This volume explores the range of Alfred North Whitehead's philosophy and his relevance to contemporary philosophical traditions.

This book offers a bold and controversial new thesis regarding the nature of prejudice. The authors' central claim is that prejudice is not simply learned, rather it is predisposed in all human beings and is thus the foundation for ethical valuation. They aim to destroy the illusion that prejudice is merely the result of learned beliefs, socially conditioned attitudes, or pathological states of development. Contrary to traditional accounts, prejudice itself is not a negative attribute of human nature, rather it is (...) the necessary precondition for the self and civilization to emerge. Defined as the preferential self-expression of valuation, prejudice gives rise to greater existential complexities and novelties that elevate selfhood and society to higher states of ethical realization. Rather than offer another contribution that highlights the destructive nature of prejudice, Mills and Polanowski address the ontological, psychological, and dialectical origins of prejudice as it manifests itself in the process of selfhood and culture. They provide an original conceptualization of the phenomenology of prejudice and its dialectical instantiation in the ontology of the individual, worldhood, and the very structures of subjectivity. As a unique synthesis of psychoanalysis, Hegelian idealism, Heideggerian existential ontology, and Whiteheadian process philosophy, prejudice is the indispensable ground for humanity to actualize its highest potentiality-for-Being. The striking result is (1) a revolutionary theory of human nature, (2) a new ethical system, and (3) the elevation of dialectical ethics to the domain of metaphysics. (shrink)

Agresja putinowskiej Rosji na Ukrainę postawiła wobec dramatycznego wyzwania nobliwą doktrynę non‑violence. Zgodnie ze sformułowanym w latach 80. XX wieku wywodem antysowieckiego dysydenta rosyjskiego Władimira Bukowskiego to nie wojna jest przeciwieństwem pokoju, lecz przemoc, a do jej powstrzymania niekiedy konieczny jest zbrojny opór, czyli prowadzenie wojny. Według Clausewitza do wywołania stanu wojny nie wystarczy militarna agresja, lecz konieczne jest przeciwstawienie się jej, czyli aktywna obrona ze strony napadniętego, chcąc zatem uniknąć wojny, nie należy stawiać oporu agresorowi. Agresja na Ukrainę złamała (...) dwie zasady prowadzenia wojen: ius ad bellum i ius in bello. Według typologii Michaela Walzera jest to zatem niesprawiedliwa wojna prowadzona niesprawiedliwymi metodami, więc przeciwstawianie się jej, także militarne, jest prowadzeniem wojny sprawiedliwej. Zgodnie z analizą Slavoja Žižka tworzy to klarowną z etycznego punktu widzenia sytuację, zło jest łatwo identyfikowalne, a przeciwstawienie się mu stanowi etyczny obowiązek. Według filozofa Étienne’a Balibara w tej sytuacji pacyfizm nie jest żadną opcją. Helplessness as Acquiescence to Evil The aggression of Putin’s Russia towards Ukraine has posed a dramatic challenge to the noble doctrine of non-violence. In line with an argument made in the 1980s by anti-Soviet Russian dissident Vladimir Bukovsky, war is not the opposite of peace; instead, violence is. Armed resistance, or warfare, is sometimes necessary to stop violence. According to Clausewitz, military aggression is insufficient to evoke a state of war; in its place, it is necessary to oppose aggression, i.e., actively mount a defense by the attacked party, thereby avoiding war requires not resisting the aggressor. However, the aggression against Ukraine broke two tenets of warfare: ius ad bellum and ius in bello. According to Michael Walzer’s typology, it is an unjust war waged by unjust methods, so resisting it, including militarily, amounts to waging a just war. According to Slavoj Žižek’s analysis, this establishes an ethically clear situation: evil is easily identifiable, and opposing it is an ethical duty. According to the philosopher Étienne Balibar, pacifism is not an option in such a situation. (shrink)

Liberalism and political polarization: The customary classification of the ideological doctri‑ nes in democratic systems, which expanded along a left–right axis, is nowadays obsolescent and has been deconstructed. At the same time, the close and strong connection between de‑ mocracy and liberalism, on which the primary model of liberal democracy was established, has been broken in many places of the world. The emerging of illiberal democracies has made the liberal component the main criterion for the classification of contemporary political systems, (...) instead of dividing them into democratic and nondemocratic systems as before. Numerous ideological options could also be classified as being contrary to the liberal one. Liberalism has thus become important in the typologies and analyses of contemporary political systems and ideological options as the opposite to those systems on many new axes. (shrink)

The article explores the concept of infodemics during the COVID-19 pandemic, focusing on the propagation of false or inaccurate information proliferating worldwide throughout the SARS-CoV-2 health crisis. We provide an overview of disinformation, misinformation and malinformation and discuss the notion of “fake news”, and highlight the threats these phenomena bear for health policies and national and international security. We discuss the mis-/disinformation as a significant challenge to the public health, intelligence, and policymaking communities and highlight the necessity to design measures (...) enabling the prevention, interdiction, and mitigation of such threats. We then present an overview of selected opportunities for applying technology to study and combat disinformation, outlining several approaches currently being used to understand, describe, and model the phenomena of misinformation and disinformation. We focus specifically on complex networks, machine learning, data- and text-mining methods in misinformation detection, sentiment analysis, and agent-based models of misinformation spreading and the detection of misinformation sources in the network. We conclude with the set of recommendations supporting the World Health Organization’s initiative on infodemiology. We support the implementation of integrated preventive procedures and internationalization of infodemic management. We also endorse the application of the cross-disciplinary methodology of Crime Science discipline, supplemented by Big Data analysis and related information technologies to prevent, disrupt, and detect mis- and disinformation efficiently. (shrink)

The initial segment of the latest volume of the _Ignatian Philosophical Yearbook _is centered on the discourse surrounding the presence of cultural heritage in the cyber domain. It explores the dissemination of this heritage by cultural institutions such as museums, libraries, and archives, as well as initiatives undertaken by Internet users. The authors scrutinize a comprehensive array of topics concerning the digital presentation of cultural artifacts, employing carefully selected examples in their discourse.

Psychological research is based on philosophical assumptions which are not always explicitly formulated. On the other hand, the results of these investigations affect philosophical thinking and the conception of human nature. For a long time it was a ruling conception in psychology that the essence of human nature consists in the existence of driving mechanisms with homeostatic properties drives or needs – which, principally, are inborn mechanisms modified by learning. The analysis of driving mechanisms founded on psychological and neuro-physiological data, (...) brought about a modification of this traditional view. Starting from the concept of need as an objective phenomenon it can be stated that the higher organisms have a special mechanisms securing the satisfaction of needs. They are drives. These mechanisms do not exist in a ready form in man but only potentially, as an ability to organize a functional unit in result of certain experience. The formation of drives includes: making connections between certain internal stimuli and some forms of activity reducing these stimuli; learning how to find things which are necessary to reduce them; and, finally, the acquisition of the ability to give verbal labels to the occurring processes. In consequence, the final form of a drive is determined by biological and social factors as well as by individual experiences. (shrink)

This study investigates performance of portfolios composed of British socially responsible investments (SRI) stocks. Using the ‘Global-100 Most Sustainable Corporations in the World’ list (known also as ‘Global-100’) to select the SRI companies, we found that, in the period 2000–2010, the returns of the SRI portfolios were on average higher compared with the corresponding returns of the market indexes. The annual average difference in returns of the SRI portfolios (with dividends) was 5.26 % and 5.69 % relative to the FTSE100 (...) and FTSE4GOOD indexes (the total return versions), respectively, but the differences in returns in the whole period, in individual years and in other sub-periods were in most cases not statistically significant. Positive performance of SRI stocks in the whole sample is, however, evidenced by risk-adjusted measures such as the modified Sharpe ratio (MSR) and certainty equivalent (CEQ) returns, as well as by incorporating various levels of transaction costs. Furthermore, a simple trading strategy relying on selection of SRI stocks from the Global-100 list would beat the market indexes in the whole period 2000–2010, even after inclusion of various levels of transaction costs. We also estimated the Fama–French and Carhart multi-factor models and found that the returns of the SRI portfolios cannot be consistently explained by conventional factors other than the market factor. (shrink)

In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB1, is an extension of systems PI, C min and B1, and a proper subsystem of Sette’s calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi.

Although it became customary to warn against confusing postmodernism with deconstructionism, it seems plausible to suggest that their central agendas are not dissimilar. Moreover, from the philosophical point of view, it is the idea of the 'deconstruction of meaning' that can be said to constitute the foundation of postmodernism understood here as an intellectual movement. It is true that grounded in the poststructuralist language analysis, deconstructionism seeks primarily to challenge the attempts inherent in the Western philosophical tradition to establish ultimate (...) meaning in a text. However, as one might have anticipated, the deconstruction of meaning of texts provided a basis for a large scale project leading to deconstruction of all 'truths', as conceived in the mainstream philosophical tradition. And it did it by questioning the coherence of the very concept of 'truth'. Eclectic as postmodernism is, it can be recognized by the fundamental assumption that there is no common denominator that guarantees the one-ness of the world, or the possibility of objective or neutral thought. This assumption would suffice to make one expect that postmodernism will challenge the very foundations of any metaphysical or religious system of beliefs. And so it does. In this paper I would like to ellucidate just one way this challange may be construed, poiting to the example of Don Cupitt, the leading exponent of the 'antirealist' critique of the discourse of theism. (shrink)

Although it became customary to warn against confusing postmodernism with deconstructionism, it seems plausible to suggest that their central agendas are not dissimilar. Moreover, from the philosophical point of view, it is the idea of the 'deconstruction of meaning' that can be said to constitute the foundation of postmodernism understood here as an intellectual movement. It is true that grounded in the poststructuralist language analysis, deconstructionism seeks primarily to challenge the attempts inherent in the Western philosophical tradition to establish ultimate (...) meaning in a text. However, as one might have anticipated, the deconstruction of meaning of texts provided a basis for a large scale project leading to deconstruction of all 'truths', as conceived in the mainstream philosophical tradition. And it did it by questioning the coherence of the very concept of 'truth'. Eclectic as postmodernism is, it can be recognized by the fundamental assumption that there is no common denominator that guarantees the one-ness of the world, or the possibility of objective or neutral thought. This assumption would suffice to make one expect that postmodernism will challenge the very foundations of any metaphysical or religious system of beliefs. And so it does. In this paper I would like to ellucidate just one way this challange may be construed, poiting to the example of Don Cupitt, the leading exponent of the 'antirealist' critique of the discourse of theism. (shrink)

The paper is a response to recent criticisms of agatheism, a new pluralistic interpretation of religious belief put forward by Janusz Salamon with the aim of accommodating the epistemological challenge of religious diversity. Agatheism is an axiologically grounded religious belief which identifies God, the Absolute or the ultimate reality religiously conceived with the ultimate good as the ultimate end of all human agency and thus an explanation of its irreducibly teleological character and a source of its meaning. Janusz (...) Salamon argues that this grounding of religious belief in the human axiological consciousness makes it immune to falsification by any future science. Replying to the concerns of the critics about about irrationality of doxastic commitment to a particular religious tradition, Janusz Salamon argues that to the extent the fundamental agatheistic religious belief is presupposed in such tradition as its doxastic core, its belief system - if internally coherent and aligned with a worldview that is consistent with undisputed scientific findings - may be considered rational, despite there being a plurality of such belief systems. (shrink)

We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable unions of (...) continuous functions with domains of type Πn0, for a fixed n<ω. For Baire class 1 functions, this generalizes analogous characterizations proved by Jayne and Rogers for n=1 and Semmes for n=2. (shrink)

The aim of the article is to present the attempts of establishing institutions of a system of worker’s self-management in the selected countries of the so-called real socialism system in Eastern Europe. The analysis considers three of those countries, namely Yugoslavia, Poland and Hungary, whose experiences in participation of the employees’ implementation were the most significant. Particular attention was paid to the evolution of socialist regimes approach to workers’ self-management. The paper tries to answer the question whether workers’ self-management posed (...) a threat to the socialist regimes persistence. The research method used in the study is an indepth survey and analysis of literature and legal acts. (shrink)

The aim of this paper is show a global strategy for defining and connecting logical criteria. Three partial criteria are distinguished: transparency for expressions, topic neutrality for consequence relation, and universality for theories. A global criterion is suggested, and proved to be fulfilled by classical and intuionistic logic.

An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

Once regarded as cellular ‘debris’ extracellular vesicles (EVs) emerge as one of the most intriguing entities in cancer pathogenesis. Intercellular trafficking of EVs challenges the notion of cancer cell autonomy, and highlights the multicellular nature of such fundamental processes as stem cell niche formation, tumour stroma generation, angiogenesis, inflammation or immunity. Recent studies reveal that intercellular exchange mediated by EVs runs deeper than expected, and includes molecules causative for cancer progression, such as oncogenes (epidermal growth factor receptor, Ras), and tumour (...) suppressors (PTEN). The uptake of oncogenic EVs (oncosomes) by various cells may profoundly change their biology, signalling patterns and gene expression, and in some cases cause their overt tumorigenic conversion. Moreover, EVs circulating in blood and present in body fluids provide an unprecedented access to the molecular circuitry driving cancer cells, and new technologies are being developed to exploit this property as a source of unique cancer biomarkers. (shrink)

In the late forties, Stanisław Jaśkowski published two papers onthe discursive sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The knownaxiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however,that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D∗2 for short, that differs from (...) D2 inmany respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness andcompleteness theorems. Additionally, we present labelled tableaux for D∗2.1. (shrink)

Does the alleged religious experience of a mystic constitute a reliable source of knowledge about the object of his or her experience? Or does it rationally justify a move from such experience to meaningful beliefs about God or the Absolute which is supposed to be the object of that experience? And are religious beliefs in need of being grounded in religious experience in order to be rationally justified? Although it seems pretty obvious that a great many adherents of all religions (...) find reasons for their beliefs in their religious traditions rather than in their personal religious experiences, one could note that usually these traditions present religious experiences of their founder figures as constituting evidence for their authenticity and truthfulness ; the supposed mystical experiences of some adherents of a given religious tradition are often treated by their co-believers as an important evidence which increases credibility of their own religious convictions. (shrink)

Does the alleged religious experience of a mystic constitute a reliable source of knowledge about the object of his or her experience? Or does it rationally justify a move from such experience to meaningful beliefs about God or the Absolute which is supposed to be the object of that experience? And are religious beliefs in need of being grounded in religious experience in order to be rationally justified? Although it seems pretty obvious that a great many adherents of all religions (...) find reasons for their beliefs in their religious traditions rather than in their personal religious experiences, one could note that usually these traditions present religious experiences of their founder figures as constituting evidence for their authenticity and truthfulness ; the supposed mystical experiences of some adherents of a given religious tradition are often treated by their co-believers as an important evidence which increases credibility of their own religious convictions. (shrink)

The article discusses the philosophical problems associated with the dualistic conception of the person dominant in traditions influenced by Platonism. The key suggestion made in the article is that opting for an embodied rather than a disembodied posthumous existence for the human person will in no way hinder the theistic philosopher when it comes to arguing that God exists in a disembodied form.

W maju 1998 roku odbyła się w Monachium międzynarodowa konferencja poświęcona zagadnieniu racjonalności teizmu. Temat to szeroko dyskutowany w ostatnich czasach, stąd wydawać by się mogło, że zorganizowanie jeszcze jednej sesji, która przyciągnęłaby uwagę środowiska filozofów religii, będzie przedsięwzięciem wyjątkowo trudnym. Tymczasem monachijska debata zasłużyła sobie na miano wydarzenia. O jej atrakcyjności zadecydował fakt, że została pomyślana jako próba ożywienia dialogu pomiędzy filozofami nawiązującymi do tradycji kontynentalnej z przedstawicielami filozofii analitycznej. Tego rodzaju ekumeniczne inicjatywy nalezą w tej dziedzinie do rzadkości. (...) Ten swoisty izolacjonizm ma wiele przyczyn, a kością niezgody jest między innymi stosunek do Kanta. Postkantowska kontynentalna filozofia religii, kładąca nacisk na epistemologię i fenomenologię doświadczenia religijnego, postrzega anglosaski renesans badań nad klasycznymi problemami teodycealnymi jako nawrót do przedkrytycznego dogmatyzmu. Z kolei niektórzy analityczni filozofowie religii zdają się uprawiać swą dyscyplinę w taki sposób, jak gdyby kopernikański przewrót Kanta uważali za niebyły, a czasem nazywają expressis verbis epoką nowożytną okresem błędów i wypaczeń. Epistemologiczne zagadnienie racjonalności religii należy do kręgu zainteresowań obydwu wymienionych tradycji, stad możliwe jest tu połączenie wysiłków w celu uporządkowania tematyki i oceny aktualnego stanu refleksji. (shrink)

Does the alleged religious experience of a mystic constitute a reliable source of knowledge about the object of his or her experience? Or does it rationally justify a move from such experience to meaningful beliefs about God or the Absolute which is supposed to be the object of that experience? And are religious beliefs in need of being grounded in religious experience in order to be rationally justified? Although it seems pretty obvious that a great many adherents of all religions (...) find reasons for their beliefs in their religious traditions rather than in their personal religious experiences, one could note that usually these traditions present religious experiences of their founder figures as constituting evidence for their authenticity and truthfulness ; the supposed mystical experiences of some adherents of a given religious tradition are often treated by their co-believers as an important evidence which increases credibility of their own religious convictions. (shrink)

The philosophical challenge that religious diversity poses for religious belief has become in recent years the focal point of a very engaging theological and philosophical debate. The debate began in the Christian context and it would be fair to say that its main issue remains the relationship of Christianity to other major religions. Traditionally Christian thinkers faced with the fact of religious plurality have assumed that Christianity is the only way to salvation, and the truth-claims of other religions can be (...) refuted by way of argument. This position is described today as 'exclusivist'. John Hick's name has become synonymous with a radically different approach to the whole issue. Hick argues that all religious traditions make contact with the same Ultimate Reality, each encountering it through a variety of culturally shaped forms of thought and experience, but all offering equally effective paths to 'salvation/liberation'. Hick's pluralistic hypothesis, although very popular in some quarters, appears to many Christian and non-Christian thinkers as highly controversial. (shrink)

The philosophical challenge that religious diversity poses for religious belief has become in recent years the focal point of a very engaging theological and philosophical debate. The debate began in the Christian context and it would be fair to say that its main issue remains the relationship of Christianity to other major religions. Traditionally Christian thinkers faced with the fact of religious plurality have assumed that Christianity is the only way to salvation, and the truth-claims of other religions can be (...) refuted by way of argument. This position is described today as 'exclusivist'. John Hick's name has become synonymous with a radically different approach to the whole issue. Hick argues that all religious traditions make contact with the same Ultimate Reality, each encountering it through a variety of culturally shaped forms of thought and experience, but all offering equally effective paths to 'salvation/liberation'. Hick's pluralistic hypothesis, although very popular in some quarters, appears to many Christian and non-Christian thinkers as highly controversial. (shrink)

An individual-based approach is used to describe population dynamics. Two kinds of models have been constructed with different distributions illustrating individual variability. In both models, the growth rate of an individual and its final body weight at the end of the growth period, which determines the number of offspring, are functions of the amount of resources assimilated by an individual. In the model with a symmetric distribution, the half saturation constant in the Michaelis–Menten function describing the relationship between the growth (...) of individuals and the amount of resources has a normal distribution. In the model with an asymmetric distribution, resources are not equally partitioned among individuals. The individual who acquired more resources in the past, will acquire more resources in the future. A single population comprising identical individuals has a very short extinction time. If individuals differ in the amount of food assimilated, this time significantly increases irrespectively of the type of model describing population dynamics. Individuals of two populations of competing species use common resources. For larger differences in individual variability, the more variable species will have a longer extinction time and will exclude less variable species. Both populations can also coexist when their variabilities are equal or even when they are slightly different, in the latter case under the condition of high variability of both species. These conclusions have a deterministic nature in the case of the model with the asymmetric distribution—repeated simulations give the same results. In the case of the model with the symmetric distribution, these conclusions are of a statistical nature—if we repeat the simulation many times, then the more variable species will have a longer extinction time more frequently, but some results will happen when the less variable species has a longer extinction time. Additionally, in the model with the asymmetric distribution, the result of competition will depend on the way of the introduction of variability into the model. If the higher variability is due to an increase in the proportion of individuals with a low assimilation of resources, it can produce a longer extinction time of the less variable species. (shrink)

Sociology has been often defined as a science of "social relations". The aim of this article is to contribute to the clarification of this concept. I take into account only two classic analytical sociologies — those developed by Max Weber and by Florian Znaniecki. These sociologies seem to me only partly useful for the analysis of macroscale (ethnic, racial, industrial, and international) problems. They refer to human individual interactions within social collectivities, and not between them. If we follow expressis verbis (...) the individualistic aspects of Weber's model and the analytical aspects of Znaniecki's theory, it would be difficult to base empirical investigations of social relations. The situation changes when we depart from the classics' ways of construction of the concepts of social relation and concentrate on the implication of the concept presented by the same authors. Fortunately, the research practices of both scholars encourage us to abandon a literal interpretation of their models. They present a variety of interesting typologies of social relations and social objects between which these relations can exist. (shrink)

This article argues that the existence of horrendous evil calls into question not just the plausibility of the most popular theodicies on offer, notably sceptical theism, but the coherence of any agatheology–that is, any theology which identifies God or the ultimate reality with the ultimate good or with a maximally good being. The article contends that the only way an agatheologian can ‘save the face of God’ after Auschwitz and Kolyma is by endorsing a non-interventionist interpretation of the Divine providence (...) which will amount to naturalisation of the discourse on evil by localising entirely in nature the causes of evil and the possible ways of its prevention. ‘Theodicy of justice as fairness’ is then presented as consistent with such naturalistic account of evils and yet compatible with a religious worldview. It justifies the Divine non-intervention by suggesting that it would not be just or fair for God to intervene on only some occasions to avert evil, if God is apparently prevented from intervening in all such cases. Since for Agatheos it is metaphysically impossible to do what is unjust or unfair, God never intervenes to avert evil. (shrink)

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

From a very young age till the last days of his life, Stanisław Staszic was occupied by the question of the relationship between God and Nature. In particular, the Polish thinker was interested in the vision of the world in which human life and Nature were seen in unison, in accordance with laws of reason and the outcomes of scientific investigations. His deliberations on Nature validated his monistic worldview, encompassed within a deistic general framework. Staszic pointed out many times that (...) natural order is the creation of God, however, earthly issues are in the hands of humans. In the last years of his life he withdrew from God. He did not accept the Church’s hierarchy, while his approach to the Creator was ambivalent. (shrink)

W tym artykule zaproponuję konstrukcję trójwartościowej logiki przekonań, którą nazywam: LSB3_1. Podam również i udowodnię kompletność LSB3_1 w odniesieniu do danej semantyki. LSB3_1 opiera się na preformalnych założeniach i intuicjach, które przedstawiono w sekcji 1. Sekcja 2 zawiera składnię i podział instrukcji LSB3_1 na wewnętrzne i zewnętrzne. Rozdział 3 przedstawia semantykę LSB3_1, a także szereg tautologii i formuł nietautologicznych w LSB3_1 wraz z ich intuicyjną interpretacją. System aksjomatyczny dla LSB3_1 i jego porównanie z silną logiką Kleene'a są przedstawione w sekcji (...) 4. Twierdzenie o kompletności dla LSB3_1 jest przedstawione w rozdziale 5. Zdefiniuję termin koniunkcyjna forma normalna i przedstawię lematy, które prowadzą do udowodnienia redukcji języka LSB3_1 wzory przed udowodnieniem twierdzenia o zupełności. (shrink)