Causal implications of Jaśkowski

Part 1 describes Stanis?aw Ja?kowski's concept of defining some often used con ditionals, namely, factorial, ewfficient and definitive implications. Part 2 contains the results strictly connected with the theory of the above implications.     

Stanisław Brzozowski’s performative criticism

Stanis?aw Brzozowski was active as philosopher and literary critic for only a few years at the turn of the twentieth century, yet his writings are still inspire contemporary thinkers and critics. In every important phase of the development of Polish literary criticism, Polish intellectuals have acknowledged Brzozowski as a writer who had the courage and critical acumen to confront modernity and examine closely contemporary trends of thought from the perspective of social and individual life. This continued presence of the celebrated critic cannot but be interesting for the researcher who is led to ask, what is so intriguing in Brzozowski’s work, why do successive generations of critics and intellectuals return to Brzozowski? Drawing on many important interpretations of Brzozowski’s work (Burek, G?owiński, Nycz), I want to show that in Brzozowski’s work it is possible to find everything contemporary criticism and thought needs, because his books contain, in nuce, projects and strategies which can be (and are) used in different ways by critics representing different ideologies and worldviews. Brzozowski worked out, or rather attempted to work out, ideas which are a source of modern critical projects but in addition his work comprises a repertoire of possibilities which contemporary critical thought can turn to its advantage. Brzozowski’s work can be also treated as a performative act, calling forth the reader’s response, in this way shedding new light on it. I also show that “performative consciousness” is both close to Brzozowski’s practice of writing and deeply rooted in his philosophical conviction. Brzozowski can be considered a representative of modernist, critical literature, in which reading and writing become a mode of experience, a privileged social discourse, and a “leaven,” an act and an activity.     

Stanisław Brzozowski on the ideal of the modern man

Stanisław Brzozowski formulated the ideal of modern man in the polemic with the contemporary man, who has ceased to believe in truth and moral values and is devoid of the will to act. For Brzozowski modernity involves the discovery of truth about the human condition: about man as an autonomous subject, a creator of values, who struggles with non-human reality. This truth was formulated in Kant’s idea of autonomy and in Marx’ idea of a collective conquest of the world of nature. For Brzozowski, ideal modern man is “the conscious labourer,” who labours because he wants to proudly impose a human law on the non-human world. At the same time Brzozowski used the term “modernity” to describe life of constant change in the modern world, understood as a set of results of man’s reign over nature. For the sake of human maturity, Brzozowski expected the truly modern man to perceive modern life as an unquestionable value. Undoubtedly, there is an evident tension in Brzozowski’s ideal of modern man between the affirmation of creativity in the world of change and the necessity of disciplined production, including unchangeable moral foundations of labour. There is also a major shift in this ideal, stemming from Brzozowski’s change of attitude towards religion.     

An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency

In this paper, I present the modal adaptive logic AJ ^r (based on S5) as well as the discussive logic D ^r ₂ that is defined from it. D ^r ₂ is a (non-monotonic) alternative for Jaśkowski’s paraconsistent system D ₂ . Like D ₂ , D ^r ₂ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, D ^r ₂ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D ₂ , this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.*Research for this paper was indirectly supported by the Flemish Minister responsible for Science and Technology (contract BIL1/8). The author is indebted to Leon Horsten, Jo?o Marcos, Jerzy Perzanowski, Liza Verhoeven, and especially to the referee and to Diderik Batens for comments and suggestions.     

Translations Between Gentzen–Prawitz and Jaśkowski–Fitch Natural Deduction Proofs

Two common forms of natural deduction proof systems are found in the Gentzen–Prawitz and Ja?kowski–Fitch systems. In this paper, I provide translations between proofs in these systems, pointing out the ways in which the translations highlight the structural rules implicit in the systems. These translations work for classical, intuitionistic, and minimal logic. I then provide translations for classical S4 proofs.

     

Around the nation’s mystic core: interactions between political concepts and the literary imagination in the works of Stanisław Brzozowski

The essay examines Stanisław Brzozowski’s ideas on mutual interactions between the sphere of culture and the realm of the political. It shows how Brzozowski made use of literary texts in order to elucidate social and political processes. In doing so, he insisted on a specific form of knowledge accessible through texts of literature and literary criticism, which are not limited by the mere “logic of notions.” Following Vico and Sorel Brzozowski detected an “irrational core” at the bases of human collectivities such as above all modern nations, and it is through literature that this core can be revealed. Brzozowski’s understanding of political ideas and concepts is informed—to a decisive degree—by the literary imagination. This can be shown by a semantic and rhetorical analysis of some of his later writings.     

Axiomatizing Jaśkowski’s Discussive Logic $$\mathbf {D_2}$$

We outline the rather complicated history of attempts at axiomatizing Ja?kowski’s discussive logic \(\mathbf {D_2}\) and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing \(\mathbf {D_2}\) in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of \(\mathbf {D_2}\) in the language Ja?kowski suggested in his second paper on discussive logic, by following a remark of da Costa and Dubikajtis. We also deal with an interesting variant of \(\mathbf {D_2}\), introduced by Ciuciura, in which negation is also taken to be discussive.     

Embedding the elementary ontology of stanisław Leśniewski into the monadic second-order calculus of predicates

LetEO be the elementary ontology of Le?niewski formalized as in Iwanu? [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function ?, defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that ? _EO A iff ? _LS ?(A) for each formulaA.     

On Jaśkowski's discussive logics

We expose the main ideas, concepts and results about Jakowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.Partially supported by grants from JNICT (Portugal) and FAPESP (Brazil), Philosophy Section. Portions of this paper were concluded while the second author visited the Math-Phys Seminar at the University of Algarve (Portugal).Presented byCecylia Rauszer     

On the logic of event-causation Jaśkowski-style systems of causal logic

Causality is a concept which is sometimes claimed to be easy to illustrate, but hard to explain. It is not quite clear whether the former part of this claim is as obvious as the latter one. I will not present any specific theory of causation. Our aim is much less ambitious; to investigate the formal counterparts of causal relations between events, i.e. to propose a formal framework which enables us to construct metamathematical counterparts of causal relations between singular events. This should be a good starting point to define formal counterparts for concepts like causal law, causal explanation and so on.Children in their simplicity keep asking why. The person of understanding has given this up; every why, he has long found out, is merely the end of a thread that vanishes into the thick snare of infinity, which no one can truly unravel, let him tug and worry at it as much as he likes.W. Busch,The Butterfly, translated by W. ArndtThe work on this paper was supported by grants from the Humboldt-Foundation, the Center for Philosophy of Science at the University of Pittsburgh and from the Fulbright-Foundation.This paper concerns a larger project on causal logic, Uwe Scheffler from Humboldt-University and I have been working on for several months. This collaboration explains the usage of plural forms wherever they occur in section 1 and 6. However, all results of this paper, if not stated explicitely otherwise, are due to its (single) author.Presented byJan Zygmunt;     

A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D<Subscript>2</Subscript>

Ja?kowski’s discussive logic D₂ was formulated with the help of the modal logic S5 as follows (see [7, 8]): \({A \in {D_{2}}}\) iff \({\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}\), where (–)^? is a translation of discussive formulae from For^d into the modal language. We say that a modal logic L defines D₂ iff \({{\rm D}_{2} = \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}\). In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (?): have the same theses beginning with ‘\({\diamond}\)’ as S5. Of course, all logics fulfilling the above condition, define D₂. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D₂ is equivalent to having the property (?). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (?). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D₂.     

Another conversion. Stanisław Brzozowski’s ‘diary’ as an early instance of the post-secular turn to religion

This essay is an attempt to analyze an important decision Brzozowski took at the end of his life, i.e. his late turn towards Catholicism, which, despite his own objections, we should nonetheless call a religious conversion. The main reason why Brzozowski resisted the traditional rhetoric of conversion lies in his often repeated conviction that faith cannot invalidate life, because “what is not biographical, does not exist at all.” Brzozowski, therefore, rejects conversion understood as a radical and abrupt revolution of the soul, which annuls everything that happened before, and turns to a model of religiosity (“Catholicism, undoubtedly”) which preserves his entire biographical past. In this manner, Brzozowski seeks his own formula of faith, more adequate to the “situation” of the modern man who lives in and through History. I argue that the model of “conversion without conversion” Brzozowski chose as representative of modern man is typically, though avant la lettre, post-secular: closer to the Jewish sources of past-oriented tschuva than to the mystical timelessness of traditionally Christian metanoia. The idea that redemption consists not in a liberation of a pure spirit but in a patient working-through of the universal history of creation is an implicit credo of the whole modern age, first fully articulated by Brzozowski and only later in the writings of Hermann Cohen, Franz Rosenzweig, and Walter Benjamin. Brzozowski emerges as a relatively early precursor of the future post-secular option whose advocates, like the author of The Diary, will not allow themselves to “lose a single moment,” either of their lives or the world’s history.     

Sur la syllogistique déontique de Zdzisław Ziemba

Sans résuméAllatum est die 12 Octobris 1970