February 18, 1994, marks the seventieth anniversary of the birth of Eval'd Vasil'evich Il'enkov. In this article, I would like to undertake a dual task: on the one hand, to trace out the general logic of Il'enkov's theoretical works; and on the other, to sketch a portrait of his personality . I would like to show that Il'enkov the man and Il'enkov the thinker are inseparable.

1. On the contradictory nature of contemporary linguistic theories and how to change it for the better -- 2. A reference-based approach to describing notional words -- 3. Basic-level concepts as the neurobiological codes for memory -- 4. Elements of a sensory grammar -- 5. On the single structure of lexical meanings of nouns and verbs -- References -- Index.

A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes (...) the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)

A classification of the global catastrophic risks of AI is presented, along with a comprehensive list of previously identified risks. This classification allows the identification of several new risks. We show that at each level of AI’s intelligence power, separate types of possible catastrophes dominate. Our classification demonstrates that the field of AI risks is diverse, and includes many scenarios beyond the commonly discussed cases of a paperclip maximizer or robot-caused unemployment. Global catastrophic failure could happen at various levels of (...) AI development, namely, before it starts self-improvement, during its takeoff, when it uses various instruments to escape its initial confinement, or after it successfully takes over the world and starts to implement its goal system, which could be plainly unaligned, or feature-flawed friendliness. AI could also halt at later stages of its development either due to technical glitches or ontological problems. Overall, we identified around several dozen scenarios of AI-driven global catastrophe. The extent of this list illustrates that there is no one simple solution to the problem of AI safety, and that AI safety theory is complex and must be customized for each AI development level. (shrink)

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

An analogy between the evolution of organisms and some complex computational problems (cryptosystem cracking, determination of the shortest path in a graph) is considered. It is shown that in the absence of a priori information about possible species of organisms such a problem is complex (is rated in the class NP) and cannot be solved in a polynomial number of steps. This conclusion suggests the need for re-examination of evolution mechanisms. Ideas of a deterministic approach to the evolution are discussed.

The paper discusses Norman Malcolm’s interpretation of Anselm’s ontological argument. Since Malcolm had shown no interest in religious or theological issues prior to publishing his article on that subject in 1960, the analysis takes clue from Malcolm’s earlier writings. By doing so, I revisit the assessment of the ontological argument as fallacious and the tendency to assess Anselm from the traditional framework initiated by Kant. As I demonstrate, Malcolm interpreted Anselm based on the method elaborated during the 1950s. That method (...) involved a synthesis between ordinary language philosophy and common sense philosophy, associated with the late Wittgenstein and Moore respectively. As I further argue, the usual objections to Malcolm’s approach ignore the main line of his reasoning: that Anselm’s ontological argument does not violate ordinary language. Indeed, the two concepts of God as “the greatest of all beings” and of the necessity of God’s existence both perfectly fit in how language works. The “God-talk” is therefore logical only in accordance with Malcoms definition of logical: an explication of the rules of ordinary language, whereas each and every argument against Anselm’s ontological proof violates ordinary language drastically. In his late works on the subject, Malcolm suggested that multiple proofs of God’s existence should be viewed as expressions of a specific philosophic pathology whose underlying drive is a justification of various forms of life. Instead of regarding this idea as “fideistic” (e.g., in K. Nielsen’s work), I propose that the very concept of ordinary language, as Malcolm developed it, makes a treatment of language games along the lines of dependence or independence obsolete. Rather, a crucial issue that Malcolm pushes to investigate is how religious statements correlate with ordinary language. (shrink)

We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, we take (...) the infinite-dimensional limit right for this inequality. Hence, uncertainty relations are derived in terms of generalized entropies. In particular, the case of measurements with a finite precision is addressed. It takes into account that in any experiment an accuracy of performed measurements is always limited. (shrink)

This paper is concerned with the logical structure of intuitionistic equality theories. We prove that De Jongh theorem holds for the theory of decidable equality, but uniform De Jongh theorem fails even for the theory of weakly decidable equality. We also show that the theory of weakly decidable equality is the weakest equality theory which enjoys Glivenko theorem.

The article is devoted to the reasoning of the „Ereignis“ phenomenon in the philosophy of M. Heidegger. It is worth to emphasize that one of the main trends in contemporary philosophy is an attempt of creation of new–non-substantial–ontology. The very specificity of such ontology lies in the fact that classical substance is replaced by the dynamical configuration of sense, which is not “purely theoretical” but “ontological” in its core. “Ontological” means, in fact, that it is impossible to separate the mode (...) of Being of phenomena from the process of thinking about them. Heidegger’s philosophy was one of the first attempts to create such ontology. It is worth to point out the three steps of the Heidegger’s studies of Being. The first, “fundamental-ontological” step is characterized primarily through the “ontological difference” between Being and entity, when the phenomenon of time represents by itself their hidden basis. During the second, “radical-ontological” period, Heidegger has already carried out his famous “turn.” In compliance with this “turn,” the truth of Being, die Lichtung, substitutes time as the “pre-ontological” basement of Being. In this case, Being itself transforms into the Event, „Ereignis“. On the third, “post-ontological” stage of studies the focal point of Heidegger’s thought is “post-ontological difference” between the Being of entity and Being itself. On this stage both Being and time are rooted in the phenomenon of „Ereignis“. The latter has been now transformed from being a “simple Event” into a “matter of fact” as the alternation of the “disclosedness” and “concealness” of Being and time. In this case, „Ereignis“ is not quasi-substantial basement of Being, time or entity but it shows itself as its “Beginning” “), when the Truth of Being is replaced by the dynamical sense configuration of the event, i.e., a “matter of fact.” Thus, Heidegger has conceptually created a new type of thnon-substantial ontology, the core of which is the phenomenon of „Ereignis“ as the dynamical singular configuration of the temporal-ontological sense of the Event itself. (shrink)

The historic or traditional Christian view of pain (suffering) and death, especially as preserved by the Christian East (i.e., the Orthodox), is radically opposed to the modern secular obsession with avoidance of pain. Everything about this life has its goal or aim in a mystical reality, the Kingdom of Heaven, for which earthly life is a preparation. While neither illness nor health are seen as ends in themselves, both are viewed as proceeding from the will of God for our benefit (...) and have no ultimate meaning or purpose outside of eternal life. Death may be a relief or an ending of suffering, but in itself it is not “good” but evil.Because they are the embodiment of lived theology, saints' lives can be a sure guide to understanding how to die as a traditional Christian. To illustrate this, I have chosen some examples from the lives of relatively recent saints. I myself am from the Russian Orthodox spiritual tradition, so all but one of my examples come from pre-Revolutionary Russia.The question is not so much whether or not a traditional Christian can countenance physician-assisted suicide, but rather, what is the meaning or purpose of pain and suffering in general. Is it part of the “work of perfection” required of those who wish to enter the Kingdom of Heaven and therefore not to be completely denied? (shrink)

Gregory Savich Skovoroda (1724-1794) belongs both to the Russian and Ukrainian philosophy. His philosophical doctrine was only revivified at the turn of the 19th-20th centuries, which was caused by the affinity of the philosophical searches of the Silver Age (beginning of the 1890s-1922) with the religious and philosophical doctrine by Gregory Skovoroda. In the history of philosophy, Gregory Skovoroda can be considered «boundary figure» marking transition from the Middle Ages to the culture of the Modernity. The article deals with the (...) thinker’s ethical doctrine, particularly, with two interpretations of nature: essential and voluntary. Moralizing was the main aim and content of the most works by Gregory Skovoroda. Practical philosophy by Gregory Skovoroda immediately sides with his understanding of nature. Volition, wish (desire), affinity, true man are its basic categories. The main aim of Skovoroda’s moralizing is to show the way to the happy life. The essential topic of the Skovoroda’s creative work are concentrated in his ethics: ontology, or doctrine of three worlds (microcosm, macrocosm, symbolic world – the Bible), exegetical method of cognition and symbolism, doctrine of nature and category of affinity, the principle of self-cognition and doctrine of the «true man», doctrine of heart and anthropology, eudemonism and problem of reality of the evil and the good in the world. According to the canons of the symbolism Skovoroda criticizes material, corporeal side of the world and gives preference to its spiritual meaning. Nevertheless, Skovoroda remains a religious thinker in his practical philosophy; he meditates per religious canons. For the 18th century Gregory Skovoroda’s doctrine had been as archaic as it became relevant at the turn of the 19th-20th centuries. (shrink)

Some are attracted to the view that repeatable artworks, such as films, novels, plays, symphonies, photographs, and the like, are a particular kind of abstracta—namely, types. This view, however, is not unproblematic. One of the most serious problems it faces is the so-called "creation problem." The core idea behind this problem is that, on the one hand, it seems reasonable to accept the claims that (1) repeatable artworks are types, (2) types cannot be created, and (3) repeatable artworks are created, (...) but, on the other hand, these claims form an inconsistent triad. A popular solution to the creation problem is that (2) can be rejected because the justification for (2) is based on a false assumption—that no type can stand in causal relations. Although this solution looks promising, it can be accepted only if its proponent can refute what might be called the "paraphrasability argument." On this argument, types are not to be regarded as capable of standing in causal relations because any discourse implying the causality of types should be paraphrased into discourse that does not imply this. My aim in this essay is to show that there is good reason to consider the paraphrasability argument sound and, hence, that the foregoing solution to the creation problem fails. (shrink)

Xenophanes claimed that God is a ball, which means that he is a perfect body. This idea is well developed in Jagannatha worship, who is a central Deity in Orissa, India. It’s a round form of Krishna, who is usually depicted in a human like form. Jagannatha, his brother Baladeva and sister Subhadra are justified as round forms because of their specific manifestation of ecstasy, that, according to aesthetical theory (rasa tattva) happened to them. Yet there are many other explanations (...) of the Jagannatha’s roundness. Round form personifies unity and diversity principle in Jagannatha worship, whose image was dear in Orissa duringlong historical period to different religious groups: Vaishnavas, Shaivaites, Jains, Buddhists and even some Muslims. Orissa also has a blending of different cultures, sub-cultures and traditions. Even now, it has 62 distinct tribal groups, that makes a largest collection of diverse tribes in a single state. As the legend goes, Jagannatha made His first appearance in the tribe of Savaras thousands of years ago. Up until now, there are cooks in the Jagannatha kitchen that are called sauviras. In worship of Jagannatha we find the model of axiological globalism, when the difference in the vision of the reality does not obscure the interior mood of wholeness, unity. (shrink)

Within the Hebbian paradigm the mechanism for integrating cell assemblies oscillating with different frequencies remains unclear. We hypothesize that such an integration may occur in cortical “interaction foci” that unite synchronously oscillated assemblies through hard-wired connections, synthesizing the information from various functional systems of the brain.

The article discusses the diversity of the subject field of the philosophy of war as well as the internal integrity of the discipline, united by the focus on the philosophical understanding of the phenomenon of war. The author shows the role of H. Lloyd, who influenced K. Clausewitz, H. Jomini and their followers’ interpretation of the meaning and content of the subject area of the philosophy of war. In the abundance of specific topics addressed by philosophers of this field, the (...) following topics should be noted: the issue of victory and defeat and their interpretation as well as the issue of historical memory. This problem is projected on contemporaneity and reflects the deep connection between peace and war, the dialectic of their relations. The interpretation of certain military and political events is of real interest in the light of the processes of distortion of historical events that have radically affected the course of history. An analysis of the motives and causes of this process is supposes to reconstruct an objective picture of relations between the subjects of international relations in various periods of history. The author finds answers in already existing concepts that have been developed in our time. It is important to mention the project of the French philosopher Charles Renouvier, who put forward the concept of “uchronia,” which became the starting point for the consideration of historical events in the “subjunctive mood.” This genre of historiosophical fantasy was picked up by famous followers – by the former President of France V. Giscard d’Estaing and others. The article provides eyewitness accounts of historical events that are historical facts and help to understand the true state of things. The article demonstrates that the philosophical study of the problem of war is important for understanding the origins and essence of relations arising from the transition between peaceful and military states. (shrink)

Recently, a number of philosophers have defended a novel, materialist view on the nature of musical works—musical perdurantism. According to this view, musical works are a peculiar kind of concreta, namely perduring mereological sums of performances and/or other concrete entities. One problem facing musical perdurantism stems from the thought that if this view is correct, then virtually no musical work can exist in a continuous, non-intermittent fashion. The aim of this paper is to expound this problem and show that it (...) cannot be plausibly solved by a musical perdurantist. (shrink)

In On the Genesis of Thought and Language, linguist Alexey Koshelev explores fundamental questions of how human concepts arise in a child, why concepts appear in a child before words, the genesis of language, and why there are so many languages. Chapter One introduces the fundamental dichotomy "visual (exogenous) vs. functional (endogenous)" cognitive units; these units are used to give non-verbal definitions of mental representations of various objects, actions, and situations. In particular, definitions of such concepts as GLASS, CHAIR, (...) BANANA, TREE, LAKE, RUN, and some others are given. Chapter Two discusses how children form concepts, hierarchical relationships, and propositions (conceptual 'utterances'). It is shown that the initial units of the child's representation of the world are pre-conceptual cognitive units--mental representations of whole situations. In the course of two consecutive cycles in the child's cognitive development, these units transform into (a) primary notions--object and motor concepts, and (b) binary role relationships. Together, they constitute the elementary language of thought which, in the process of thinking, is used to build conceptual structures--propositions. It is further demonstrated that, immediately after the formation of thought, the child begins to develop his native language in which concrete and motor concepts become initial meanings of nouns and verbs, while propositions become the meanings of the child's expressions. The chapter concludes with a contrastive analysis of the proposed approach and Aristotle's and Chomsky's views on thought and language. Chapter Three analyzes how a community's culture affects its language. It is demonstrated that the progress of a community, the main constituent of the civilizational component of its culture, enhances the development of the content component of language by extending the range of its lexical and grammatical meanings. In the context of this analysis, Daniel Everett's (2008) hypothesis that culture affects language structure is discussed. In the subsequent sections, models of the development of human and social activity are offered. These models comprise three components: Activity (main component), Thought, and Language (auxiliary components that ensure the successful realization of activities). The models are illustrated with examples of some concrete societies. (shrink)

When discussing the French Revolution and Napoleon in his lectures from 1933 to 1939, Alexandre Kojève had in mind events in Russia. The clash between the “old order,” with its Masters, and the worker Slaves corresponded for him more with the images of pre-revolutionary Russian journalism than with the wigged aristocrats and French bourgeoisie of the end of the eighteenth century. In his lectures, behind Napoleon, as a revolutionary emperor, there exists, however secretly or openly, the figure of Stalin, with (...) his plans for the “building of socialism in one country,” his five-year plans, collectivization, and terror. Kojève’s ontology and anthropology diverge both from Hegel’s version of the two as well as with Marxism, incorporating different theses from Nietzsche and Heidegger’s Daseinanalytik. Just as in The Phenomenology of Spirit, terror plays a central role in interpreting revolution, yet it is conceived in the spirit of a Heideggerian “being-toward-death.” The relation between Master and Slave begins with fear of death, and it is destroyed by fear of death in the face of revolutionary terror. In this article, Kojève’s philosophy converges with the various versions of “left Nietzscheanism,” which were particularly widespread in prerevolutionary Russia. (shrink)

I argue that St. Augustine of Hippo was the first in the history of Christian spirituality who expressed a key tendency of Christian mysticism, which implies a gradual intellectual ascent of the human soul to God, consisting of the three main stages: external, internal, and supernal. In this ascent a Christian mystic proceeds from the knowledge of external beings to self-knowledge, and from his inner self to direct mystical contemplation of God. Similar doctrines may be found in the writings of (...) the Greek Fathers. Although there are many similarities in the overall doctrine and in particular details between them, it does not imply the direct impact of Augustine’s theological thought on the Greek Fathers but rather the influence of the Neoplatonic philosophy on both Western and Eastern Christianity, in particular, of Plotinus’ theory of intellectual cognition. (shrink)

Quantum mechanics is one of the most successful theories of physics. But the creators of quantum mechanics had to reject realism in order to describe some paradoxical quantum phenomena. Einstein considered the rejection of realism unacceptable, since according to his understanding, realism is the presupposition of every kind of physical thinking. The dispute about the permissibility of rejecting realism has largely determined the modern understanding of quantum theory and even led to the emergence new quantum information technologies. Many modern authors (...) are sure that realism can be refute experimentally. Some authors are sure even that real technologies can be created on the basis of this refutation. The well-known GHZ theorem is considered critically in this work the authors of which are sure that realism can be refute experimentally. (shrink)

The article is devoted to the analysis, and introduces the publication, of one of the texts of the documentary complex ‘The Verkhne-Uralsk Political Isolator Notebooks’ – the ‘Theses on Economic Policy’ of 1933. The article (DOI: 10.1163/1569206X-00002252) covers the history of the discovery of this complex of documents reflecting the ideological and political life of imprisoned members of the Opposition of the Bolshevik Leninists (Trotskyists) in the early 1930s, and discusses the context of their creation. On the basis of archival (...) materials, the biography of one of the authors of the Theses – the agricultural economist, and a member of the Siberian opposition centre, F.P. Sasorov – is reconstructed. It is noted that Sasorov held a special position among the Bolshevik Leninists, determined by his economic views. He belonged to the current whose adherents were called ‘neo-Nepists’ by their opponents. This current advocated not just a return to the NEP cancelled by Stalin, but also an expansion of its scope, and this position is presented and argued for in the ‘Theses on Economic Policy’. A comparison of the views of Sasorov and his co-author G.A., stated in the Theses, including on the explanation of the crisis and the liquidation of the NEP, the policy of out-and-out collectivisation and forced industrialisation, with the views of Leon Trotsky, allows us to conclude that the thought of the imprisoned oppositionists developed independently, and not always in accordance with the guidelines of their exiled thought leader. The article also examines the forecasts of the development of the economic and socio-political situation in the USSR presented in the Theses. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions to solve (...) nonlinear problems on Hilbert spaces. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square integrable functions (...) of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

The paper considers Plato’s theory of language through the prism of the Timaeus’ metaphysics. It is argued that the apparent contradictions of Plato’s philosophy of language are the consequence of the two-fold nature of language, and that the metaphysical scheme proposed by Plato in the Timaeus can shed a light on his coherent theory of language. The linguo-metaphysical isomorphism of the Timaeus presupposes that (1) words and material elements have their own meaning and nature respectively; (2) they can be reduced (...) to an infinite variety of amorphic sounds and receptacle; (3) the participation in truth is possible only at the level of narrative and universe. According to this scheme the universe (κόσμος), as well as any speech (λόγος), can be explained by the reduction to its constituent elements, but it will be only necessary explanation. Whereas for Plato, the true understanding of cosmos and logos is possible only on the level of the coherent unity of the whole, which represents the ideal paradigm in the best possible way. (shrink)

This article gives a general characteristic of the publications of the Russian philosophers in the oldest Kantian Journal “Kant-Studien”. The study embraces the entire period of the existence of this magazine, from the very beginning down to our days. In general, after compiling all materials related to Russia published in “Kant-Studien”, I became aware of get a picture of a significant presence of Russian philosophers in this periodical. This gives me a good reason to conclude that even if the impact (...) of the Russian philosophical thought on the international Kant studies was not decisive, then, at least, it was tangible. This influence was due to the phenomenon which was later called the “Silver Age of Russian philosophy”, as well as the phenomenon of Russian emigration, arising as a result of wars and revolutions in Russia and the exodus of the Russian philosophers of the West, where one of their main initial shelters was Germany. (shrink)

The article is related to the revealing of the intent of Hegel’s “Science of Logic”. As authors take it, there is an attempt to imagine the fundamental level of reasoning, where there is no opposition between cognition and its object. In this dimension there is no need to substantiate compatibility between them — it is a level of primary foundation of knowledge. Consequently, any knowledge at this level may be characterized as “Ultimate”. That being said, place of such knowledge is (...) not taken by several specific statements, but by the certain way of organizing those “mental definitions” that are already used by common human sense. To organize these definitions, to arrange them into consistently deployed sequence of logical notions, there is need to abort the search for the primary foundation for knowledge inherent in philosophy from its very origins. This attempt was reflected in Kant's theory of knowledge, where the problem of the reliability of knowledge was solved due to self-limitation in the process of cognition — it was necessary to stop before a certain line, beyond which thought leaves “the limits of possible experience” and falls into the area of insoluble contradictions (antinomies). Hegel's Logic, which, according to the authors, is in a kind of “symbiosis” with the Kantian program, consists in considering these insoluble contradictions precisely as a “symptom” of achieving the primary foundation of knowledge. It is in the collision with an insoluble contradiction that the definitions are organized in the necessary logical sequence, and that fundamental level is reached where there is no opposition between cognition and its object. (shrink)

The research identifies the amount of headline/article discrepancies in the corpora of western and Russian online articles on sensitive political topics. A quarter of the western headlines and nearly half of the Russian headlines distort the publications they introduce. Language means and manipulative strategies employed by different sides vary considerably. Extensive use of expressive language and style variation are seen as leading causes of distortions in the western corpus. The rich imagery used by the authors forms emotional implicatures that affect (...) the reader’s perception of the issue. In contrast, information substitution, subjective modality and selective citations are identified as major causes of distortions in the Russian corpus. Contributors to Russian news outlets rely on general rather than language manipulation strategies, including frequent use of logical fallacies and wrong generalizations. These techniques establish false logical sequences and wrong causative implicatures that compromise objective reporting. The underlying motives of the journalists’ creating false emotional and causative implicatures in the headlines lies beyond the scope of the study; however, it is assumed that intentional change of the information introduced by the headline could be viewed as a covert misinformation attempt. (shrink)

Qumran Hebrew: An Overview of Orthography, Phonology, and Morphology. By Eric D. Reymond. Resources for Biblical Study, vol. 76. Atlanta: Society of Biblical Literature, 2014. Pp. xvii + 309. $37.95.

In the course of the last 20 years, the problem of Kant’s view of races has evolved from a marginal topic to a question which affects his critical philosophy in general, including the anthropology and its influence on contemporary social studies. The goal of our paper is to examine the anthropological role of Kant’s concept of race from the largely overlooked or underestimated perspective of his Lectures on Anthropology. Taking into account the differences between Kant’s approach in the early lectures (...) of the 1770s and early 1780s and the lectures of the late 1780s in the light of the development of the idea of race in Kant’s works, we will demonstrate that several key elements of Kant’s 1780s theory of race presented in his published works can be found in his early lectures. On the other hand, we will prove that Kant gradually abandons racial hierarchies and moral characteristics of races in his anthropological lectures of the late 1780s and in the Anthropology from the Pragmatic Point of View, shifting his focus to more nuanced descriptions of morals of different nations. (shrink)

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional (...) manifold produces a family of functional equations on different spaces of functions. (shrink)