ABSTRACTWith over 560 citations reported on Google Scholar by April 2018, a publication by Juslin and Gabrielsson presented evidence supporting performers’ abilities to communicate, with hig...

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)

Jerzy Perzanowski s ideas were based on an original blend of logic and ontology in what he called onto/logic, where the slash is meant to suggest a quotient of ontology by logic. Perzanowski began as a logician, his early works being on modal logic, then gradually shifted his interest to logical philosophy, meaning not so much philosophy of logic as philosophy informed by logic. Perzanowski was a rare breed of analytical philosopher who thought that a philosophical theory of everything (...) was worthwhile. In this systematic spirit, he began with method. He presented his method of total analysis and synthesis quite simply: reduce the object of research to its simplest possible constituents, and then combine them in some way. Better still, combine them in every possible way, thereby producing a space of possibilities analogous to (and in certain cases identical with) the logical space. Thus, analysis and synthesis differ from a trivial disassembly and reassembly.". (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)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

Chciałem Go pożegnać. Kilkakrotnie próbowałem napisać choć parę słów. O Nim samym. Okazało się, że nie potrafię. Udało mi się tylko przedstawić Jego poglądy na reizm Tadeusza Kotarbińskiego, ale uczyniłem to gdzie indziej. Muszę tu poprzestać na ofiarowaniu Mu tego, co napisałem na Jego dziewięćdziesiąte urodziny, w osiemdziesięciolecie naszej przyjaźni.

Author: Sawicki Jerzy Title: THELEOGICAL PRINCIPLE IN KANT’S METHODOLOGY (Zasada teleologiczna w metodologii Kanta) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 281-292 Keywords: KANT, THELEOGICAL PRINCIPLE, FINALISM, MECHANICISM Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The work contains a concise of I. Kant’s views on the problem of the laws of nature and the theleological principle presented in this context, which Kant proposes in the character of a regulative methodological postulate. (...) The analysis of fundamental philosophical notions (the law of nature, necessity, causality, purpose) carried out from the position of an extreme aprioristic rationalism leads Kant to the conclusion about the basic impossibility of educing the conception of purpose (in relation to nature) from aprioristic transcendental laws, ie. such laws which the theoretical reason imposes to the nature by necessity. However, the fact of a total functioning of an organism does not fit, according to Kant, into the frames of a mechanically understood causality. Kant tries to solve this problem choosing the way of conclusion by analogy and finally he suggests to introduce into the living nature a specific causal relation in which the purposes constitute a particular kind of causes and results at the same time. That conception oscillates between mechanicism and theological finalism, and the fitting of a science system into the frames of aprioristic categories does not permit a finally decide about the supremacy of one or the other way of seeing the world. However, nevertheless, the perceiving and stressing of the peculiarity of organic symptoms, the formulation of the postulate about their unreductability to the law of a mechanical type constitute unquestionable and great merit of the author of the Criticism of the Judgment Authority. The idea of the totality of organism, though involved in subjective idealistic non consequences of Kant’s conceptions has in the given historical period all features of a deep and progressive thought, outpacing and inspiring several later research ideas, both in philosophy and in natural science. (shrink)

Book review: Lukas Benedikt Kraus, Der Begriff des Kontinuums bei Bernard Bolzano, Beiträge zur Bolzano-Forschung, vol. 25, Academia Verlag, Sankt Augustin 2014, pp. 112.

W wyniku przemian społecznych w wielu krajach demokratycznych, a zwłaszcza w Stanach Zjednoczonych jako kolebce demokracji, dostrzega się zmiany nie tylko ideowe, ale i obrazu samego społeczeństwa, podkreślając choćby zmiany tradycyjnych cnót mieszczańskich społeczeństwa kapitalistycznego. W tym kontekście warto więc zauważyć, ze wszelkie przeobrażenia i „nowinki" odbywają się na bazie poszanowania podstawowych zasad systemu, tj. demokracji, wolnego rynku oraz wyraźnej dominacji drogi ewolucyjnej, a nie rewolucyjnej, co dla czytelnika polskiego może stanowić pozytywny aspekt wychowawczy. W niniejszym studium teoretyczne koncepcje filozoficzne (...) filozofów Johna Rawlsa i George'a C. Lodge'a są zestawione z działalnością polityka praktyka Johna Fitzgeralda Kennedy’ego, który choć nie jest filozofem teoretykiem, to jednak należy do głównych przedstawicieli tzw. liberalizmu jakościowego. Jego pozycja w życiu społeczno-politycznym Stanów Zjednoczonych Ameryki Północnej umożliwiła spopularyzowanie tego nurtu liberalnego w życiu publicznym społeczeństwa amerykańskiego. (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)

The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox and a precise representation of the axiom of restriction in set theory proposed much earlier by Abraham Fraenkel. We discuss the main features of Suszko's contribution and hint at its possible further applications.

S. Jaśkowski introduced the discussive propositional calculus D₂ as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories. D₂ has afterwards been extended to a first-order predicate calculus and to a higher-order logic. In this paper we present a natural version of D₂, in the sense of Jaśkowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus. A semantics for the new calculus is also presented.

S. Jakowski introduced the discussive prepositional calculus D 2as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D 2has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the (...) quoted paper). In this paper we present a natural version of D 2, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented. (shrink)

Jerzy Franczak comprehensively presents Jacques Rancière's thought by emphasizing the relations between politics and literature. The detailed analysis considers the context of modern aesthetics and political philosophy, which is why the book introduces further protagonists, such as Louis Althusser, Michel Foucault, Pierre Bourdieu, or Jean-François Lyotard. Franczak first reconstructs Rancière's original philosophy of literature so as to then immediately apply it in readings of select world literature masterpieces by Gustav Flaubert, Max Jacob, Bertold Brecht, Vladimir Nabokov, and Philip Roth.