximum likelihood and Bayes methods. These two methods are used to construct the point and interval estimators with the help of the MCMC method. The developed results are measured and compared under Monte Carlo studying. Also, a data set is analyzed for illustration purposes. Finally, some comments are presented to describe the numerical results. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept (...) label can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept (...) label can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

Seven hundred adolescents with mean age of 15.3 years. Multigroup confirmatory factor analysis was performed to assess measurement invariance of the MSPSS scale across Chinese and South Asian ethnic minority samples. Results show that the original three-factor structure of the MSPSS was supported in both samples. Measurement invariance was supported in terms of configural, metric, and partial scalar invariance. Given partial scalar invariance was achieved, the latent mean differences were compared across samples. Chinese adolescents had higher levels of (...) all three types of social support when compared with their South Asian ethnic minority counterparts. The present study attempts to assess the measurement invariance of the MSPSS across ethnic groups in Asian society, which sheds light on future research that involves perceived social support among adolescents in Chinese culture contexts. (shrink)

The recently developed technique of Bohrification associates to a (unital) C*-algebra Athe Kripke model, a presheaf topos, of its classical contexts;in this Kripke model a commutative C*-algebra, called the Bohrification of A;the spectrum of the Bohrification as a locale internal in the Kripke model. We propose this locale, the ‘state space’, as a (n intuitionistic) logic of the physical system whose observable algebra is A.We compute a site which externally captures this locale and find that externally its points may be (...) identified with partial measurement outcomes. This prompts us to compare Scott-continuity on the poset of contexts and continuity with respect to the C*-algebra as two ways to mathematically identify measurement outcomes with the same physical interpretation. Finally, we consider the not-not-sheafification of the Kripke model on classical contexts and obtain a space of measurement outcomes which for commutative C*-algebras coincides with the spectrum. The construction is functorial on the category of C*-algebras with commutativity reflecting maps. (shrink)

Comparing the relative sensitivity of direct and indirect measures of learning is proposed as the best way to provide evidence for unconscious learning when both conceptual and operative definitions of awareness are lacking. This approach was first proposed by Reingold & Merikle (1988) in the context of subliminal perception. In this paper, we apply it to a choice reaction time task in which the material is generated based on a probabilistic finite-state grammar (Cleeremans, 1993). We show (1) that participants progressively (...) learn about the statistical structure of the stimulus material over training with the choice reaction time task, and (2) that they can use some of this knowledge to predict the location of the next stimulus in a subsequent “generation” task. However, detailed partial correlational analyses of the correspondence between performance during the reaction time task and the statistical structure of the training material showed that large effects remained even when controlling for explicit knowledge as assessed by the generation task. Hence we conclude (1) that at least some of the knowledge expressed through reaction time performance can not be characterized as conscious, and (2) that even when associations are found at a global level of analysis, dissociations can still be obtained when more detailed analyses are conducted. Finally, we also show that participants are limited in the depth of the contingencies they can learn about, and that these limitations are shared by the Simple Recurrent Network model of Cleeremans & McClelland (1991). (shrink)

For any ordinal δ, let λδ be the least inaccessible cardinal above δ. We force and construct a model in which the least supercompact cardinal κ is indestructible under κ-directed closed forcing and in which every measurable cardinal δ < κ is < λδ strongly compact and has its < λδ strong compactness indestructible under δ-directed closed forcing of rank less than λδ. In this model, κ is also the least strongly compact cardinal. We also establish versions of this result (...) in which κ is the least strongly compact cardinal but is not supercompact. (shrink)

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not (...) as popular as it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are (...) given. (shrink)

A partial ordering in the class of observables (∼ positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter (...) definition, be justified operationally. The nonideality notion is compared to other quantum estimation theoretic methods. Measures for the amount of nonideality are derived from information theory. (shrink)

Social desirability bias is a pervasive measurement challenge in the social sciences and survey research. More clarity is needed to understand the performance of social desirability scales in diverse groups, contexts, and cultures. The present study aims to contribute to the international literature on social desirability measurement by examining the psychometric performance of a short version of the Marlowe-Crowne Social Desirability Scale in a nationally representative sample of teachers in Kazakhstan. A total of 2,461 Kazakhstani teachers completed the MCSDS – (...) Form C in their language of choice. The results failed to support the theoretical unidimensionality of the original scale. Instead, the results of Random Intercept Item Factor Analysis model suggest that the scale answers depend more on the method factor rather than the substantial factor that represents SDB. In addition, an alternative explanation indicates that the scale seems better suited to measuring two SDB correlated factors: attribution and denial. Internal consistency coefficients demonstrated unsatisfactory reliability scores for the two factors. The Kazakhstani version of the MCSDS – Form C was invariant across geographic location, language, and partially across age groups. However, no measurement invariance was demonstrated for gender. Despite these limitations, the analysis of the Kazakhstani version of the MCSDS – Form C presented in this study constitutes a first step in facilitating further research and measurement of SDB in post-Soviet Kazakhstan and other collectivist countries. (shrink)