I analyse three most interesting and extensive approaches to theoretical models: classical ones—proposed by Peter Achinstein and Michael Redhead, and the rela-tively rareanalysed approach of Ryszard Wójcicki, belonging to a later phase of his research where he gave up applyingthe conceptual apparatus of logical semantics. I take into consideration the approaches to theoretical models in which they are qualified as models representing the reality. That is why I omit Max Black’s and Mary Hesse’s concepts of such models, as (...) those two concepts belong to the analogue model group if we consider the main function of the model of a given class as its classification criterion. My main focus is on theoretical models with representative functions as these very models and, in a broader context, the question of representation. (shrink)

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there are at least two (...) approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)

My paper refers to Leszek Kołakowski’s Main Currents of Marxism: Its Origin, Growth, and Dissolution (Oxford: Clarendon Press 1987). Kołakowski’s intention was to write a textbook on the history of Marxism based on his lectures but his book is much more than that. It is a philosophical treatise in which Marx’s doctrine of mankind and the program of its liberation are critically analysed and reinterpreted. The core of Marx’s philosophy is the idea of man and the belief that the real (...) existence of humans is not identical with their essence. Kołakowski shows that this belief is rooted in mythological thinking, the Platonic tradition, and in the Christian thought. A moral that follows from Kołakowski’s critical analysis of Marx’s doctrine is that man has never lived in a paradise and yet he perceives himself as banished thereof; that he will never enter a paradise and yet he cannot live without the faith that this is somehow possible. Therefore, what he should do is to have a minimum of common sense and skepticism related to it, for they would protect him against the traps laid by false prophets repeatedly asserting that they know the means to construct the paradise today or at least tomorrow. (shrink)

Divus Augustus Pater. The cult of divine Augustus under the rule of the Julio-Claudian dynasty -/- Summary The cult of divine Augustus was one of the most important phenomena of ideological nature under the rule of the Julio-Claudian dynasty. The crucial point of its development was the apotheosis conducted on 17 September 14 AD. The new cult was derived greatly from numerous borrowings from the rites of various gods of the Roman Pantheon. As divus, Augustus received a separate priest, a (...) private priestess, and a college of priests. The first flamen Augustalis became Germanicus. The holder of this title enjoyed many privileges. It seems unlikely, however, that flamen Augustalis controlled the entire cult of divine Augustus. This was the role of the emperor as both the supreme priest and the inheritor of political power. Sodales Augustales also had special cult functions. This religious fraternity had a mixed private-state character just like many of the institutions of the early principate. It was a cult college of gens Iulia and, most of all, of Augustus. From its beginning it enjoyed high prestige. The members of this religious fraternity were recruited among the Senate elite and the family of the emperor. Sacerdos divi Augusti occupies a different place in the priesthood established to worship Augustus. This female priesthood, despite its humble cult and political role, is of great interest to scholars. In spite of discerning investigations by researchers, there seem to have been only two priestesses in the Julio-Claudian dynasty – Julia Augusta, the widow of the creator of the principate, and Antonia Augusta. There is even no certainty that the latter had preformed the function at all. Augustus, as a god, was given a separate temple under a Senate decree. However, the construction work went slowly ahead. Therefore, divus Augustus was initially worshipped in other places of worship. At first, it was the temple of Mars Ultor. He was also worshipped in the sacrarium on the Palatine. One encounters certain difficulties when trying to identify the places of Augustus’ worship in Rome. Ultimately, there seem to have been two sacraria in the capital of the Empire. There is no certainty, however, whether yet another temple was located next to the templum novum divi Augusti on the Palatine. In trying to analyse the phenomenon of the divinity of the Roman emperors, and Augustus in particular, it is necessary to refer to the genesis of Emperor worship. Within the framework of official religion it is important to distinguish such elements as genius and numen. Although the consecratio act conducted by the Senate meant the crossing of the boundary between the human Augustus and the divine Augustus, it is important to remember that Augustus had prepared his apotheosis for a long time and already enjoyed divine honours during his lifetime. Certain elements of Augustus worship developed under his rule continued to exist for some time after the death of the creator of the principate. Augustus divinity was guarded by the law of maiestas. At the beginning of the rule of Tiberius it mostly protected divus Augustus himself. Gradually, despite some opposition, the law began to serve the ruling emperor. There is little certainty of how many cases were brought under the crimen laesae maiestatis against those who insulted the divine Augustus. The issue of trials for offending the law of maiestas is accounted for one-sidedly by ancient historians, which complicates the work of contemporary researchers. There is, however, no denying that for Tiberius (Augustus’ successor) the trials on the charge of maiestas turned out to be a trap. The cult of divus Augustus was approved throughout the Empire. Nevertheless, some weaker voices of opposition could be heard. These were present in the Senate circles cherishing the memory of the last defenders of the Republic, as well as among some ethnic and religious communities. The latter included Judaism and emerging Christianity. The political consequences of Augustus’ deification were very serious. He significantly contributed to the ruling of the Julio-Claudian dynasty for over 50 years. The main reason for that was the fact that in the Rome of that time the tradition of power succession was not yet well-grounded. Directly after the principate creator’s death, his consecratio took place – he was assigned priests and many godly honours and a temple was erected in his honour. These actions obviously took place under Augustus’ successor Tiberius who, during his rule, constantly tried to emulate the divine predecessor and referred to his decrees on numerous occasions. Tiberius was the emperor who contributed to the cult of his adoptive father to the greatest extent. However, one cannot fail to notice that his actions were somehow ambiguous. It has to be remembered that, in addition to his sincere respect for the divine Augustus, Tiberius also tried to use the authority of the creator of the principate to strengthen his power. This is exemplified by the motto imprinted on coins: DIVVS AVGVSTVS PATER. Caligula took a different approach to the Augustan cult. When assuming power after Tiberius, he was in a different position. The 20-year rule by Augustus’ successor greatly contributed to the strengthening of the idea of the principate ’s stability in the minds of the Romans. This allowed Caligula to pay less heed to the Senate aristocracy, as well as other institutional elements of the Republic. Under these circumstances, the cult of Augustus underwent modifications. Divus Augustus still remained at the heart of the religious propaganda of the Roman state and gens Iulia, but also other members of the family of the young Emperor received a number of honours drawing them closer to the world of gods. Drusilla, for that matter, was made a diva. By this, the idea of domus Augusta received a new confirmation. Caligula himself did not cease to participate in, and support, the rites performed to worship his divine grandfather. The available sources lead us to believe that Augustus constituted for the young princeps a role model and a character to which he often compared himself with. For Claudius, the use of the cult of divine Augustus was important as a tool to strengthen political power. But due to the fact that his personal links with divus Augustus were rather weak, Claudius focused on the cult of his grandmother Livia, Augustus’ wife. He also emphasised the function of sacerdos divi Augusti which his mother Antonia Augusta was to fulfil. Claudius faced the task of the ‘reconstruction’ of the cult of Augustus which had deteriorated, especially during the second part of Caligula’s rule. Claudius took a different direction in imitating Augustus than his two predecessors. Augustus’ model was very capacious, allowing him to find examples which could be adjusted to fit his own political goals and personality. Claudius avoided the stiffness characteristic of Tiberius and, at the same time, respected Augustus’ traditions which he Caligula inadvertently abused. Claudius’ attitude to Augustus is not quite clear. Undoubtedly he kept alive the memory of the first princeps, however, there is a lack of testimony about the new honours conferred on divine Augustus during the rule of this Emperor. Almost all of them concentrate around the person of Claudius or his family. There are, however, no honours conferred on the creator of the principate. This type of attitude caused the cult of divine Augustus to be eclipsed by the cult of the ruling Emperor. Nero, the last representative of the Julio-Claudian dynasty descended, unlike Claudius, directly from the line of Augustus. The new emperor deified his predecessor by using the model of Augustus’ apotheosis. In the first part of his rule he drew greatly from the Augustus model of exercising power. Nero ’s ideological platform seems to be the richest in comparison with other emperors of the Julio-Claudian dynasty. The tradition of links with divus Augustus was, however, only one of many different elements. With time, the tradition appeared to play a still smaller role. The departure from the Augustus model took place on many levels. Some of the steps were very radical, whereas others were less significant. The most serious was the elimination of the members of gens Iulia and gens Claudia, and those who could prove their kinship with both the houses. The devastation in Nero ’s closest family put an end to the concept of domus Augusta. Formally, the Emperor did not renounce the divine creator of the principate but, in practice, the idea of the new domus Augusta no longer aimed at presenting Augustus’ descendants united in a single family. Nero was now alone and any creation of ideological concepts of power under those circumstances had to be based around him. These actions ended in disaster. By giving up the Augustan model, Nero lost the support of the army and, as a result, lost power. Apart from the worship of the state religion in the capital, divus Augustus was the subject of a provincial and municipal cult. Here, the worship of divine Augustus was often a continuation, sometimes in an extended form, of the honours Augustus had been granted during his lifetime. In the cult of divus Augustus, in the provinces one can observe a mutual interweaving of elements copied from the capital model and local traditions. The beginning of the provincial cult of Augustus dates back to the rule of Tiberius. The crucial point for the establishment of the provincial cult in the West was the request of the citizens of Hispania Tarraconensis to build a temple for divine Augustus. It is important to emphasise here that he was appointed on a local initiative. In the East, the genesis of the provincial cult is related to the functioning of koinon. In comparison with the western regions, the cult here was characterised not only by longer history but also an extensive system of priesthood and rich ritual. The intensity of development of municipal and private cult in the West depended on the level of social and economic development of the regions. It assumed the most complex forms in the provinces with well-developed city life – generally in the eastern provinces. Whereas the cult of divine Augustus in the western municipal provinces was similar in character to the cult of the principate’s creator in Italy. The greatest testimony to the cult’s development comes from relatively strongly romanised and, at the same time, the wealthiest regions which had been part of the Empire for a long time. These included the mainly proconsular Africa, Spain and Narbonese Gaul. The sources coming from these regions constitute not only an illustration of the development of the cult of divine Augustus and members of domus Augusta, but are also a sign of the processes of romanisation of great numbers of city populations. It is necessary to note that outside Rome we do not encounter an isolated cult of divine Augustus. Whenever we deal with information concerning temples or rituals dedicated to the deified creator of the principate, other members of the family are also worshipped. In fact, during the whole rule of the Julio-Claudian dynasty we actually deal with the cult of divine Augustus in close association with the worship of domus Augusta – domus divina. (shrink)

Author: Mordarski Ryszard Title: THE LAST ESOTERIC THINKER. LEO STRAUSS’S REMARKS ON THE ESOTERIC CHARACTER OF GOTTHOLD EPHRAIM LESSING’S WORKS (Ostatni ezoterysta. Uwagi Lea Straussa o ezoterycznym charakterze twórczości Gottholda Ephraima Lessinga) Source: Filo-Sofija year: 2006, vol:.6, number: 2006/1, pages: 135-152 Keywords: LEO STRAUSS, LESSING, ESOTERIC CHARACTER, MAIMONIDES Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:According to Leo Strauss, the great thinkers of the political philosophy from Plato, through al-Farabi and Maimonides, (...) to Hobbes, Locke, and J.J. Rousseau distinguished between exoteric, or public, writing and esoteric, or private, writing. The last thinker who was well aware of that distinction and applied it to express his own thought was G.E. Lessing. In the article the author discusses Strauss’s thesis concerning esoteric writing and presents the reasons why Lessing might be regarded as the last esoteric thinker. Finally, the author attempts to interpret Lessing’s last writings, especially his play Nathan the Wise, in the light of Strauss’s thesis. (shrink)

my goal here is to provide a detailed analysis of the methods of inference that are employed in De prospectiva pingendi. For this purpose, a method of natural deduction is proposed. the treatise by Piero della Francesca is a manifestation of a union between the ne arts and the mathematical sciences of arithmetic and geometry. He de nes painting as a part of perspective and, speaking precisely, as a branch of geometry, which is why we nd advanced geometrical exercises here.

SPIS TREŚCI Ryszard Moń Wstęp -/- Rozdział 1: Lękam się świata bez filozofii. O nieodzowności humanistyki w dobie techniki i globalizacji -/- 1.1 Konieczność filozofii 1.2 Narodziny sztuk wyzwolonych 1.3 Uniwersytet domem humanistyki 1.4 Upadek humanistyki 1.5 Uniwersytet – biznes i korporacyjna logika 1.6 Kognitywny kapitalizm 1.7 Złowroga moc etatyzmu 1.8 Pragmatyzm a ideały kształcenia 1.9 Demokracja – dialog, kultura, światopogląd 1.10 Humanistyka na straży demokracji 1.11 Edukacja filozoficzna w szkole 1.12 Podsumowanie – filozofia jako fundament -/- Rozdział 2: (...) Czy starożytna paideia może być alternatywą dla współczesnej pedagogiki? Antyczne metody wychowawcze i ich obecna rola -/- 2.1 Filozofia jako sposób życia 2.2 Rola ćwiczeń duchowych w paidei starożytnej Grecji oraz starożytnego Rzymu 2.3 Antyczna paideia a aktualne wzorce kształcenia -/- Rozdział 3: Problem ujawniania przez nauczyciela własnej tożsamości moralnej w nauczaniu etyki i filozofii -/- 3.1 Nauczyciel na lekcjach filozofii i etyki 3.2 Etyka, moralność i tożsamość 3.3 Matthew Lipmana filozofowanie z dziećmi i młodzieżą 3.4 Filozofia! Ale jaka? 3.5 Nauczyciel-filozof 3.6 Tożsamość moralna nauczyciela -/- Rozdział 4: Język i filozofia. O Naturalnym Metajęzyku Semantycznym i jego związkach z filozofią -/- 4.1 Naturalny Metajęzyk Semantyczny – rozważania wstępne 4.2 Inspiracje filozoficzne koncepcji NMS 4.3 Naturalny Metajęzyk Semantyczny – cel i założenia koncepcji 4.4 Kierunki rozwoju NMS 4.5 Jak wykorzystać NMS w dydaktyce filozofii? -/- Rozdział 5: Metody problemowe na lekcji etyki i filozofii jako możliwe działanie prewencyjne -/- 5.1 Metody rozwiązywania problemów – informacje ogólne 5.2 Rozwiązywanie problemów poznawczych 5.3 Rozwiązywanie problemów decyzyjnych 5.4 Rozwiązywanie problemów praktycznych 5.5 Nauczanie i uczenie się metodą „układanki” 5.6 Metoda wychowania bez porażek 5.7 Rola nauczyciela 5.8 Kształcenie umiejętności rozwiązywania problemów 5.9 Oceny i wartościowania 5.10 Podsumowanie Rozdział 6: Trudności w uczeniu się – profilaktyka i terapia -/- 6.1 Trudności w uczeniu się 6.2 Specyficzne trudności w uczeniu się 6.3 Niepowodzenia szkolne 6.4 Profilaktyka i terapia -/- Aneks – konspekty lekcji o tematyce filozoficznej i etycznej. (shrink)

In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as linguistic (...) systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach -- advocated by Carnap, Hempel and Nagel -- and the non- statement or semantic approach --advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wojcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is 'adequate' to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of 'theoretical entities' without relapsing into the metaphysics typical of the usual scientific realist approaches. (shrink)

In this essay, the author considers intertextuality in contemporary musical work, conceptualizing it not only as a critical category and as an artistic convention, but also as an aesthetic strategy. Listening for texts, as it were, opens the work for influences and gives it new purposes. The multiple texts, which are mutually interdependent, alter each other’s meaning and are “read” and “re-read” during aesthetic experience. Depending on the listener, these meanings are more or less pronounced; some are seen as primary, (...) while others are seen as secondary. Sometimes they are co-dependent and meaningful together, but sometimes they shy each other out. The multilayered quality of the work is acknowledged and seen as important even before individual meanings can be discovered. The author proposes a look at intertextuality in reference to musical works by Steve Reich,. The author uses Ryszard Nycz’s definition of intertextuality and confronts it with Umberto Eco’s idea of interpretation and the structural openness of art. Putting forward a concept of listening-in as a necessary element of receiving and understanding certain musical works, she suggests accepting an intertextual aesthetic strategy for a satisfactory aesthetic experience. Assuming the presence of multiple texts, which are different in character and meaning, and accepting their interdependence, changes the reception of the work and colors its qualities. The challenge is not only to seek out different texts hidden behind the purely musical face of the work but to find out the way they influence each other, knowing full well that the major or minor role those texts play depend on the listener as much as on the author. (shrink)

Poniższa dyskusja odbyła siȩ we wrześniu 2018 w Szkole Głównej Handlowej w Warszawie. Skupiła zarówno badaczy problematyki polityki senioralnej, ekspertów, analityków. Dyskusjȩ moderował i zaplanował Andrzej Klimczuk, zwi¸a}zany z SGH, natomiast zaproszenie do dyskusji przyjȩli: Barbara Szatur-Jaworska, polityk społeczny i gerontolog z Uniwersytetu Warszawskiego, Paweł Kubicki, ekonomista, SGH, Marek Niezabitowski, socjolog z Politechniki Śl¸a}skiej, Ryszard Majer, polityk społeczny, Agnieszka Cieśla, architektka i urbanistka, Politechnika Warszawska, Marzena Rudnicka, fundatorka oraz prezeska Krajowego Instytutu Gospodarki Senioralnej. Paneliści podczas dyskusji analizowali nastȩpuj¸a}ce zagadnienia: (...) I. pocz¸a}tki polityki senioralnej, jej definiowanie, dokumenty strategiczne państwa, II. rola samorz¸a}dów w animowaniu działań w obrȩbie polityki senioralnej oraz organizacji pozarz¸a}dowych, III. powstanie i rola ustawy o seniorach, IV. zróżnicowanie środowiska osób w wieku senioralnym, V. działania w innych krajach w obrȩbie polityki senioralnej, VI. zmiany w świadomości społecznej, ewolucja postaw wobec osób starszych, starości, starzenia siȩ, VII. rynek produktów i usług dla seniorów, VIII. aktywność seniorów, formalna i nieformalna, infrastruktura aktywności, IX. mieszkalnictwo dla osób starszych i starzej¸a}cej siȩ ludności X. rola państwa i samorz¸adu w polityce senioralnej, dialog z władz¸a, partnerstwo publiczno-prywatne, XI. wyzwania i kierunki rozwoju polityki senioralnej, XII. deficyt usług opiekuńczych XIII. polityka senioralna i emerytalna, XIV. konwergencja i dywergencja w polityce senioralnej. ** The following discussion took place in September 2018 at the Warsaw School of Economics. It focused on both senior politics, experts, and analysts. The discussion was moderated and planned by Andrzej Klimczuk, associated with the Warsaw School of Economics, and invited to the discussion: Barbara Szatur-Jaworska, social politician and gerontologist from the University of Warsaw, Paweł Kubicki, economist, Warsaw School of Economics, Marek Niezabitowski, sociologist from the Silesian University of Technology, Ryszard Majer, social politician, Agnieszka Cieśla, architect and urban planner, Warsaw University of Technology, Marzena Rudnicka, founder and president of the National Institute of Senior Management. Panelists during the discussion analyzed the following issues: I. Beginnings of the senior policy, its definition, strategic documents of the state, II. The role of local governments in animating activities within the framework of senior policy and non-governmental organizations, III. Creation and role of the law on seniors, IV. Diversification of the environment of seniors, V. Activities in other countries within the framework of the senior policy, VI. Changes in social awareness, the evolution of attitudes towards older people, old age, ageing, VII. The market for products and services for seniors, VIII. Seniors’ activity, formal and informal, activity infrastructure, IX. Housing for older people and ageing population X. The role of the state and self-government in the senior policy, dialogue with the authorities, public-private partnership, XI. Challenges and directions of development of the senior policy, XII. The deficit of care services, XIII. Senior and pension policy, XIV. Convergence and divergence in the senior policy. (shrink)

W swoim artykule przedstawiłam w skróconej formie problem społeczeństwa żydowskiego z przełomu lat 1933-1945 na terenie niemieckiego miasta Bayreuth, znanego w świecie jako miejsce corocznych festiwali wagnerowskich. Osoby zajmujące się historią, a w szczególności okresem II wojny światowej oraz ci, których pasjonuje z różnych powodów muzyka Ryszarda Wagnera, natkną się z pewnością na ślady historii miasta Bayreuth, będącego w tym czasie niemal świątynią kultu ideologii nazistowskiej. To tu właśnie tworzył wybitny, a zarazem uwielbiany przez Hitlera Niemiec: Ryszard Wagner. Fakt (...) ten pełnił dość istotną funkcję wspomagającą manipulację masami ludzkimi. Przypisywanie kompozytorowi oraz jego sztuce antysemityzmu okazało się czystym środkiem do celu, jakim było wyniszczenie narodu żydowskiego. Podsycanie nienawiści, propaganda, bojkoty ze strony nazistów, brutalna dyskryminacja społeczeństwa żydowskiego i niszczenie jego długowiecznego dobytku kulturowego przyniosło zamierzone efekty w postaci emigracji tej ludności na zachód, do Ameryki, Kanady oraz Izraela. Liczne deportacje i eksterminacja Żydów sprawiły, że niewielu wróciło po wojnie do Bayreuth. Szybko odrodziła się tu jednak kultura żydowska i znalazła po wojnie pełną akceptację społeczeństwa. Warto dodać, że Bayreuth cieszy się dziś ogólnym uznaniem w świecie muzyki. Co roku napływają tu rzesze zwolenników twórczości Ryszarda Wagnera z całego świata, podziwiając piękno jego muzyki oraz urocze krajobrazy Zielonego Wzgórza. (shrink)

This paper discusses two novels by contemporary writer Inga Iwasiów (b. 1963), Bambino (2008) and Ku słońcu [Towards the Sun] (2010), in the context of geopolitical, ideological, social and psycho-cultural transformations as they specifically affect different generations of inhabitants of the Polish city of Szczecin (pre-1945 German Stettin) from 1945 until the first decade of the 21st century. Bambino covers the years 1945–1981, but also contains flashbacks to pre-war memory of Stettin and to the suppressed experiences of the new post-war (...) inhabitants, as well as ‘flash-forwards’ to post-1989, post-communist reality; Ku słońcu covers 1981 to the first decade of 2000s. It shows how the novels portray these transformations through the experience primarily of women (but not only) — in Bambino, through the main protagonists: Ula (formerly Ulrike), Anna and Marysia, and through that of the hidden narrator Magda (Marysia’s daughter born in the same year as the author, Iwasiów, 1963); and in Ku słońcu, primarily through the experience of Magda herself, as well as through that of two generations of ‘feminist’ academics: Małgorzata and Sylwia (in which it is hard not to perceive the personal experience of the author, though she is at pains to emphasize elsewhere that her work is a collective biography of the city, not so much of herself). The analysis follows Katarzyna Chmielewska’s supposition that contemporary Polish fiction dealing with the past ‘constantly oscillates between memory and genealogy’, and that it raises raw issues not yet addressed by historians; it also derives inspiration from the new ‘postdependency’ studies proposed by Hanna Gosk and Ryszard Nycz. It also attempts to capture the specific nature of Iwasiów’s use of language, her style of feminism, her method of portraying place, and the connections in her prose between place and memory. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...) types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)