Hale proposes a neo-logicist definition of real numbers by abstraction as ratios defined on a complete ordered domain of quantities (magnitudes). I argue that Hale's definition faces insuperable epistemological and ontological difficulties. On the epistemological side, Hale is committed to an explanation of measurement applications of reals which conflicts with several theorems in measurement theory. On the ontological side, Hale commits himself to the necessary and a priori existence of at least one complete ordered domain of quantities, which is extremely (...) implausible because science treats the logical structure of quantities as subject to experimentally and theoretically motivated refinements and revisions. (shrink)

Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data. These challenges are incomplete in two respects: they do not show that chaotic regimes are unpredictable in principle and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this paper (...) we appeal to an asymptotic analysis of state space trajectories and their numerical approximations to show that chaotic regimes are deterministically unpredictable even with unbounded resources. Additionally, we explain why stochastic models of chaotic systems, while predictively successful in some cases, are in general predictively as limited as deterministic ones. We conclude by suggesting that the way in which scientists deal with such principled obstructions to predictability calls for a more comprehensive approach to theory validation, on which experimental testing is augmented by a multifaceted mathematical analysis of theoretical models, capable of identifying chaos-related predictive failures as due to principled limitations which the world itself imposes on any less-than-omniscient epistemic access to some natural systems. (shrink)

Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry as an inexact non-demonstrative science (...) is argued to be a consequence of his attempt to discredit geometrical proofs of infinite divisibility of extension by anchoring the meaning of geometrical concepts in inherently inexact qualitative measurement procedures. This measurement-based attack on the exactness and certainty of geometry is analyzed and shown to be both self-refuting and inconsistent with the general epistemological framework of the Treatise. The revised conception of geometry as a demonstrative science in the first Enquiry is then interpreted as Hume's response to the failure of his earlier attempt to discredit geometrical proofs of infinite divisibility of extension. (shrink)

The central argument for functionalism is the so-called argument from multiple realizations. According to this argument, because a functionally characterized system admits a potential infinity of structurally diverse physical realizations, the functional organization of such systems cannot be captured in a law-like manner at the level of physical description (and, thus, must be treated as a principally autonomous domain of inquiry). I offer a rebuttal of this argument based on formal modeling of its premises in the framework of automata theory. (...) In this formal model I exploit the so-called minimal (universal) realizations of automata behaviors to show that the argument from multiple realizations is not just invalid but is refutable, in the sense that its premises (when made formally precise) entail the very opposite of the functionalist's conclusion. (shrink)

Putnam's ``model-theoretic'' argument against metaphysical realism presupposes that an ideal scientific theory is expressible in a first order language. The central aim of this paper is to show that Putnam's ``first orderization'' of science, although unchallenged by numerous critics, makes his argument unsound even for adequate theories, never mind an ideal one. To this end, I will argue that quantitative theories, which dominate the natural sciences, can be adequately interpreted and evaluated only with the help of so-called theories of measurement (...) whose epistemological and methodological purpose is to justify systematic assignments of quantitative values to objects in the world. And, in order to fulfill this purpose, theories of measurement must have an essentially higher order logical structure. As a result, Putnam's argument fails because much of science turns out to rest on essentially higher order theoretical assumptions about the world. (shrink)

In today's philosophy of science, scientific theories are construed as abstract mathematical objects: formal axiomatic systems or classes of set-theoretic models. By focusing exclusively on the logico-mathematical structure of theories, however, this approach ignores their essentially cognitive nature: that theories are conceptualizations of the world produced by some cognitive agents. As a result, traditional philosophical analyses of scientific theories are incapable of coherently accounting for the relevant relations between highly abstract and idealized models in science and concrete empirical phenomena in (...) the world. ;As a more accurate and comprehensive alternative to traditional analyses of scientific theorizing, the dissertation proposes and develops a conception of scientific theories which makes explicit the essential role of cognitive agents--theorizers--in generating abstract scientific models and systematically relating such models to experimentally controlled parts of the world. ;Specifically, by utilizing the conceptually powerful formal framework of the Theory of Categories, the new approach clarifies and makes formally precise the cognitive status of several important aspects of scientific theorizing, including the notion of a scientific model as theorizers' mathematical conceptualization of the world jointly determined by theorizers' physical interactions with the world and their cognitive access to mathematical objects, the distinction between models in science and models in pure mathematics, the distinction between provisional and successful scientific models, the notion of a systematic correspondence between successful scientific models and the world which does not impose upon the world the mathematical structure of scientific models, and the way in which theorizers' modeling strategy determines the general structure of scientific knowledge. (shrink)

The main aspect of the intuitionist ontology of mathematicsis the conception of mathematical objects as products of the human mind. This paper argues that so long as the existence of mathematical objects is made dependent on thehuman mind , the intuitionist ontology is refutable in that it is inconsistent with our well-confirmed beliefs about what is physically possible. At the same time, it is also argued that the intuitionistś attempt to remove this inconsistency by endowing the mind with various highly (...) idealized features and capacities will erase any significant ontological difference between Intuitionism and Platonism. (shrink)

In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources of mathematical analysis) are used as a unified mathematical framework for modeling (a) the time-dependent behavior of natural systems, (b) interactions between natural systems and measuring instruments, (c) error and uncertainty in measurement, and (d) the formal propositional language for describing and reasoning about measurement results. We also discuss how a celebrated theorem in analysis, known as Gelfand (...) representation, guarantees that autonomously specified algebras of quantities can be interpreted as algebras of observables on a suitable state space. Such an interpretation is then used to support (i) a realist conception of quantities as objective characteristics of natural systems, and (ii) a realist conception of measurement results (evaluations of quantities) as determined by and descriptive of the states of a target natural system. As a way of motivating the analytic approach to measurement, we begin with a discussion of some serious philosophical and theoretical problems facing the well-known representational theory of measurement. We then explain why we consider the analytic approach, which avoids all these problems, to be far more attractive on both philosophical and theoretical grounds. (shrink)

Using the two cases of the Icelandic Health Sector Database and Russian initiatives in biobanking, the article criticizes the view of narratives and imaginaries as a sufficient and unproblematic means of shaping public understanding of genetics and justifying population-wide projects. Narrative representations of national biobanking engage particular imaginaries that are not bound by the universal normative framework of human rights, promote affective thinking, distract the public from recognizing and discussing tangible ethical and socioeconomic issues, and harm trust in science and (...) technology. In the Icelandic case, the presentation of the project in association with national imaginaries concealed its market identity and could lead to the commodification of biodata. In the Russian case, framing in terms of "genetic sovereignty" and "civilizational code" offers pretexts for state securitization. Adherence to normative framework of human rights and public discussion of genetics in an argumentative and factual mode can counter these trends. (shrink)

The article discusses the book by A. Yurchak, in which he offers a scientific explanation of the causes and process of the completion of socialist culture and the death of the USSR. The author analyzes the central concept used in this explanation — “authoritative discourse”, showing that the latter is interpreted in two ways: within the framework of the semiotic approach outlined by John Austin, and the “dispositive” approach developed by Michel Foucault. Based on the analysis of the case from (...) the book, the author offers his own reconstruction and concepts (“schemas”, “life world”, “sociality”) that can complement Yurchak’s research. A comparison of the latter’s explanation and the explanation of sociologist Leonid Ionin, carried out during the period of perestroika and reforms, made it possible to clarify Yurchak’s approach and methodology. (shrink)

Представим себе берег реки, на берегу пасутся дикие кабаны. Светит солнце, лес шумит от порывов ветра и так далее. По вашему мнению, это не является картиной реальности, пока в нее не введен наблюдатель - человек.

An online game of chess against a human opponent appears to be indistinguishable from a game against a machine: both happen on the screen. Yet, people prefer to play chess against other people despite the fact that machines surpass people in skill. When the philosophers of 1970’s and 1980’s argued that computers will never surpass us in chess, perhaps their intuitions were rather saying “Computers will never be favored as opponents”? In this paper we analyse through the introduced concepts of (...) psychological affordances and psychological interplay, what are the mechanisms that make a human-human interaction more meaningful than a human-computer interaction. We claim that an HH chess game consists of two intertwined, but independent simultaneous games—only one of which is retained in the HC game. To help with the analysis we introduce the thought experiment of a Preferential Engagement Test which is inspired by, but non-equivalent to, the Standard Turing Test. We also explore how the PET can illuminate, and be illuminated by, various philosophies of mind reading: Theory Theory, Simulation Theory and Mind Minding. We propose that our analysis along with the concept of PET could illuminate in a new way the conditions and challenges a machine must face before it can replace humans in a given occupation. (shrink)

This research is devoted to the study of scientific and methodological aspects of providing students with physical education. The research is based on the works of Russian teachers who have adopted the experience of the new higher education program for bachelor's degree. The starting point for the development of new concepts is the latest edition of the Federal State Educational Standard for Higher Education. The purpose of the study is to analysis of the scientific and methodological support of physical education (...) of students under the Federal State Educational Standard program. In the course of the research, we study the most important aspects of the formation of physical skills with the help of basic and additional types of interaction between a teacher and students. Scientific novelty lies new look at complex education, which includes an expanded set of methods, technologies for the development of cognitive interest, activity, physical skills and motivation for active recreation, a healthy lifestyle. The design technology of 2021, based on the method of new generation projects by Evgenia Semyonovna Polat, is a separate factor. The result of the study was the definition of the scientific and methodological aspects of providing physical education in the main and additional types of interaction between the teacher and students, including physical culture, sports, elite sports, competitive tests, project technology and distance learning format. (shrink)

The author discusses the concept of an ideal object. The statement of O.I. Genisaretsky is quoted and problematized, stating that the obligatory feature that has been preserved for the object and the terms "object" and "ideal object" is, apparently, its representability or visibility. The author shows that ideal objects began to be created during the formation of ancient philosophy and thinking. Faced with contradictions, ancient thinkers dealt with this situation in different ways. If Protogoras recognized the right of the reasoners (...) to receive contradictions and, accordingly, to consider the world contradictory, then Parmenides considered the world consistent, arguing that the criterion for the correctness (truth) of knowledge is not a reasoning person, but this world, existence, which still needs to be reached with the help of correct thought. It was within the framework of the implementation of the Parmenides program that ideal objects began to be created, which, as the author shows, performed three main functions: they allowed us to think consistently, to know the world and its phenomena, to comprehend and interpret empirical phenomena (facts) in a different way. Based on the case of Plato's "Feast", the semiotic schemes on the basis of which Plato creates ideal objects are analyzed. It is argued that it is impossible to build ideal objects, bypassing schemes, since their inventors (creators) are people. By solving problems, they synthesize meanings belonging to different areas of consciousness. The analysis of Galileo's "Conversations" allowed the author to suggest that the construction of ideal objects is due to the historical type of philosophical or scientific thinking. The author considers it necessary, before claiming to create a modern doctrine of ideal objects, to analyze the main typical cases of the construction of these objects in philosophy and science, and such an analysis can make significant adjustments to the understanding of the nature and features of this concept. Nevertheless, he suggests, it is already clear that the construction of ideal objects is an important link in philosophical, scientific and a number of other types of thinking. (shrink)

The article aims at clarifying the historical status and cognitive potentials of such a genre of contemporary historiography of philosophy as biographical encyclopedia (dictionary). Based on extensive bibliographic material, the author demonstrates that in the late XX – early XXI centuries in the English-speaking countries there was a real outbreak of interest in encyclopedias and dictionaries, compiled from personalized articles about the life and works of philosophers of certain epochs, countries, trends, etc. According to the author, the increasing popularity of (...) this genre can be considered as a logical continuation of the historical and biographical turns that took place in the Anglo-American (analytic) philosophy in the 1980s and 1990s, respectively. The author specifically emphasizes that it caused the appearance of a significant number of encyclopedias and dictionaries, which contain the well-known facts as well as the significant elements of scholar novelty. The article also shows that similar tendencies have taken place in the contemporary Ukrainian historiography of philosophy. It is shown that Ukrainian experts also made their own significant contribution to the development of this genre. They have successfully developed a special approach, which presupposes the focus on life and works of the representatives of a particular academic institution. The intellectual value of this approach is demonstrated by the example of the recently published two-volume encyclopedia “Kyiv Theological Academy in Names: 1819-1924”. It contains a systematic and very informative presentation of the biographies of many representatives of the national philosophy, whose activities were associated with this institution. The author also shows that from the perspective of the historiography of philosophy, the general methodological foundations of this encyclopedic research is a matter of special interest. (shrink)

Geared toward undergraduate majors in math, computer science, and computer engineering, this text employs discrete mathematics to introduce basic knowledge of proof techniques. Exercises with hints. 2019 edition.

In the Club of Rome report Come on! Capitalism, Short-Termism, Population and the Destruction of the Planet (2018) Kant, along with other “old” Enlighteners, is presented as the father of a world-view which led to the destabilisation of the environment in which humanity exists. The authors of the report argue that the “old Enlightenment” with its individualism, faith in the market and a consumerist attitude to nature should be scrapped. I maintain that this assessment of Kant’s philosophy is groundless and (...) that his ideas allow us both to conduct a more profound diagnosis of the crisis and to propose a more solidly founded strategy of overcoming it. First, I sum up the position of the authors concerning the loss of sustainability of development which they attribute to the philosophy of Enlightenment. Next, I outline the history and content of the notion of “sustainable development” and offer an analysis of the sources of progressivist commitment to the conquest of nature which lie outside Modern Times in the idea of the “cultural mandate”. Then I present the Kantian diagnosis of the causes of the crisis which attributes it to humankind’s failure to “mature”. I compare the idea of “the full world” formulated by the authors of the report with the idea of the “the world come of age” and their diagnosis of “capitalism — short-termism — depletion of resources” with the Kantian assessment of the attempts to escape from the predicaments of the present into the past or the future. I draw attention to Kant’s solutions to some of the specific problems indicated in the report. Instead of the strategy of “return of the cultural mandate”, proposed at this time by the authors of the report, the Kant­ian answer to the crisis is a “Copernican turn” and re-direction of the cultivating effort to the inner moral development of the human being. (shrink)

In biomedical measurement, biomarkers are used to achieve reliable prediction of, and useful causal information about patient outcomes while minimizing complexity of measurement, resources, and invasiveness. A biomarker is an assayable metric that discloses the status of a biological process of interest, be it normative, pathophysiological, or in response to intervention. The greatest utility from biomarkers comes from their ability to help clinicians (and researchers) make and evaluate clinical decisions. In this paper we discuss a specific methodological use of clinical (...) biomarkers in pharmacological measurement: Some biomarkers, called ‘surrogate markers’, are used to substitute for a clinically meaningful endpoint corresponding to events and their penultimate risk factors. We confront the reliability of clinical biomarkers that are used to gather information about clinically meaningful endpoints. Our aim is to present a systematic methodology for assessing the reliability of multiple surrogate markers (and biomarkers in general). To do this we draw upon the robustness analysis literature in the philosophy of science and the empirical use of clinical biomarkers. After introducing robustness analysis we present two problems with biomarkers in relation to reliability. Next, we propose an intervention-based robustness methodology for organizing the reliability of biomarkers in general. We propose three relevant conditions for a robust methodology for biomarkers: (R1) Intervention-based demonstration of partial independence of modes: In biomarkers partial independence can be demonstrated through exogenous interventions that modify a process some number of “steps” removed from each of the markers. (R2) Comparison of diverging and converging results across biomarkers: By systematically comparing partially-independent biomarkers we can track under what conditions markers fail to converge in results, and under which conditions they successfully converge. (R3) Information within the context of theory: Through a systematic cross-comparison of the markers we can make causal conclusions as well as eliminate competing theories. We apply our robust methodology to currently developing Alzheimer’s research to show its usefulness for making causal conclusions. (shrink)

The article offers an attempt to understand the present state of Kant’s legacy in Russia on the threshold of the Tercentenary. An explanans is found in the metaphors of “ tabula rasa ” and “unplowed virgin soil,” first used by Leibniz in relation to Russia in his letters and memoranda addressed to tsar Peter I and other members of the Russian elite, which became the country’s “absolute metaphors to live by” up to present time. Several known and unknown episodes from (...) the history of the reception of Kantian ideas, his followers in Russia, and the transformation of the urban environment of Kant’s life in Königsberg, as it was becoming Kaliningrad, are presented through the prism of this metaphor. Without hoping to make specific recommendations of any use from such metaphorical grounds, this study aims to emphasize the depth, interconnectedness, and basic, metaphysical tension of the relationship between Europe and Russia, which cannot be terminated at will by either side, or by a third party. In a situation where the sides are doomed to dialog, Kant, appropriated by Russia as its “subject,” occupies the unique position of mediator of philosophical understanding and peaceful action. (shrink)

It is shown that the power set of $\kappa$ ordered by the subset relation modulo various versions of the non-stationary ideal can be embedded into the partial order of Borel equivalence relations on $2^\kappa$ under Borel reducibility. Here $\kappa$ is an uncountable regular cardinal with $\kappa^{<\kappa}=\kappa$.

In experimental settings, scientists often “make” new things, in which case the aim is to intervene in order to produce experimental objects and processes—characterized as ‘effects’. In this discussion, I illuminate an important performative function in measurement and experimentation in general: intervention-based experimental production (IEP). I argue that even though the goal of IEP is the production of new effects, it can be informative for causal details in scientific representations. Specifically, IEP can be informative about causal relations in: regularities under (...) study; ‘intervention systems’, which are measurement/experimental systems; and new technological systems. (shrink)

This article reevaluates the mystical techniques and experiences peculiar to Abraham Abulafia’s Kabbalah and attempts to offer an alternative approach to their dominant understanding, which largely depends on Moshe Idel’s work. Current scholars of Jewish mysticism have a habit of highlighting the “unique character” of Abulafia’s mystical practices while asserting that they cannot be compared with the induction techniques and the psychophysical phenomena typical of hypnosis. While generally agreeing with the scholars discussed that the hyperactivation of the mind found in (...) Abulafian Kabbalah contrasts sharply with the mental relaxation attained through the mystical practices of other religious traditions, the present study takes issue with the current view of Abulafian Kabbalah’s relation to hypnotic procedures, processes, and states. This work addresses the issues present with the current view and offers a more inclusive model for interpreting Abulafia’s Kabbalah, drawing from psychiatrist Roland Fischer. (shrink)