In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

We show that the properties of [relative] semisimplicity and congruence 3-permutability of a [quasi]variety with equationally definable [relative] principal congruences (EDP[R]C) can be characterized syntactically. We prove that a quasivariety with EDPRC is relatively semisimple if and only if it satisfies a finite set of quasi-identities that is effectively constructible from any conjunction of equations defining relative principal congruences in the quasivariety. This in turn allows us to obtain an ‘axiomatization’ of relatively filtral quasivarieties. We also show that (...) a variety is 3-permutable and has EDPC if and only if there is a single pair of quaternary terms satisfying two simple equations, and whose equality defines principal congruences in the variety. Finally, we combine both results to obtain a neat characterization of semisimple, 3-permutable varieties with EDPC, which is applied to solve a problem posed by Blok and Pigozzi in the third paper of their series on varieties with EDPC. (shrink)

In this paper we pursue the study of the variety of m -generalized Łukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Łukasiewicz algebras of order n . Given , we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Łukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the principal congruences (...) on A via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of . After showing that for m > 1 and n > 2, the variety of Łukasiewicz algebras of order n is a proper subvariety of , we prove that is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability. (shrink)

In this paper we investigate the computational complexity of deciding if the variety generated by a given finite idempotent algebra satisfies a special type of Maltsev condition that can be specified using a certain kind of finite labelled path. This class of Maltsev conditions includes several well known conditions, such as congruence permutability and having a sequence of n Jónsson terms, for some given n. We show that for such “path defined” Maltsev conditions, the decision problem is polynomial-time (...) solvable. (shrink)

We consider various classes of algebras obtained by expanding idempotent semirings with meet, residuals and Kleene-*. An investigation of congruence properties (e-permutability, e-regularity, congruence distributivity) is followed by a section on algebraic Gentzen systems for proving inequalities in idempotent semirings, in residuated lattices, and in (residuated) Kleene lattices (with cut). Finally we define (one-sorted) residuated Kleene lattices with tests to complement two-sorted Kleene algebras with tests.

A varietyV satisfies a strong Malcev condition ∃f1,…, ∃fnθ where θ is a conjunction of equations in the function variablesf1, …,fnand the individual variablesx1, …,xm, if there are polynomial symbolsp1, …,pnin the language ofVsuch that ∀x1, …,xmθ is a law ofV. Thus a strong Malcev condition involves restricted second order quantification of a strange sort. The quantification is restricted to functions which are “polynomially definable”. This notion was introduced by Malcev [6] who used it to describe those varieties all of (...) whose members have permutable congruence relations. The general formal definition of Malcev conditions is due to Grätzer [1]. Since then and especially since Jónsson's [3] characterization of varieties with distributive congruences there has been extensive study of strong Malcev conditions and the related concepts: Malcev conditions and weak Malcev conditions.In [9], Taylor gives necessary and sufficient semantic conditions for a class of varieties to be defined by a Malcev condition. A key to the proof is the translation of the restricted second order concepts into first order concepts in a certain many sorted language. In this paper we show that, given this translation, Taylor's theorem is an easy consequence of a result of Tarski [8] and the standard preservation theorems of first order logic. (shrink)

We write$\mathcal {S}_n(A)$for the set of permutations of a setAwithnnon-fixed points and$\mathrm {{seq}}^{1-1}_n(A)$for the set of one-to-one sequences of elements ofAwith lengthnwherenis a natural number greater than$1$. With the Axiom of Choice,$|\mathcal {S}_n(A)|$and$|\mathrm {{seq}}^{1-1}_n(A)|$are equal for all infinite setsA. Among our results, we show, in ZF, that$|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$for any infinite setAif${\mathrm {AC}}_{\leq n}$is assumed and this assumption cannot be removed. In the other direction, we show that$|\mathrm {{seq}}^{1-1}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setAand the subscript$n+1$cannot be reduced ton. Moreover, (...) we also show that “$|\mathcal {S}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setA” is not provable in ZF. (shrink)

This study examined the extent to which the impact of green transformational leadership on employee green behavior through follower perceptions of value congruence. Path analyzing on data from 193 subordinate-leader dyads showed that followers’ value congruence with their leader mediated the effects of green transformational leadership on employee green behavior. Results also supported that green identity moderated the indirect effect of green transformational leadership on employee green behavior through value congruence, such that the indirect effect was more (...) positive when green identity was high than when it was low. These findings provided valuable contribution to green transformational leadership, value congruence and employee green behavior by exploring the relationship between them. Practical implications and directions for future research are also discussed. (shrink)

The article presents an analysis of a mystical practice of letter permutation conceived as part of the practice of “kavannah” in prayer. This practice was articulated by a 13th century anonymous ecstatic kabbalist writing in Catalonia. The anonymous author draws on earlier sources in the kabbalah and Ashkenazi spirituality. The article explores the wider connection between ecstasy and ritual, particularly prayer in the earlier stages of Judaism and its development in medieval theology and kabbalah. The anonymous author describes a unique (...) permutation technique capable of inducing ecstatic experiences as part of the liturgical ritual. (shrink)

How are permutation arguments for the inscrutability of reference to be formulated in the context of a Davidsonian truth-theoretic semantics? Davidson takes these arguments to establish that there are no grounds for favouring a reference scheme that assigns London to “Londres”, rather than one that assigns Sydney to that name. We shall see, however, that it is far from clear whether permutation arguments work when set out in the context of the kind of truth-theoretic semantics which Davidson favours. The principle (...) required to make the argument work allows us to resurrect Foster problems against the Davidsonian position. The Foster problems and the permutation inscrutability problems stand or fall together: they are one puzzle, not two. (shrink)

Objective: Theory and research suggest that the pursuit of personal goals that do not fit a person's affect-based implicit motives results in impaired emotional well-being, including increased symptoms of depression. The aim of this study was to evaluate an intervention designed to enhance motive-goal congruence and study its impact on well-being. Method: Seventy-four German students (mean age = 22.91, SD = 3.68; 64.9% female) without current psychopathology, randomly allocated to 3 groups: motivational feedback (FB; n = 25; participants learned (...) about the fit between their implicit motives and explicit goals), FB + congruence-enhancement training (CET; n = 22; participants also engaged in exercises to increase the fit between their implicit motives and goals), and a no-intervention control group (n = 27), were administered measures of implicit motives, personal goal commitments, happiness, depressive symptoms, and life satisfaction 3 weeks before (T1) and 6 weeks after (T2) treatment. Results: On two types of congruence measures derived from motive and goal assessments, treated participants showed increases in agentic (power and achievement) congruence, with improvements being most consistent in the FB+CET group. Treated participants also showed a trend-level depressive symptom reduction, but no changes on other well-being measures. Although increases in overall and agentic motivational congruence were associated with increases in affective well-being, treatment-based reduction of depressive symptoms was not mediated by treatment-based agentic congruence changes. Conclusion: These findings document that motivational congruence can be effectively enhanced, that changes in motivational congruence are associated with changes in affective well-being, and they suggest that individuals’ implicit motives should be considered when personal goals are discussed in the therapeutic process. (shrink)

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these (...) congruence lattices satisfy the Jónsson–Kiefer property. (shrink)

In this note, it is shown that the set of kernel ideals of a K n, 0-algebra L is a complete Heyting algebra, and the largest congruence on L such that the given kernel ideal as its congruence class is derived and finally, the necessary and sufficient conditions that such a congruence is pro-boolean are given.

This exploratory study examines awareness of the other party''s instrumental, terminal, and work values by members of supervisor and employee dyads. Subjective estimates of value congruence, provided by either member of the dyad, correlated with actual value congruence scores determine conscious awareness levels in all cases. Results demonstrate supervisory awareness of employee terminal values, but not work values or instrumental values, even though these latter value types probably possess the greatest relevance to achieving organizational goals. Further, employees possess (...) awareness of supervisor work values but not instrumental or terminal values. These findings challenge traditional assumptions underlying the functionalism position on organizational culture that appears in the literature most frequently read by practicing managers. (shrink)

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993 ) concerning the modelling conditions for the axioms of assertion A → (( A → B ) → B ) (there called c 6) and permutation ( A → ( B → C )) → ( B → ( A → C )) (there called c 7). We show that the modelling conditions for assertion and permutation proposed (...) in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001 ), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections. (shrink)

We write and for the cardinalities of the set of permutations with n non‐fixed points and the set of subsets with n elements, respectively, of a set which is of cardinality, where n is a natural number greater than 1. With the Axiom of Choice, and are equal for all infinite cardinals. We show, in ZF, that if is assumed, then for any infinite cardinal. Moreover, the assumption cannot be removed for and the superscript cannot be replaced by n. We (...) also show under that for any infinite cardinal, implies is Dedekind‐infinite. (shrink)

We continue the research of the relation $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ on the set $\beta \mathbb {N}$ of ultrafilters on $\mathbb {N}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as an order on the set of $=_{\sim }$ -equivalence classes, where $\mathcal {F}=_{\sim }\mathcal {G}$ means that $\mathcal {F}$ and $\mathcal {G}$ are mutually $\hspace {1mm}\widetilde {\mid }$ -divisible. Here we introduce a new tool: a relation of congruence modulo (...) an ultrafilter. We first recall the congruence of ultrafilters modulo an integer and show that $=_{\sim }$ -equivalent ultrafilters do not necessarily have the same residue modulo $m\in \mathbb {N}$. Then we generalize this relation to congruence modulo an ultrafilter in a natural way. After that, using iterated nonstandard extensions, we introduce a stronger relation, which has nicer properties with respect to addition and multiplication of ultrafilters. Finally, we introduce a strengthening of $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ and show that it also behaves well with respect to the congruence relation. (shrink)

Corporate social responsibility has grown on the corporate agenda and is at the heart of today’s corporate culture. While much research has examined CSR strategies and effects, the effects of post-crisis CSR communication have received relatively little academic attention. Therefore, this paper uses two experimental studies to examine several key contingency factors that influence consumers’ responses to post-crisis CSR initiatives. Results suggest that consumers demonstrate more favorable responses when a company launches a CSR initiative congruent with the crisis issue, or (...) when the crisis is the result of an accident rather than a transgression. Further, the congruence between the crisis issue and the pre-crisis CSR initiative moderates the consistency effects between pre- and post-crisis initiatives. Such findings should be understood by considering the mediating role of corporate CSR motives’ consumer attributions, which was evidenced in this study. This study theoretically contributes to an improved understanding of the underlying mechanism of the post-crisis CSR information process and managerially contributes to the strategic development of effective post-crisis CSR initiatives given a particular situation. (shrink)

Let M be a model of ZFAC (ZFC modified to allow a set of atoms), and let N be an inner model with the same set of atoms and the same pure sets (sets with no atoms in their transitive closure) as M. We show that N is a permutation submodel of M if and only if N satisfies the principle SVC (Small Violations of Choice), a weak form of the axiom of choice which says that in some sense, all (...) violations of choice are localized in a set. A special case is considered in which there exists an SVC witness which satisfies a certain homogeneity condition. (shrink)

Although charismatic leadership theorists have long argued that leader–follower value congruence plays a central role in the development of charismatic relationships, few studies have tested this proposition. Using data from two studies involving a total of 329 CEOs and 1807 members of their top management teams, we tested the hypothesis that value congruence between leaders and their followers is empirically linked to follower perceptions of the charisma of their leader. Consistent with a relational perspective on charismatic leadership, strong (...) support was found for the hypothesis that perceived value congruence between leaders (CEOs) and their followers (members of their top management teams) is positively related to follower perceptions of the degree of charisma possessed by the leader. Conversely, only limited support was found for the hypothesis that actual value congruence is linked to perceptions of charismatic leadership. Implications of these findings for research and practice are discussed. (shrink)

The multi-disciplinary interest in social responsibility on the part of individuals and organizations over the past 30 years has generated several descriptors of corporate social responsibility and employee social responsibility. These descriptors focus largely on socially responsible behavior and, in some cases, on socially responsible identity. Very few authors have combined the two concepts in researching social responsibility. This situation can lead to an oversimplification of the concept of CSR, thereby impeding the examination of congruence between employees and organizations (...) with regard to social responsibility. In this article, we connect two dimensions of social responsibility—identity and behavior—to build a Social Responsibility Matrix consisting of four patterns for classifying the social responsibility of employees and employers: Low Social Responsibility, Identity-based Social Responsibility, Behavior-based Social Responsibility, and Entwined Social Responsibility. The positioning of employers and employees on the same matrix is vital for assessing the level of congruence between employers and employees with regard to social responsibility and for discussing the possible outcomes for both parties. These identity and behavior-based patterns, determinants, and levels of congruence connecting employees and employers form the foundation for the multi-dimensional, dynamic ESR–CSR Congruence Model, as exemplified in a case study. This contribution enhances the existing literature and models of CSR, in addition to improving the understanding of employee–employer congruence, thereby broadening the array of possibilities for achieving positive organizational outcomes based on CSR. (shrink)

Permutation invariance is often presented as the correct criterion for logicality. The basic idea is that one can demarcate the realm of logic by isolating specific entities—logical notions or constants—and that permutation invariance would provide a philosophically motivated and technically sophisticated criterion for what counts as a logical notion. The thesis of permutation invariance as a criterion for logicality has received considerable attention in the literature in recent decades, and much of the debate is developed against the background of ideas (...) put forth by Tarski in a 1966 lecture (Tarski 1966/1986). But as noted by Tarski himself in the lecture, the permutation invariance criterion yields a class of putative ‘logical constants’ that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutation invariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutation invariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, especially some modal operators. (shrink)

An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended de Morgan algebras.

It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.

Following the research of Liedtka (1989), this paper examines the impact of her values congruence model on managers'' work attitudes and perceptions of ethical practices within their firms. A nationwide cross-section of managers (N=1,059) provides the sample for the study. Consonance or clarity about both personal value systems and organizational value systems were found to be more important and, in the absence of one or the other, clarity of personal values were shown to have a more positive impact than (...) organizational value clarity. (shrink)

To improve upon previous methodology, participants in musically induced happy, sad, or neutral moods were asked to recall childhood and recent autobiographical memories in response to pleasant, unpleasant, and neutral word cues. Symmetrical mood-congruent memory effects were observed when events were rated from the perspective of when they actually occurred (i.e., then), because memories rated as being unpleasant then tended to be rated as more pleasant now. Finally, pleasant and unpleasant cue words facilitated retrieval of childhood memories more than did (...) neutral cues. These findings suggest that symmetrical mood congruence can be observed when accounting for such factors as the valence of retrieval cues and the perspective from which experiences are rated, given that memories appear to undergo change in affective labelling. (shrink)

Many scholars have focused on understanding ways of how to suppress knowledge hiding by employees. Existing studies have demonstrated that mindfulness could effectively inhibit employees’ knowledge hiding. This study aims to investigate the impact of leader–subordinate mindfulness congruence on subordinate knowledge hiding and its internal mechanisms. Based on the role theory, we collected 169 leadership data and 368 employee data at three time-points through collecting questionnaire of matching leaders and subordinates. In addition, we used polynomial regression and response surface (...) analysis to validate our research hypotheses. The results demonstrated that: Compared with the “high leader–high subordinate” mindfulness congruence condition, subordinates in the “low leader–low subordinate” mindfulness congruence condition were more likely to exhibit knowledge hiding. Compared with the “low leader–high subordinate” mindfulness incongruence, subordinates under the “high leader–low subordinate” mindfulness incongruence are more likely to exhibit knowledge hiding. The more incongruent the mindfulness between the leader and the subordinate is, the more likely an employee is to exhibit knowledge hiding. Emotional exhaustion mediated the correlation between leader–subordinate mindfulness congruence and knowledge hiding. When the gender of the leader and the subordinate is different, the impact of mindfulness congruence on the inhibition of emotional exhaustion is stronger. This study provides a new perspective for researching the impact of mindfulness on individual behavior and provides a new idea for the research related to inhibiting knowledge hiding. (shrink)

While there is no principle of evil (archē kakou) for Plato, evil does exist in the Platonic framework in various ways, and these help to illuminate other important and overlooked features of Platonic thought: human freedom and the ability to choose and act. Using the Timaeus as the basis of investigation, this paper examines the world-soul and its relation to the human soul in order to understand Plato’s notion of congruency between parts and the whole. It specifically highlights the importance (...) of the three fundamental characteristics of the cosmos—singularity, proportionalism, and completeness—and their ability to explain the human being. The paper argues that Plato understands evil as basic incongruence on all levels, but specifically active incongruence on the human level. The incongruence between the human and the cosmic levels of evil reveals perhaps the most important aspect of the Platonic framework, the possibility for progress toward the good. (shrink)

We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control triggered by the detection of conflict on the preceding situation. We tested whether these conflict monitoring processes can operate implicitly (...) in an implicit learning procedure, modulating the expression of knowledge of which participants are not aware. We reanalyze recently published data, and present an experiment with a probabilistic sequence learning procedure, both showing consistent effects of implicit sequence learning. Despite being implicit, the expression of learning was reduced or completely eliminated right after trials incongruent with the learned sequence, thus showing that sequential congruency effects can be obtained even when the source of congruency itself remains implicit. (shrink)

Several reaction time (RT) studies report faster responses when responses to temporal information are arranged in a spatially congruent manner than when this arrangement is incongruent. The resulting space–time congruency effect is commonly attributed to a culturally salient localization of temporal information along a mental timeline (e.g., a mental timeline that runs from left to right). The present study aims to provide a compilation of the published RT studies on this time–space association in order to estimate the size of its (...) effect and the extent of potential publication bias in this field of research. In this meta-analysis, three types of task are distinguished due to hitherto existing empirical findings. These findings suggest that the extent to which time is made relevant to the experimental task has a systematic impact on whether or not the mental timeline is activated. The results of this meta-analysis corroborate these considerations: First, experiments that make time a task-relevant dimension have a mean effect size of d = 0.46. Second, in experiments in which time is task irrelevant, the effect size does not significantly deviate from zero. Third, temporal priming studies have a surprisingly high mean effect size of d = 0.47, which, however, should be adjusted to d = 0.36 due to publication bias. (shrink)

Masked priming experiments occasionally revealed surprising effects: Participants responded slower for congruent compared to incongruent primes. This negative congruency effect was ascribed to inhibition of prime-induced activation [Eimer, M., & Schlaghecken, F. . Response faciliation and inhibition in subliminal priming. Biological Psychology, 64, 7–26.] that sets in if the prime activation is sufficiently strong. The current study tests this assumption by implementing manipulations designed to vary the amount of prime-induced activation in three experiments. In Experiments 1 and 3, NCEs were (...) observed despite reduced prime-induced activation. Experiment 2 revealed no NCE with at least similar prime strength. Thus, the amount of prime activation did not predict whether or not NCEs occurred. The findings are discussed with regard to the inhibition account and the recently proposed account of mask-induced activation [cf. Lleras, A., & Enns, J. T. . Negative compatibility or object updating? A cautionary tale of mask-dependent priming. Journal of Experimental Psychology: General, 133, 475–493; Verleger, R., Jaskowski, P., Aydemir, A., van der Lubbe, R. H. J., & Groen, M. . Qualitative differences between conscious and nonconscious processing? On inverse priming induced by masked arrows. Journal of Experimental Psychology: General, 133, 494–515]. (shrink)

Harry Eckstein’s long-standing (but ever-changing) hypothesis that a nation’s political stability is a function of “congruence” between the “authority patterns” exhibited by the government and those displayed by nearly every sort of institution under that government’s aegis involved a highly complex politico-psychological theory. As a result, it was quite difficult either to confirm or disconfirm. While there have been a number of suggested revisions that apparently simplify his thesis, they suffer either from vagueness or a failure to take democracy (...) to be a system that requires an actual commitment to majoritarianism. In this paper a revision is offered that utilizes a small number of completely dichotomous variables that are easily subject to empirical tests. This revised theory (of “consonance” rather than congruence) is also explicitly majoritarian, enabling it to shed light on the essential nature of democratic regimes. (shrink)

In this paper we use Hobby's duality for semi-De Morgan algebras, to characterize those algebras having only principal congruences in the classes of semi-De Morgan algebras, demi-pseudocomplemented lattices and almost pseudocomplemented lattices. This work extends some of the results reached by Beazer in [3] and [4].

I offer a variant of Putnam’s “permutation argument,” originally an argument against metaphysical realism. This variant is called the “natural permutation argument.” I explain how the natural permutation argument generates a form of referential inscrutability which is not resolvable by consideration of “natural properties” in the sense of Lewis’s response to Putnam. However, unlike the classical permutation argument (which is applicable to nearly all interpretations of all first-order theories), the natural permutation argument only applies to interpretations which have some special (...) symmetries. I give an analysis of the interpretations to which the natural permutation argument does apply, and I explain how, when it fails to apply, the referential inscrutability generated by permutation arguments is resolvable by a Lewisian strategy. In order to demonstrate how these problems of referential inscrutability play out in an a priori setting relevant to philosophy, I discuss the applicability of the natural permutation argument in set-theoretic reasoning. I use the well-known Kunen inconsistency theorem to show that, in Zermelo–Fraenkel set theory, the Axiom of Choice is sufficient to resolve referential inscrutability. I then explain how, as a result of a recent theorem of Daghighi–Golshani–Hamkins–Jeřábek, in certain non-well-founded set theories the natural permutation argument does yield an intractable inscrutability of reference. (shrink)

Morality can hardly perform a function, which is discussed in this chapter, unless it offers directives that not only can but frequently do differ from those of self-interest itself. The idea of potential congruence asserts that the relation between morality and the interests of the individual agent is characterized by a high degree of mutual accommodation, so that the frequency and severity of conflict between these two perspectives is significantly reduced. Conflicts are nevertheless possible in principle, but the extent (...) to which they arise in practice is not fixed or immutable. Instead, the frequency of conflict depends to a considerable degree on the character of the prevailing social and political institutions. Achieving convergence between morality and self-interest is in part a social and political task. The account of the “priority” of morality developed by Thomas Scanlon in his book What We Owe to Each Other is similar in a number of respects to this chapter's account of potential congruence. (shrink)

Is there a nontrivial automorphism of the Turing degrees? It is a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be. Here we consider instead how an automorphism might be induced by a function on reals, or even by a function on integers. We show that a permutation of ω cannot induce any nontrivial automorphism of the Turing degrees of members of 2ω, and in fact any permutation that induces the trivial automorphism must (...) be computable.A main idea of the proof is to consider the members of 2ω to be probabilities, and use statistics: from random outcomes from a distribution we can compute that distribution, but not much more. (shrink)

In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation (...) argument and the identifiability thesis, (ii) the validity of the permutation argument, and (iii) the truth of the identifiability thesis. In this paper, we undertake a detailed technical study of the two main lines of interpretation, and gather some evidence for favoring one interpretation over the other. (shrink)

In previous work, we have introduced and studied a lifting property in congruence–distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence–distributive algebras; in this paper we introduce and study this property, which we have called the Factor Congruence Lifting Property. We also define the Boolean (...) Lifting Property in varieties with \ and \ having Boolean Factor Congruences and no skew congruences, and prove that it coincides to the Factor Congruence Lifting Property in the congruence–distributive case; we particularize this result to bounded distributive lattices and residuated lattices. (shrink)

We identify the \-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \ of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \-ideal, prime \-ideal, and falsity ideal coincide.

The paper exposes the relevance of permuting conversions (in natural-deduction systems) to the role of such systems in the theory of meaning known as proof-theoretic semantics, by relating permuting conversion to harmony, hitherto related to normalisation only. This is achieved by showing the connection of permuting conversion to the general notion of canonicity, once applied to arbitrary derivations from open assumption. In the course of exposing the relationship of permuting conversions to harmony, a general definition of the former is proposed, (...) generalising the specific cases of disjunction and existential quantifiers considered in the literature. (shrink)

Part 1 of this exploratory study demonstrated that for terminal, instrumental, and work values, supervisors could only accurately assess the extent to which their terminal values are congruent with their employees, whereas, employees could only accurately describe degrees of alignment with their supervisors' work values. Thus, supervisors appear to possess conscious awareness of the terminal values held by their employees and employees similarly possess conscious awareness of their supervisors' work values. Part 2 of the study examined what each of these (...) two parties might do with their conscious knowledge concerning value congruence with the other member. Supervisor ratings and employee self-ratings concerning employee job performance, citizenship, climate fit, working relationship (LMX), and other issues, were correlated with supervisor terminal value congruence estimates and employee work value congruence estimates respectively. For supervisors, only one significant finding was noted, indicating a positive relationship between the supervisors' awareness of terminal value congruence with the employee and the supervisors' estimate of the employee's potential for future promotion. For employees, seven hypotheses received support demonstrating relationships between the employees' awareness of supervisor/employee work value congruence and self-ratings of work behaviours, citizenship behaviours, volunteerism behaviours, work climate behaviours, work climate attitudes, work climate organizational-wide attitudes, and the supervisor/employee working relationship. Implications for management and future research are discussed. (shrink)

Part 1 of this exploratory study demonstrated that for terminal, instrumental, and work values, supervisors could only accurately assess the extent to which their terminal values are congruent with their employees, whereas, employees could only accurately describe degrees of alignment with their supervisors’ work values. Thus, supervisors appear to possess conscious awareness of the terminal values held by their employees and employees similarly possess conscious awareness of their supervisors’ work values. Part 2 of the study examined what each of these (...) two parties might do with their conscious knowledge concerning value congruence with the other member. Supervisor ratings and employee self-ratings concerning employee job performance, citizenship, climate fit, working relationship (LMX), and other issues, were correlated with supervisor terminal value congruence estimates and employee work value congruence estimates respectively. For supervisors, only one significant finding was noted, indicating a positive relationship between the supervisors’ awareness of terminal value congruence with the employee and the supervisors’ estimate of the employee’s potential for future promotion. For employees, seven hypotheses received support demonstrating relationships between the employees’ 0awareness of supervisor/employee work value congruence and self-ratings of work behaviours, citizenship behaviours, volunteerism behaviours, work climate behaviours, work climate attitudes, work climate organizational-wide attitudes, and the supervisor/employee working relationship. Implications for management and future research are discussed. (shrink)