ArgumentThis paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal (...) law is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain. (shrink)

From the viewpoint of its Stalinist-era creators, the IKKN/INS could at best be described as a mixed success. Despite heroic efforts, it failed to train the cadres that might have permeated Polish scholarship with Marxism-Leninism. If it was the major channel for transmitting Soviet experience to Polish academia, then Poland's universities would not learn to be Soviet—the Polish historian Jerzy Halbersztadt has made the point that the institute was the only direct conduit of Soviet experience into Polish academic life. It (...) even had a major role in educating some of Poland's most famous critical thinkers, although they, unlike their master Adam Schaff, seem less fond of reminiscing about the institute. Leszek Koŀakowski writes that he does not regard his role in the ideological struggles of the early 1950s as a “source of pride”.90The legacy of the IKKN/INS has also been a mixed one. It was not only a “foundry of revisionists”. For every future critical thinker of world repute, it graduated several cadres who served the PZPR loyally over decades. Adam Schaff recognises this dual legacy. Looking back on a long and active life, he has called the institute a “pearl in my crown”.91 Its members filled top party and government posts throughout the history of People's Poland. Andrzej Werblan served as Central Committee secretary and a member of the Politburo, Sylwester Zawadzki became minister of justice, Stanisŀaw Wroński was minister of culture, Mieczysŀaw Jagielski was the Politburo member who negotiated the Gdańsk accords, Stanisŀaw Kania succeeded Edward Gierek, and Mieczysŀaw Rakowski acted as General Jaruzelski's Party First Secretary.92Undoubtedly much of the institute's strange course is to be attributed to the designs of Adam Schaff. Despite his Moscow training, Schaff retained an attachment to the Polish academic milieu which had formed him. He may have believed in Stalinist doctrine, but he also believed that this doctrine would show its superiority in competition with other views—even if the competition was far from a fair one. Of course, Schaff tried to retain ultimate control, and to play, as he now calls himself, the “grey eminence”. Nevertheless, his was a very unstalinist way of propagating Stalinism, and he must be given credit for helping to keep a spirit of intellectual inquiry alive in Poland during the dark years of the early 1950s.Yet Schaff tends to exaggerate his personal role in educating philosophers, dissidents and critical thinkers. This tendency is itself a legacy of the Stalinist period and its concentration of power. Stalinists view the present as their personal creation and therefore reject all criticisms of the past. At the final meeting of the Crooked Circle Club in 1962, Schaff encountered unwonted criticism from, among others, Andrzej Walicki. Schaff shot back at him: “You are ours, you are our creation, a creation of socialism ... we educated you, and we didn't do such a bad job.” But far from being a “creation” of Schaff's, the non-party member Walicki had been denied admission to graduate studies in philosophy. He felt relieved when those in attendance, who knew him better than Schaff did, burst out laughing.93The point is that the Polish intellectual world maintained its integrity outside the IKKN/INS, and in the end it was the institute which merged into the Polish intelligentsia, rather than the opposite. After 1957 the non-Marxist sociologists and philosophers made their way back to academia, and were joined by many former INS staff members. The basic unity of Polish social science training, and of the Polish intelligentsia, was restored.94Of course in a larger sense the fate of the IKKN/INS had little to do with the designs of its master. Schaff admits as much, proclaiming that “I did this because I did not know what I was doing!” If he had been asked to start such a project five years later, the answer would have been: “No!”95 The fatal flaw of the Institute for Training Scientific Cadres was cadres: Poland did not have them. By 1956, Schaff and the party leadership, and perhaps Soviet advisers as well, had learned that one could not create an elite party scientific institution almost out of nothing. It would either be party or scientific, because apparatchiki could not become scientists, scientists would not become apparatchiki, and students could not produce teachers. In the Stalinist period, Polish intellectual life had stood in the shadow of the party; yet during the Thaw the relationship was reversed—increasingly the tiny party training institute was engulfed by the shadow of the resurgent Polish universities. Talented young people, even those in the party, made their way into the traditional higher educational establishment.The IKKN/INS did not, therefore, fail because of its own failings, nor succeed because of its own successes. It was a failed part of a failed whole. To succeed, “mild” revolution would have required decades, and Poland's Stalinists had only a few years. To make matters worse—or better, depending on viewpoint—they did not use these years in a conventional Stalinist manner. Under Schaff's guidance and at somewhat erratic Soviet bidding, the institute became an awkward series of half-measures, reminiscent of much of Polish Stalinism. When Poland's communists fell back and regrouped in 1956, the IKKN/INS occupied a lonely position they preferred to abandon. (shrink)

STRESZCZENIE Opracowanie zmierza do udzielenia odpowiedzi na pytanie, czym – z punktu widzenia struktury procesu wykładni i struktury wchodzących w grę wartości konstytucyjnych – różni się ograniczanie wolności i praw w ramach stosowania „zwykłych środków konstytucyjnych”, od ograniczania wolności i praw dopuszczalnego w stanach nadzwyczajnych. Podjęta zostaje problematyka dotyczącą kwestii materialnych, a poza zakresem rozważanych zagadnień pozostają kwestie dotyczące formalnych warunków dopuszczalności ograniczeń, jak publiczne ogłoszenie zagrożenia czy możliwość wprowadzania ograniczeń w aktach podustawowych. Stawiane tezy są polemiczne wobec poglądów, że (...) zawieszenie wolności lub praw jest skrajnym typem ograniczania i następuje wtedy, gdy wolności czy prawa „już nie ma”, lub że zawieszenie zakłada ograniczenie istoty wolności lub prawa. Okazuje się, że można sensownie mówić o zawieszaniu wolności lub praw także wówczas, gdy są one ograniczane w niewielkim tylko stopniu. Ponadto, możliwe jest zawieszanie, które nie prowadzi do ograniczenia istoty wolności lub prawa. Argumentuje się, że istotą zawieszania wolności lub praw w stanach nadzwyczajnych jest zakwestionowanie podstawowego ich przymiotu, jakim jest – uznawana w prawie międzynarodowym – nienaruszalność „całych” poszczególnych praw człowieka, która jest czymś innym od nienaruszalności ich istoty. Przy okazji prowadzona jest refleksja teoretycznoprawna nad zagadnieniem zawieszania wolności lub praw. Zawieszenie okazuje się czymś istotnie różnym od czasowej utraty mocy obowiązującej przepisów dotyczących wolności czy praw. Ich ciągłe obowiązywanie znajduje wyraz, na przykład, w zasadzie proporcjonalności mającej zastosowanie do zawieszanych wolności lub praw. -/- Extraordinary Measures and Restrictions of Constitutional Freedoms and Rights ABSTRACT The study aims to answer the question on the difference between limitation of freedoms and rights in ordinary situations and their suspension (derogation) when extraordinary measures are introduced. This question is considered from the point of view of the structure of the interpretation process and the structure of the constitutional values. Consideration is given to issues relating to material aspects. However, issues relating to formal conditions for the admissibility of restrictions, such as public announcement of a threat or the possibility of introducing restrictions in sub-statutory acts, are not examined. The theses put forward are critical of the view that suspension of freedoms or rights is an extreme type of limitation and a freedom or a right "is no longer there", and of the view that suspension presupposes violation of the essence of freedom or right. It can be argued that it makes sense to talk about the suspension of freedoms or rights also when they are only slightly restricted. Moreover, it is possible to suspend a freedom or a right without violating their essence. It is argued that suspension of freedoms or rights leads to questioning of their basic characteristic that is their inviolability as recognized in international law. However, this inviolability of freedoms or rights is something different from the inviolability of their essence. In terms of the theory of law, the suspension of freedoms or rights turns out to be something significantly different from the temporary loss of the binding force of the respective provisions. Their continued validity is reflected, for example, in the application of the principle of proportionality to the suspended freedoms or rights. (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.

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.

I claim that objective consequentialism faces a problem stemming from the existence in some situations of a plurality of chances relevant to the outcomes of an agent’s acts. I suggest that this phenomenon bears structural resemblance to the well-known Reference Class problem. I outline a few ways in which one could attempt to deal with the issue, suggesting that it is the higher-level chance that should be employed by OC.

In his paper, the author analyses some premises of liberal concept of equality and its philosophical origins. He attempted to show affinities and differences between liberal and conservative approaches to legal equality. He argues that economic inequality is compatible with political and legal liberties within conservative political philosophy. Victorian lawyer James Fitzjames Stephen proved that fraternity is an ambiguous ideal conceived from utilitarian perspective mainly because that it would be political naïvete to expect love from our citizens instead of justice (...) and respect. (shrink)

The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.

In vorliegender Arbeit wird von mir die Gedanke von Nietzsche als Philosophie aufgezeigt, deren die oberste Wert und Wesen unbedingte und hinausgehende über die Rahmen des anwesendes Daseins die Schaffung ist. Meine Arbeit fange ich damit an, die Tiefe und Ausdehnung dieser Problematik im Werk "Also sprach Zarathustra" darzustellen. Dann überlege ich die Schwierigkeiten, die vor der konstitutiven für Erfahrung des Wesens von der Schaffung stehen, die Schwierigkeiten, die vor allem aus den Begrenzungen von der Natur der Sprache und des (...) Bewußtseins als die Vorstellung folgen. In Bezug auf die Auslegungen von Deleuze und Heidegger zeige ich weiter die Problematik der Schaffung in der Perspektive des Werdens und des Ereignisses, die eng mit der ahistorisch verstandenen Frage der Zeit zusammengehängt wird. Sehr wichtige Rolle spielt hier das Begriff der Zukunft, das der gesehenen im Gedächtnis und in der vergangenheit Grundlage der Zeit entgegengesetzt wird. Die Zukunft als schöpferischer und zugleich destruktiver Abgrund drückt hier eigene Sphäre von der Konstituierung der Zeit aus. Gemaß dahinter wird diesen Artikel mit den berlegungen geschlossen, die der Möglichkeit mystischen Auslegungen der Gedanken von Nietzsche im Zusammenhang mit der Frage der Schaffung betreffen. (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.

This paper considers the rediscovery of Hegel currently taking place in the analytic philosophy. Going back to the Hegelian texts themselves, I will try to show how they can help to decisively solve some problems of contemporary philosophy. I will concentrate on the theme of knowledge, and especially mathematical knowledge, in relation to Hegelian dialectical logic.

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)

We extend a result by Gallow concerning the impossibility of following two epistemic masters, so that it covers a larger class of pooling methods. We also investigate a few ways of avoiding the issue, such as using non-convex pooling methods, employing the notion of imperfect trust or moving to higher-order probability spaces. Along the way we suggest a conceptual issue with the conditions used by Gallow: whenever two experts are considered, whether we can trust one of them is decided by (...) the features of the other! (shrink)

In recent years part of the literature on probabilistic causality concerned notions stemming from Reichenbach’s idea of explaining correlations between not directly causally related events by referring to their common causes. A few related notions have been introduced, e.g. that of a “common cause system” (Hofer-Szabó and Rédei in Int J Theor Phys 43(7/8):1819–1826, 2004) and “causal (N-)closedness” of probability spaces (Gyenis and Rédei in Found Phys 34(9):1284–1303, 2004; Hofer-Szabó and Rédei in Found Phys 36(5):745–756, 2006). In this paper we (...) introduce a new and natural notion similar to causal closedness and prove a number of theorems which can be seen as extensions of earlier results from the literature. Most notably we prove that a finite probability space is causally closed in our sense iff its measure is uniform. We also present a generalisation of this result to a class of non-classical probability spaces. (shrink)

My Ph.D. dissertation written under the supervision of Prof. Tomasz Placek at the Institute of Philosophy of the Jagiellonian University in Kraków. In one of its most basic and informal shapes, the principle of the common cause states that any surprising correlation between two factors which are believed not to directly influence one another is due to their common cause. Here we will be concerned with a version od this idea which possesses a purely probabilistic formulation. It was introduced, in (...) the form of a general principle, by Hans Reichenbach in his posthumously published book "The Direction of Time". The central notion of the principle in Reichenbach's formulation, and of the current essay, is that of screening off: two correlated events are screened off by a third event if conditioning on the third event makes them probabilistically independent. Reichenbach's principle marks also the beginning of a new field of philosophy: namely, that of ``probabilistic causality''. For the most part, the current essay can be seen as an effort at checking how far one can go with the purely statistical notions revolving around Reichenbach's idea of common cause. In short, the answer is ``surprisingly far''; in some classes of probability spaces all correlations between ``interesting'' events possess explanations of such sort. However, this fact lends itself to opposing interpretations; more on that in the conclusion. Chapters 6 and 7 contain mathematical results concerning these issues. The screening-off condition requires an equality of a probabilistic nature to hold; chapter 8 is a short discussion of slightly weakened versions of the condition, which hold if the sides of the above mentioned equality differ to a small degree. In chapter 2, after some mathematical preliminaries, we study the various formulations of the principle which might be said to stem from the original idea of Reichenbach. We also examine a few of the most salient counterarguments, which undermine at least some of the formulations. Chapter 3 is of a formal nature, dealing with various probabilistic notions which can be thought of as generalizations of Reichenbach's concept of common cause. The next chapter concerns the relationship between the idea of common causal explanation and the Bell inequalities. In chapter 5 we briefly present the form of Reichenbach's principle which can be found in the field of representing causal structures by means of directed acyclic graphs. (shrink)

We tackle two open questions from Leitgeb and Pettigrew (2010b) regarding what the belief update framework described in that paper mandates as correct responses to two problems. One of them concerns credences in overlapping propositions and is known in the literature as the “simultaneous update problem”. The other is the well known “Judy Benjamin” problem concerning conditional credences. We argue that our results concerning the problems point to deficiencies of the framework. More generally, we observe that the method of minimizing (...) inverse relative entropy seems to work better than (or at least equally well as) its competitors in many situations. (shrink)

Dans la carte des conflits numériques – logiciel libre, open source, théorie de la propriété –Échelle Inconnue relate son expérience de bataille pour le QR-code (encodeur et décodeur libre en ligne, donc gratuit et réalisable par tous) contre le système de « Flash code » payant, érigé comme standard national, commercialisé par Orange. Ce récit, victorieux dans la ville de Rouen, a amené une vingtaine de collectivités territoriales à préférer utiliser le site d’Échelle Inconnue pour élaborer leur code, amenant Orange (...) à abandonner ses rêves de code fermé et payant. (shrink)

Various notions of independence of observables have been proposed within the algebraic framework of quantum field theory. We discuss relationships between these and the recently introduced notion of logical independence in a general operator-algebraic context. We show that C*-independence implies an analogue of classical independence.

In French, the word « expérience » has two different meanings, which often merge into each other: whether one hears it as « to experience » or as « to experiment », one will take it towards lay knowledge and techniques of struggle, or towards scientific protocols and techniques of governance. This article rides on this ambiguity, putting the two sides of this notion to the service, and to the test, of an analysis of practices and policies dealing with the (...) issue of drugs. On this specific question, the two meanings of political « expérience » are both maximally divergent and intimately tied to each other. (shrink)

Hegel i Nietzsche twierdzili, że żyją w czasach przełomu, który wymusi pojawienie się nowego etapu w dziejach ludzkości. Sytuację człowieka współczesnego określa „fakt” roztrzaskania dotychczasowych horyzontów oraz konieczność stworzenia, lub odkrycia, horyzontów nowych. Postulują oni zatem ustanowienie nowego celu ludzkości. Filozofia polityki winna stać się częścią tego ogólnokulturowego projektu. Tym samym rzucają wyzwanie współczesnej filozofii politycznej, która zrzeka się prawa do ustanawiania takiego celu. Obaj są też przekonani – znów wbrew twierdzeniom współczesnym – że cel ów może i powinien być (...) ugruntowany w naturze całej rzeczywistości i w naturze człowieka. W ich założeniu ma to być cel człowieka empirycznego, historycznego, człowieka, który osiągnął bolesną świadomość tego, że to on był twórcą tych wartości, które dotąd uznawał za obiektywne. Potrzeba sformułowania nowego celu każe Heglowi i Nietzschemu powrócić do klasycznego pojmowania filozofii polityki, do postrzegania w doskonałości człowieka ideału, któremu ma być podporządkowana polityczna działalność. Właściwe rozumienie miejsca człowieka w świecie, ujęcie go jako istoty stwarzającej horyzonty i przekształcającej zgodnie z nimi rzeczywistość, pozwala według nich dotrzeć do prawdy o bycie jako całości, do konstytuującej go zasady samo-rozwoju, będącego zarazem samo-przezwyciężaniem i samo-przekraczaniem. Zaakceptowanie tej prawdy o świecie pozwala ugruntować w nim ideał doskonałości, który można od tej pory ujmować jako istotowy cel człowieka, i żądać podporządkowaniu mu całej kulturowej działalności, w tym także – filozoficzno-politycznej teorii i praktyki. (shrink)

This paper investigates the application of artificial intelligence (AI) language models in writing policy briefing notes within the context of public administration by juxtaposing the technologies’ performance against the traditional reliance on human expertise. Briefing notes are pivotal in informing decision-making processes in government contexts, which generally require high accuracy, clarity, and issue-relevance. Given the increasing integration of AI across various sectors, this study aims to evaluate the effectiveness and acceptability of AI-generated policy briefing notes. Using a structured evaluation-by-experts methodology, (...) the research scrutinizes and compares the output of three leading AI language models—OpenAI’s ChatGPT, Google’s Gemini, and Mistral’s Le Chat—across ten critical dimensions reflective of policy briefing notes quality. These dimensions encompass both structural and content-related aspects, ranging from linguistic precision to the depth and applicability of the generated information. The discussion is anchored in the technology acceptance model (TAM) theory and its extensions, which offer a theoretical framework for understanding the factors influencing the adoption and usefulness of technology in public administration. Our comparative analysis reveals that while AI models exhibit notable competencies in meeting some structural and linguistic benchmarks, they fail to address the nuances and depth required by policy experts for undertaking informed decision-making adequately. This discrepancy underscores the enduring value of human expertise in synthesizing complex information and navigating ethical considerations, even as AI enhances efficiency in certain aspects of the policy briefing note crafting process. (shrink)

This is a summary of a talk delivered at the Winter School of Logic held in Rabka, 24.02 – 04.03.1986 by the Department of Logic of the Jagiellonian University. We wish to announce here several results on embeddability of quotient algebras of certain kind into algebras of some varieties related to the class of Heyting algebras. A “by product” is the deduction theorem for a large family of intermediate consequence operations.

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.