Philosophy of science is the object of metaphilosophical investigations. Metaphilosophy is the philosophy of philosophy. Philosophy is an archetypical thinking of being or an experience-of-being. History of Greek-European tradition of philosophy has three archetypes of thinking: objectivity, subjectivity, and inter-subjectivity. They are three archetypical contexts of interpretations of the concept of a philosophy of science too. Is philosophy of science part of philosophy? Is philosophy ofscience part of epistemology? What are methods of philosophy of science? These questions are the topics (...) of metaphilosophy. The topic of a scientific fact is a focal point of contemporary epistemology and philosophy of science. Is a scientific fact a fallible knowledge? The nature of a scientific fact is discussed in keeping with to the opposition of fallibilism and infallibilism. If fallibilism is universal quality of knowledge then there is a problem: is a scientific fact a fallible knowledge too? We are understanding and make clear the nature of a scientific fact by correlation of facts with: (1) data and evidence; (2) languages and theories; (3) methods of empirical investigations; (4) values, norms, and conventions of scientific investigations. Philosophy of science communicates with philosophy ofeconomics as the contemporary branch of philosophy. Its problems arise from the relationship of philosophy and philosophy of science with economics and practice. (shrink)

The article examines the system-methodological and conceptual foundations of the psychological activity theory that arose in the Soviet Union under the influence of the ideology of Marxism-Leninism. The author demonstrates the process of incorporation of Marxism-Leninism dogmas into the canonical form of the activity theory as a scientific knowledge that does not need any scientific confirmation. The pseudoscientific discourse that arose at the same time served to strengthen the position of the ideologists of the bureaucratic system, who found “objective confirmations” (...) of the truth of Marx’s teachings in the data of psychological science. The scientific community, subjected to ideological transformation, tried to defend itself from the destructive influence of ideology, giving rise to special forms of relations in the scientific and psychological environment, which led to the struggle and confrontation of scientific schools and groups. As a result of ideological expansion, psychological knowledge has become to some extent a tool for the bureaucratic system to overpower scientific dissent. That was clearly manifested in the discussion on the results of the Zagorsk experiment, in which an incorrect, partially falsified, attempt was made to prove the development of the human psyche of children born deaf and blind. The influence of ideology can also be traced in the confrontation of scientific schools in physics, genetics, biology and physiology. The article discusses prospects and new trends in the development of the activity theory after exclusion of the ideological concepts of Soviet socialism from its systemconceptual foundations. We observe the formation of new psychological concepts that reflect non-classical and post-non-classical forms of scientific rationality. Attempts are made to create and study the models of the psyche developed within the framework of the theory of organized complexity and the concepts of autopoietic self-organization and evolution. (shrink)

By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...) the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (shrink)

This essay serves as an intellectual biographical introduction to the special issue devoted to one of the leading Russian contemporary philosophers, Vyacheclav S. Stepin. The essay discusses Stepin's philosophical works and his chief contributions to such fields as philosophy and methodology of science, epistemology, and philosophical ontology among others. The authors also reflect on Stepin's academic leadership and his role as an organizer of research in philosophy in the contemporary Russia.

The intensive process of differentiation of knowledge that has in the past decade come to include philosophy has had the results, inter alia, that ethics, esthetics, and empirical sociology have undergone a kind of secondary "branching off" from the philosophy of society and culture . On the level of teaching this had the consequence that a department of esthetics and ethics was carved out of the department of historical materialism at the Philosophical Faculty of Moscow University, and was subsequently divided (...) into departments of esthetics and ethics, respectively. It was thus that the independent department of ethics made its appearance for the first time in the history of Moscow University. This occurred in 1969, and recently the department of Marxist- Leninist ethics marked its modest first decade. (shrink)

The study contains the review, analysis, assessment of the current state and prospects for further scientific study of the materials of the Russian state archives, including the personal funds of philosophers and philosophical institutions of Russia in the 19th-20th centuries, which are of the greatest relevance to historians of Russian philosophy. In this regard, on the one hand, the study considers the largest research and scientific-publishing historical and philosophical projects, testifying to the already achieved results of the scientific development of (...) vast arrays of archival documents; on the other hand, a number of collections of Russian state archives (federal, regional, municipal, departmental) have been monitored in order to identify archival collections that were little or insufficiently studied from this point of view. The results of the collective research presented in the article can be considered as the beginning of a large systematic work on the analytical mapping of the content of Russian archival collections relevant to the problems of the history of Russian philosophy. The study shows the importance and productivity of conducting parallel research work both with the personal funds of Russian philosophers of the 19th-20th centuries, and with funds containing documentation of philosophical institutions (magazine editorial offices, faculties, departments, research institutes, publishing houses of philosophical literature, professional and thematic associations of philosophers). In this regard, the question was raised about the need to develop historical and philosophical archiving and source studies in Russia, to include this set of subjects into the system of training historians of philosophy, and also about the need to coordinate the joint efforts of historians of Russian philosophy towards the formation of an archive of Russian philosophy as a significant and publicly available mapped resource. The results obtained in the course of the study should contribute to the emergence of the history of Russian philosophy as a dynamically developing branch of Russian science to a qualitatively new source study and methodological level, necessary for solving the large-scale research tasks, related, in particular, to the scientific preparation of academic collections of works by Russian philosophers and the development of modern fundamental history of Russian philosophy. (shrink)

The most enigmatic feature of polytene chromosomes is their banding pattern, the genetic organization of which has been a very attractive puzzle for many years. Recent genome‐wide protein mapping efforts have produced a wealth of data for the chromosome proteins of Drosophila cells. Based on their specific protein composition, the chromosomes comprise two types of bands, as well as interbands. These differ in terms of time of replication and specific types of proteins. The interbands are characterized by their association with (...) “active” chromatin proteins, nucleosome remodeling, and origin recognition complexes, and so they have three functions: acting as binding sites for RNA pol II, initiation of replication and nucleosome remodeling of short fragments of DNA. The borders and organization of the same band and interband regions are largely identical, irrespective of the cell type studied. This demonstrates that the banding pattern is a universal principle of the organization of interphase polytene and non‐polytene chromosomes.Editor's suggested further reading in BioEssaysCaught in the act: Rapid, symbiont‐driven evolution AbstractFunction and evolution of sex determination mechanisms, genes and pathways in insects Abstract. (shrink)

We show that for every computable limit ordinal α, there is a computable structure A that is $\Delta _\alpha ^0 $ categorical, but not relatively $\Delta _\alpha ^0 $ categorical (equivalently. it does not have a formally $\Sigma _\alpha ^0 $ Scott family). We also show that for every computable limit ordinal a, there is a computable structure A with an additional relation R that is intrinsically $\Sigma _\alpha ^0 $ on A. but not relatively intrinsically $\Sigma _\alpha ^0 $ (...) on A (equivalently, it is not definable by a computable $\Sigma _\alpha $ formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α. (shrink)

The question of the Russian man – his past, present and future – is the central one in the philosophy of history. Unfortunately, at present this area of philosophy is not suffciently developed in Russia. Partly the reason for this situation is the lack of understanding by researchers of the role played by Russian classical literature and its philosophizing writers in historiosophy. The Hunting Sketches, a collection of short stories by I.S. Turgenev, is a work still undervalued, not fully considered (...) not only in details but also in general meanings. And this is understandable because it is the frst systematic encyclopedia of Russian worldview, which is not envisaged by the literary genre. To a certain extent, Turgenev’s line is continued by I. Goncharov, L. Tolstoy, F. Dostoevsky, A. Chekhov. This article examines the philosophical nature of The Hunting Sketches, its structure and content. According to author’s opinion, stories can be divided into ten groups according to their dominant meanings. Thus, in The Hunting Sketches the main Russian types are depicted: “natural man,” rational, submissive, cunning, honest, sensitive, passionate, poetic, homeless, suffering, calmly accepting death, imbued with the immensity of the world. In the image and the comments of the wandering protagonist, Ivan Turgenev reveals his own philosophical credo, which he defnes as a moderate liberalism – freedom of thought and action, without prejudice to others. (shrink)

The modification of Frege's semantics that consists in using only one reference (Bedeutung, denotate) truth instead of two references truth and falsity is proposed. According to Frege 1) every true sentence stands for truth, 2) every false sentence stands for falsity. We modify the second statement: 2*) every false sentence doesn't stand for truth. The modification of sentential logic interpretation will consist in change of semantic rules: a) every formula A stands either for truth or falsity, b.1) the formula A (...) has value T iff the formula A stands for truth, b.2) the formula A has value F iff the formula A stands for falsity. Let’s change rules a) and b.2) on: a*) every formula A either stands or doesn't stand for truth, b.2*) the formula A has value F iff the formula A doesn't stand for truth. So, we have only one reference but still two values. The proposed approach can be extended to non-classical cases, for which the bivalence principle doesn't take place. An ordered pair of the sentences A, ~A is put in correspondence to the sentence A. Each sentence of ordered pair can either stands or doesn't stand for truthindependently from the other. Thus for each pair of sentences we have four possible variants of reference which are generate four functional values. (shrink)

The paper discusses the Strawsonian concept of descriptive metaphysics and its various implementations in conceptions of I. Kant, R.G. Collingwood and P.F. Strawson, their similarities and differences. Particular attention is paid to the analysis of Kant's transcendental philosophy (resp. transcendental idealism), or its metaphysics of appearance as a pioneer version of descriptive metaphysics and its comparison with the version of descriptive metaphysics of P. Strawson himself.

Volume 57, Issue 1, February 2019, Page 1-2.

In recent decades, perspectivism has developed into an epistemological research program claiming its independence. This autonomy stems from Perspectivism’s potential ability to resolve the contradictions between realist and constructivist programs. Perspectivism is based on the idea that the object depends on perspective, which constitutes any subjective attempt to cognize it. Perspectivists reconstruct and explain the factors involved in the formation of perspective, identifying the conditionality of epistemic acts, using concepts such as “position”, “point of view”, “view”, “angle”, “horizon”, “focus”, “picture”, (...) “context”, “aspect”, etc. Although these concepts are part of the perspectivist’s toolkit, their meanings and interrelation have so far been taken for granted and have not yet been critically and comprehensively analyzed. The purpose of this article is to take steps toward clarifying the conceptual basis for defending perspectivism as an epistemological program. Once consistently uncovered and correlated in a conceptual model, Perspectivist concepts can be used as a tool for a detailed analysis of theories, positions, and beliefs. The article begins with a preliminary description of the concept of perspectivism and its brief history as an epistemological program. In particular, the first modern attempts to outline perspectivist epistemology are described in the works of F. Kaulbach (1990), W. Stegmaier (2008), and M. Massimi (2017, 2020). The problem of identifying the special a priori status of perspectivist notions as a strategy for justifying the autonomy of Perspectivism is then posed. A method for demonstrating such a status, based on Kant’s transcendentalism and P. Strawson’s descriptive metaphysics, is then suggested. (shrink)

Philosophical Thought in Russia in the Second Half of the 20th Century is the first book of its kind that offers a systematic overview of an often misrepresented period in Russia's philosophy. Focusing on philosophical ideas produced during the late 1950s – early 1990s, it reconstructs the development of genuine philosophical thought in the Soviet period and introduces those non-dogmatic Russian thinkers who saw in philosophy a means of reforming social and intellectual life. Covering such areas of philosophical inquiry as (...) philosophy of science, philosophical anthropology, the history of philosophy, activity approach as well as communication and dialogue studies, the volume presents and thoroughly discusses central topics and concepts developed by Soviet thinkers in that particular fields. Written by a team of internationally recognized scholars from Russia and abroad, it examines the work of well-known Soviet philosophers (such as Mikhail Bakhtin, Evald Ilyenkov and Merab Mamardashvili) as well as those important figures (such as Vladimir Bibler, Alexander Zinoviev, Yury Lotman, Georgy Shchedrovitsky, Genrich Batishchev, Sergey Rubinstein, and others) who have often been overlooked. By introducing and examining original philosophical ideas that evolved in the Soviet period, the book confirms that not all Soviet philosophy was dogmatic and tied to orthodox Marxism and the ideology of Marxism-Leninism. It shows Russian philosophical development of the Soviet period in a new light, as a philosophy defined by a genuine discourse of exploration and intellectual progress, rather than stagnation and dogmatism. In addition to providing the historical and cultural background that explains the development of the 20th-century Russian philosophy, the book also puts the discussed ideas and theories in the context of contemporary philosophical discussions showing their relevance to nowadays debates in Western philosophy. With short biographies of key thinkers, an extensive current bibliography and a detailed chronology of Soviet philosophy, this research resource provides a new understanding of the Soviet period and its intellectual legacy 100 years after the Russian Revolution. (shrink)

Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. (...) More importantly, the measure predicts a new effect ("abnormal deflation"). Two studies show that people's judgments do, in fact, show this new effect. Taken together, the patterns of people's causal judgments thereby provide support for the proposed explanation. (shrink)

While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions under (...) which Bayesian agents would be rational. The proposal is illustrated with a characterization of costs inspired by thermodynamics. (shrink)

Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) and as a source of scientific hypotheses about how mental processes in fact work. The latter project, often called rational analysis, depends for its success on a fine-grained characterization of the computational problem facing a decision maker, which may in turn depend on realistic assumptions about what the relevant agent is like. As a consequence, resource rationality involves a delicate, but often fruitful interplay between the normative and the descriptive. (shrink)

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in a community, (...) especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease’s endemicity in the community, either suppressive or supportive. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and (...) only if the subject’s comparative judgments preclude representation by a standard probability measure. (shrink)

Listening to someone from some distance in a crowded room you may experience the following phenomenon: when looking at them speak, you may both hear and see where the source of the sounds is; but when your eyes are turned elsewhere, you may no longer be able to detect exactly where the voice must be coming from. With your eyes again fixed on the speaker, and the movement of her lips a clear sense of the source of the sound will (...) return. This ‘ventriloquist’ effect reflects the ways in which visual cognition can dominate auditory perception. And this phenomenological observation is one what you can verify or disconfirm in your own case just by the slightest reflection on what it is like for you to listen to someone with or without visual contact with them. (shrink)

Background A morally sound framework for benefit-sharing is crucial to minimize research exploitation for research conducted in developing countries. However, in practice, it remains uncertain which stakeholders should be involved in the decision-making process regarding benefit-sharing and what the implications might be. Therefore the study aimed to empirically propose a framework for benefit-sharing negotiations in research by taking HIV vaccine trials as a case. Methods The study was conducted in Tanzania using a case study design and qualitative approaches. Data were (...) collected using in-depth interviews (IDI) and focus group discussions (FGD). A total of 37 study participants were selected purposively comprising institutional review board (IRB) members, researchers, community advisory board (CAB) members, a policymaker, and HIV/AIDS advocates. Deductive and inductive thematic analysis approaches were deployed to analyze collected data with the aid of MAXQDA version 20.4.0 software. Results The findings indicate a triangular relationship between the research community, researched community and intermediaries. However, the relationship ought to take into consideration the timing of negotiations, the level of understanding between parties and the phase of the clinical trial. The proposed framework operationalize partnership interactions in community-based participatory research. Conclusion In the context of this study, the suggested framework incorporates the research community, the community being researched, and intermediary parties. The framework would guarantee well-informed and inclusive decision-making regarding benefit-sharing in HIV vaccine trials and other health-related research conducted in resource-limited settings. (shrink)

This paper explains how to use a new software tool for argument diagramming available free on the Internet, showing especially how it can be used in the classroom to enhance critical thinking in philosophy. The user loads a text file containing an argument into a box on the computer interface, and then creates an argument diagram by dragging lines from one node to another. A key feature is the support for argumentation schemes, common patterns of defeasible reasoning historically know as (...) topics . Several examples are presented, as well as the results of an experiment in using the system with students in a university classroom. (shrink)

Recently, we have faced the outbreak of the coronavirus disease 2019 in the world, which has attracted the attention of all people. Stress has become a word familiar to all people. The stressors of life are relatively clear and some of them cannot be eliminated by humans. One of the stressors in the life of humans is the COVID-19 pandemic. Doctors believe that the virus is controllable but its prevalence is quicker and deadlier than other viruses. In addition, the virus (...) puts the elderly and those with underlying diseases at extreme risk. Therefore, more care is seriously required to protect members of society. However, this psychological imbalance caused by the virus is associated with stress and anxiety. Lack of proper management of this stress will be associated with emotional impacts, physiological impacts, cognitive impacts and behavioural impact.Contribution: Given the importance of this topic, this study aimed to evaluate the relationship between religious beliefs and coping with COVID-19-related stress amongst Muslim students in three cities of Russia – Ingushetia, Chechnya and the Republic of Dagestan – in 2020. Data were collected using questionnaires, the validity and reliability of which were previously confirmed. According to the results, religious beliefs had an impact on stress coping by p = 0.657. In other words, students’ ability to cope with stress improved by 0.657 units, with each unit of enhancement in their religious beliefs. (shrink)

The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most important (...) cause of cyclical crises stems from strong structural disproportions that develop during economic booms. These are not only disproportions between different economic sectors, but also disproportions between different societal subsystems; at present these are also disproportions within the World System as a whole. The proposed model of business cycle is based on its subdivision into four phases: – recovery phase (which could be subdivided into the start sub-phase and the acceleration sub-phase); – upswing/prosperity/expansion phase (which could be subdivided into the growth sub-phase and the boom/overheating sub-phase); – recession phase (within which one may single out the crash/bust/acute crisis subphase and the downswing sub-phase); – depression/stagnation phase (which we could subdivide into the stabilization subphase and the breakthrough sub-phase). The article provides a detailed qualitative description of macroeconomic dynamics at all the phases; it specifies driving forces of cyclical dynamics and the causes of transition from one phase to another (including psychological causes); a special attention is paid to the turning point from the peak of overheating to the acute crisis, as well as to the turning point from the downswing to recovery. The proposed mathematical model of Juglar cycle takes into account the following effects that are typical for the market economy: • positive feedbacks between various economic processes; • presence of a certain inertia, time lags in reactions of the economic subsystem to the change in conditions; • amplification by the financial subsystem of positive feedbacks and time lags in the economic subsystem; • excessive reaction to changing conditions during the acute crisis sub-phase. The authors suggest that the current crisis turns out to be rather similar to classical Juglar crises; however, there is also a significant difference, as the current crisis occurs at a truly global scale. Yet, due to this truly global scale of the current crisis, the possibilities of regulation with the national state's measures have turned out to be ineffective,whereas the suprastate regulation of financial processes hardly exists. It is shown that all these have led to the reproduction of the current crisis according to a classical Juglar scenario. (shrink)

Robert Kimball, in “What’s Wrong with Argumentum Ad Baculum?” (Argumentation, 2006) argues that dialogue-based models of rational argumentation do not satisfactorily account for what is objectionable about more malicious uses of threats encountered in some ad baculum arguments. We review the dialogue-based approach to argumentum ad baculum, and show how it can offer more than Kimball thinks for analyzing such threat arguments and ad baculum fallacies.

Against those who question that ethical character should be considered as convincing factor of the human constitution based on empirical reasons, Obiora F. Ike gives good arguments, based on the agenda of the human development and education across the planet, to reaffirm some truth about character formation. There should be no question that simplifications, related to some sort of skepticism over the moral character, are at best purely theoretical fanciness, at worst irresponsible. Passivity in a world made of urgent challenges (...) around education and economic inequalities is not acceptable. Our need to believe, to trust and to act in the real world, lead us to praise some dogmatism on the ground assumption that we act accordingly to our [moral] character. Education has shown us the value of developing moral character. Cross-situational consistency of integrity needs to be shared across cultures, against the impression that it opens a room for abuses, as integrity is also a social construct. (shrink)

In [8], the third author defined a reducibility$\le _w^{\rm{*}}$that lets us compare the computing power of structures of any cardinality. In [6], the first two authors showed that the ordered field of reals${\cal R}$lies strictly above certain related structures. In the present paper, we show that$\left \equiv _w^{\rm{*}}{\cal R}$. More generally, for the weak-looking structure${\cal R}$ℚconsisting of the real numbers with just the ordering and constants naming the rationals, allo-minimal expansions of${\cal R}$ℚare equivalent to${\cal R}$. Using this, we show that (...) for any analytic functionf,$\left \equiv _w^{\rm{*}}{\cal R}$. $is noto-minimal.). (shrink)

For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This (...) role of Cantor's theory is compared with the role of Galois theory in algebraic geometry. (shrink)

The provability logic of a theory $T$ is the set of modal formulas, which under any arithmetical realization are provable in $T$. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$. We make an analogous modification for interpretability logics. We first study provability logics with restricted realizations and show that for various natural candidates of $T$ and restriction set $\Gamma$, the result is the logic of linear frames. However, for the theory Primitive (...) Recursive Arithmetic (PRA), we define a fragment that gives rise to a more interesting provability logic by capitalizing on the well-studied relationship between PRA and I$\Sigma_1$. We then study interpretability logics, obtaining upper bounds for IL(PRA), whose characterization remains a major open question in interpretability logic. Again this upper bound is closely related to linear frames. The technique is also applied to yield the nontrivial result that IL(PRA) $\subset$ ILM. (shrink)

0. The ancient and honorable role of philosophy as a servant to the learning, development and use of scientific knowledge, though sadly underdeveloped since Grassmann, has been re-emerging from within the particular science of mathematics due to the latter's internal need; making this relationship more explicit (as well as further investigating the reasons for the decline) will, it is hoped, help to germinate the seeds of a brighter future for philosophy as well as help to guide the much wider learning (...) of mathematics and hence of all the sciences. 1. The unity of interacting opposites "space vs. quantity", with the accompanying "general vs. particular" and the resulting division of variable quantity into the interacting opposites "extensive vs. intensive", is susceptible, with the aid of categories, functors, and natural transformations, of a formulation which is on the one hand precise enough to admit proved theorems and considerable technical development and yet is on the other hand general enough to admit incorporation of almost any specialized hypothesis. Readers armed with the mathematical definitions of basic category theory should be able to translate the discussion in this section into symbols and diagrams for calculations. 2. The role of space as an arena for quantitative "becoming" underlies the qualitative transformation of a spatial category into a homotopy category, on which extensive and intensive quantities reappear as homology and cohomology. 3. The understanding of an object in a spatial category can be approached through definite Moore-Postnikov levels; each of these levels constitutes a mathematically precise "unity and identity of opposites", and their ensemble bears features strongly reminiscent of Hegel's Science of Logic. This resemblance suggests many mathematical and philosophical problems which now seem susceptible of exact solution. (shrink)

In Morals By Agreement, David Gauthier concludes that under certain conditions it is rational for an agent to be disposed to choose in accordance with a fair cooperative scheme rather than to choose the course of action that maximizes his utility. This is only one of a number of important claims advanced in that book. In particular, he also propounds a distinctive view concerning what counts as a fair cooperative arrangement. The thesis concerning the rationality of adopting a cooperative disposition (...) is, however, logically independent of his substantive view of a fair cooperative scheme and is itself central to the project as a whole. Gauthier's concern is to establish that certain moral principles are those that fully rational, self-interested persons would agree to take as regulative of their dealings with one another – that a contractarian approach, in this sense, can provide an adequate basis for a theory of morality. (shrink)