We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We (...) focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...) that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain (...) ordering on ideals. (shrink)

We present several naturally defined σ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such σ-ideals.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 111 One fascinating item is the author's extensive account of the most violent and extended controversy in the history of aesthetics---the veneration of images and the disputes between the Iconoclasts and the Iconophiles. This sometimes physical battle raged for over 100 years! The Byzantine society, obviously, took art seriously. Tatarkiewicz' great labor is an object lesson in historiography and bibliographic technique. At one and the same time (...) it demonstrates how much of value remains to be discovered by careful adherence to the detail of scholarship, while it also displays how much fruitful scholarship depends upon a brilliant and profoundly informed mind. Such a work, in short, could only have descended from a fully mature scholar. Publication of these volumes underscores the continuing need for publication of significant translations waiting to be made. When can we return to those conditions which make possible this kind of international scholarly achievement? The Humanities Press is now offering these two volumes for $10.00. ALLAN SHIELDS Cali/ornia State University, San Diego Tempo, Coscienza e Essere nella filosofia di Aristotele. By Luigi Ruggiu. (Brescia: Paideia Editrice, 1970. Pp. xxviii+662. L. 6,000.) Ruggiu gives us here a careful and extended account of Aristotle's view of time with special attention to the necessary connections that obtain between time and consciousness, and time and beilag. Ruggiu is also interested in saying something about the origins of later Western conceptions of time and what he calls the nihilistic tendency which runs through them. The reader who (wishing to follow Ruggiu in this 690 page enterprise) begins by trying to get a sense of the architectonic of the essay, is immediately advised to skip E. Severino's somewhat misleading preface. In his own very useful Introduction, Ruggiu rightly notes that Aristotle's review of the aporia in the notion of time found that his predecessors had tended to assimilate (or reduce) time to non-being. But Ruggiu neglects to emphasize something that would have been very helpful at this stage, and which is altogether required, for the understanding of Aristotle's view of time. This is, that Aristotle himself assimilates time, not to non-being but to change and motion. It is also fundamental to Aristotle's philosophy of time, just as it is to his philosophy as a whole, that it acknowledges the primacy of change in the realm of the conditional. Let it be emphasized, then, that generation or change in Aristotle are not from nothing into something, or from something into nothing but from one thing into another. Ruggiu is trying to recover the sense of being in Aristotle which transcends the oppositions between idealism and naturalism, subjectivism and objectivism, and which is the matrix of Aristotle's sense of, and doctrine about, time. He finds that from Plotinos to the present, the prevailing interpretation of Aristotle's conception of time has been a spatial one in which, for instance, temporal succession has been reduced to spatial co-existence. Plotinos, of course, accepted the distinction found in Aristotle between the eternal sort of being which is outside of time and the being which is in time. But in trying to deduce temporal being from eternal being Plotinos is found guilty, by Ruggiu, both of equivocating between radically opposed senses of being and of developing his notion of time on the basis of the denial of time (quite like some modern mathematical philosophers of physics). Others have been equally mistaken in approaching Aristotle with the belief that consciousness is the basis of time. But the substrate of time, in Aristotle, is change, not conscious being. According to Ruggiu time in Aristotle is more than just a mode of being whose essence consists in succes- I 12 HISTORY OF PHILOSOPHY sion, for the reason that time conditions the very way in which we conceptualize being. The relations between being, time, and consciousness are, so to say, intrafoundational. Existing things or processes can, of course, be thought of as not existing; so, there is a sense or mode (namely, possibility) in Aristotle in which things disappear. Ruggiu (p. 411) understands Aristotle to mean by "the possible" that which does not now exist... (shrink)

The article is devoted to the memory of Vyacheslav Semenovich Stepin and Nikita Nikolaevich Moiseev, whose multifaceted work was integrally focused on philosophical, interdisciplinary and transdisciplinary research of the key ideas and principles of universal human-dimensional evolutionism. Other remarkable Russian scientists V.I. Vernadsky, S.P. Kurdyumov, S.P. Kapitsa, D.S. Chernavsky worked in the same tradition of universal evolutionism. While V.I. Vernadsky and N.N. Moiseev had been the originators of that scientific approach, V.S. Stepin provided philosophical foundations for the ideas of those (...) remarkable scientists and thinkers. The scientific legacy of V.S. Stepin and N.N. Moiseev maintained the formation of a new quality of research into the philosophy of science and technology as well as into the philosophy of culture. This new quality is multidimensional and it is difficult to define unambiguously, but we presume the formation of those areas of philosophical knowledge as constructively oriented languages of interdisciplinary and transdisciplinary co-participation of philosophy in the convergent-evolutionary development of scientific knowledge in general. In this regard, attention is paid to V.S. Stepin’s affirmations about non-classical nature of modern social and humanitarian knowledge. Quantum mechanics teaches us that the reality revealed through it is a hybrid construct, or symbiosis, of both mean and object of cognition. Therefore, the very act of cognitive observation constructs quantum reality. Thus, it is very close to the process of cognition in modern sociology and psychology. V.S. Stepin insisted that these principles are applicable to all complex selfdeveloping systems, and such are all “human-dimensional” objects of modern humanities. In all the phases of homeostasis changes, or crises, there is necessarily a share of chaos, instability, uncertainty in the selection process of future development scenarios, which is ineliminably affected by our observation. Therefore, a cognitive observer in the humanities should be considered as a concept of post-non-classical rationality, that is as an observer of complexity. (shrink)

Recenzio Kiraly V. Istvan Death and History c. konyverol.

Glava 1. Osmyslenie "ideala" russkim kosmizmom -- Glava 2. Analiz osnovnykh filosofsko-antropologicheskikh ideĭ v russkoĭ religioznoĭ filosofii -- Glava 3. Idei kosmizma v russkoĭ religioznoĭ filosofii -- Glava 4. V.I. Vernadskiĭ o sootnoshenii nauki, filosofii i religii -- Glava 5. Mifologicheskoe i nauchnoe v izuchenii obraza protopopa Avvakuma -- Glava 6. Ėkonomicheskoe razvitie i nravstvennai︠a︡ degradat︠s︡ii︠a︡ cheloveka i obshchestva v format︠s︡ionnom podkhode Karla Marksa i Fridrikha Ėngelʹsa.

Review the Istvan Kiraly V.'s book: Death and History.

v. 1. Obrazovanie v sud'bakh narodov. Education in the fates of nations -- v. 2. Razdumyi︠a︡. Thoughts -- v. 3. Krutogori︠a︡mi zhizni. Steep roads of the life -- v. 4. Ėstetika i tvorchestvo. Aesthetics and creativity -- v. 5. T︠S︡ivilizat︠s︡ii︠a︡ v zhizni planety. The civilization in the life of our planet.

Throughout Christianity, its activities are in one way or another connected to the historical reality of its time. Usually, for different epochs, the strength of these bonds was different, but during the Middle Ages, they were significantly stronger than before and after. It is here that perhaps the most important moment was the rise of Christianity, which spread over a relatively short period of time almost throughout Europe. It was then - and never again in all its history - that (...) the Church was able to participate in the formation of all aspects of its contemporary life, in accordance with its spirit. When solving this task, it inevitably came in close contact with the "world" and the various forms in which it was represented. (shrink)

Рассматриваются актуальные проблемы философской антропологии, проводится анализ парадоксов и противоречий, возникающих при изучении человека, тех кардинальных сдвигов в культуре, которые открыли новые стороны человеческого бытия. Для студентов.