Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions.

The aim of the paper is to give a new definition of real number. The logical type of any number defined is that of the function B = h(A) which assigns to a class of sets A a class of sets B. I give some conditions which the function h has to fulfill to be considered as number; an intuitive sense of the conditions is as follows: a function, which is number, assigns a class of sets of measure h·m to (...) a class A of sets of equal measure, where m is the measure of A. (shrink)

In 1934 Stanisław Jaśkowski published his groundbreaking work on natural deduction. At the same year Gerhard Gentzen also published a work on the same topic. We aim at presenting of Jaśkowski’s system and provide a comparison with Gentzen’s approach. We also try to outline the influence of Jaśkowski’s approach on the later development of natural deduction systems.

In this brief note we would like to outline the main events of life and the main achievements of Stanisław Jaśkowski one of the important Polish logician and mathematician of the first half of twentieth century.

A universally free logic is a system of quantification theory, with or without identity, whose theses remain logically true if the domain of quantification is empty and some of the singular terms present in the language do not denote existing objects. In the West, logics satisfying and ones satisfying were developed starting in the 1950s. But Stanisław Jaśkowski preceded all this work by some twenty years: his paper “On the Rules of Supposition in Formal Logic” of 1934 can be (...) regarded as containing, at least implicitly, the first universally free logic. The system proposed there is an inclusive logic as it is, and a straightforward extension of it is also free. (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)

I am honoured with and touched by the invitation of delivering the opening address of this Congress. Firstly, to see paraconsistent logic flourishing and growing, as we can readily see by simply glacing over the programme of this conference, is among one of my greatest joys. Secondly, and equally important, because this congress takes place in the University of Toruń.I am honoured for having lectured here, a most congenial and stimulating place, and could not think of a better place for (...) a conference dedicated to the memory of Stanisław Jaśkowski. In particular, I am delighted for having had a correspondence with him, and although I was deprived of the pleasure of meeting him personally, I was fortunate enough for having collaborated with some of his disciples, such as L. Dubikajtis and T. Kotas. All and all, Toruń in particular and Poland in general are for me a second home, for all the kindness and care everyone has shown to me over several years, since my very first visit to this country. (shrink)

The concept of inconsistency has become recently the subject of many studies focused on the principle ex contradictione sequitur quodlibet which is a hallmark of the classical inconsistency. Stanisław Jaśkowski was the first who took a non-classical standpoint toward this principle building a system of propositional logic which rejects this classical principle. Rejecting it implies important consequences for the concept of classical negation, and poses the question in which properties the op-eration of negation should be endowed. The intention of (...) this article is to define the concept of inconsistency as well as the concept of negation in a way satisfying the main intuitions natural language users connect with the two notions occurring in propositions containing vague concepts. The vagueness of natural language dis-course leads to the phenomenon of the seeming contradiction characteristic of natural language. A non-standard consequence relation for such a language has been defined in terms of preferential semantics making use of the concept of most classical model. This non-standard consequence relation is applied to the ethical discourse. The concepts introduced in this article have been used to an interpretation of the contradictories of Plato's Parmenides, as well as to the rejection of dialetheism. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement of (...) mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

Wollen (Libertarianism and conjoined twins) argues that libertarianism premised on absolute property rights founders where physical boundaries between two persons cannot be discerned, as is the case with conjoined twins. In this rejoinder, we make a three-pronged argument against Wollen’s claim. First, it is demonstrated that even if conjoined twins really do not hold self-ownership rights against one another, they still have one bodily ownership right against the rest of the world. Second, two alternative resolutions of Wollen’s hypothetical dispute between (...) conjoined twins that derive from two different versions of libertarianism are set forth. Third, it is shown that the quandaries engendered by the existence of conjoined twins not only are not specific for libertarianism but there also are political philosophies to which conjoined twins pose even greater a challenge. (shrink)

Liberalism and marxism are two forms of economism, which separate economic activity from ethics. The social teaching of the Church accepted continued by pope Benedict XVI recognizes the necessity of free market and limited intervention of the state in economy, but first of all postulates creativity of civil society in the field of economic life. The main arguments for observance of moral rules in the economic activity are following: 1. Every conscious and free men’s action is responsible for the effects (...) – economic activity cannot be any exception; 2. The same ethics ought to be applied in the individual-private life and in the public domain – also economy; 3. Ethos of economic activity is connected with three virtues – truth, love and justice (also social justice); 4. Christian-personalistic ethics is based on the principles auxialiarity (personalism) and common good (solidarity). Economic activity completely separated from ethics is inhuman. (shrink)

The book by professor Stanisław Kowalczyk, renowned scholar in the field of social philosophy, is, without doubt, one of the most important studies on the idea of freedom. The concept of freedom is as old as mankind. It has many meanings and has been interpreted in many different ways. For instance, we also have the word „liberty," which means „freedom or right" and is synonymous with the word freedom, which means „the condition of being free." The author indicates that in (...) our times the notion of freedom is most frequently used; however, it is often misused or deceptive. Mass media and people of all walks of life talk of liberty; everyone talks of freedom and, for many, it is the highest value. Longing for freedom is rooted in the heart of every human being, for freedom is an existential correlate and the fulfilment of the rational human being. The semantic confusion about the notion of freedom leads to many misuses of the concept. Personalism, as a philosophical concept in which a person stands in the centre of all discussion, serves as a framework for the author's delineation on the concept of freedom. He further states that the appropriate understanding of this value is possible in the context of the personalistic interpretation of a human being. This is the focus of this informative and insightful book. (shrink)

The article reviews the book Philosophia Vitam Alere. Prace dedykowane Profesorowi Romanowi Darowskiemu SJ z okazji 70-lecia urodzin, edited by Stanisław Ziemiański S.J.

Sport plays today an eminent role in man's life and in societies. Various sciences have made it the subject-matter of their reflection, i.e. psychology, sociology, the natural and humanistic sciences, art, philosophy, and theology. The present work seeks to answer some fundamental questions connected with the phenomenon of sport: what is it for man? whether and when does it serve the social integration of a community? what are the premises and principles of the ethics of sportive activity? what is the (...) aesthetic dimension of sport? what are the relations between sport and religious faith? The philosophical profile is dominant in the book, taking into consideration various aspects of sport: anthropological, social, axiological, and theological. (shrink)

Visual targets which follow a prime stimulus and a mask can be identified faster when they are incompatible rather than compatible with the prime . According to the self-inhibition hypothesis, the initial activation of the motor response is elicited by the prime based on its identity. This activation leads to benefits for compatible trials and costs for incompatible trials. This motor activation is followed by an inhibition phase, leading to an NCE if perceptual evidence of the prime is immediately removed (...) by the mask. The object-updating and mask-triggered inhibition hypotheses emphasize the role of the mask content . We show that the NCE may appear even if nonmasking neutral flankers are presented instead of a mask. Moreover, although with target-like flankers the NCE is larger, it occurred if flankers and targets are built from dissimilar elements. Therefore, masks/flankers can evoke an inhibition phase independently of whether or not they remove evidence for the prime and whether they are similar to the targets. (shrink)

Author: Czerniak Stanisław Title: CAN WE RIGHTLY SPEAK ABOUT “KAZIMIERZ HOFFMAN’S PHILOSOPHY”? (SOME REMARKS CONCERNING THE PUBLICATION POZNAWANIE KAZIMIERZA HOFFMANA) (Filozofia Kazimierza Hoffmana? Refleksje na marginesie książki Poznawanie Kazimierza Hoffmana) Source: Filo-Sofija year: 2011, vol:.15, number: 2011/4, pages: 1038-1046 Keywords: KAZIMIERZ HOFFMAN, IDEA OF DIVINE, EXISTENCE, POETRY Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The article shows the philosophical background of Kazimierz Hoffman’s poetry. The author points to Hoffman’s idea of the Divine, (...) which creates all possible objects in the world and incessantly sustains their existence, treating it as the crucial point of his philosophical stance. Another question is devoted to a possible relationship between Hoffman’s philosophical views and the traditions of the philosophy of life and phenomenology. Worth examining are also some similarities between Hoffman’s concept of donation and the ethical standpoint of E. Lévinas. In conclusion to those considerations one could claim that in Hoffman’s poetry we experience an interesting kind of mysticism uniting the contemplation of the absolute order with the aesthetic, perfectionist attempts to write the “ideal poem” and to connect the metaphysical insight with the experimental form. In the article the author quotes extensively the most important hermeneutic conclusions contained in the book Poznawanie Kazimierza Hoffmana (“The Understanding of Kazimierz Hoffman”). (shrink)

There have been many papers on the Jesuit relationship with the State and with the civil powers in the Western Countries. But there are no such elaborations concerning Poland. However, it was not a central aim, the Jesuits had to engage in the political situation of the country where they did His apostolic work though they did not commit themselves personally in the policy. The Jesuits had their own concept of the State and the state policy. And they showed great (...) caution in preparing the policy treaties in order to save impartiality. (shrink)

Choice reaction times to visual stimuli may be influenced by preceding subliminal stimuli . Some authors reported a straight priming effect i.e., responses were faster when primes and targets called for the same response than when they called for different responses. Others found the reversed pattern of results. Eimer and Schlaghecken [Eimer, M. & Schlaghecken, F. . Links between conscious awareness and response inhibition: evidence from masked priming. Psychonomic Bulletin & Review, 9, 514–520.] showed recently that straight priming occurs whenever (...) a prime is not efficiently masked thereby the information provided by the prime is accessible for consciousness. In the present study, a hypothesis is tested that straight priming is due to mediation of consciousness. To test this hypothesis, prime validity was manipulated. We showed that even when no mask was used so that participants could fully and consciously perceive the prime and participants were informed that primes were mostly invalid, for the short prime–target ISI interval straight priming occurred. The priming was inverse when the ISI was 800 ms. This indicates that participants were able to use the information provided by the prime to prepare the response opposite to that cued by the prime but only if the time between the prime and the target was long enough. (shrink)