A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

It is consistent that there is a set mapping from the four-tuples of ω n into the finite subsets with no free subsets of size t n for some natural number t n . For any $n it is consistent that there is a set mapping from the pairs of ω n into the finite subsets with no infinite free sets. For any $n it is consistent that there is a set mapping from the pairs of ω n into ω (...) n with no uncountable free sets. (shrink)

For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that |p(x)|<|S(x)|<|seq^1-1(x)|<|seq(x)|, where p(x) is the powerset of x, seq(x) is the set of all finite sequences of elements of x, and seq^1-1(x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind infinite set (...) x such that |S(x)|<|[x]^3| and such that there exists a surjection from x onto S(x). (3) There is an infinite set x such that there is a finite-to-one function from S(x) into x. (shrink)

In this article, cluster analysis is used to explore the conflicting results reported when the Defining Issues Test is used to explain moral reasoning ability in business situations. Using a convenience sample, gender, age, work experience, and ethics training were examined to determine their impact on the level of moral reasoning ability as measured by the Defining Issues Test. Using the whole sample, a significant difference was found for average P scores reported for males and females, but no significant (...) differences were found based on age, work experience, and ethics training. However, the sample fell into distinct clusters that identified distinct male and female groupings. While females naturally fell into two distinct high- and low-moral reasoning ability clusters, male clusters were dominated more by work experience and ethics training. Clearly there are other factors mitigating the level of moral reasoning ability for males which require further exploration. The findings suggest that while the P score provides an initial point of comparison, the real benefit to the test is in exploring what is different for males and females in terms of training needs, and the impact of work experience on the moral reasoning ability, and most importantly, how to make ethics training enticing. Recommendations for future research are also discussed. (shrink)

We prove a combinatorial result for models of the 4-fragment of the Simple Theory of Types , TST4. The result says that if is a standard transitive and rich model of TST4, then satisfies the 0,0,n-property, for all n≥2. This property has arisen in the context of the consistency problem of the theory New Foundations . The result is a weak form of the combinatorial condition that was shown in Tzouvaras [5] to be equivalent to the consistency of (...) NF. Such weak versions were introduced in Tzouvaras [6] in order to relax the intractability of the original condition. The result strengthens one of the main theorems of Tzouvaras [5, Theorem 3.6] which is just equivalent to the 0,0,2-property. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: Adding a theory of truth to a finitely axiomatized theory T is more or less equivalent to a (...) kind of abstract consistency statement. A large part of the interest of the paper lies in the way syntactic theories are 'disentangled' from object theories. (shrink)

This study examined whether holding a status-consistent or status-inconsistent position affected the work satisfaction of college-educated, white-collar employees. The status-consistent group contained 128 women and 118 men. The status-inconsistent group was composed of 89 women and 102 men. Our results indicated that workers in occupations in which the majority of workers are the same gender had significantly higher levels of work satisfaction than those in status-inconsistent occupations. However, subsequent analyses revealed that men and women employed in occupations in which (...) the majority of workers are men had higher levels of work satisfaction than those employed in women-dominated occupations. These findings held when controlling for other work-satisfaction factors, such as individual earnings, hours worked per week, and length of time employed. We suggest that the effect of status consistency on work satisfaction is mediated by the cultural value attached to the occupations men dominate. (shrink)

In addition to beliefs, people have attitudes of confidence called credences. Combinations of credences, like combinations of beliefs, can be inconsistent. It is common to use tools from probability theory to understand the normative relationships between a person’s credences. More precisely, it is common to think that something is a consistency norm on a person’s credal state if and only if it is a simple transformation of a truth of probability. Though it is common to challenge the right-to-left direction (...) of this biconditional, I argue in this paper that the left-to-right direction is false for standard versions of probability theory. That is, I make the case that there are consistency constraints on credal states that are not simple transformations of truths of standard versions of probability theory. I do so by drawing on a newly discovered type of credal attitude, a quantificational credence, and by showing how the consistency norms on this attitude can’t be represented as simple transformations of truths of standard versions of probability theory. I conclude by showing that a probability theory that could avoid the result would have to be strikingly different from the standard versions—so different that I suspect many would hesitate to call it a theory of probability at all. (shrink)

People sometimes explain behavior by appealing to an essentialist concept of the self, often referred to as the true self. Existing studies suggest that people tend to believe that the true self is morally virtuous; that is deep inside, every person is motivated to behave in morally good ways. Is this belief particular to individuals with optimistic beliefs or people from Western cultures, or does it reflect a widely held cognitive bias in how people understand the self? To address this (...) question, we tested the good true self theory against two potential boundary conditions that are known to elicit different beliefs about the self as a whole. Study 1 tested whether individual differences in misanthropy—the tendency to view humans negatively—predict beliefs about the good true self in an American sample. The results indicate a consistent belief in a good true self, even among individuals who have an explicitly pessimistic view of others. Study 2 compared true self-attributions across cultural groups, by comparing samples from an independent country and a diverse set of interdependent countries. Results indicated that the direction and magnitude of the effect are comparable across all groups we tested. The belief in a good true self appears robust across groups varying in cultural orientation or misanthropy, suggesting a consistent psychological tendency to view the true self as morally good. (shrink)

This paper presents proof that Buss's S22 can prove the consistency of a fragment of Cook and Urquhart's PV from which induction has been removed but substitution has been retained. This result improves Beckmann's result, which proves the consistency of such a system without substitution in bounded arithmetic S12. Our proof relies on the notion of "computation" of the terms of PV. In our work, we first prove that, in the system under consideration, if an equation is proved (...) and either its left- or right-hand side is computed, then there is a corresponding computation for its right- or left-hand side, respectively. By carefully computing the bound of the size of the computation, the proof of this theorem inside a bounded arithmetic is obtained, from which the consistency of the system is readily proven. This result apparently implies the separation of bounded arithmetic because Buss and Ignjatović stated that it is not possible to prove the consistency of a fragment of PV without induction but with substitution in Buss's S12. However, their proof actually shows that it is not possible to prove the consistency of the system, which is obtained by the addition of propositional logic and other axioms to a system such as ours. On the other hand, the system that we have considered is strictly equational, which is a property on which our proof relies. (shrink)

DNA arrays are now widely used in academia and industry, and expression profiling is recognised as a major tool for basic research as well as for drug development. It is also likely, in the near future, that DNA arrays will be used in clinical laboratories for diagnostic and prognostic purposes. Since several types of arrays are being used, the coherence of results obtained using these diverse platforms becomes an important issue: to what extent can data obtained in different laboratories (...) and with different equipment be combined? Several recent papers address this issue and demonstrate that the expected agreement is not necessarily found. Consistent results can be obtained, but this requires careful identification of the genes assessed by the arrays, and scrupulous adherence to strict experimental procedures. BioEssays 26:1236–1242, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

In a stimulating paper, Piccione and Rubinstein (1997) argued how a decision maker could undertake dynamically inconsistent choices when, in an extensive form decision problem, she has a particular type of imperfect recall named absentmindedness. Such memory limitation obtains whenever information sets include decision histories along the same decision path. Starting from work focusing on the absentminded driver example, and independently developed by Segal (2000) and Dimitri (1999), the main theorem of this article provides a general result of dynamically consistent (...) choices, valid for a large class of finite extensive form decision problems without nature. (shrink)

In this paper, we prove the following:Theorem. Let M be a rosy dependent theory and letp,pbe non-þ-forking extensions ofp∈Switha0a1; assume thatp∪pis consistent and thata0,a1start a þ-independent indiscernible sequence. Thenp∪pis a non-þ-forking extension ofp.We also provide an example to show that the result is not true without assuming NIP.

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These (...) class='Hi'>results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

Gödel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz [Herbrand consistency and bounded arithmetic, Fundamenta Mathematical vol. 171 (2002), pp. 279-292]. In that paper, it was shown that one cannot always shrink the witness of a bounded formula logarithmically, but in the presence of Herbrand consistency, for theories I∆₀+ Ωm, with m ≥ 2, any (...) witness for any bounded formula can be shortened logarithmically. This immediately implies the unprovability of Herbrand consistency of a theory T ⊇ I∆₀ + Ω₂ in t itself. In this paper, the above results are generalized for I∆₀ + Ω₁. Also after tailoring the definition of Herbrand consistency for I∆₀ we prove the corresponding theorems for I∆₀. Thus the Herbrand version of Gödel's second incompleteness theorem follows for the theories I∆₀ + Ω₁ and I∆₀. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize (...) nicely to languages containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Managers often encounter situations that require them to make decisions with ethical implications that affect the organization as well as the managers themselves. The issue we address in this study concerns whether the ethical consistency of managerial decisions is situation dependent. That is, are the decisions managers make ethically consistent when they are faced with different ethical situations? We hypothesize that managerial decisions will vary depending on the type of ethical situation they encounter. We also hypothesize that gender plays (...) a role in determining the ethical consistency of managerial decisions. Results of statistical analyses support our hypotheses. (shrink)

Syntactic templates serve as schemas, allowing speakers to describe complex events in a systematic fashion. Motion events have long served as a prime example of how different languages favor different syntactic frames, in turn biasing their speakers toward different event conceptualizations. However, there is also variability in how motion events are syntactically framed within languages. Here, we measure the consistency in event encoding in two languages, Spanish and Swedish. We test a dominant account in the literature, namely that variability (...) within a language can be explained by specific properties of the events. This event-properties account predicts that descriptions of one and the same event should be consistent within a language, even in languages where there is overall variability in the use of syntactic frames. Spanish and Swedish speakers (N= 84) described 32 caused motion events. While the most frequent syntactic framing in each language was as expected based on typology (Spanish: verb-framed, Swedish: satellite-framed, cf. Talmy,2000), Swedish descriptions were substantially more consistent than Spanish descriptions. Swedish speakers almost invariably encoded all events with a single syntactic frame and systematically conveyed manner of motion. Spanish descriptions, in contrast, varied much more regarding syntactic framing and expression of manner. Crucially, variability in Spanish descriptions was not mainly a function of differences between events, as predicted by the event-properties account. Rather, Spanish variability in syntactic framing was driven by speaker biases. A similar picture arose for whether Spanish descriptions expressed manner information or not: Even after accounting for the effect of syntactic choice, a large portion of the variance in Spanish manner encoding remained attributable to differences among speakers. The results show that consistency in motion event encoding starkly differs across languages: Some languages (like Swedish) bias their speakers toward a particular linguistic event schema much more than others (like Spanish). Implications of these findings are discussed with respect to the typology of event framing, theories on the relationship between language and thought, and speech planning. In addition, the tools employed here to quantify variability can be applied to other domains of language. (shrink)

Against the charge that Kant's doctrine of radical evil is inconsistent and alien to his practical philosophy, my aim is to show its necessity within the critical system. First, I undermine the alleged vacuity of Kant's notion of evil by showing that, already in the Groundwork, an evil will is the necessary conceptual correlate of a good will. "Good" and "evil" characterize the agent's form of willing and represent the source of value of right and wrong actions. Then, I show (...) how the doctrine of radical evil derives from Kant's notion of evil. That evil lies at the level of an individual Gesinnung is the result of Kant's radicalizing the use of transcendental freedom. That there is a propensity to evil in the whole species is the result of Kant's naturalizing the principles of his moral psychology. Although Kant is not clear about this distinction, the consistency of his doctrine depends on indicating that an "evil Gesinnung" and the "propensity to evil" are not equivalent concepts. Rather, they refer to different units of moral analysis, the individual and the whole species, and represent a failure to comply with different types of moral obligation: the duty to realize the good and the duty to realize the highest good. The correlation between units of moral analysis and types of obligation explains the isomorphism that Kant detects between them, as well as their logical independence, without which the individual's choice of Gesinnung would be analytically contained in the species' choice of moral nature . Finally, to account for the problem of moral self-constitution I argue for the necessity of assuming a transcendental volitional structure, the unity of acknowledgement or "I will". At the different levels of analysis, this structure organizes the will's manifold intentions according to unifying principles that allow it to recognize them as its own. Although Kant does not mention it, the "I will" is a necessary assumption to account for the continuity of choice and for its possible imputation to an agent. (shrink)

In this study, Consistency and Balance Model (CBM) is proposed and introduced. In the context of the model, the importance of consistency is emphasized in morality just like in Philosophy. Therefore, CBM gives the reason prominence in morality to ensure the consistency and according to CBM the emotion, the intuition and the conscience in addition to the reason, are also important. In order to see the principles determined by the reason in human behaviors, two kinds of classification (...) are developed for the virtues that is defined as the middle of excess and defect. The first of them is the triple classification of virtues that draws attention to the false existence of virtues and determines the opposite of virtues as forming dichotomy. The latter is the tetrad classification, which is based on the duality of two means that propose to consider the virtues together. The Contrast is considered as the central concept in the first classification and the integration is considered as the central concept in the second classification. Then it is offered that the virtues may be evaluated consistently in the social, global and theological contexts. However, the ideal morality with objective qualities and the real morality with subjective qualities are produced in order to reach the universal morality that is determined by the reason, then the consistency and the integration are proposed for them. Similarly, consistency and integration are proposed in the dualities of principle-virtue, abstract-concrete, intention-outcome, universality-locality, objectivity-subjectivity throughout the study. Finally, it is pointed out that the reasonableness of applying consistency in morality has exceptions.Summary: Philosophy is the logical, systematic and consistent thinking that focuses on specific questions and topics to reach the reality. When this basic tendency of philosophy is applied to morality, logical, systematic and consistent actions are expected to emerge. Accordingly, a new model called as Consistency and Balance Model (CBM) is proposed and introduced in this article. By this model, the importance of consistency is emphasized in morality just like in philosophy. Therefore, CBM gives the reason prominence in morality to ensure thought, expression and behavior consistency. According to CBM the human emotion, the divine intuition and the solid conscience in addition to reason are required to determine the virtues. CBM, which is a synthesis of the good intention and the reason, aims to constitute the sensible and good actions. According to CBM, which has a holistic structure, if a person can adopt the virtue as a principle and reflect the virtue in all of his behaviors during his whole life, he can be defined as consistently virtuous.CBM defines the good with the concepts of consistency and balance. According to CBM, the good is the mean of excess and defect. In this respect, CBM is based on Aristotle’s mean idea. However, CBM aims to develop it with new content. Two important questions arise during the identification of the evil: 1. Is it bad that nothing happens? 2. Is it bad that something is wrong? The point of defect represents the absence and the point of excess represents the fallacy in the entity. Both of them are bad in morality. The middle of them is the virtue. In order to see the principles determined by the reason in human behaviors, two kinds of classification are developed for the virtues which are defined as the middle of excess and defect. The first is the triple classification of virtues that draws attention to the false existence of virtues and determines the opposite of virtues as forming dichotomy. The triple classification, which forms a dichotomy as an empty pattern that can be applied to all virtues, is determined as over virtue-virtous-virtueless. According to CBM the opposite of the mean is always clearly the point of defect and implicitly the point of excess. Therefore, it is important to determine extremes of virtues. The point of defect can be briefly denoted as virtueless. The point of excess can be denoted as in fact virtueless, pretending as virtuous, masked virtue and over virtue. The latter is the tetrad classification, which is based on the duality of two means. In this classification, it is possible to produce new and better virtues by considering two virtues together. The Contrast is considered as the central concept in the first classification and the integration is considered as the central concept in the second classification.The principle is seen as a guarantee for the consistency in philosophy. CBM points out that a similar situation should be in ethics. According to Kant, the invisible internal principles of the actions are more important than the actions themselves to determine the moral value. The principle does not vary according to the individual and the condition, on the contrary, the individual is shaped by the principle and all individuals benefit equally from the outcome of the principle. Thus, the abuse of the rights of individuals with arbitrary treatments and double standards are prevented. In this democratic environment formed by the principle not only the owner of the power, but all right holders can get their rights. In this respect, the adherence to the principle is the guarantee of the rights and the freedom by establishing a balance between the rule and the freedom.Aristotle’s virtue and Kant’s principle are discussed in a holistic manner in this study. Thus, it is aimed that the principles in the human mind and the virtues in human actions are consistent in themselves and ultimately the union of the principles and the virtues can be ensured. Besides, the concepts of the ideal morality and the real morality are introduced in this article. The ideal morality takes place on the objective basis of the good and the truth, which is absolute, universally and unarguably accepted by everyone. The ideal morality with its objective qualities can be seen as the target that people know and want to achieve. The real morality is the morality that is shaped in the people or society in all its positive and negative aspects, which also includes the subjectivity of them as their own realities. The real morality with subjective qualities is the morality that occurs in life. CBM aims at the integrity and the consistency between the ideal morality and the real morality to reach the universal morality. In this article, the virtues are divided into two parts as material and spiritual. Then it is offered that the virtues may be evaluated consistently in the principal, individual, social, global and theological contexts. In this context, on the one hand it is aimed that the principal, individual, social, global and theological virtues are consistent within themselves and on the other hand they all are consistent within each other. In this classification the principal and theological morality have objective qualities and the individual and social morality have subjective qualities. CBM aims at an objectivity that incorporates subjectivity within the consistency and integrity of the principal, individual, social, global and theological morality. CBM aims to achieve the ultimate morality by integrating the starting point as the principal morality and the end point as the theological morality and to make them clear in the individual and social morality. As a result, CBM confirms the mean found by reason, by the revelation given by God. In other words, the morality that God has already there and always presents and the morality that the human mind finds here and now coincide. The consistency and integration are also proposed in the dualities of principle-virtue, abstract-concrete, intention-outcome, universality-locality, objectivity-subjectivity in the article. However, consistency, which is the central concept of the article, can form the basis for possible criticisms. But, it can be foreseen that the possible criticisms oriented to CBM would come from an extreme consistency perception that detaches the concept of consistency from reality without careful consideration. For this reason it should be kept in mind that it is wrong to expect excessive consistency in human behavior and to accept the ideal morality as absolute by neglecting the real morality. Finally, it is pointed out that the reasonableness of applying the consistency in morality has exceptions. (shrink)

There are two ways of representing rational belief: qualitatively as yes-or-no belief, and quantitatively as degrees of belief. Standard rationality conditions are: consistency and logical closure, for qualitative belief, satisfaction of the probability axioms, for quantitative belief, and a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open-mindedness, and invariance under independent conceptual expansions. Restrictions of the (...) Lockean thesis that have been suggested in the literature cannot remove the inconsistency. In the outlook we discuss two alternative ways of dealing with this problem: restricting conjunctive closure or going for a dual system account. (shrink)

Taking the BCS Hamiltonian written in second-quantized form, a modified form of Umezawa's self-consistent field theory method is applied, and a unitarily nonequivalent representation is selected in which the Hamiltonian obviously describes a superconducting system. This result is not at all obvious, since the original Hamiltonian is completely symmetric, and there is no reason a priori for expecting it to describe an asymmetric superconducting configuration. All higher order terms are accounted for, and in doing so, one finds the existence of (...) the energy-gap condition for Cooper pairs. The representation is picked out without using the adiabatic theorem or pair approximation, as is typically done in the self-consistent method for superconductivity. (shrink)

Early versions of satellite and radiosonde datasets suggested that the tropical surface had warmed more than the troposphere, while climate models consistently showed tropospheric amplification of surface warming in response to human-caused increases in greenhouse gases. We revisit such comparisons here using new observational estimates of surface and tropospheric temperature changes. We find that there is no longer a serious discrepancy between modeled and observed trends in the tropics. Our results contradict a recent claim that all simulated temperature trends (...) in the tropical troposphere are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”.This emerging reconciliation of models and observations has two primary explanations. First, because of changes in the treatment of buoy and satellite information, new surface temperature datasets yield slightly reduced tropical warming relative to earlier versions. Second, recently developed satellite and radiosonde datasets now show larger warming of the tropical lower troposphere. In the case of a new satellite dataset from remote sensing systems, enhancedRSS warming is due to an improved procedure of adjusting for inter-satellite biases. When the RSS-derived tropospheric temperature trend is compared with four different observed estimates of surface temperature change, the surface warming is invariably amplified in the tropical troposphere, consistent with model results. Even if we use data from a second satellite dataset with smaller tropospheric warming than in remote sensing systems RSS, observed tropical lapse rates are not significantly different from those in all model simulations.Our results contradict a recent claim that all simulated temperature trends in the tropical troposphere and in tropical lapse rates are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”. (shrink)

Marcus argues that moral dilemmas are real, but that they are not the result of inconsistent moral principles. Moral principles are consistent just in case there is some world where all principles are 'obeyable.' They are inconsistent just in case there is no world where all are 'obeyable.' What this logical point is meant to show is that moral dilemmas do not make moral codes inconsistent. She also discusses guilt, and argues that guilt is still appropriate even in cases of (...) conflict, even when the agent thinks the right thing to do is clear. (shrink)

This article concerns the proposal and testing of a Slovak version of the Ideological Consistency Scale, which is a 10-item scale originally developed by the Pew Research Centre (2017). Its psychometric properties are investigated on a Slovak sample (N = 101). Its fit to the Rasch model with conditional maximum likelihood is tested. The Slovak version of the scale is shown to be a reliable and useful instrument for measuring ideological attitudes. The ideological attitudes of the Slovak respondents are (...) compared with those of the American sample. The results show that the political polarization in Slovakia is not strong: few Slovak respondents could be identified as being either consistently conservative or consistently liberal, and the majority exhibited mixed attitudes, tending slightly to display liberal opinions. (shrink)

There are two standard ways to establish consistency in set theory. One is to prove consistency using inner models, in the way that Gödel proved the consistency of GCH using the inner model L. The other is to prove consistency using outer models, in the way that Cohen proved the consistency of the negation of CH by enlarging L to a forcing extension L[G].But we can demand more from the outer model method, and we illustrate (...) this by examining Easton's strengthening of Cohen's result:Theorem 1. There is a forcing extensionL[G] of L in which GCH fails at every regular cardinal.Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton's model L[G] and V? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only hold in universes which are incompatible with the universe of all sets. Ideally, we would like L[G] to not only be compatible with V, but to be an inner model of V.We say that a statement is internally consistent iff it holds in some inner model, under the assumption that there are innermodels with large cardinals. (shrink)

BackgroundThe Chinese version of the Mini-Mental State Examination and the Beijing version of the Montreal Cognitive Assessment are the most commonly used scales to screen for Alzheimer’s disease among Chinese patients; however, their consistency varies according to populations and languages. Equivalent conversion of MMSE-C and MoCA-BJ scores is important for meta-analysis.Materials and methodsMMSE-C and MoCA-BJ scoring were performed on the enrolled patients with AD. Consistency analysis of MMSE-C and MoCA-BJ scores of patients in the conversion groups was performed. (...) The circle-arc method was used to convert the MMSE-C scores of the conversion groups into MoCA-BJ scores, and the conversion formula was generated. The MMSE-C data of the verification group was converted to MoCA-BJ according to the formula, and the consistency analysis of the original MoCA-BJ of the verification group and the converted MoCA-BJ was performed to verify the conversion model.ResultsThe results of the consistency analysis of MMSE-C and MoCA-BJ in group A showed that the correlation coefficients of the total group, high education years subgroup, medium education years subgroup, and low education years subgroup were 0.905, 0.874, 0.949, and 0.874, respectively, with high consistency and statistical significance. After applying the circle-arc method for equivalent conversion, the consistency analysis results of the original and the converted MoCA-BJ of the patients in group B of the total group, high education years subgroup, medium education years subgroup, and low education years subgroup were 0.891, 0.894, 0.781, 0.909, respectively, with high consistency and statistical significance.ConclusionWe established and validated a model of MMSE-C and MoCA-BJ score conversion for Chinese patients with AD using the circle-arc method. This model could be useful for multi-centers clinical trials and meta-analysis. (shrink)

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, (...) a generalization of delta sets. All of our results are theorems in ZFC. (shrink)

In response to a recent rebuttal of Okon and Sudarsky presented in Griffiths, we defend the claim that the Consistent Histories formulation of quantum mechanics does not solve the measurement problem. In order to do so, we argue that satisfactory solutions to the problem must not only not contain anthropomorphic terms at the fundamental level, but also that applications of the formalism to concrete situations should not require any input not contained in the description of the situation at hand at (...) the fundamental level. Our assertion is that the Consistent Histories formalism does not meet the second criterion. We also argue that the so-called second measurement problem, i.e., the inability to explain how an experimental result is related to a property possessed by the measured system before the measurement took place, is only a pseudo-problem. As a result, we reject the claim, defended in Griffiths, that the capacity of the Consistent Histories formalism to solve it should count as an advantage over other interpretations. (shrink)

The fact that “natural” theories, i.e. theories which have something like an “idea” to them, are almost always linearly ordered with regard to logical strength has been called one of the great mysteries of the foundation of mathematics. However, one easily establishes the existence of theories with incomparable logical strengths using self-reference . As a result, PA+Con is not the least theory whose strength is greater than that of PA. But still we can ask: is there a sense in which (...) PA+Con is the least “natural” theory whose strength is greater than that of PA? In this paper we exhibit natural theories in strength strictly between PA and PA+Con by introducing a notion of slow consistency. (shrink)

Language is highly dynamic: It unfolds over time, and we can use it to achieve a wide variety of communicative goals, from telling a story to trying to persuade another person. One aspect of language that has gained increasing popularity among researchers in the last several decades is the individual language style (LS) represented by an individual’s use of function words (e.g., pronouns, articles). Previous approaches to LS mostly focus on LS of one individual in isolation, paying less attention to (...) the fact that language emerges from interaction with others. The aim of this paper is twofold: First, we integrate LS into a dynamical theoretical framework and present an innovative methodological approach. Second, this paper aims to address how interactive conversation—as an aspect of the communicative setting—changes an individual’s LS. We use recurrence quantification analysis to look at structure in patterns of LS in monologs and conversations of 118 participants. Our results showed that LS significantly differs from monolog to conversation, and post hoc analyses further revealed that the change in LS is greater for conflict than for friendly conversations. The difference between monologs and conversations is reflected more strongly in the dynamics (i.e., structure and complexity) of LS than the proportion of function words used. Theoretical implications and directions for future studies are discussed. (shrink)