In this paper, we study the employment of $\Sigma _1$ -sentences with certificates, i.e., $\Sigma _1$ -sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some detail and illustrate their use by reproving some classical results and proving some new ones. An example of such a classical result is Vaught’s theorem of the strong effective inseparability of $\mathsf {R}_0$. We also develop the new idea of a (...) theory being $\mathsf {R}_{0\mathsf {p}}$ -sourced. Using this notion, we can transfer a number of salient results from $\mathsf {R}_0$ to a variety of other theories. (shrink)

We study effectively inseparable (abbreviated as e.i.) prelattices (i.e., structures of the form$L = \langle \omega, \wedge, \vee,0,1,{ \le _L}\rangle$whereωdenotes the set of natural numbers and the following four conditions hold: (1)$\wedge, \vee$are binary computable operations; (2)${ \le _L}$is a computably enumerable preordering relation, with$0{ \le _L}x{ \le _L}1$for everyx; (3) the equivalence relation${ \equiv _L}$originated by${ \le _L}$is a congruence onLsuch that the corresponding quotient structure is a nontrivial bounded lattice; (4) the${ \equiv _L}$-equivalence classes of 0 and 1 (...) form an effectively inseparable pair of sets). Solving a problem in (Montagna & Sorbi, 1985) we show (Theorem 4.2), that ifLis an e.i. prelattice then${ \le _L}$is universal with respect to all c.e. preordering relations, i.e., for every c.e. preordering relationRthere exists a computable functionfreducingRto${ \le _L}$, i.e.,$xRy$if and only if$f\left( x \right){ \le _L}f\left( y \right)$, for all$x,y$. In fact (Corollary 5.3)${ \le _L}$is locally universal, i.e., for every pair$a{ < _L}b$and every c.e. preordering relationRone can find a reducing functionffromRto${ \le _L}$such that the range offis contained in the interval$\left\{ {x:a{ \le _L}x{ \le _L}b} \right\}$. Also (Theorem 5.7)${ \le _L}$is uniformly dense, i.e., there exists a computable functionfsuch that for every$a,b$if$a{ < _L}b$then$a{ < _L}f\left( {a,b} \right){ < _L}b$, and if$a{ \equiv _L}a\prime$and$b{ \equiv _L}b\prime$then$f\left( {a,b} \right){ \equiv _L}f\left( {a\prime,b\prime } \right)$. Some consequences and applications of these results are discussed: in particular (Corollary 7.2) for$n \ge 1$the c.e. preordering relation on${{\rm{\Sigma }}_n}$sentences yielded by the relation of provable implication of any c.e. consistent extension of Robinson’s systemRorQis locally universal and uniformly dense; and (Corollary 7.3) the c.e. preordering relation yielded by provable implication of any c.e. consistent extension of Heyting Arithmetic is locally universal and uniformly dense. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively (...) enumerable set, if X intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

We show the non-arithmeticity of 1st order theories of lattices of Σ n sentences modulo provable equivalence in a formal theory, of diagonalizable algebras of a wider class of arithmetic theories than has been previously known, and of the lattice of degrees of interpretability over PA. The first two results are applications of Nies’ theorem on the non-arithmeticity of the 1st order theory of the lattice of r.e. ideals on any effectively dense r.e. Boolean algebra. The theorem on degrees of (...) interpretability relies on an adaptation of techniques leading to Nies’ theorem. (shrink)

This paper belongs to the research on the limit of the first incompleteness theorem. Effectively inseparable (EI) theories can be viewed as an effective version of essentially undecidable (EU) theories, and EI is stronger than EU. We examine this question: Are there minimal effectively inseparable theories with respect to interpretability? We propose tEI, the theory version of EI. We first prove that there are no minimal tEI theories with respect to interpretability (i.e., for any tEI theory T, we can (...) effectively find a theory which is tEI and strictly weaker than T with respect to interpretability). By a theorem due to Pour-EI, we have that tEI is equivalent with EI. Thus, there are no minimal EI theories with respect to interpretability. Also, we prove that there are no minimal finitely axiomatizable EI theories with respect to interpretability. (shrink)

In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the following twelve important metamathematical properties of arithmetical theories: Rosser, EI (effectively inseparable), RI (recursively inseparable), TP (Turing persistent), EHU (essentially hereditarily undecidable), EU (essentially undecidable), Creative, $\textbf{0}^{\prime }$ (theories with Turing degree $\textbf{0}^{\prime }$), REW (all RE sets are weakly representable), RFD (all recursive functions are definable), RSS (all recursive sets are strongly representable), RSW (all (...) recursive sets are weakly representable). Given any two properties $P$ and $Q$ in the above list, we examine whether $P$ implies $Q$. (shrink)

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC a = {x/ xa} andC b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).

_Relevance_. The starting point for embedding CSR as part of the management culture is the vision and values. But first, you need to understand what 'values' means in CSR terms. Companies spend time and effort in creating their mission, vision and values statements, but these are often only from a commercial and internal viewpoint. To achieve CSR values, managers need to take an objective external vie", identifying their various stakeholders, and the company's impacts upon them [1]. Management culture is part (...) of an organizational culture that includes both formal and informal elements of the organizational culture. Management culture reflects the level of the organization’s managerial system development, modernity, efficiency and functionality. It depends on this level how innovations will be implemented in the organization’s management and whether they will be implemented at all, and how effectively the objectives will be solved and the aims will be implemented [2]. Summarizing the results of various research made in different countries, it becomes clear that large companies are not always inclined to coordinate their activities with stakeholders because of their institutional weakness. Research aim: assess the level of cultural and social responsibility of organisational management and discuss their links. Research methods. Analysis of scientific literature, questionnaire survey. Research results. The findings of the research carried out in other countries proved that organizations evaluate not all aspects of corporate social responsibility, and this is influenced by the lack of the employees, as one part of the stakeholders, strong institutional capacity. The quantitative research found that the administration of both groups of companies inadequately evaluate corporate social responsibility activities, there is no feedback guaranteed, there is insufficient care about the relations with employees who are one part of stakeholders, their physical environment and psychological condition. There is no effective internal audit system of social responsibility which should be developed to guarantee feedback, and corporate social responsibility has not become an inseparable part of organizational culture. Having evaluated the weaknesses and the positive trends of management culture and social responsibility characteristics of groups of companies, it should be stated that firstly, management culture expression has influence when aiming for corporate social responsibility; secondly, corporate social responsibility can be regarded as an integral derivative of management culture realized in organizations’ management practice. However, there are also significant differences. There were set personal managerial personnel culture and management knowledge significant amounts of estimates, associated with different approaches to other management work criteria according to which the management culture condition is diagnosed. The clearer dynamics of indicator estimates of the second group of companies leads to the conclusion that the management culture is still being formed, but without clear direction vector. Processes are not clearly focused and uncoordinated. The standards, regulations existing in the second group are not sufficiently linked to the activities practice, so they do not guarantee the optimality of processes, unlike in the first group of companies, where there is a standard peculiar management culture, although the estimates of indicators diagnosing it are not particularly high. In such a situation, the questions of investment in the modernization of management, optimization of working processes remain relevant, unresolved, but the effectiveness of their payoff remains uncertain. Human resources in management policy of both groups of companies are under-estimated; in order to create favorable conditions for their effective use, communication and the interrelationship functionality problems are acute. Organizations (larger problems fixed in the second group of companies) are not adequately prepared to implement corporate social responsibility organization-wide, as management work is not optimally organized, the managerial personnel lacks knowledge and skills working with human resources. Even in the evaluation of formal aspects of corporate social responsibility standards implementation possibilities, the situation existing in groups of companies and organizational abilities of leaders would not allow to realize them systematically and effectively. In this case, corporate social responsibility values would remain more as a declarative form and not the organization’s management culture inseperable part, and a natural, balanced way of functioning of processes based on this philosophy. Though in the second group of companies there is clearer dynamics according to separate management culture parameters, the apparent orientation to modernization of activities shows more open to innovation, in which the elimination of drawbacks and purposeful development can serve the realization of corporate social responsibility more effectively. In both groups of companies the highlighted declarative corporate social responsibility policy trends contradict the actual practice of social responsibility in relations with the organization's internal and external stakeholders. This partly confirms theoretical insights presented in Lithuanian scientific works, which emphasize marketing direction of corporate social responsibility as a general cultural dominant. However, this aspect has not been developed yet in the case of the discussed groups of companies, and the research results lead to the conclusion that organizations lack basic knowledge of corporate social responsibility and motivation to realize them in practice, and the high level of clustering and internal corruption impedes social responsibility transfer to the strategic level. The lack of development of dialogue culture between stakeholders (subjects) became apparent in management culture problem areas and can become a formidable obstacle to the implementation of both individual social responsibility initiatives and installing in complex. This is true in the sense that the organizations do not have universal support from employees, and the procedures are carried out in a superficial manner and have a formal character. Corporate social responsibility is a valuable organization's internal culture category, but this base is not strong enough and balanced. Corporate social responsibility in the activities of both groups of companies (and especially - the first) can be considered still developing and has not taken clear shapes yet. According Hoskins (2006) CSR is a means of developing a management culture. However, the fundamental CSR success factor is that it is a living management process. The strategy needs to be reviewed regularly, and implemented across business units and all CSR components. The delivery of CSR practice is a critical activity. If any of the components are weak, then they detract from the effectiveness of the other components. Like all cultural aspects, CSR is only as strong as its weakest link A CSR management system is essential for CSR to become embedded within the business culture. CSR should not be a separate central activity, but become part of the business process and practice for all business units. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

This fine book is a comprehensive and careful survey of the current situation in the methodology of economics. It is directed primarily at economists and students of economics. Indeed, the economist who reads it with the care it deserves will have a better grip on matters of methodology in economics than most philosophers of science, but philosophers and historians of science will also find the work rewarding and interesting. Though a few examples may be beyond the economically untutored reader, they (...) are not essential to the exposition, and other examples are accessible and enlightening: the brief discussions of Paul Samuelson's revealed preference approach and Julie Nelson's criticism of Gary Becker's work on economics of the family are good instances. Chapter 2, “The Methodological Tradition in Economics,” is a calm and brief introduction to its subject.Until quite recently practicing scientists, economists among them, and philosophers of science presupposed several strong theses about science and knowledge: that all genuine knowledge is scientific; that the objects of this knowledge are eternal and free of context; that all knowledge and all science is one, unified at least by a common scientific method; that, though not infallible, this method is progressive—it approaches truth as a limit—and operates in independence of the nonscientific beliefs and values of its practitioners. These principles cannot be presupposed today. Those who would accept any of them must be ready to meet serious criticisms. The import of this contemporary Methodenstreit as it affects economics is the dominant theme of Reflection without Rules. The reader is left with the conviction that the science of economics and the study of its methodology are inseparable and that it was only dedicated and myopic attachment to The Legend that kept this messy business at bay. Nor can there be any return to the age of innocent division of labor—economists to economics, philosophers to methodology.There are too many topics treated in the book even to list in a brief review. There are calm and clear accounts of Thomas Kuhn's work; of logical positivism ; of the deep effects of the collapse of The Legend on Walrasian equilibrium models; of Daniel Hausman's work on the nature of economics; of the strong program, which strives to reduce scientific activity to the effects of the social interests of scientists; of Alvin Goldman's reliabilism and social epistemology ; and of the important differences between pre‐ and post‐Legend views of science and knowledge.The question of values in science arises for economics in a special and pointed way, for economics studies many sorts of values. It also, at least since Adam Smith, deals in the unintended collective consequences of individual intentional actions. Economics evidently consists in the largely unintended consequences of the intentional actions of individual economists, and, once The Legend is discredited, economics is seen to navigate the very currents that it studies. This opens the door to the virtuous possibility of self‐criticism in tune with the strong naturalism of contemporary epistemology.It is not the least virtue of Reflection without Rules that its author wears his impressive erudition gracefully and well. The book is sophisticated and at the same time naive in the best sense. It will fortunately be the standard reference for work in the methodology of economics for some time to come. (shrink)

An elementary theory T in a language L is (strongly) finitely inseparable if the set of logically valid sentences of L and the set of T-finitely refutable sentences are recursively inseparable. In §1 we establish a sufficient condition for the elementary theory of a class of BA's with operators to be finitely inseparable. This is done using the methods developed independently by M. Rabin and D. Scott (see [6]) on the one hand and by Ershov on the other (see [2]).

In a recent paper, Montagna proved the undecidability of the first-order theory of diagonalisable algebras. This result is here refined — the set of finitely refutable sentences is shown effectively inseparable from the set of theorems. The proof is quite simple.

This paper will first introduce first-order mereotopological axioms and axiomatized theories which can be found in some recent literature and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about (...) other properties stronger than undecidability. (shrink)

We show that any partial order with a Σ3 enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤tt on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co-embeddable.

We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW + . Next, we show that POW + can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the (...) weaker theory. (shrink)

From Plato through the nineteenth century, the West could draw on comprehensive political visions to guide government and society. Now, for the first time in more than two thousand years, Tracy B. Strong contends, we have lost our foundational supports. In the words of Hannah Arendt, the state of political thought in the twentieth and twenty-first centuries has left us effectively “thinking without a banister.” _Politics without Vision_ takes up the thought of seven influential thinkers, each of whom attempted (...) to construct a political solution to this problem: Nietzsche, Weber, Freud, Lenin, Schmitt, Heidegger, and Arendt. None of these theorists were liberals nor, excepting possibly Arendt, were they democrats—and some might even be said to have served as handmaidens to totalitarianism. And all to a greater or lesser extent shared the common conviction that the institutions and practices of liberalism are inadequate to the demands and stresses of the present times. In examining their thought, Strong acknowledges the political evil that some of their ideas served to foster but argues that these were not necessarily the only paths their explorations could have taken. By uncovering the turning points in their thought—and the paths not taken—Strong strives to develop a political theory that can avoid, and perhaps help explain, the mistakes of the past while furthering the democratic impulse. Confronting the widespread belief that political thought is on the decline, Strong puts forth a brilliant and provocative counterargument that in fact it has endured—without the benefit of outside support. A compelling rendering of contemporary political theory, _Politics without Vision_ is sure to provoke discussion among scholars in many fields. (shrink)

A central argument of the _Leviathan_ has to do with the political importance of education. Hobbes wants his book to be taught in universities and expounded much in the manner that Scripture was. Only thus will citizens realize what is in their hearts as to the nature of good political order. Glory affects this process in two ways. The pursuit of glory _by a citizen_ leads to political chaos and disorder. On the other hand, _God’s_ glory is such that one (...) can do nothing but acquiesce to it. The Hobbesian sovereign shares some of the effects of glory that God has naturally; this, however, has to be supplemented by awe and that but fear. (shrink)

Objective:A growing body of evidence supports the effectiveness of body-oriented interventions in educational contexts, showing positive influences on social-emotional competence. Nevertheless, there is a lack of systematization of the evidence regarding preschool years. This is a two-part systematic review. In this first part, we aim to examine the effects of BOI on preschoolers' social-emotional competence outcomes.Data Sources:Searches were conducted in Pubmed, Scopus, PsycInfo, ERIC, Web of Science, Portal Regional da BVS and CINAHL.Eligibility Criteria:English, French and Portuguese language articles published between (...) January 2000 and October 2020, that evaluated the effects of BOI implemented in educational contexts on social-emotional competence of preschool children. Only randomized controlled trials or quasi-RCT were included.Data Extraction and Synthesis:Two reviewers independently completed data extraction and risk-of-bias assessment. The level of scientific evidence was measured through the Best Evidence Synthesis.Results:Nineteen studies were included. There was strong evidence that BOI do not improve anger/aggression, delay of gratification and altruism. Nevertheless, there was moderate evidence that BOI effectively improve other social-emotional outcomes, such as empathy, social interaction, social independence, general internalizing behaviors, and general externalizing behaviors. The lack of scientific evidence was compromised by the methodological quality of the studies.Conclusion:BOI effectively improve specific social-emotional competences of preschool children.Systematic Review Registration:PROSPERO, identifier CRD42020172248. (shrink)

ABSTRACTEffects of metaphorical framing of political issues on opinion have been studied widely by two approaches: a critical-discourse approach and a response-elicitation approach. The current article reports a systematic literature review that examines whether these approaches report converging or diverging effects. We compared CDA and REA on the metaphorical frames that were studied and their reported effects. Results show that the CDA frames are typically more negative, nonfictional, and extreme than REA frames. Reported effects in CDA and REA studies differ (...) in terms of presence, directionality, and strength, with CDA typically reporting strong effects in line with the frame, compared to REA. These differences in effects can be explained by the different frame characteristics. However, differences in the methods applied by CDA and REA could be responsible for these differences as well. In all, we conclude that the research field is fragmented on the impact of metaphors in politics. (shrink)

Various arguments have been given against positive euthanasia, but little attention has been given to the question of whether these arguments are uniformly effective in all contexts. There appears to be a range of cases, involving non-voluntary killing of irreversibly unconscious patients, in which these arguments do not succeed. Various reasons have been given in support of positive killing in such cases. It can be argued that there is a range of cases for which a policy of allowing positive (...) killing is morally required. However, currently there are legal obstacles to implementing such a policy. (shrink)

This study examined the effect of emotional context on the semantic memory of subsequent emotional words during discourse comprehension in two eye-tracking experiments. Four-sentence discourses were used as experimental materials. The first three sentences established an emotional or neutral context, while the fourth contained an emotional target word consistent with the preceding emotional context's valence. The discourses were presented twice using the text change paradigm, where the target words were replaced with strongly - or weakly-related words during the second presentation. (...) Thus, four conditions were included in the present study: Emotional-strongly-related, Emotional-weakly-related, Neutral-strongly-related and Neutral-weakly-related. In Experiment 1, negative contexts and negative target words were used, whereas in Experiment 2, positive contexts and positive target words were used. The results revealed a semantic relatedness effect, whereby the strongly-related words have lower change detection accuracy, longer reading times and more fixations in both Experiments 1 and 2. Furthermore, across both experiments, the magnitude of the semantic relatedness effect was greater in the emotionally congruent contexts than in the neutral contexts. These results suggest that emotional context could increase efforts to change the discrimination of subsequent words and demonstrate an important role of emotional context on semantic memory during discourse processing. (shrink)

This study investigated whether perspective-taking reduces belief bias independently of argument strength. Belief bias occurs when individuals evaluate belief-consistent arguments more favourably than belief-inconsistent arguments. Undergraduates read arguments that varied with respect to belief-consistency and strength about the topic of climate change. After participants read each argument, those in the perspective-taking condition rated the argument's strength from a perspective of a climate scientist and then from their own perspectives, whereas those in the no perspective-taking condition only rated the arguments from (...) their own perspectives. Perspective-taking eliminated belief bias for weak arguments, but not for strong arguments. Theoretical and practical implications of the results are discussed, and directions for future research are provided. (shrink)

This paper studies effective aspects of Jacobson radicals of rings and their applications from the viewpoint of reverse mathematics. First, we propose four radicals of rings, showing that the first order (resp., second order) left and right Jacobson radical coincide in (resp., ). Second, we study Jacobson radicals in left (resp., right) local rings and show that the second order left and right Jacobson radical of left (resp., right) local rings coincide within. Third, we apply our results about Jacobson (...) radicals of rings and local rings to study properties of left (resp., right) strongly indecomposable modules; furthermore, we study effective aspects of typical lemmas and theorems related to strongly indecomposable modules, and show that proves the Fitting Lemma as well as the Krull‐Schmidt‐Azumaya Theorem and that proves the Krull‐Schmidt Theorem. (shrink)

Each of the following claims has been defended in the scientific literature on free will and consciousness: your brain routinely decides what you will do before you become conscious of its decision; there is only a 100 millisecond window of opportunity for free will, and all it can do is veto conscious decisions, intentions, or urges; intentions never play a role in producing corresponding actions; and free will is an illusion. In Effective Intentions Alfred Mele shows that the evidence (...) offered to support these claims is sorely deficient. He also shows that there is strong empirical support for the thesis that some conscious decisions and intentions have a genuine place in causal explanations of corresponding actions. In short, there is weighty evidence of the existence of effective conscious intentions or the power of conscious will. Mele examines the accuracy of subjects' reports about when they first became aware of decisions or intentions in laboratory settings and develops some implications of warranted skepticism about the accuracy of these reports. In addition, he explores such questions as whether we must be conscious of all of our intentions and why scientists disagree about this. Mele's final chapter closes with a discussion of imaginary scientific findings that would warrant bold claims about free will and consciousness of the sort he examines in this book. (shrink)

Despite the voluminous literature on biological functions produced over the last 40 years, few philosophers have studied the concept of function as it is used in neuroscience. Recently, Craver (forthcoming; also see Craver 2001) defended the causal role theory against the selected effects theory as the most appropriate theory of function for neuroscience. The following argues that though neuroscientists do study causal role functions, the scope of that theory is not as universal as claimed. Despite the strong prima facie (...) superiority of the causal role theory, the selected effects theory (when properly developed) can handle many cases from neuroscience with equal facility. It argues this by presenting a new theory of function that generalizes the notion of a ‘selection process’ to include processes such as neural selection, antibody selection, and some forms of learning—that is, to include structures that have been differentially retained as well as those that have been differentially reproduced. This view, called the generalized selected effects theory of function, will be defended from criticism and distinguished from similar views in the literature. (shrink)

The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relativity and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen “bridge” article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Feynman time-symmetric approach is questioned.

As a result of numerous, highly publicized, ethical breaches, firms and their agents are under ongoing scrutiny. In an attempt to improve both their image and their ethical performance, some firms have adopted ethical codes of conduct. Past research investigating the effects of ethical codes of conduct on behavior and ethical attitudes has yielded mixed results. In this study, we again take up the question of the effect of ethical codes on ethical attitudes and find strong evidence to suggest (...) that business professionals employed at firms with ethical codes of conduct are significantly less accepting of ethically questionable behavior toward most stakeholders. One notable exception relates to ethical actions toward customers. (shrink)

Shared genetic inheritance results in a high correlation in the heights of brothers, but experiences in childhood and adolescence can intervene. Poor diet, disease, and heavy labor can prevent the achievement of height potentials. If families cannot control variations in these conditions, the heights of brothers will be less strongly correlated. We use heights measured at military conscription examinations from three communities in nineteenth-century Belgium. The Generalized Estimating Equation procedure allows us to estimate effects of covariates on mean heights as (...) well as the correlations within families. Both average height and the correlation of brothers’ heights differed by socioeconomic status. Members of the local elite were taller and the heights of brothers in those families were more strongly correlated. This suggests that elite families were much better able to control the environmental challenges faced by their offspring. (shrink)

Household structure may have strong effects on reproduction. This study uses household demographic data for 59 women in a Caribbean village to test evolutionary hypotheses concerning variation in reproductive strategies. Father-absence during childhood, current household composition, and household economic status are predicted to influence age at first birth, number of mates, reproductive success, and pair-bond stability. Criterion variables did not associate in a manner indicative of r- and K-strategies. Father-absence in early childhood had little influence on subsequent reproduction. Household (...) wealth and alloparenting were positively associated with age at first birth. Alloparenting was negatively associated with reproductive success. Women in long-term conjugal unions had higher reproductive success than did single women. Number of adult male kin resident in the household was negatively associated with women’s number of mates. (shrink)

Effective altruism has become a worldwide phenomenon. The movement combines empathy and reason in the attempt to improve the world. Adherents don’t let moral gut instincts dictate their altruistic efforts, but use evidence and reflection to do the most good they can. Effective altruism originated, and primarily grew, in strongly secular environments—such as philosophy departments or Silicon Valley. So far, a religious perspective on this movement has been lacking. What can people of faith learn from effective altruism? (...) What may they criticise? What can effective altruism in turn take from religion? This volume offers a first examination of these questions, covering various Christian as well as Jewish and Buddhist perspectives. (shrink)

The side-effect effect is the seemingly irrational tendency for people to say harmful side effects were more intentional than helpful side effects of the same action. But the tendency may not be irrational. According to the Tradeoffs Justification Model, judgments of a person's intentions to cause harm depend on how that person decided to act, and on whether the reasons for acting justified causing the harmful consequences. Across three experiments (N = 660), unjustified harms were viewed as more intentional than (...) justified harms. If the person had a choice of what to do and knowingly caused harm for no good reason, people judged that the person must have actually desired and intended to cause the harm. However, if the person had a strong, compelling reason (e.g., to ransom his daughter from kidnappers) that the observer deemed to have justified causing the harm, then observers thought the harm was weakly intended at most. Taboo harms that violated sacred moral values were especially likely to be seen as intentional because most reasons do not adequately justify violating a sacred value. (shrink)

According to the so-called Classical Theory, concepts are mentally represented by individually necessary and jointly sufficient application conditions. One of the principal empirical objections against this view stems from evidence that people judge some instances of a concept to be more typical than others. In this paper we present and discuss four empirical studies that investigate the extent to which this ‘typicality effect’ holds for the concept of basic needs. Through multiple operationalizations of typicality, our studies yielded evidence for a (...) strong effect of this kind: Participants tended to recall the same core examples of the concept in a free-listing task. They judged some basic needs to be more typical than others. The items that were judged to be more typical were listed more frequently in the free-listing task. These items were listed earlier on in the free-listing task. Typical basic needs, as well as non needs, were classified faster than atypical basic needs in a reaction time study. These findings suggest that the concept of basic needs may have a non-classical structure. If so, the quest for a simple and robust intensional analysis of the concept may be futile. (shrink)

Recent downward trends in corporate giving have renewed interest in the factors that shape corporate philanthropy. This paper examines the relationships between charitable contributions, firm size and industry. Improvements over previous studies include an IRS data base that covers a much broader range of firm sizes and industries as compared to previous studies and estimation using an instrumental variable technique that explicitly addresses potential simultaneity between charitable contributions and profitability. Important findings provide evidence of a cubic relationship between charitable giving (...) and firm size and evidence of strong industry effects. The plus-minus-plus regression coefficient sign pattern for the cubic firm size model suggests that small and large firms give more relative to total receipts with lower giving ratios among medium size firms. One interpretation for this finding is that small firms are close to the communities they serve while high visibility creates a need for large firm philanthropy. Strong industry effects provide evidence of inter-industry differences in giving culture and/or different public relations requirements across industries. (shrink)

Empirical support is offered for the claim that the original Knobe effect, whereby our intentional action ascriptions exhibit certain asymmetries in light of our moral attitudes, can be successfully cancelled. This is predicted by the view that the Knobe effect can be explained in purely pragmatic terms (Adams and Steadman 2004a, 2004b, 2007). However, previous cancelling studies (Adams and Steadman 2007; Nichols and Ulatowski 2007) have failed to identify evidence of cancellability. The key to the successful cancelling strategy presented here (...) is to provide subjects with the opportunity to assent to statements that involve sufficiently strong forms of moral censure. (shrink)

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the (...) least non-trivial normal ideal. (shrink)

In transparent orthographies, persistent reading fluency difficulties are a major cause of poor reading skills in primary school. The purpose of the present study was to investigate effects of a syllable-based reading intervention on word reading fluency and reading comprehension among German-speaking poor readers in Grade 4. The 16-session intervention was based on analyzing the syllabic structure of words to strengthen the mental representations of syllables and words that consist of these syllables. The training materials were designed using the 500 (...) most frequent syllables typically read by fourth graders. The 75 poor readers were randomly allocated to the treatment or the control group. Results indicate a significant and strong effect on the fluency of recognizing single words, whereas text-level reading comprehension was not significantly improved by the training. The specific treatment effect provides evidence that a short syllable-based approach works even in older poor readers at the end of primary school. (shrink)

This paper examines the relationship between organizational ethical culture in two large international CPA firms, auditors'' personal values and the ethical orientation that those values dictate, and judgments in ethical dilemmas typical of those that accountants face. Using an experimental task consisting of multiple judgments designed to vary in "moral intensity" (Jones, 1991), and unique as well as tried-and-true approaches to variable measurements, this study examined the judgments of more than three hundred participants in our study. ANCOVA and path analysis (...) results indicate that: (1) Ethical judgments in situations of high moral intensity are affected by personal values and by environmental variables, such as the professional code of conduct (direct and indirect effects) and previous ethics instruction (direct effect only). (2) Corporate ethical culture, and a relatively strong firm rules-orientation, affect auditors'' idealism but not relativism, and therefore indirectly affect ethical judgments. Jones'' (1991) moral intensity argument is supported: differences in the characteristics of specific judgment tasks apparently result in different decision processes. (shrink)

This study investigates the influence of teacher competence on 3rd?grade students? reading achievement in public and independent schools in Sweden. The data come from the Swedish participation in PIRLS 2001 (Progress in Reading Literacy Study 2001) and comprise some 10,000 students. Students in independent schools achieved better on the reading test than did students in public schools, but when parents? education was controlled for, the effect on students? achievement of school type disappeared. Teacher certification for teaching in the early grades (...) had a strong effect on students? mean reading test scores in both school types, while no significant effects of teacher experience, age, gender, in?service training or cooperation could be established. Though school type had no influence of itself, it was a mediating factor for both parents? education and teachers? education. These effects, however, worked in opposite directions. (shrink)

Food safety has become a major development challenge and a key influence on the strategic behavior of food companies. The study seeks to analyze the effect of perceived institutional pressures on the governance of food safety and the effect this may have on food safety performance in emerging food supply chains. The research develops a conceptual framework that links perceived institutional pressures, degree of food manufacturer-supplier relationships, food safety practices, and food safety output. The hypothesized relationships were tested in the (...) Middle Eastern context, where food safety concerns are rising. Accordingly, a survey was carried out to collect data from food quality/safety managers representing 94 food processors across Lebanon. The study finds that perceived institutional pressures have a direct and strong effect on the degree of integration in the agro-food supply chain, and such an integration, in turn, increases the intensity of food safety practices and food safety performance. However, in the absence of strong manufacturer-supplier relationships, perceived institutional pressures do not lead to improved food safety performance. The study suggests that long-term food manufacturer-supplier relationship is necessary if agro-food chain actors are to respond to established regulatory demands, industry practices, and social norms. (shrink)