We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to ∅. We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C ≥ |x|-c. The ‘only if' direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity. Next we prove some results (...) on lowness. Among other things, we characterize the 2-random sets as those 1-random sets that are low for Chaitin's Ω. Also, 2-random sets form minimal pairs with 2-generic sets. The r.e. low for Ω sets coincide with the r.e. K-trivial ones. Finally we show that the notions of Martin-Löf randomness, recursive randomness, and Schnorr randomness can be separated in every high degree while the same notions coincide in every non-high degree. We make some remarks about hyperimmune-free and PA-complete degrees. (shrink)

We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and super-lowness for sets of natural numbers. A computable non-decreasing unbounded function h is called an order function. Informally, a set A is strongly jump-traceable if for each order function h, for each input e one may effectively enumerate a set Te of possible values for the jump JA, and the number of values enumerated is at most h. A′ (...) is well-approximable if can be effectively approximated with less than h changes at input x, for each order function h. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and strong jump-traceability in terms of Kolmogorov complexity. We also investigate other properties of these lowness properties. (shrink)

We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent (...) to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal. (shrink)

A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.

A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let ${\mathcal {D}}$ (...) be the mass problem of infinite bit sequences y such that for each computable bit sequence x, the bit sequence $ x {\,\leftrightarrow\,} y$ has asymptotic lower density at most p = y$ ). We show that all members of this family of mass problems parameterized by a real p with $0 p$ for each computable set x. We prove that the Medvedev complexity of the mass problems ${\mathcal {B}}$ is the same for all $p \in $, by showing that they are Medvedev equivalent to the mass problem of functions bounded by ${2^{2}}^{n}$ that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type $\text {IOE}$ : we show that for any order function g there exists a faster growing order function $h $ such that $\text {IOE}$ is strictly above $\text {IOE}$ in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance, ${\mathfrak {d}} $ is the least size of a set G of bit sequences such that for each bit sequence x there is a bit sequence y in G so that $\underline \rho >p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relationsR,S, a componentwise reducibility is defined byR≤S⇔ ∃f∀x, y[x R y↔fS f].Here,fis taken from a suitable class of effective functions. For us the relations will be on natural numbers, andfmust be computable. We show that there is a${\rm{\Pi }}_1^0$-complete equivalence relation, but no${\rm{\Pi }}_k^0$-complete fork≥ 2. We show that${\rm{\Sigma }}_k^0$preorders arising naturally in the above-mentioned areas are${\rm{\Sigma }}_k^0$-complete. This includes polynomial timem-reducibility on (...) exponential time sets, which is${\rm{\Sigma }}_2^0$, almost inclusion on r.e. sets, which is${\rm{\Sigma }}_3^0$, and Turing reducibility on r.e. sets, which is${\rm{\Sigma }}_4^0$. (shrink)

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...) main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

Ukazał się kolejny, X tom Rocznika Edyty Stein. Trzeba o tym napisać nie tylko ze względu na jego zawartość. Z wydaniem tego jubileuszowego numeru został zamknięty okres, w którym redakcja Rocznika spoczywała w rękach J. S. de Murillo. Nowym naczelnym redaktorem jest od tego numeru Ul. Dobhan. W roku 1993 ukazał się I. tom Rocznika Edyty Stein, którego redakcja na zlecenie Zakonu Karmelitańskiego objął hiszpański karmelita J. S. de Murillo. Rocznik miał stanowić swego rodzaju „otwarte forum" dla współpracy między filozofię (...) i teologię, jak również pedagogikę i sztukę, nawiązujących do myśli i ducha Edyty Stein. Koncepcja Rocznika szła - jeśli można tak powiedzieć - „w szerokość", tak, aby próbować wgłębiać się w myśli Edyty Stein aż po granice możliwości. Ale co to właściwie znaczy? Czy na końcu takiego eksperymentu myślowego będziemy jeszcze mieć do czynienia z myślą Edyty Stein? Odpowiedzi na te istotne pytania i zamyślenia nad kształtem Rocznika doprowadziły do zmiany jego kierownictwa i tym samym do zmiany jego koncepcji. (shrink)

Ukazał się kolejny, X tom Rocznika Edyty Stein. Trzeba o tym napisać nie tylko ze względu na jego zawartość. Z wydaniem tego jubileuszowego numeru został zamknięty okres, w którym redakcja Rocznika spoczywała w rękach J. S. de Murillo. Nowym naczelnym redaktorem jest od tego numeru Ul. Dobhan. W roku 1993 ukazał się I. tom Rocznika Edyty Stein, którego redakcja na zlecenie Zakonu Karmelitańskiego objął hiszpański karmelita J. S. de Murillo. Rocznik miał stanowić swego rodzaju „otwarte forum" dla współpracy między filozofię (...) i teologię, jak również pedagogikę i sztukę, nawiązujących do myśli i ducha Edyty Stein. Koncepcja Rocznika szła - jeśli można tak powiedzieć - „w szerokość", tak, aby próbować wgłębiać się w myśli Edyty Stein aż po granice możliwości. Ale co to właściwie znaczy? Czy na końcu takiego eksperymentu myślowego będziemy jeszcze mieć do czynienia z myślą Edyty Stein? Odpowiedzi na te istotne pytania i zamyślenia nad kształtem Rocznika doprowadziły do zmiany jego kierownictwa i tym samym do zmiany jego koncepcji. (shrink)

Book Reviewed in this article: Traditional Sayings in the Old Testament. By Carole R. Fontaine. Pp. viii, 279, Sheffield, The Almond Press, 1982, £17.95, £8.95. The First Day of the New Creation: The Resurrection and the Christian Faith. By Vesilin Keisch. Pp.206, Crestwood, New York, St Vladimirs Seminary Press, 1982, £6.25. The First Day of the New Creation: The Resurrection and the Christian Faith. By Vesilin Keisch. Pp.206, Crestwood, New York, St Vladimir's Seminary Press, 1982, £6.25. The Resurrection of Jesus: (...) A Jewish Perspective. By Pinchas Lapide. Pp.160, London, SPCK, 1983, 4.95. Easter Enigma. By John Wenham. Pp.162, Exeter, Paternoster Press, 1984, £2.95. The Anastasis: the Resurrection of Jesus as an Historical Event. By J. Duncan M. Derrett. Pp.xiv, 166, Shipston‐on‐Stour, P. Drinkwater, 1982, £5.00. The Open Heaven: A Study of Apocalyptic in Judaism and Early Christianity. By Christopher Rowland. Pp. xii, 562, London, SPCK, 1982, £22.50. Christianity Rediscovered: An Epistle from the Masai. By Vincent J. Donovan. Pp. viii, 200, London, SCM Press, 1982, £5.50. Basics of a Roman Catholic Theology. By William A. Van Roo, S.J. Pp.387, Rome, Gregorian University Press, 1982, $21.00. Charisms and Charismatic Renewal: a Biblical and Theological Study. By Francis A. Sullivan. Pp.184, Dublin, Gill & Macmillan, 1982, £5.95. Holiness and Politics. By Peter Hinchliff. Pp.214, London, Darton, Longman and Todd, 1982, £8.95. Rational Theology and the Creativity of God. By Keith Ward. Pp.240, Oxford, Blackwell, 1982, £14.00. The Point of Christology. By S.M. Ogden. Pp.xii, 193, London, SCM Press, 1982, £5.95. Fullness of Humanity: Christ's Humanness and Ours. By T.E. Pollard. Pp.126, Sheffield, The Almond Press, 1982, £9.95, £5.95. Milton's Good God: A Study in Literary Theodicy. By Dennis Richard Danielson. Pp.xi, 292, Cambridge University Press, 1982, £20.00. Biblical Tradition in Blake's Early Prophecies: The Great Code of Art. By Leslie Tannenbaum. Pp.xiii, 373, Princeton University Press, 1982, £17.60. The Inner Journey of the Poet and Other Papers. By Kathleen Raine, edited by Brian Keeble. Pp.xii, 208, London, George Allen and Unwin, 1982, £9.95.iVol. 34: Horayot and Niddah. Translated by Jacob Neusner. Pp.xiii, 243, Chicago, The University of Chicago Press, 1982, £17.50. Holy Land Pilgrimage in the Later Roman Empire A.D. 312–460. By Ed. Hunt. Pp. £+ 269, Oxford University Press, 1982, £16.50. Constantine versus Christ: The Triumph of Ideology. By Alistair Kee. Pp.186, London, SCM Press, 1982, £5.95. Society and the Holy in Late Antiquity. By Peter Brown. Pp.347, London, Faber and Faber, 1982, £10.50. Elishe: History of Vardan and the Armenian War. Translation and commentary by Robert W. Thomson. Pp.x, 353, 1 map, Cambridge, Harvard University Press, 1982, £21.00. Ireland in Early Mediaeval Europe: Studies in Memory of Kathleen Hughes. Edited by Dorothy Whitelock, Rosamond McKitterick and David Dumville. Pp.x, 406, Cambridge University Press, 1982, £39.00. Letters from Ireland 1228–1229 by Stephen of Lexington. Translated with an introduction by B.W. O'Dwyer. Pp.vii, 292, Kalamazoo, Cistercian Publications, 1982, $24.95. The Occupation of Celtic Sites in Ireland by the Canons Regular of St Augustine and the Cistercians. By Geraldine Carville. Pp.ix, 158, Kalamazoo, Cistercian Publications, 1982, $13.95. Chartres: The Masons who built a Legend. By John James. Pp.200, London, Routledge and Kegan Paul, 1982, £17.50. Temples, Churches and Mosques: A Guide to the Appreciation of Religious Architecture. By J.G. Davies. Pp.x, 262, Oxford, Basil Blackwell, 1982, £12.50. The Murdered Magicians: The Templars and their Myth. By Peter Partner. Pp.xxi, 209. Oxford University Press, 1982, £12.95. The Italian Crusades: The Papal‐Angevin Alliance and the Crusades Against Christian Lay Powers, 1254–1343. By Norman Housley. Pp.xi, 293, Oxford, Clarendon Press: Oxford University Press, 1982, £17.50. The Westminster Chronicle, 1381–1394. Edited and Translated by L.C. Hector and Barbara F. Harvey. Pp.lxxvii, 563. Oxford, the Clarendon Press, 1982, £42.00. Frömmigkeitstheologie am Anfang des 16. Jahrhunderts. By Berndt Hamm. Pp.xv, 378, Tübingen, J.C.B. Mohr, 1982, 168 DM. Erasmi Opera omnia, IX, 2: Desiderii Erasmi Roterodami Apologia respondens ad ea quae Iambus Lopis Stunica taxavrat in prima duntaxat Novi Testamenti aeditione. Edited by Henk Jan de Jonge. Pp.292, Amsterdam, North‐Holland Publishing Company, 1983, 280 guilders. The Christian Polity of John Calvin. By Harro Höpfl. Pp.x, 303, Cambridge University Press, 1982, £27.50. Concerning the Eternal Predestination of God. By John Calvin, translated with an Introduction by J.K.S. Reid. Pp.191, Cambridge, James Clarke & Co., 1982, £5.95. Spanish Protestants and Reformers in the Sixteenth Century: A Bibliography. By A. Gordon Kinder. Pp.108, London, Grant & Cutler, 1983, £6.80. Moderate Puritans and the Elizabethan Church. By Peter Lake. Pp.viii, 357, Cambridge University Press, 1982, £27.50. Resistance and Compromise: The Political Thought of Elizabethan Catholics. By Peter Holmes. Pp.viii, 279, Cambridge University Press, 1982, £22.50. Dutch Puritanism: A History of English and Scottish Churches of the Netherlands in the Sixteenth and Seventeenth Centuries. By Keith L. Sprunger. Pp.xiii, 485, Leiden, E.J. Brill, 1982, 172 guilders. John Toland and the Deist Controversy. By Robert E. Sullivan. Pp.viii, 355, Cambridge, Harvard University Press, 1982, £19.95. Radical Sects of Revolutionary New England. By Stephen A. Marini. Pp. 213, Cambridge, Harvard University Press, 1982, £11.55. Religion and Society in North America: An Annotated Bibliography. Edited by Robert deV: Brunkow. Pp.xi, 515, Santa Barbara, ABC‐Clio; Oxford, EBC‐Clio, 1983, £57.75. Charles Lowder and the Ritualist Movement. By Lida Ellsworth. Pp.vi, 234, London, Darton, Longman & Todd, 1982, £17.95. How the Pope became Infallible: Pius IX and the Politics of Persuasion. By August Bernhard Hasler. Pp.xi, 383, New York, Doubleday, 1981, $14.95; London, Sheldon Pres, 1982, £15.00. Hauptsache der Papst ist katholisch. Edited by Bruno Nies. Pp.104, Salzburg, Otto Müller, 1982, öS 140. Religious Change in Contemporary Poland: Secularization and Politics. By Maciej Pomian‐Srednicki. Pp.227, London, Routledge & Kegan Paul, 1982, £12.50. World Christian Encyclopedia: A Comparative Survey of Churches and Religions in the Modern World. Edited by David B. Barrett. Pp.1010, Nairobi, Oxford University Press, 1982, £55.00. Probability and Evidence. By Paul Horwich. Pp.vii, 146, Cambridge University Press, 1982, £15.00. Philosophical Foundations of Probability Theory. By Roy Weatherford. Pp.xi, 282, London, Routledge and Kegan Paul, 1982, £15.00. The Origins of Greek Thought. By Jean‐Pierre Vernant. Pp.144, London, Methuen, 1982, £9.95. Portraying Analogy. By J.F. Ross. Pp.xi, 244, Cambridge University Press, 1981, £20.00. The Marriage of East and West. By Bede Griffiths. Pp.224, London, Collins, 1982, £5.95. The Religious Experience: A Socio‐Psychological Perspective. By C.D. Batson & W.L. Ventis Pp.ix, 356, New York, Oxford University Press, 1982, £18.50,£9.95. (shrink)

English summary: It was not until the publication of Schelling''s Munich and Berlin lectures that we learned the decisive source for his theory of an identity of identity or identity doubled in itself. Schelling referred to what he called an older logic that was still acquainted with the figure of reduplication, for instance in Leibniz and Wolff. Philosophers in this tradition employed this term to refer to the specification of an aspect under which the subject-term is being considered. An often (...) quoted example: As consul, Fabius Maximus has authority over his father, but as son he stands under his fathers authority. Schelling gave the following turn to reduplication: Nature as nature does not coincide with the mind; and the mind as mind does not coincide with nature. Both have different truth conditions, so as to integrate an essential moment of difference into the identity formula. There is an X, however, which is strictly (seamlessly) identical with itself (the absolute subject = X) while transitively being both of them in turn; and it is only via X that the relata (nature and mind) are indirectly identified with each other: X is B and X is A (and X is strictly identical to itself). In addition to this, Schelling held a view of predication as kind of identification. He became acquainted with this view at the Tubingen Seminary through his teacher Gottfried Ploucquet. This insight helps us understand why Schelling reasonably thought that the identity-formula A=A is the genuine matrix of all veridical judgments. Taken together with his conviction that judging (Kant''s relative position) is a minor (or inferior) form of existential being (Kant''s absolute position) sheds light on why in 1806 Schelling made the radical contention in his Aphorisms: The strict sense of being (absolutely posited seamless self-sameness) is taken over by the looser sense of the copulative is which identifies subject and predicate; yes, this copula alone is existence itself and nothing else. Why should Schelling''s conception of nature-mind identity interest recent philosophers of mind? Because Schelling presents an ontologically neutral solution: Identity is a symmetrical relation that does not favor mind or matter, and prevents the idealistic reduction of nature to the mind. Nor can we conceive of the nature-mind identity as a fact inwardly disclosed to the mind (McGinn, Levine). Consciousness remains an enigma for itself; so does its identity with nature. Schelling teaches us that identity theories are not justified by self-evidence, but by an inference to the best explanation. German description: Nie ist genau erklart worden, was Schelling unter Identitat von Natur und Geist verstand. Dabei hat er sein reifes Denken Identitatssystem genannt und sich zeitlebens um kein zweites Problem begrifflich ahnliche Muhe gegeben. Da er aber seine Uberlegungen in Schriften verpackte, deren grosser systematischer Ausgriff sie schier erdruckte, ist, was er bis hinein in die Weltalter-Periode daruber herausfand, kaum eigens gewurdigt oder auch nur klar benannt worden. Die Schellingliteratur arbeitete entweder historisch oder liess sich vom Systemgedanken oder einzelnen in die Augen springenden Problemen blenden (z. B. Natur, Organismus, Freiheit, Existenz). Dabei ist Schellings Starke in einzelnen entscheidenden Argumenten versteckt, die, waren sie bekannt, die gegenwartige, auch analytische Diskussion durchaus zu inspirieren vermochten. Wir konnen heute urteilen, dass schon der junge Schelling in seiner Schrift Form der Philosophie eine differenzsensitive Form der Identitat im Sinn hatte, die er in den kommenden Jahrzehnten immer genauer auszubuchstabieren unternahm. Seine eigentlichen Quellen hat er kunstvoll verborgen. Es sind erstens die Identitatstheorie der Pradikation seines Universitatslehrers Ploucquet, die den Stiftlern in Tubingen eingeblaut wurde und die ihre merkwurdige Fixierung auf die ganz unkantische Auffassung vom Urteil als Subjekt-Pradikat-Identifikation (mit quantifiziertem Pradikator) erklart. Und zweitens Schellings Entdeckung einer alteren Logik, die mit der Figur der reduplicatio arbeitete. - So auch das Absolute: Als Geist ist es nicht Natur (und umgekehrt; Aussagen uber beide haben unterschiedliche Wahrheitsbedingungen), aber Geist und Natur werden beide vom Absoluten gewesen (transitiv ins Sein gehoben), und dies Absolute ist im striktest denkbaren Sinne mit sich identisch. So lasst sich die Schelling''sche Formel von der Identitat der Identitat und Differenz dem gesunden Menschenverstand vermitteln und Schellings aufrichtiger Jugendgedanke (Marx) aktualisieren. Er schneidet respektabel ab im Wettbewerb mit allerlei heutigen Leib-Seele-Identitatstheorien. (shrink)

Autor prezentuje własną interpretację fenomenologicznej zagadki „w sobie” przedmiotu rzeczywistego i samego świata. Rozwiązanie tej zagadki ma rozstrzygające znaczenie dla właściwego zrozumienia fenomenologii transcendentalnej. Według Husserla, rzecz transcendentna jest „w sobie” w odniesieniu do faktycznego doświadczenia, ponieważ jej esse nie rozpływa się w percipi i może istnieć nawet wtedy, gdy nie jest faktycznie doświadczana. „W sobie” przedmiotu realnego nie oznacza jednak jego istnienia poza wszelkim możliwym sposobem dania w świadomości, ale jest idealną jednością daną w nieskończonej wielości rzeczywistych i możliwych (...) przejawów tego samego dopuszczającego określenia x. Wszystkie przedmioty realne są jednostkami sensu, ale sens nie przenika przedmiotu w nieskończoności jego przejawów, a w konsekwencji niewyczerpywalne x jako nosiciel tożsamości przedmiotu zawiera nadwyżkę wykraczającą poza sens. Zasadnicza teza artykułu brzmi, że „w sobie” rzeczy transcendentnej i świata realnego odpowiada czystemu x i jego nadwyżce przekraczającej sensy noematyczne. (shrink)

W artykule autor analizuje teorię autorytetu przedstawioną przez Trinkaus Zagzebski. Teoria ta podkreśla rolę zaufania w uzasadnianiu zdań, m.in. wskazując na ograniczenia stanowiska egoizmu poznawczego, dla którego ideałem jest sytuacja, w której podmiot, uzasadniając swe przekonania, polega tylko na własnych zdolnościach poznawczych. Trinkaus Zagzebski broni uniwersalizmu poznawczego, wg którego już sam fakt, że osoba x, głosi że p, jest prima facie racją za p. W tekście autor wskazuje na słabe punkty uniwersalizmu i konkluduje, że albo uznamy to stanowisko z jego (...) konsekwentnym odrzuceniem tezy o równości podmiotów poznających, albo też mimo wszystko opowiemy się za egoizmem poznawczym. Autor uznaje przy tym, że amerykańska filozofka daje nam wskazówki, jak ulepszyć owo stanowisko, by nie prowadziło ono do twierdzeń sprzecznych z intuicją. (shrink)

Given two infinite binary sequences A,B we say that B can compress at least as well as A if the prefix-free Kolmogorov complexity relative to B of any binary string is at most as much as the prefix-free Kolmogorov complexity relative to A, modulo a constant. This relation, introduced in Nies [14] and denoted by A≤LKB, is a measure of relative compressing power of oracles, in the same way that Turing reducibility is a measure of relative information. The equivalence classes (...) induced by ≤LK are called LK degrees and there is a least degree containing the oracles which can only compress as much as a computable oracle, also called the ‘low for K’ sets. A well-known result from Nies [14] states that these coincide with the K-trivial sets, which are the ones whose initial segments have minimal prefix-free Kolmogorov complexity. We show that with respect to ≤LK, given any non-trivial sets X,Y there is a computably enumerable set A which is not K-trivial and it is below X,Y. This shows that the local structures of and Turing degrees are not elementarily equivalent to the corresponding local structures in the LK degrees. It also shows that there is no pair of sets computable from the halting problem which forms a minimal pair in the LK degrees; this is sharp in terms of the jump, as it is known that there are sets computable from which form a minimal pair in the LK degrees. We also show that the structure of LK degrees below the LK degree of the halting problem is not elementarily equivalent to the or structures of LK degrees. The proofs introduce a new technique of permitting below a set that is not K-trivial, which is likely to have wider applications. (shrink)

Według standardowej koncepcji krzywdy, inkorporującej test kontrfaktyczny, osoba B została skrzywdzona, jeśli na skutek działania x osoby A znalazła się w gorszej sytuacji niż ta, w której znajdowałaby się, gdyby osoba A nie zrealizowała tego działania. Zastosowanie tej koncepcji do wyborów prokreacyjnych napotyka jednak dwa poważne problemy teoretyczne: tzw. problem nie-istnienia, będący także istotą spraw sądowych z tytułu „wrongful life”, oraz problem nie-tożsamości, opisany przez Derka Parfita. Problemy te ujawniają, że standardowa koncepcja krzywdy prowadzi do wniosków, które są całkowicie sprzeczne (...) z powszechnie podzielanymi intuicjami dotyczącymi obowiązków moralnych rodziców wobec przyszłych dzieci. Celem niniejszego artykułu jest analiza alternatywnej koncepcji krzywdy – tzw. krzywdy progowej. Wykazane zostanie, że koncepcja ta jest oporna na problem nie-istnienie, ale nie jest w stanie w sposób satysfakcjonujący rozwiązać problemu nie-tożsamości. (shrink)

Filozofia rosyjska zrodziła się w X wieku z chwilą przyjęcia przez Rosję prawosławia. Nie wszyscy historycy zgadzają się z tym poglądem. Przede wszystkim odmawiają filozoficznego charakteru pierwszej refleksji dotyczącej człowieka, Boga, świata, podkreślając jej teologiczne pochodzenie. Tymczasem średniowieczna Ruś, podobnie jak Europa tamtych czasów, problemy filozoficzne rozpatrywała na gruncie teologii. Dopiero dalsze losy tych dwóch nauk potoczyły się innymi drogami. Prawosławna filozofia na tyle przeniknęła kulturę rosyjską, że zadecydowało to o jednej z jej osobliwości, wyrażającej się w przekonaniu o współistnieniu (...) wiary i rozumu. Dziewiętnasto- i dwudziestowieczni rosyjscy filozofowie powracali i odwoływali się do poglądów Ojców Kościoła. Najważniejsze idee rosyjskie wypłynęły z średniowiecznej myśli religijnej. (shrink)

Według standardowej koncepcji krzywdy, inkorporującej test kontrfaktyczny, osoba B została skrzywdzona, jeśli na skutek działania x osoby A znalazła się w gorszej sytuacji niż ta, w której znajdowałaby się, gdyby osoba A nie zrealizowała tego działania. Zastosowanie tej koncepcji do wyborów prokreacyjnych napotyka jednak dwa poważne problemy teoretyczne: tzw. problem nie-istnienia, będący także istotą spraw sądowych z tytułu „wrongful life”, oraz problem nie-tożsamości, opisany przez Derka Parfita. Problemy te ujawniają, że standardowa koncepcja krzywdy prowadzi do wniosków, które są całkowicie sprzeczne (...) z powszechnie podzielanymi intuicjami dotyczącymi obowiązków moralnych rodziców wobec przyszłych dzieci. Celem niniejszego artykułu jest analiza alternatywnej koncepcji krzywdy – tzw. krzywdy progowej. Wykazane zostanie, że koncepcja ta jest oporna na problem nie-istnienie, ale nie jest w stanie w sposób satysfakcjonujący rozwiązać problemu nie-tożsamości. (shrink)

In the individual, social, and political dimensions, the shaping of the liberal tradition has met up with and will continue to meet up with the presence of the Roman Catholic Church with its own philosophy. Yet has this always led to sharp conflict between Catholicism and liberalism? Has the social thinking of the Church evolved in its assessment of the liberal tradition and vice versa? Have there been points in common in the two systems of thinking? In contrast, where have (...) sparks appeared? Does Catholicism support the stability of liberal democracy? A response to these questions comprises the primary aim of the work at hand. Herein is a presentation and appraisal of one of the most interesting and continually lively clashes, accompanied by a portrayal of both Catholicism and liberalism. Analysis will be conducted at the level of social philosophy, through incidental political practice, and from the historical perspective – all of which together will enable illustration of the dynamic relationship between Catholicism and liberalism. Due to the scope of liberalism, the analysis of the Catholicism-liberalism relationship will be limited solely to the philosophy of politics and of economics. Such a restricted social philosophy involves the following issues: the genesis, essence, and characteristics of social policy; its ultimate justification or lack thereof; the relationship between the political society and its members; the types of structured political communities; the genesis, nature and duties of political authorities; the definition of the law, its foundations and limitations; the essence and properties of economic life; types of ownership; and, finally, the relations taking place between politics and economics. The problem inherent in an encounter between the social thinking of the Roman Catholic Church and liberalism appear to be especially meaningful in the context of the Polish discourse regarding the new order, its theoretical bases and institutions, projects for the realization of individual freedom, and the superiority or inferiority of values in today’s pluralistic universe. This matter is of great consequence and significance – not only intellectually but above all practically – and manifests itself in political, economic, and cultural life. Nonetheless, for decades now, Polish research into this issue has been entangled in occasional conflicts of a worldview and political nature. In turn, there is a lack of understanding and objective theoretical reflection on the subject. In fact, there are no publications which attempt to understand liberalism and assess the validity of the accusations against it. The vast amount of literature devoted to this problem most frequently opens, right from the start, with arguments stemming from either a Marxist or Catholic apologetics. The liberal credo is not identified with the philosophy of politics, but rather the theory of pro-capitalist economics. This, as a result, not only misrepresents the crux of liberalism, but also narrows the catalogue of responses by the Church on this very topic – starting with the encyclical Rerum novarum (1891) by Pope Leo XIII. In order to resolve this problem, the analysis will be rooted in the broader philosophical and historical context. In other words, it will look into liberalism on the one hand, and into those Church documents in which that institution first spoke of liberalism on the other. The discussions and deliberations contained within this volume are laid out in an introduction, four chapters, and a conclusion. The introduction includes the theoretical bases and methodological assumptions of this work, taking into account the principles of philosophical reflection and analysis. The fundamental chapters present the evolution of an attitude towards liberalism in the social teachings of the Roman Catholic Church – from Pius VI to John Paul II – taking under consideration the key moments and figures in the development of liberalism (e.g., John Locke, John Stuart Mills, John Rawls). In this time period four stages of a Catholic reference to liberalism will be distinguished. The first three constitute: 1) animosity and condemnation (from Pius VI to Pius IX), 2) criticism accompanied by tolerance (from Leo XIII to Pius XII, and 3) criticism accompanied by limited concord (from John XXIII to Paul VI). Today, and with increasing frequency, voices are heard speaking of the teachings of John Paul II as marking a new caesura in the Catholic-liberalism relationship. Hence it is worth re-evaluating and re-analyzing if such opinions are justified. The volume closes with a conclusion comprising an attempt to answer the following questions. Are Catholic accusations addressed at liberalism correct or not? Has liberalism turned out to be a philosophy open to criticism and capable of modification as the weak points in liberal theory and practice are disclosed? Can Catholic values enrich the liberal political order? Can Catholic moral-religious norms, introduced into the realm of political responsibilities, endanger the foundations of the liberal system? Reviewing the evolution of Catholicism as well as liberalism, has Catholicism found its place amidst the pluralistic harmony of liberal democracy? Kształtowanie się tradycji liberalnej napotykało i będzie napotykać na promowaną przez Kościół rzymskokatolicki filozofię, zarówno w wymiarze indywidualnym, społecznym, jak i politycznym. Czy zawsze prowadziło to do ostrego sporu między katolicyzmem a liberalizmem? Czy społeczna myśl Kościoła ewoluowała w swojej ocenie tradycji liberalnej i vice versa? Czy w obu systemach myślowych istniały punkty wspólne? Czego dotyczyły ogniska zapalne? Czy katolicyzm wspiera stabilność liberalnej demokracji? Te pytania sprawiły, że głównym celem niniejszej pracy jest prezentacja i ocena jednego z najbardziej interesujących i wciąż aktualnych sporów, a pośrednio przedstawienie dwóch filozofii – katolicyzmu i liberalizmu. Analiza tego sporu prowadzona jest na płaszczyźnie filozofii społecznej, incydentalnie – praktyki politycznej w ujęciu historycznym, co umożliwia ukazanie dynamiki relacji między katolicyzmem i liberalizmem. Z powodu zakresu liberalizmu w analizie relacji katolicyzm – liberalizm praca ta ogranicza się jedynie do filozofii polityki i filozofii gospodarki. Tak okrojona filozofia społeczna interesuje się następującymi problemami: genezą, istotą i cechami społeczności politycznej, jej ostatecznym uzasadnieniem lub brakiem takowego oraz relacjami między społeczeństwem politycznym a jego członkami, typami ustrukturyzowania wspólnoty politycznej, genezą, naturą i zadaniami władzy politycznej, definicją prawa, jego podstawą i ograniczeniami, istotą i właściwościami życia gospodarczego, rodzajami własności, stosunkami zachodzącymi między polityką a ekonomią. Problem spotkania myśli społecznej Kościoła katolickiego z liberalizmem wydaje się szczególnie znaczący również w kontekście polskich dyskusji o tworzącym się ładzie, jego teoretycznych podstawach i instytucjach, projekcie realizacji indywidualnej wolności oraz wyższości i niższości wartości w dzisiejszym, pluralistycznym uniwersum. Problem ten ma olbrzymie znaczenie nie tylko intelektualne, ale przede wszystkim praktyczne, objawiające się na poziomie życia politycznego, ekonomicznego i kulturowego. Jednak od wielu dziesięcioleci polskie studia nad tym zagadnieniem są uwikłane w doraźne konflikty o charakterze światopoglądowym i politycznym, natomiast brakuje rozumiejącej i obiektywnej refleksji teoretycznej na ten temat. Właściwie nie ma publikacji próbujących zrozumieć liberalizm i ocenić zasadność stawianych mu zarzutów. Ogrom literatury poświęcony temu problemowi najczęściej zawiera prace już na wstępie wychodzące z pozycji apologetycznie marksistowskich czy katolickich. Utożsamia się w nich credo liberalizmu nie z filozofią polityki, lecz z teorią ekonomii prokapitalistycznej, co nie tylko zakłamuje istotę liberalizmu, lecz także zawęża katalog wypowiedzi Kościoła na jego temat, rozpoczynając je od encykliki Rerum novarum (1891) Leona XIII. Aby sprawę wyjaśnić w niniejszej książce, analiza jest umieszczona w szerszym kontekście filozoficznym i historycznym, czyli „ma wgląd”, z jednej strony w liberalizm, z drugiej – w dokumenty Kościoła, w których on po raz pierwszy zabrał głos w sprawie liberalizmu. Rozważania zawarte w niniejszej pracy podzielone są na wstęp, cztery rozdziały i zakończenie. We wstępie prezentuję podłoże teoretyczne i założenia metodologiczne rozprawy, przestrzegając zasad refleksji i analizy filozoficznej. Rozdziały przedstawiają ewolucję stosunku do liberalizmu w społecznej nauce Kościoła rzymskokatolickiego, od czasów Piusa VI do Jana Pawła II, z uwzględnieniem ważniejszych momentów rozwoju myśli liberalnej (John Locke, John Stuart Mill, John Rawls). W omawianym okresie wyróżniam cztery etapy katolickiego odniesienia do liberalizmu: pierwszy – wrogości i potępienia (od Piusa VI do Piusa IX), drugi – krytyki, ale zarazem tolerowania (od Leona XIII do Piusa XII), trzeci – krytyki, choć i ograniczonej zgody (od Jan XXIII do Pawła VI) i czwarty – powszechnie oceniany jako przełom w katolickiej percepcji liberalizmu (pontyfikat Jana Pawła II). Całość rozważań zamknie zakończenie, którego treścią jest próba odpowiedzi na pytania: czy katolickie zarzuty pod adresem liberalizmu są trafne czy też nie? Czy liberalizm okazał się filozofią otwartą na krytykę, zdolną do modyfikacji pod wpływem ujawniania słabych stron teorii lub praktyk liberalnych? Czy wartości katolickie mogą wzbogacić liberalny porządek polityczny? Czy też katolickie normy moralno-religijne, wprowadzone w obręb obowiązków politycznych, zagrażają fundamentom ustroju liberalnego? Czy zarówno wobec ewolucji katolicyzmu, jak i liberalizmu katolicyzm odnalazł się w pluralistycznej harmonii liberalnej demokracji? (shrink)

In 1945–46, representatives of the U.S. government made similar discoveries in both Germany and Japan, unearthing evidence of unethical experiments on human beings that could be viewed as war crimes. The outcomes in the two defeated nations, however, were strikingly different. In Germany, the United States, influenced by the Canadian physician John Thompson, played a key role in bringing Nazi physicians to trial and publicizing their misdeeds. In Japan, the United States played an equally key role in concealing information about (...) the biological warfare experiments and in securing immunity from prosecution for the perpetrators. The greater force of appeals to national security and wartime exigency help to explain these different outcomes. (shrink)

Critics and author, Alvin Goldman’s response to Knowledge in the Social World.

This article sympathetically explores the phenomenological pragmatism of Robert E. Innis in Consciousness and the Play of Forms and Pragmatism and the Forms of Sense. Disputing both the realistic view that perception underlies semiosis and deconstructionist reversals of this, Innis claims they are inextricably interwoven. He forges an alliance between pragmatists Peirce and Dewey, and Continental phenomenologists Polanyi, Bühler, and Cassirer, a "polyphony" that also yields a richly aesthetic critique of technology. By restricting his analysis to a methodological "frame," Innis (...) overlooks a metaphysical tension between Polanyi's realism and Cassirer's idealism, though potentially resolvable in Dewey's transactional philosophy. (shrink)

M. Bonnefond-Coudry has performed a great service by compiling a list of senators who are known to have spoken in the senate in the first century b.c. Yet her list for the year 50 invites a thoroughgoing revision. Beside the rubric ‘supplicatio à Cicéron’ she gives the following list: Cato, Hirrus, Balbus, Lentulus , Domitius , Scipio, Favonius. She also notes that Pompey spoke at a session late in the year , and maintains that Scipio spoke on 1 December.

The praetorship of L. Rupilius is of great importance only to the biography of L. Rupilius. His consular candidacy has a wider significance, since his repulsa represents a reverse for his most prominent supporter, Scipio Aemilianus. As the praetorship is not explicitly mentioned in the sources, its terminus non post quem is fixed by the consular candidacy. Scholarly treatment of the question is hard to come by. The terminus post quem for the candidacy of Lucius is his brother's candidacy ; (...) the terminus ante quem, Scipio's death : Cicero tells us that Scipio brought about the election of P. Rupilius, but failed to make his brother Lucius consul. Broughton classified L. Rupilius as ‘Pr. by 133 ’, and in this seems to have followed Münzer, who indeed considered L. Rupilius ‘Praetor gegen 620 = 134’, but added that he was a candidate ‘urn das Consulat für 623 =131 oder noch eher für 624 = 130’. Of course, if L. Rupilius was a candidate in 131 for a consulship of 130, then he was praetor by 133. A candidacy in 1294 can be safely ruled out: Scipio died in the first half of the year, in spring or early summer. But we cannot rule out candidacy in 130 for 129: Scipio might have preferred L. Rupilius to either consul of that year. The latest possible date for the praetorship of L. Rupilius is therefore 132. (shrink)

In the 13th and 14th centuries CE the Śrīvaiṣṇava Hindu community of south India struggled to integrate the traditional values of the older brahmanical hierarchical system with the devotional egalitarianism that had come to the fore with fresh force in the Tamil vernacular tradition in the 7th and 8th centuries and thereafter. One of the most vexed aspects of this integration pertained to caste, and whether devotionalism foreclosed a continuation of traditional caste distinctions: do divine love and grace mandate radical (...) egalitarianism? Śrīvaiṣṇava theologians were divided on the issue, some more conservative, some more radical in their rhetoric about continuity and change. Yet, as this essay argues, none were willing to go to the extremes either of dismissing caste structures entirely or of entirely subordinating devotion to caste. New values were to take primary place, while old norms were to be reinterpreted and given new meanings. Analyzing well-known examples from the tradition they argued instead a balance between norms and exceptions, treating violations of caste as occasions to glorify the power of devotion but without predicting the end of caste altogether. Attention to this case sheds light on caste and devotion in the Hindu context, the nature of ethical debate in India, and consequently too ways in which rhetoric functions more widely in ethical analysis. (shrink)