In this paper we prove that any Δ30 degree has an increasing η -representation. Therefore, there is an increasing η -representable set without a strong η -representation.

In the framework of a cosmological model of the Universe filled with a nonrelativistic particle soup, we easily reproduce inflation due to the quantum potential. The lightest particles in the soup serve as a driving force of this simple, natural and promising mechanism. It is explicitly demonstrated that the appropriate choice of their mass and fraction leads to reasonable numbers of e-folds. Thus, the direct introduction of the quantum potential into cosmology of the earliest Universe gives ample opportunities of successful (...) reconsideration of the modern inflationary theory. (shrink)

The progress towards mathematization or, in a broader context, towards an increased “objectivity” is one of the main trends in the development of biological systematics in the past century. It is commonplace to start the history of numerical taxonomy with the works of R. R. Sokal and P. H. A. Sneath that in the 1960s laid the foundations of this school of taxonomy. In this article, I discuss the earliest research program in this field, developed in the 1920s by the (...) Russian entomologist and biometrician Eugen (Evgeniy Sergeevich) Smirnov. The theoretical and methodological grounds of this program are considered based on the published works of Smirnov as well as some archival sources. The influence of Smirnov’s evolutionary (mechano-Lamarckian) convictions on the development of this project of “exact systematics” is analyzed as well as the author’s attempts to establish a novel concept of “mathematical essentialism” in animal taxonomy. The probable causes of the failure of Smirnov’s project are viewed from both externalist and internalist perspectives, including the opposition to the use of quantitative methods in biology by some of the Lysenkoist ideologists in the USSR. A brief comparison of Smirnov’s research program with that developed 40 years later by Sokal and Sneath is provided. (shrink)

The structure of Russian science of the XIX century was dominated by state forms of its organization. At the same time, there were also a few private (non-governmental) forms of research communities. One of the little-studied phenomena of scientific privacy is the so-called “kruzhok” (a little circle in Russian). The article examines the history of the formation and activity of one of such “kruzhoks”, formed in the 1880s–1890s around Grand Duke Nikolai Mikhailovich, who was seriously engaged in research in the (...) field of lepidopterology (the branch of entomology studying butterflies, Lepidoptera). The role and significance of this “kruzhok” for the development of descriptive entomology in the situation of its weak institutionalization in Russia at the end of the XIX century are briefly considered, the course of scientific research of the Grand Duke and his entourage and the reasons for the termination of their activity are discussed. The history of this informal association is interpreted by us as a manifestation of the purposeful life-making of the Grand Duke, who thus tried to professionalize his hobby and enter the scientific community of entomologists on an equal footing, without breaking with his social environment and without going beyond the behavioral norms established by society for persons of his status. It is shown that the Nikolai Mikhailovich’s “kruzhok” became not only an instrument of his life-making, but also an influential center of Russian lepidopterology, the development of which was thereby given a powerful impetus. (shrink)

For a non-zero natural number n, we work with finitary $$\Sigma ^0_n$$ -formulas $$\psi (x)$$ without parameters. We consider computable structures $${\mathcal {S}}$$ such that the domain of $${\mathcal {S}}$$ has infinitely many $$\Sigma ^0_n$$ -definable subsets. Following Goncharov and Kogabaev, we say that an infinite list of $$\Sigma ^0_n$$ -formulas is a $$\Sigma ^0_n$$ -classification for $${\mathcal {S}}$$ if the list enumerates all $$\Sigma ^0_n$$ -definable subsets of $${\mathcal {S}}$$ without repetitions. We show that an arbitrary computable $${\mathcal {S}}$$ (...) always has a $${{\mathbf {0}}}^{(n)}$$ -computable $$\Sigma ^0_n$$ -classification. On the other hand, we prove that this bound is sharp: we build a computable structure with no $${{\mathbf {0}}}^{(n-1)}$$ -computable $$\Sigma ^0_n$$ -classifications. (shrink)

A low linear order with no computable copy constructed by C. Jockusch and R. Soare has Hausdorff rank equal to $2$. In this regard, the question arises, how simple can be a low linear order with no computable copy from the point of view of the linear order type? The main result of this work is an example of a low strong $\eta $ -representation with no computable copy that is the simplest possible example.

A stable classification of practical principles into mutually exclusive types is foundational to Kant’s moral theory. Yet, other than a few brief hints on the distinction between maxims and laws, he does not provide any elaborate discussion on the classification and the types of practical principles in his works. This has led Onora O’Neill and Lewis Beck to reinterpret Kant’s classification of practical principles in a way that would clarify the conceptual connection between maxims and laws. In this paper I (...) argue that the revised interpretations of O’Neill and Beck stem from a mistaken reading of the fundamental basis of the classification of practical principles. To show this, I first argue that Kant distinguishes between maxims and laws on the bases of validity and reality. I then argue that although a practical principle necessarily has the feature of validity, its reality in actually moving the agents to action sufficiently makes a principle a practical principle. If this is so, I argue that the classification of practical principles must be based on the extent to which they are effective in human agents. Such a classification yields us three exhaustive and mutually exclusive types namely, “maxims that are not potential laws”, “maxims that are potential laws” and “laws that are not maxims”. (shrink)

We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some (...) transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type. (shrink)

Introduction. Anthropotechnical turn in culture is based on educational practices that characterize a person as a subject and at the same time as an object of educational and corrective influence. Theoretical basis. We use the method of categorical analysis, which allows revealing the main outlook potentials of anthropotechnical turn as an essential transformation of modern socio-culture. Originality. For the first time, we conducted a categorical analysis of the glossary of anthropotechnical turn as dialectic of active and passive in the personal (...) and social modes such as education. Conclusions. The anthropotechnical turn of modern socio-culture means the actualization of the dialectic of active and passive in the process of socialization and formation of a person in a modern society. The world-view potential of the anthropotechnical turn is producing a new maxim and stratagem of person's behaviour through the formation of a new way of self-identification and self-esteem. The modern educational system, given the theory of anthropotechnical rotation, should change the content of timological energies from obedience to self-actualization and self-improvement. A prerequisite for this task is the change in the motivation of the education sector and the improvement of the social status of the teacher as an intellectual and leader of opinion. The analysis of the specificity of the information society and its determinatory impact on the individual provides grounds for identifying modern culture as a culture of lost opportunities. Thus, the main cause of disorientation and ignorance of a person is not the lack of information, but the lack of motivation. Therefore, the fundamental principles of anthropotechnical turn are productive in solving pressing problems of our time. (shrink)

Purpose. The purpose of the article is the analysis of the reasons and grounds of the crisis in the sphere of meaning-making, as well as searching answers to the questions about the meaning of human life in the contemporary world, which are maximally relevant in connection with the escalation of global problems, revealing the points of convergence between various theoretical positions, evaluation of their heuristic potential. Theoretical basis of the research is the historical-philosophical, comparative and system approaches, as well as (...) the analysis of philosophical insights in the field of global studies. Originality. Originality lies in the fact that this article is the first attempt to conduct comprehensive analysis in the problem of the sense of the Existence as it is presented in the first quarter of the 21st century and to relate it with the modern social situation that is characterized by a complex range of interconnected and interdependent anthropological problems of our time. Authors emphasize that the main reason in the crisis of meaning is that a man has lost touch with his roots, which is wildlife. He has created an artificial structure, civilization to satisfy his needs and finds no way to the transcendental, which is the true House of his being. Conclusions. A human must refuse from false self-conceit concerning his potential omniscience and omnipotence, cease dictating his own rules to the Existence, determine the boundaries of his freedom and try to clearly realize his place in the objective structure of being. The global situation can change for the better only if a dramatic change in the area of meaning-making happens. The decisive force, which may encourage nudging to the positive changes, can be either the free will of people who have realized the criticality of the situation or external natural and social circumstances that will make people reorganize radically. The proper prioritizing, a deep awareness of universal goals and solidarity between people could be the value basis that will become the foundation to find the meaning and create a more favorable future. (shrink)

The term 'Machiavellianism', used to designate a tough politics knowing no ethical barriers, entered firmly into circulation as far back as the sixteenth century. It was the negative reaction to the maxims in The Prince that defined the initial attitude toward Machiavelli's doctrine, and the internal polemic with this initial assessment has spawned an endless stream of literature endeavoring to justify in one way or other the ill-starred secretary of the Florentine Republic. In sheer number of publications, pro-Machiavelli views exceed (...) anti-Machiavelli views by many times. And yet questions remain; the original negative reaction is not eradicated, just as the striving for apologetics is not eradicated. (shrink)

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

The empirical findings in Collins and Porras'' study of visionary companies, Built to Last, and the normative claims about the purpose of the business firm in Centesimus Annus are found to be complementary in understanding the purpose of the business firm. A summary of the methodology and findings of Built to Lastand a short overview of Catholic Social Teaching are provided. It is shown that Centesimus Annus'' claim that the purpose of the firm is broader than just profit is consistent (...) with Collins and Porras empirical finding that firms which set a broader objective tend to be more successful than those which pursue only the maximization of profits. It is noted however that a related finding in Collins and Porras, namely that the content of the firm''s objective is not as important as internalizing some objective beyond just profit maximization, can lead to ethical myopia. Two examples are provided of this: the Walt Disney Company and Philip Morris. Centesimus Annus offers a way to expose such myopia, by providing guidance as to what the purpose of the firm is, and therefore as to what kinds of objectives are appropriate to the firm. (shrink)

I have argued elsewhere that our conception of phenomenal consciousness commits us to simple phenomenal experiences that in some sense constitute our complex experiences. In this paper I argue that the temporal boundaries of simple phenomenal experiences cannot be conceived as fuzzy or vague, but must be conceived as instantaneous or maximally sharp. The argument is based on an account of what is involved in conceiving fuzzy temporally boundaries for events generally. If the argument is right, and our conception of (...) phenomenal consciousness is assumed to reflect the facts about consciousness, then since the temporal boundaries of neurophysiological events can be conceived as fuzzy, considerable pressure can be applied to neurophysiological identity theories, as well as to dualist accounts that posit temporal correspondence with neurophysiological events. (shrink)

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, and (...) the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections. (shrink)

Is there any interesting sense in which we can speak of an act as 'evil', in contrast to simply "morally bad' or "immoral"? In ordinary language, we typically judge actions as evil that somehow differ significantly, in terms of degree or intensity, from commonplace wrongdoing. If taken to an extreme, however, this view simply reduces the difference between evil and immoral acts to a mere quantitative analysis. At worst, it leads to a wholly trivial account of evil as just those (...) actions we tend to regard as "really bad". In this paper, I outline a distinctively Kantian theory of evil that instead defends a fundamental qualitative difference between evil and more ordinary immoral actions, locating the main distinction in terms of the structure of the agent's will itself Broadly understood, this strategy endorses a Kantian account of "evil as dehumanization" in which a "material" -- as opposed to purely "formal" -- difference exists between the respective maxims of the immoral and the evil agent. In such instances, unlike typical cases of Kantian immoral actions, direct violation of another person's humanity qua human somehow comprises a necessary part of the "material object" of an evil agent's will. (shrink)

As is well known, Plotinus's philosophy served as the starting point for the development of all Neoplatonism. It created the basic schema that set the framework for the thought of all later representatives of this tendency from Porphyry to Damascius. The doctrine of the transcendence of the One, of the three original hypostases, the application of the categories of Plato's Parmenides in the construction of ontology—all this and much else besides became the property of the Neoplatonic schools, which were scattered (...) throughout the Roman empire, and was incorporated partly into the Christian theology, which was then in the process of formation. Naturally, as a result of its wide dissemination and the change in its cultural and social environment, Plotinus's legacy appeared in a different light and took on new forms; through these changes in form we can try to understand the difference in content. For this purpose Plotinus's treatise on the virtues is of special interest. The point is that Porphyry relies precisely on this treatise and at times even literally borrows large fragments from it in setting out the doctrine concerning the virtues in the thirty-second maxim . The same treatise serves as a basis for Marinus in his biography of Proclus. The aim of my lecture is to analyze the content of the treatise and its interpretations. (shrink)

Misrepresentations can be innocuous or even useful, but Kant’s corollary to the formula of universal law appears to involve a pernicious one: “act as if the maxim of your action were to become by your will a universal law of nature”. Humans obviously cannot make their maxims into laws of nature, and it seems preposterous to claim that we are morally required to pretend that we can. Given that Kant was careful to eradicate pernicious misrepresentations from theoretical metaphysics, the (...) imperative to act as if I have this supernatural power has typically been treated as an embarrassment meriting apology. The wording of the corollary may be vindicated, however, by recognizing that “as if” (als ob) is a technical term both in the Critique of Pure Reason and here. It signals a modal shift from the assertoric to the problematic mode of cognition, one that is necessitated by the attempt to incorporate the natural effects of a free will into a universal moral imperative that is philosophically practical. In this paper I sketch how the modal shift makes sense of the corollary as a subjectively necessary, philosophically practical idealization of the extension of human freedom into nature, one that accurately represents a necessary parameter of moral conduct: moral ambition. (shrink)

Consider an election in which each of the n voters casts a vote consisting of a strict preference ranking of the three candidates A, B, and C. In the limit as n→∞, which scoring rule maximizes, under the assumption of Impartial Anonymous Culture (uniform probability distribution over profiles), the probability that the Condorcet candidate wins the election, given that a Condorcet candidate exists? We produce an analytic solution, which is not the Borda Count. Our result agrees with recent numerical results (...) from two independent studies, and contradicts a published result of Van Newenhizen (Economic Theory 2, 69–83. (1992)). (shrink)

Some ideas expressed in the collective monograph Universality in Morality (2020), edited by Ruben Apressyan, are here critically examined. The book is based on the results of a large-scale study by professional ethical philosophers devoted to the question of the nature of universality in morality and the mechanisms of universalisation of individual maxims and norms from antiquity to modern ethical theories, represented above all by the analytical tradition in philosophy. Of great interest is the analysis of related phenomena in morality, (...) which makes it possible to determine the causes and nature of the transformation of morality in different eras and the accompanying change in the terminological apparatus of absolute ethical universalism, considered to be the starting point in the analysis of key modern concepts of moral universality. The article also suggests possible avenues for continued research in this area which could prompt modifications not only to the history of the concept of universality in morality, but also to our assessment of the contribution of individual authors and entire eras to the progress of human civilisation. This concerns above all the moral theory of contractarianism and the Enlightenment. Focus on their ideas goes a long way to determining the direction of current historical-philosophical research that reconstructs the history of ethical teachings and individual concepts. The importance attached today to a new view of the theory of the social contract, considered not only from socio-political but also from moral positions, forces us to approach in a new way the question concerning the universality of the key philosophical categories developed within this theory throughout its history. Elaborating the ideas set forth in the monograph, the author also stresses the relevance of the problem of justifying the thesis about the moral law as an analogue of the universal law of nature in the modern context. (shrink)

In this paper, I analyzed the discussion on the principle of universalizability which took place in moral philosophy in 1970–1980s. In short, I see two main problems that attracted more attention than others. The first problem is an opposition of universalizability and generalization. M.G. Singer argued for generalization argument, and R.M. Hare defended universalizability thesis. Hare tried to refute Singer’s position, using methods of ordinary language philosophy, and claimed that in ethics generalization is useless and misleading. I have examined Singer’s (...) defense and concluded that he was right and Hare was mistaken. Consequently, generalization argument is better in clarification of the relationship between universality and morality than Hare’s doctrine of universalizability, and hence the universality of moral principles is not incompatible with the existence of exclusions. The second problem is the substantiation of the application of categorical imperative in the theory of relevant act descriptions and accurate understanding of the difference between maxims and non-maxims. In Generalization in Ethics, Singer drew attention to this theme and philosophers have proposed some suggestions to solve this problem. I describe ideas of H.J. Paton, H. Potter, O. O’Neill and M. Timmons. Paton coined the teleological-law theory. According to Potter, the best criterion for the relevant act descriptions is causal one. O’N eill suggested the inconsistency-of-intention theory. Timmons defended the causal-law theory. My claim is that the teleological-law theory and the causal-law theory fail to solve the relevant act descriptions problem and the causal criterion and the inconsistency-of-intention theory have their limits. From this, I conclude that these approaches cannot be the basis for clarifying the connection between universality and morality, in contrast to Singer’s approach, which, therefore, is better than others to clarify the nature of universality in morality. (shrink)

As the need for business to address pressing social and ecological issues intensifies, so does the importance of enhancing the development of sustainable marketing. The current dominant approach to sustainable marketing is based on a Triple Bottom Line (TBL) profit‐centric worldview, which suggests that firms can simultaneously improve their financial well‐being as they reduce negative social and ecological externalities. However, whereas the scope of TBL marketing is limited to sustainability initiatives that enhance profits, there is a growing need for—and interest (...) in—developing a sustain‐centric approach to marketing that relaxes the need to maximize financial well‐being in order to optimize social and ecological well‐being. Even so, because of the dominance of the profit‐centric worldview, hallmarks of sustain‐centric marketing practices remain under‐developed and may even lend themselves to becoming inauthentically mimicked on a piecemeal basis by greenwashing profit‐centric firms. We provide an exploratory empirical study of marketing practices evident in two sustain‐centric firms and draw implications to advance theory for both sustain‐centric and profit‐centric marketing. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Feminist Studies 44, no. 2. © 2018 by Feminist Studies, Inc. 333 Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair Refusing to Account: Toward a Pedagogy of Tectonic Instability The increasing commoditization of knowledge and corporatization of the academy have led to a drastic restructuring of higher education, and in particular, of public institutions of learning. There is a striking similarity to the strategies enacted across institutions, each (...) governed by modes of efficiency and profitability. These moves have included a preference for larger classes, curriculum decisions that are governed by seats rather than pedagogical possibilities, an expansion of online offerings, tuition increases, and ramped-up bureaucratization, with the latter being accompanied by fewer faculty hires, a greater dependence on contingent faculty, and a swell in the ranks of senior administrative staff. This restructuring has held very specific consequences for women ’s studies programs. While larger classes are not inherently at odds with a student-centered feminist pedagogy, they do require adjustments in order to achieve similar results with our students, and they do exact greater physical and emotional labor from us as instructors. These restructuring strategies have also positioned the field in a Catch22 in that a number of issues that we have lobbied to have valued within the academy have now come into the university’s line of vision only to be redeployed as part of the university’s public relations branding agenda. There are numerous examples if we would but look: campuses that are spotted with banners portraying faculty and students of color —a visual map to the institution’s “embrace of diversity”; committees 334 Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair that are convened to review the institution’s sexual harassment policy while simultaneously refusing the involvement of women’s studies academics in the process, for whom these are scholarly and intellectual areas of study; the introduction of multicultural general education curricula, where the study of “difference” amounts to a banal presence of one or more categories of “otherness” in syllabi. This list is not exhaustive but the similarity that threads through is the commodification and the PR-ization of issues that sit at the heart of the field of women’s studies. Such cooptation notwithstanding, in this economic climate of profit maximization, small, interdisciplinary programs and departments such as women’s studies, ethnic studies, and LGBT studies have become woefully vulnerable to mergers, downsizing, and elimination.1 Our own program, now defunct, attests to this growing reality.2 So what then is the story to be told for a program that no longer exists? As alumna of Clark University’s now defunct women’s studies doctoral program, we consider the ways in which Clark, under the guidance of Cynthia Enloe, worked to move the field toward a more transnational bent. While we begin with an engagement with Clark’s specific institutional vulnerabilities, we use Clark’s commitment to a transnational praxis as our comparative point of departure to note the ways in which the importance and acuity of a transnational feminist critique have seeped away from the field. At various points in the article, we discuss how our individual trajectories emerged out of a transnational feminist sensibility. We interrogate the ways that the dominant logics of the field continue to be complicit with the very inequities and modes of representation critiqued within transnational feminist discourses. We point to the role that our scholarly pursuits play in an ongoing effort to hold the field accountable to a transnational feminist critique. Finally, 1. See Miranda Joseph, Debt to Society: Accounting for Life under Capitalism (Minneapolis, MN: University of Minnesota Press, 2014); and Chandra Talpade Mohanty, “Privatized Citizens, Corporate Academies, and Feminist Projects,” in Feminism without Borders: Decolonizing Theory, Practicing Solidarity (Durham, NC: Duke University Press, 2003). 2. The doctoral program at Clark began in 1992 and closed in 2008, graduating twenty-six PhDs and training many more who have gone on to make significant contributions at NGOs among other locations. For example, Parissara Liewkeat and Barbara Schulman have held positions with the International Labor Organization and Amnesty International, respectively. Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair 335 we look back at our own training... (shrink)

Starting from the premise that firms are distinct in terms of their capacity to create innovations, this article explores the rationale for R&D cooperation and the choice between alliances that involve information sharing, cost sharing or both. Defining innovative capability as the probability of creating an innovation, it examines firm strategy in a duopoly market, where firms have to decide whether or not to cooperate to acquire a fixed cost R&D infrastructure that would endow each firm with a firm-specific innovative (...) capability. Furthermore, since emerging industries are often characterized by high technological uncertainty and diverse firm focus that makes the exploitation of spillovers difficult, this article focuses on a zero spillover context. It demonstrates that asymmetry has an impact on alliance choice and social welfare, as a function of ex-post market competition and fixed costs of R&D. With significant asymmetry no alliance may be formed, while with similar firms the cost sharing alliance is dominant. Finally, it ascertains the settings under which the equilibrium outcome is distinct from that maximizing social welfare, thereby highlighting some conditions under which public investment in a technology park can be justified. (shrink)

The author argues that despite universal and formal character of the foundation of Kant's ethics, its principles appear to be compatible with recognition of the possibility of lying for philanthropic reason. To have an effect in the world, our obligations must necessarily have empirical components that point to specific conditions, under which the maxim will have a moral worth. One of such condition may be the requirement that probable consequences of the action will not clash with other obligations.

The sources of the real conflict between science and various kinds of undertakings in occultism pretending to be science date back to the end of the 16th and beginning of the 17th centuries, when modern scientific method was barely taking shape. The natural philosophy of the 16th century, which put forth natural magic in place of divine magic, was the ideological antipode of the new science in process of formation. The pantheistic reinterpretation of monotheistic Christian creationism is a characteristic feature (...) of constructs in natural philosophy with their striving toward maximal substantialization of the nonmaterial. Thus, for example, the rationalist mystic of natural philosophy, Girolamo Cardano, returns in his work to the medieval notion of the world soul, but understands by it an entirely material substance which he identifies with light and heat. (shrink)

During each school semester, students face an onslaught of material to be learned. Students work hard to achieve initial mastery of the material, but when they move on, the newly learned facts, concepts, and skills degrade in memory. Although both students and educators appreciate that review can help stabilize learning, time constraints result in a trade-off between acquiring new knowledge and preserving old knowledge. To use time efficiently, when should review take place? Experimental studies have shown benefits to long-term retention (...) with spaced study, but little practical advice is available to students and educators about the optimal spacing of study. The dearth of advice is due to the challenge of conducting experimental studies of learning in educational settings, especially where material is introduced in blocks over the time frame of a semester. In this study, we turn to two established models of memory—ACT-R and MCM—to conduct simulation studies exploring the impact of study schedule on long-term retention. Based on the premise of a fixed time each week to review, converging evidence from the two models suggests that an optimal review schedule obtains significant benefits over haphazard (suboptimal) review schedules. Furthermore, we identify two scheduling heuristics that obtain near optimal review performance: (a) review the material from μ-weeks back, and (b) review material whose predicted memory strength is closest to a particular threshold. The former has implications for classroom instruction and the latter for the design of digital tutors. (shrink)

Over a period of 22 years (1934-1955), the mathematician Kurt Gödel wrote down philosophical remarks, the so-called Maximen Philosophie (Max Phil). They are preserved in 15 notebooks in Gabelsberger shorthand. The first booklet contains general philosophical considerations, booklets two and three consist of Gödel's individual ethics. The following books show that Gödel developed a philosophy of science in which he places his discussions on physics, psychology, biology, mathematics, language, theology and history in the context of a metaphysics. A complete, historical-critical (...) edition of Gödel's Philosophical Notebooks is now being prepared for the first time at the Kurt Gödel Research Centre of the Berlin-Brandenburg Academy of Sciences and Humanities. One volume will be published each year as part of this edition. Volume 5 is particularly interesting because Gödel reveals his satisfaction with it at the beginning of 'Maximen V'. He states that he has arrived at independent thought here, which has not primarily come about through discussion with other authors. Furthermore, in addition to numerous remarkable philosophical considerations, there is a previously unknown interpretation of his (second) incompleteness theorem that goes beyond the mathematical one. (shrink)

Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...) and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable. (shrink)

W. V. Quine calls some general methods of science maxims: general defeasible principles that call on us to approximate, maximize, or minimize a state and that are interpreted and weighed in context-sensitive ways. On my reading, his empiricism asks us to maximize accepting overall theories empirically equivalent to ours but to minimize accepting sentences that both do not affect the empirical content of our overall theory and do not simplify our overall theory. His naturalism asks us to maximize accepting sentences (...) that are solely supported by standards that support our best current scientific theory. Drawing on the Quine archive at Houghton Library at Harvard, I support and apply these interpretations by investigating his rapidly evolving later work on empirical content and empirical equivalence, including some of his views on translation in this later work and his vacillation between what he calls the ecumenical and sectarian attitudes. (shrink)

This paper is about David Gauthier’s concept of constrained maximization. Attending to his most detailed and careful account, I try to say how constrained maximization works, and how it might be changed to work better. In section I, that detailed account is quoted along with amplifying passages. Difficulties of interpretation are explained in section II. An articulation, a spelling out, of Gauthier's account is offered in section III to deal with these difficulties. Next, in section IV, constrained maximization thus articulated (...) is tested on several choice problems and shown to be seriously wanting. It appears that there are prisoners’ dilemmas in which constrained maximizers would not cooperate to mutual advantage, but would interact sub-optimally just as straight-maximizers would. ‘Coordination problems’ are described with which constrained maximizers might, especially if transparent to one another, not be able to cope–problems in which they might not be able to make up their minds to do anything at all. And I prove that there are prisoners’ dilemmas that, though possible for real agents and for straight maximizers, are not possible for constrained maximizers, so that agents’ internalising dispositions of constrained maximization could not be of help in connection with such possibly impending dilemmas. Taking constrained maximization as it stands, there are many problems for which it does not afford the ‘moral solutions’ with which Gauthier would have it replace Hobbesian political ones. After displaying these shortcomings of constrained maximization as presently designed, I sketch, in section V, possible revisions that would reduce them, stressing that these revisions would not be cost-free. Whether finishing the job of fixing up and making precise constrained maximization would be worth the considerable trouble it would involve lies beyond the issues taken up in this paper. So, of course, do substantive comparisons of constrained maximization, perfected and made precise, and straight maximization. (shrink)

The iterative concept of set is standardly taken to justify ZFC and some of its extensions. In this paper, we show that the maximal iterative concept also lies behind a class of further maximality principles expressing the maximality of the universe of sets V in height and width. These principles have been heavily investigated by the first author and his collaborators within the Hyperuniverse Programme. The programme is based on two essential tools: the hyperuniverse, consisting of all countable transitive models (...) of ZFC, and V -logic, both of which are also fully discussed in the paper. (shrink)

In recent years, one of the main thrusts of set-theoretic research has been the investigation of maximality principles for V, the universe of sets. The Hyperuniverse Programme (HP) has formulated several maximality principles, which express the maximality of V both in height and width. The paper provides an overview of the principles which have been investigated so far in the programme, as well as of the logical and model-theoretic tools which are needed to formulate them mathematically, and also briefly shows (...) how optimal principles, among those available, may be selected in a justifiable way. (shrink)

In transfinite arithmetic 2n is defined as the cardinality of the family of all subsets of some set v with cardinality n. However, in the arithmetic of recursive equivalence types 2N is defined as the RET of the family of all finite subsets of some set v of nonnegative integers with RET N. Suppose v is a nonempty set. S is a class over v, if S consists of finite subsets of v and has v as its union. Such a (...) class is an intersecting class over v, if every two members of S have a nonempty intersection. An IC over v is called a maximal IC , if it is not properly included in any IC over v. It is known and readily proved that every MIC over a finite set v of cardinality n ≥ 1 has cardinality 2n-1. In order to generalize this result we introduce the notion of an ω-MIC over v. This is an effective analogue ot the notion of an MIC over v such that a class over a finite set v is an ω-MIC iff it is an MIC. We then prove that every ω-MIC over an isolated set v of RET N ≥ 1 has RET 2N-1. This is a generalization, for while there only are χ0 finite sets, there are ϰ isolated sets, where c denotes the cardinality of the continuum, namely all the finite sets and the c immune sets. MSC: 03D50. (shrink)

In this paper, following an idea of Christophe Chalons. I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence varphi holding in some forcing extension $V^P$ and all subsequent extensions $V^{P\ast Q}$ holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme $(\lozenge \square \varphi) \Rightarrow \square \varphi$ , and is equivalent to (...) the modal theory S5. In this article. I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that $V_\delta \prec V$ for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is $\square MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ , which asserts that $MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ holds in V and all forcing extensions. From this, it follows that $0^\#$ exists, that $x^\#$ exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain. (shrink)

What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...) set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics. (shrink)