We prove that a number of axioms, each a consequence of PFA (the Proper Forcing Axiom) are equivalent. In particular we show that TOP (the Thinning-out Principle as introduced by Baumgartner in the Handbook of set-theoretic topology), is equivalent to the following statement: If I is an ideal on ω 1 with ω 1 generators, then there exists an uncountable $X \subseteq \omega_1$ , such that either [ X] ω ∩ I = ⊘ or $\lbrack X\rbrack^\omega \subseteq I$.

In lieu of an abstract, here is a brief excerpt of the content:A Brief History of Medical Ethics Code in PolandJacek A. Piątkiewicz (bio)On March 15, 1934 a Parliamentary Act authorized the General Medical Chambers, a body incorporating all Polish physicians, to establish general rules of medical ethics. These rules governed medical conduct in Poland until 1950, when the Communist government dissolved the General Medical Chambers.From 1950 to 1989 the only medical organization in Poland tolerated by the Communist government (...) was the Polish Medical Association, which included about 30% of the country's physicians. In 1967 this group produced the "Collection of Ethico-deontological principles of the Polish Physician" which constituted a kind of code of medical ethics. This collection was a compromise between objective ethical principles and the demands of the Communist regime. For example, Principle 1 of the Collection stated that the physician "had to observe the ethico-deontological principles obligatory in socialist society."During round-table talks in early 1989 with representatives of the Communist government, the Solidarity movement argued for the revival of autonomous medical organizations like the Medical Chambers. On May 17, 1989 an Act of Parliament re-established the group. The Act (article 33, part 1) also stipulated that the National Congress of Physicians, the legislative body of Medical Chambers, establish rules of medical ethics. The Act (article 15, part 1) also states that all practicing Polish physicians are obliged to observe these rules.When the revived Chambers began its work in January 1990, its governing body—the General Medical Council—created a Commission to prepare a draft of a medical ethics code. After a year and a half of work, the Commission completed its draft, which received preliminary acceptance by the General Medical Council. [End Page 361]On December 13-14, 1991 the Extraordinary Second National Congress of Physicians was held in Bielsko-Biala (South Poland) and one of the main items on the agenda was the Code. Every article of the Code was discussed exhaustively throughout the second day of the meeting, and close to midnight the Code, including the Physician' Oath, was approved by an overwhelming majority (449 for, 75 against, 58 abstaining).Some of the liveliest discussion centered on Article 37, which relates to abortion. The delegates realized that the Code was inconsistent with a 1956 Act on abortion then under discussion in the Parliament which was not as restrictive as the Code. They decided to defer implementation of the Code for five months, until May 3, 1992. As described in the following text by Robert Baker, Article 37 has now been appealed and a decision resolving the discrepancy would have to come from Poland's Constitutional Tribunal or its Parliament. [End Page 362]Jacek A. Piątkiewicz Jacek A. Piątkiewicz, M.D., Ph.D., is Chairman of the Legislative Commission of the General Medical Council of Poland in Warsaw.Copyright © 1993 The Johns Hopkins University Press... (shrink)

Leszek Kolakowski discusses, in a highly original way, the arguments for and against the existence of God as they have been conducted through the ages. He examines the critiques of religious belief, from the Epicureans through Nietzsche to contemporary anthropological inquiry, the assumptions that underlie them, and the counter-arguments of such apologists as Descartes, Leibniz, and Pascal. His exploration of the philosophy of religion covers the historical discussions of the nature and existence of evil, the importance of the concepts (...) of failure and eternity to the religious impulse, the relationship between skepticism and mysticism, and the place of reason, understanding, and in models of religious thought. He examines why people, throughout known history, have cherished the idea of eternity and existence after death, and why this hope has been dependent on the worship of an eternal reality. He confronts the problems of meaning in religious language. (shrink)

Résumé L’auteur interroge la relation complexe que la peinture de Bernard Villers entretient avec la culture du livre et avec la pratique de l’édition. En effet, le livre – dans tous les sens du terme – a profondément marqué sa démarche de peintre. Il s’agit donc d’analyser l’impulsion que le livre a pu donner à la pratique et aux stratégies picturales. Plusieurs aspects de cette fascination pour la possibilité de faire de la peinture en faisant des livres sont donc passés (...) en revue à la recherche d’une cohérence : les inspirations littéraires, l’inscription du livre dans le quotidien, le livre comme objet, etc., mais surtout l’utilisation du recto et du verso en peinture. (shrink)

The problem of idealization in empirical sciences is very rarely taken up in works concerned with the methodology of those sciences. It seems to be common knowledge that in advanced natural sciences references are made to concepts such as “perfectly rigid body,” “material point,” “perfect gas,” etc., but it remains a fact that the most important methodological concepts, concepts which have determined the present-day form of the philosophy of science, have been advanced without regard to the peculiarities of the procedure (...) mentioned above. And yet a moment's consideration suffices to raise doubts as to Carnap's physicalism and/or Popper's falsificationism if we just realize the trivial and commonly known truth that empirical sciences resort to idealizationism. For how are we to imagine a reduction of idealizational concepts to observation terms? And how are we to imagine that theorems which include idealizational concepts imply observation statements which refute, or at least are at variance with, those theorems? But it is a fact that such doubts have neither been raised by the authors of the conceptions mentioned above, nor have they been raised against them. (shrink)

First lecture: The end -- Second lecture: The means -- Third lecture: The achievements.

Leszek Kolakowski delves into some of the most intellectually vigorous questions of our time in this remarkable collection of essays garnished with his characteristic wit. Ten of the essays have never appeared before in English. "Exemplary.

Since its introduction by Hans Reichenbach, many philosophers have claimed to refute the idea – known as the common cause principle – that any surprising correlation between any two factors that do not directly influence one another is due to some common cause. For example, falsity of the principle is frequently inferred from falsifiability of Bell’s inequalities. The author demonstrates, however, that the situation is not so straightforward. There is more than one version of the principle formulated with the use (...) of different variants of Reichenbach-inspired notions; their falsity still remains an open question. The book traces different formulations of the principle and provides proofs of a few pertinent theorems, settling the relevant questions in various probability spaces. In exploring mathematical and philosophical issues surrounding the principle, the book offers both philosophical insight and mathematical rigor. (shrink)

The current heated debate on the deteriorating status of the university raises a range of pertinent questions, including: What role can the humanities play in culture today in the face of the crisis of higher education? To answer this question, the authors begin by problematizing the relationship between culture, the humanities, and education. In the second part of the paper, they examine the changing role of the humanities in conjunction with the understandings of culture, and outline three salient ways in (...) which culture is conceived of today. Subsequently, they focus on the loss of the dominant status that culture suffered when everyday life was discovered in modernity. In the third part, they argue that everyday life, or rather social representations of everyday life and its practices, are currently becoming the chief criterion for assessing culture, the humanities, and education. However, everyday life remains complex both in theoretical conceptualizations and in research observations. For example, everyday life harbors a range of risks and anxieties which are veiled by its own obviousness and reinforced by socialization. The authors conclude that, given this, everyday life in democratic societies calls for the work of understanding, support, affirmation, and criticism, in which the humanities can retain their superior status. In the fourth part, the authors discuss non-consensual democracy, critical community, and the pedagogy of asylum as the forms of organization and action that promote an auspicious interconnection of culture, the humanities, and education. (shrink)

We introduce the notion of a Minkowskian Branching Structure ("MBS" for short). Then we prove some results concerning the phenomenon of funny business in its finitary and infinitary variants.

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory [math] of [E. Jeřábek, Approximate counting by hashing in bounded arithmetic, J. Symb. Log. 74(3) (2009) 829–860]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We give a purely computational (...) characterization of this class and show that, relative to an oracle, it does not contain the problem CPLS, a strengthening of PLS. As CPLS is provably total in the theory [math], this shows that [math] does not prove every [math] sentence which is provable in bounded arithmetic. This answers the question posed in [S. Buss, L. A. Kołodziejczyk and N. Thapen, Fragments of approximate counting, J. Symb. Log. 79(2) (2014) 496–525] and represents some progress in the program of separating the levels of the bounded arithmetic hierarchy by low-complexity sentences. Our main technical tool is an extension of the “fixing lemma” from [P. Pudlák and N. Thapen, Random resolution refutations, Comput. Complexity, 28(2) (2019) 185–239], a form of switching lemma, which we use to show that a random partial oracle from a certain distribution will, with high probability, determine an entire computation of a [math] oracle machine. The introduction to the paper is intended to make the statements and context of the results accessible to someone unfamiliar with NP search problems or with bounded arithmetic. (shrink)

At the beginning of Book I of the Nicomachean Ethics, Aristotle says that “the good is the same for an individual as for a city”. The good in question is εὐδαιμονία – the highest good achievable for human beings. In Book X, we learn that contemplative activity meets best the requirements set for eudaimonia. Even if we agree that contemplative activity is the good for an individual, how should we understand the claim that contemplation is also the good for a (...) city? I start by reminding readers that for Aristotle the Nicomachean Ethics is essentially a political enquiry and should be read together with his Politics. I focus on the teleological character of his political philosophy and the interlinking of the concepts of the good, nature, form, end and function. Then, I look at Aristotle’s two closely-connected statements that polis exists by nature and that men are political animals. Having taken into account Aristotle’s opinion regarding the imperfection of this world, which is exemplified by the vulnerability of human lives to fortune, luck and accidents, I conclude that Alasdair MacIntyre’s concept of the political community as a common project explains well how contemplation could be the end of polis. Only very few individuals can achieve the highest good and they can do it only if they have the support of the political community. But all the inhabitants of a polis structured towards achieving the highest good benefit from living in a well-ordered community whose constitution reflects the objective hierarchy of goods. (shrink)

Wychodząc od metaforycznego (figuralnego) ujęcia problemu zła, w oparciu o wybrane przemyślenia Leszka Kołakowskiego, rozważania składające się na artykuł zmierzają do namysłu nad „złem w polityce” w sensie niedomagań i nadużyć wolności: pokus władzy autokratycznej i totalitarnej. Dotyczą antropologicznego i politycznego przekraczania granic wolności kosztem (aż do zniesienia) wolności innych. Evil Politics or Trouble with the Devil. Reflections on the Political Demonology of Leszek Kołakowski Proceeding from a metaphorical (figurative) account of the problem of evil, and based on (...) class='Hi'>Leszek Kołakowski’s selected thoughts, this paper’s considerations aim to deliberate on “evil in politics” in the spirit of the shortcomings and excesses of freedom: namely, the lure of autocratic and totalitarian power. At issue is how the bounds of freedom are anthropologically and politically transgressed at the expense (to the point of abolishing) the freedom of others. (shrink)

We show, under the assumption that factoring is hard, that a model of PV exists in which the polynomial hierarchy does not collapse to the linear hierarchy; that a model of S21 exists in which NP is not in the second level of the linear hierarchy; and that a model of S21 exists in which the polynomial hierarchy collapses to the linear hierarchy. Our methods are model-theoretic. We use the assumption about factoring to get a model in which the weak (...) pigeonhole principle fails in a certain way, and then work with this failure to obtain our results. As a corollary of one of the proofs, we also show that in S21 the failure of WPHP (for Σb1 definable relations) implies that the strict version of PH does not collapse to a finite level. (shrink)

Since its first introduction by Hans Reichenbach, many philosophers have claimed to refute the common cause principle. The situation is not so straightforward, though: validity of the principle remains an open question. The book traces different formulations of the principle, and provides proofs of a few pertinent theorems, settling the relevant questions in various probability spaces. It offers both philosophical insight and mathematical rigor.

According to the commonsensical model of educating researchers, young researchers must first acquire the knowledge achieved thus far and then solve new problems by developing applications of the accepted theory. This model, which presupposes a positivist theory of science, is incapable of explaining why the major breakthroughs in science have been carried out by young researchers. On the idealizational view of science, it becomes clear that commonsensical model must be rejected and replaced with an alternative, according to which the primary (...) duty of young researchers is to revise the existing theories. It is the young researchers who are usually creative enough, ignorant enough, and exhibit a sufficient degree of nonconformism, to be capable of developing really new scientific theories. (shrink)

This paper investigates the prospects of developing a branching modal framework while keeping with the spirit of Humean Supervenience. It is argued that such an approach is bound to face hard problems regarding haecceitism and the notion of recombination. Possible directions for future philosophical developments of branching frameworks are suggested.

Niniejszy artykuł przedstawia poglądy oryginalnego polskiego filozofa z pierwszej połowy XX stulecia – Jana Stachniuka. Wyróżniającymi elementami tej koncepcji z zakresu filozofii społecznej są jego rozważania dotyczące kultury, swoistej,,wspakultury”, historiozofii, roli mitów w społecznym bycie.

The present paper is intended to take up the basic issue in Marxist epistemology: does the development of human cognition include mechanisms that ensure the attainment of, or approximation to, the absolute truth?But to take up this issue we have to define the concept of absolute truth. This is why the paper begins with comment on the assumptions we adopt. This is followed by explanations of the concept of the absolute truth and that of relative truth and some of derivative (...) concepts, too. Section 3 is concerned with the problem of whether the absolute truth is attainable, and with the role played in the process by the correspondence principle, which is reconstructed in a specified way. (shrink)

Leszek Kolakowski discusses, in a highly original way, the arguments for and against the existence of God as they have been conducted through the ages. He examines the critiques of religious belief, from the Epicureans through Nietzsche to contemporary anthropological inquiry, the assumptions that underlie them, and the counter-arguments of such apologists as Descartes, Leibniz, and Pascal. His exploration of the philosophy of religion covers the historical discussions of the nature and existence of evil, the importance of the concepts (...) of failure and eternity to the religious impulse, the relationship between skepticism and mysticism, and the place of reason, understanding, and in models of religious thought. He examines why people, throughout known history, have cherished the idea of eternity and existence after death, and why this hope has been dependent on the worship of an eternal reality. He confronts the problems of meaning in religious language. (shrink)

We study the first-order consequences of Ramsey’s Theorem fork-colourings ofn-tuples, for fixed$n, k \ge 2$, over the relatively weak second-order arithmetic theory$\mathrm {RCA}^*_0$. Using the Chong–Mourad coding lemma, we show that in a model of$\mathrm {RCA}^*_0$that does not satisfy$\Sigma ^0_1$induction,$\mathrm {RT}^n_k$is equivalent to its relativization to any proper$\Sigma ^0_1$-definable cut, so its truth value remains unchanged in all extensions of the model with the same first-order universe.We give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^n_k$for$n \ge (...) 3$. We show that they form a non-finitely axiomatizable subtheory of$\mathrm {PA}$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _{\ell +3}$fragment for$\ell \ge 1$lies between$\mathrm {I} \Sigma _\ell \Rightarrow \mathrm {B} \Sigma _{\ell +1}$and$\mathrm {B} \Sigma _{\ell +1}$. We also give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k + \neg \mathrm {I} \Sigma _1$. In general, we show that the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k$form a subtheory of$\mathrm {I} \Sigma _2$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _4$fragment is strictly weaker than$\mathrm {B} \Sigma _2$but not contained in$\mathrm {I} \Sigma _1$.Additionally, we consider a principle$\Delta ^0_2$-$\mathrm {RT}^2_2$which is defined like$\mathrm {RT}^2_2$but with both the$2$-colourings and the solutions allowed to be$\Delta ^0_2$-sets rather than just sets. We show that the behaviour of$\Delta ^0_2$-$\mathrm {RT}^2_2$over$\mathrm {RCA}_0 + \mathrm {B}\Sigma ^0_2$is in many ways analogous to that of$\mathrm {RT}^2_2$over$\mathrm {RCA}^*_0$, and that$\mathrm {RCA}_0 + \mathrm {B} \Sigma ^0_2 + \Delta ^0_2$-$\mathrm {RT}^2_2$is$\Pi _4$- but not$\Pi _5$-conservative over$\mathrm {B} \Sigma _2$. However, the statement we use to witness failure of$\Pi _5$-conservativity is not provable in$\mathrm {RCA}_0 +\mathrm {RT}^2_2$. (shrink)

Leszek Kołakowski explores 23 questions asked by great philosophers, introducing us to the great ideas and philosophers of Western thought.

"[An] important essay by a philosopher who more convincingly than any other I can think of demonstrates the continuing significance of his vocation in the life of our culture."--Karsten Harries, The New York Times Book Review With The Presence of Myth , Kolakowski demonstrates that no matter how hard man strives for purely rational thought, there has always been-and always will be-a reservoir of mythical images that lend "being" and "consciousness" a specifically human meaning. "Kolakowski undertakes a philosophy of culture (...) which extends to all realms of human intercourse--intellectual, artistic, scientific, and emotional. . . . [His] book has real significance for today, and may well become a classic in the philosophy of culture."-- Anglican Theological Review. (shrink)

Celem artykułu jest próba rekonstrukcji rozwoju duchowego Zaratustry, głównego bohatera dzieła Nietzschego Tako rzecze Zaratustra. Ów rozwój polega na osiąganiu trzech stadiów świadomości: fazy konformistycznego wielbłąda, przepełnionego negacją lwa i finalnie dziecka afirmującego życie. Metodologia badań zastosowana w artykule opiera się na analizie, rekonstrukcji i syntezie tekstu Tako rzecze Zaratustra. Przeprowadzone badania osadzone są w kontekście tezy Heideggera o komplementarności głównych aspektów nietzscheanizmu: woli mocy i wiecznego powrotu. Zaratustra, aby przeistoczyć się w lwa, a następnie w dziecko, będzie musiał odkryć (...) i zaakceptować ową komplementarność. Głównym antagonistą proroka jest duch ciężkości, symbolizujący negację życia i destruktywną miłość bliźniego. (shrink)