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)

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)

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents (...) a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present. (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)

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 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.

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)

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)

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)

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)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous (...) subsets of R with the relation of embeddability. We prove that for every finite model L , : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1 , and { U 0 ,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2. (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)

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)

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)

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)

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)

We introduce the large-cardinal notions of ξ-greatly-Mahlo and ξ-reflection cardinals and prove (1) in the constructible universe, L, the first ξ-reflection cardinal, for ξ a successor ordinal, is strictly between the first ξ-greatly-Mahlo and the first Π1ξ-indescribable cardinals, (2) assuming the existence of a ξ-reflection cardinal κ in L, ξ a successor ordinal, there exists a forcing notion in L that preserves cardinals and forces that κ is (ξ+1)-stationary, which implies that the consistency strength of the existence of a (...) (ξ+1)-stationary cardinal is strictly below a Π1ξ-indescribable cardinal. These results generalize to all successor ordinals ξ the original same result of Mekler–Shelah [A. Mekler and S. Shelah, The consistency strength of every stationary set reflects, Israel J. Math.67(3) (1989) 353–365] about a 2-stationary cardinal, i.e. a cardinal that reflects all its stationary sets. (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)

The Wigner’s friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner’s friend thought experiment in detail and show that the reasoning process from each agent that leads to the no-go theorem is inconsistent. The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information. We then apply the (...) relational formulation of quantum measurement to resolve the inconsistent descriptions from different agents. In relational formulation of quantum mechanics, a measurement is described relative to an observer. Synchronization of measurement result is a necessary requirement to achieve consistent descriptions of a quantum system from different observers. Thought experiments, including EPR, Wigner’s Friend and it extended version, confirm the necessity of relational formulation of quantum measurement when applying quantum mechanics to composite system with entangled but space-like separated subsystems. (shrink)