The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...) which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

This paper is a continuation of Part I under the same title. Its Chapter III contains results given in the following publications: U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131. G. Bryll, Związki logiczne pomiędzy zdaniami nauk empirycznych (Logical relations between sentences of empirical sciences). Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia (...) i Monografie, Nr 22 (1969), 155-216. This chapter contains an attempt to formalize some questions of methodology of empirical sciences. The theory T is enriched here not only by new definitions but also by a new primitive term and new axioms. The most important notion defined in this chapter is the set IndX of all inductive conclusions obtained on the basis of sentences of the set X. The function CnI defined by the equality: CnI X = X u IndX, satisfies the axioms of the general theory of deductive systems. The set CnI X can be understood as a system of empirical sciences in a narrower sense. This paper is a development of the considerations of G. Bryll, included in the above-listed article by this author. (shrink)

The paper tackles two problems. The first one is to grasp the real meaning of Jerzy Kalinowski’s theory of normative sentences. His formal system K 1 is a simple logic formulated in a very limited language . While presenting it Kalinowski formulated a few interesting philosophical remarks on norms and actions. He did not, however, possess the tools to formalise them fully. We propose a formulation of Kalinowski’s ideas with the use of a set-theoretical frame similar to the one (...) presented by Krister Segerberg in his A Deontic Logic of Action. At the same time we enrich the language used by Kalinowski with more operators on actions and present an adequate axiomatisation of the resulting system. That allows us to disclose some unrevealed aspects of Kalinowski’s theory. The most important one is a relation between acts which we call moral indiscernibility. Our second problem is a proper understanding of moral indiscernibility. We show how a repertoire of agent’s actions, defined with the use of simple observable elements of actions, can be filtrated by the relation of moral indiscernibility. That allows us to understand the consequences of Kalinowski’s claim that not doing something good is always bad. (shrink)

The paper analyzes the philosophical consequences of the recent discovery of direct violations of the time–reversal symmetry of weak interactions. It shows that although we have here an important case of the time asymmetry of one of the fundamental physical forces which could have had a great impact on the form of our world with an excess of matter over antimatter, this asymmetry cannot be treated as the asymmetry of time itself but rather as an asymmetry of some specific physical (...) process in time. The paper also analyzes the consequences of the new discovery for the general problem of the possible connections between direction of time and time-asymmetric laws of nature. These problems are analyzed in the context of Horwich’s Asymmetries in time: problems in the philosophy of science argumentation, trying to show that existence of a time–asymmetric law of nature is a sufficient condition for time to be anisotropic. Instead of Horwich’s sufficient condition for anisotropy of time, it is stressed that for a theory of asymmetry of time to be acceptable it should explain all fundamental time asymmetries: the asymmetry of traces, the asymmetry of causation, and the asymmetry between the fixed past and open future. It is so because the problem of the direction of time has originated from our attempts to understand these asymmetries and every plausible theory of the direction of time should explain them. (shrink)

The present note is intended to draw the reader's attention to the analysis of the relation between Newtonian Mechanics and Special Relativity Mechanics (henceforth to be referred to as NM and SRM), given by Philipp Frank, one of the classics of Logical Empiricism (in Frank [1938]). Frank's analysis of the relation between NM and SRM is interesting in many ways. Firstly, it shows clearly that problems of disruptive changes and of conceptual disparity were known to and discussed by Logical Empiricists (...) and that, therefore, some of them at least were not at all blinded to 'dynamic' problems of changes in actual science by their view of physical theories as interpreted axiomatic systems and did not deal with those theories as 'static, frozen in logical mold'. Secondly, it reveals some of the reasons for the Logical Empiricist rejection of what came to be known later as the incommensurability claim. (shrink)

Прототетика Ст. Лесневского является обобщением двузначного исчисления предложений. Выступают в ней рядом с терминами этого исчисления функторы (как постоянные так и переменные) всех тех семантических категорий какие могут быть определены, когда точкой исхода является категсрия предложений.В этом труде представлены три системы прототетики. Основным термином двух из них является импликация, ссновным термином третьей системы эквивалентность. Системы с основным термином импликации разнятся гравилами вывода. В одной из них действует так наз. правило проверки, в другой прабило зкстенсиональности. Первое из этих правил является обобщением (...) следующего правила вывода исчисления предложений, обогащенного тєрминами 0 и 1:Вь'ражение ϕ является тезисом системы, когда тезисами системы являются оба выражения возникнувшие из ϕ через подстановку некоторой его переменной символов 0 и 1.На основании правила экстенсиональности тезисами системы являются правила экстенсиональности сформулированные для функторов любых семантических категсрий свойственных грототетике.В этом труде даются доказательства эквивалентности трех систем протстетики и доказательство их полноты.Значительная часть результатов из опытов Лесневского, представленных в этом труде, не была до сих пор опубликована. Обрабатывая эти результаты я пользовался записками составленными по лекциях Лесневского, его учениками. Оригинальные записки Лесневского подвєрглись уничтожению во еремя варшавского восстания. (shrink)

The old-fashioned concept of state is shown to be inadequate and misleading. Replacing it by a concept of information and taking advantage of the invariance of the mechanical description under time reversal puts the problems of the interpretation of quantum mechanics in a new light. A more realistic interpretation appears to be possible. Moreover, a new explanation of the Einstein-Podolsky-Rosen paradox is presented, too.

The paper consists of two parts. The first critically analyses Meyer’s [2005] version of the triviality objection to presentism (according to which, presentism is either trivial or untenable), and tries to show that his argument is untenable because – contrary to what he claimed – he did not take into account the entire possible spectrum of interpretations of the presentist’s thesis. In the second, positive part of the paper, it is shown that a leading form of tensed theory of time (...) postulates the same ontology as presentism and that it avoids the triviality problem which means that it can be used to generate an alternative formulation of presentism which is no longer vulnerable to the triviality objection. (shrink)

The paper examines the relations between presentism and the thesis concerning the existence of the flow of time. It tries to show that the presentist has to admit the existence of the passage of time and that the standard formulation of presentism as a singular thesis saying that only the present exists is insufficient because it does not allow the inference of the existence of the passage of time. Instead of this, the paper proposes a formulation of presentism with the (...) aid of the notion of becoming; not only does a formulation state the existence of the flow of time in such a way as to avoid the question of the rate of the passage of time, it also allows the inference of the existence of only present things and events. The paper demonstrates that the proposed conception of presentism also has other virtues, such as homogeneity, non-triviality, and ability to express dynamicity of presentists’ image of the world which testify for it. (shrink)

Resumo Este artigo analisa, as recentes versões, da objecção à existência de um fluxo do tempo, com base na pergunta: “Com que velocidade flui o tempo?”. O autor mostra que as soluções existentes para o problema não são plausíveis e, que em vez disso, a resolução deve ser encontrada numa nova concepção de fluxo temporal, que evite tais dificuldades. A teoria metafísica proposta desenvolve as ideias de Broad e Prior sob um novo enquadramento, que invalida a objecção resultante da questão (...) sobre o ritmo da passagem do tempo e das respostas “segundo a segundo”. Neste texto também se procura mostrar, que esta teoria metafísica, aqui proposta, possui outras virtudes que testemunham a seu favor. Palavras-chave : existência dinâmica, fluxo do tempo, presentismo, velocidade de passagem do tempoThe paper analyzes some recent versions of the objection to the existence of the flow of time based on the question: “How fast does time flow?”. It shows that the replies given to the problem are implausible and instead proposes a solution for the issue in the form of a conception of the flow of time which can avoid such a difficulty. The proposed metaphysical theory develops the ideas of Broad and Prior in a radical way and invalidates the objection resulting from the question about the rate of passage and answers “second per second”. The paper also tries to show that this metaphysical theory has other virtues which testify in favor of it. Keywords : flow of time; rate of time’s passage; presentism; dynamic existence. (shrink)

The aim of this paper is to make presentism a dynamic view of reality by basing it on a notion of dynamic existence, that is, on a notion of existence which has a dynamic character. The paper shows that both of the notions of existence which are used in metaphysical theories of time have a static character and, while such a notion is useful for eternalists, it is useless for presentists if they want to make their view able to remain (...) in agreement with our everyday experience and self-consistent. It is demonstrated that both empirical and theoretical arguments indicate that the presentist should replace the notion of this static existence with the notion of a dynamic existence and that this maneuver allows the presentist to treat his/her existential thesis as equivalent to the thesis that time flows. Not only does this strategy allow us to express presentism in a simple, homogenous way which remains in agreement with our experience, but also permits us to solve some of the difficult problems which presentism faces, such as, for example, the objection of triviality and the question about the rate of time passage. Moreover, such an approach to presentism allows us to solve fundamental metaphysical problems concerning time such as the problem of the openness of the future and the fixity of the past, direction of causation, and relations between presentism and persistence through time by endurance. (shrink)

It is often claimed that the debate between presentism and eternalism is merely verbal, because when we use tensed, detensed or tenseless notions of existence, there is no difference in the accepted metaphysical statements between the adherents of both views. On the contrary, it is shown in this paper that when we express their positions making use, in accordance with intentions of the presentists and the eternalists, of the tensed notion of existence (in the case of the presentists) and the (...) detensed or tenseless notion (in the case of the eternalists), the controversy remains deep and very important for us, because both ontological claims express a different attitude to the existence of the flow of time. It is shown that not only does the proposed approach to presentism and eternalism exactly express the intentions of the adherents of both views but it also offers a better understanding of them joining together seemingly different theses maintained by the presentists and the eternalists, and explaining at the same time the dynamism of the presentists' ontology. The paper takes for granted that we should assess metaphysical theories in a similar way as we assess scientific theories, that is on the basis of their explanatory value. (shrink)