In the paper we study the method of Socratic proofs in the intuitionistic propositional logic as a reduction procedure. Our approach consists in constructing for a given sequent α a finite tree of sets of sequents by using invertible reduction rules of the kind: ? is valid if and only if ?1 is valid or... or ?n is valid. From such a tree either a Gentzen-style proof of α or an Aristotle-style refutation of α can also be extracted.

This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world (...) semantics of quantum counterfactuals using David Lewis's famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactuals semantics to strengthen Bell's theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell's theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation. (shrink)

A general theory of refutation systems is given. Some applications (concerning maximality and minimality in lattices of logics) are also discussed.

The concept of proper multiple-conclusion entailment is introduced. For any sets X, Y of formulas, we say that Y is properly mc-entailed by X iff Y is mc-entailed by X, but no A ∈ Y is single-conclusion entailed by X. The concept has a natural interpretation in terms of question evocation. A sound and complete axiom system for the propositional case of proper mc-entailment is presented.

In this paper we study the method of refutation rules in the modal logic K4. We introduce refutation rules with certain normal forms that provide a new syntactic decision procedure for this logic. As corollaries we obtain such results for the following important extensions: S4, the provability logic G, and Grzegorczyk''s logic. We also show that tree-type models can be constructed from syntactic refutations of this kind.

The purpose of the paper is to study syntactic refutation systems as a way of characterizing normal modal propositional logics. In particular it is shown that there is a decidable modal logic without the finite model property that has a simple finite refutation system.

The goal of this paper is to generalize specific techniques connected with refutation rules involving certain normal forms. In particular, a method of axiomatizing both a logic L and its complement −L is introduced.

In Section 2 I give a criterion of decidability that can be applied to logics (i.e. Tarski consequence operators) without the finite model property. In Section 3 I study ukasiewicz-style refutation procedures as a method of obtaining decidability results.This method also proves to be more general than Harrop's criterion.

Axiomatic proof/refutation systems for the paraconsistent modal logics: KN4 and KN4.D are presented. The completeness proofs boil down to showing that every sequent is either provable or refutable. By constructing finite tree-type countermodels from refutations, the refined characterizations of these logics by classes of finite tree-type frames are established. The axiom systems also provide decision procedures for these logics.

A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.

The goal of this paper is to analyse Implicational Relevance Logic from the point of view of refutability. We also correct an inaccuracy in our paper “The RM paraconsistent refutation system”.

The purpose of the paper is to make a few remarks on the following aspects of refutation rules: a characteristic property of a logic, elegant and constructive completeness proofs. In particular a new constructive completeness proof for the provability logic G is given.

The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.

Quantum mechanics tells us that states involving indistinguishable fermions must be antisymmetrized. This is often taken to mean that indistinguishable fermions are always entangled. We consider several notions of entanglement and argue that on the best of them, indistinguishable fermions are not always entangled. We also present a simple but unconventional way of representing fermionic states that allows us to maintain a link between entanglement and non-factorizability.

I will argue that physicians have an ethical obligation to justify their conscientious objection and the most reliable interpretation of the Polish legal framework claims that conscientious objection is permissible only when the justification shows the genuineness of the judgment of conscience that is not based on false beliefs and arises from a moral norm that has a high rank. I will demonstrate that the dogma accepted in the Polish doctrine that the reasons that lie behind conscientious objection in medicine (...) cannot be evaluated or controlled by anyone is based either on a mistaken interpretation of the Constitution or on the unreliable concept of conscience. I will refer to the legal regulations concerning military refusals that require from objectors to reveal and justify their views. Finally, I will demonstrate why conscientious objection under uncertainty does not deserve acceptance, because it is based on a specific version of the precautionary principle. (shrink)

Cet article vise à présenter les principales étapes de l’histoire des traductions polonaises des dialogues de Platon, qui sont intimement liées à l’histoire de la Pologne et à la renaissance de la vie académique dans l’entre-deux-guerres. L’attention se porte en particulier sur les travaux de traductions de F.A. Kozłowski, A. Bronikowski, S. Lisiecki et W. Witwicki, qui représentaient diverses approches et appliquaient des méthodes différentes pour rendre les textes de Platon en polonais. Le développement de cette série de dialogues accessibles (...) au public polonais dans différentes traductions a suscité des discussions sur les méthodes mêmes pour rendre Platon. Chaque nouveau dialogue était discuté et examine par les philologues classiques, les enseignants, les spécialistes de littérature, et même les théologiens, et seulement accessoirement par les philosophes. Bien que de nouvelles traductions de Platon commencent de plus en plus à apparaître, les productions anciennes, en particulier celles de Witwicki, restent populaires et sont encore largement lues. (shrink)

We study the monadic fragment of second order intuitionistic propositional logic in the language containing the standard propositional connectives and propositional quantifiers. It is proved that under the topological interpretation over any dense-in-itself metric space, the considered fragment collapses to Heyting calculus. Moreover, we prove that the topological interpretation over any dense-in-itself metric space of fragment in question coincides with the so-called Pitts' interpretation. We also prove that all the nonstandard propositional operators of the form q $\mapsto \exists$p ), where (...) F is an arbitrary monadic formula of the variable p, are definable in the language of Heyting calculus under the topological interpretation of intuitionistic logic over sufficiently regular spaces. (shrink)

According to latitudinarianism, S’s belief that x is F is about x solely in virtue of S’s believing a proposition that ascribes F- ness to x. Saul Kripke (2011b) has recently objected to this view by arguing that it entails that S believes of arbitrary objects that they are F. In this paper I revisit Ernest Sosa’s (1995a, 1995b) notion of associative aboutness to put forward a novel account of mental reference, called ‘associative exportation,’ that evades the troublesome consequence pointed (...) out by Kripke, while preserving the spirit of latitudinarianism. In particular, the proposed view: (1) does not invoke any form of acquaintance with the object of belief; (2) validates a weak reducibility thesis of de re belief to de dicto; (3) is compatible with the observation that our unreflective aboutness judgments are latitudinarian; (4) offers new insights about the notorious tallest- spy objection. (shrink)

Traditional views concerning musical meaning, in the field of philosophy, quite often oscillate around the discussion of whether music can transfer meaning (and if so if it happens by a means similar to language). Philosophers have provided a wide range of views – according to some, music has no meaning whatsoever, or if there is any meaning involved, it is only of a formal/structural significance. According to the opposing views, music can contain meaning similarly to language and what is more, (...) sometimes it can be even richer than language, as in music we are – arguably – able to encode “emotional meanings”. In recent years, several approaches – also speculative – to the old philosophical question have been proposed by evolutionary psychologists, one of the most controversial views being that of Stephen Pinker’s famous metaphor for music as “auditory cheesecake”. This anti-adaptationist view has been challenged f. ex. by Geoffrey Miller or Ian Cross. In this chapter, I enlist some main philosophical views on the titular problem and investigate some evolutionary-paradigm-based propositions for its solution, to examine whether – both from explanatory and methodological standpoints – the philosophy of music could gain something from recent developments in evolutionary psychology. (shrink)

For a free filter F on $$\omega $$, let $$N_F=\omega \cup \{p_F\}$$, where $$p_F\not \in \omega $$, be equipped with the following topology: every element of $$\omega $$ is isolated whereas all open neighborhoods of $$p_F$$ are of the form $$A\cup \{p_F\}$$ for $$A\in F$$. The aim of this paper is to study spaces of the form $$N_F$$ in the context of the Nikodym property of Boolean algebras. By $$\mathcal{A}\mathcal{N}$$ we denote the class of all those ideals $$\mathcal {I}$$ on (...) $$\omega $$ such that for the dual filter $$\mathcal {I}^*$$ the space $$N_{\mathcal {I}^*}$$ carries a sequence $$\langle \mu _n:n\in \omega \rangle $$ of finitely supported signed measures such that $$\Vert \mu _n\Vert \rightarrow \infty $$ and $$\mu _n(A)\rightarrow 0$$ for every clopen subset $$A\subseteq N_{\mathcal {I}^*}$$. We prove that $$\mathcal {I}\in \mathcal{A}\mathcal{N}$$ if and only if there exists a density submeasure $$\varphi $$ on $$\omega $$ such that $$\varphi (\omega )=\infty $$ and $$\mathcal {I}$$ is contained in the exhaustive ideal $$\text{ Exh }(\varphi )$$. Consequently, we get that if $$\mathcal {I}\subseteq \text{ Exh }(\varphi )$$ for some density submeasure $$\varphi $$ on $$\omega $$ such that $$\varphi (\omega )=\infty $$ and $$N_{\mathcal {I}^*}$$ is homeomorphic to a subspace of the Stone space $$St(\mathcal {A})$$ of a given Boolean algebra $$\mathcal {A}$$, then $$\mathcal {A}$$ does not have the Nikodym property. We observe that each $$\mathcal {I}\in \mathcal{A}\mathcal{N}$$ is Katětov below the asymptotic density zero ideal $$\mathcal {Z}$$, and prove that the class $$\mathcal{A}\mathcal{N}$$ has a subset of size $$\mathfrak {d}$$ which is dominating with respect to the Katětov order $$\le _K$$, but $$\mathcal{A}\mathcal{N}$$ has no $$\le _K$$ -maximal element. We show that, when $$\mathcal {I}$$ is a density ideal, $$\mathcal {I}\not \in \mathcal{A}\mathcal{N}$$ holds if and only if $$\mathcal {I}$$ is totally bounded if and only if the Boolean algebra $$\mathcal {P}(\omega )/\mathcal {I}$$ contains a countable splitting family. Our results shed some new light on differences between the Nikodym property and the Grothendieck property of Boolean algebras. (shrink)

In their philosophical projects that address the concept of law, Immanuel Kant, Johann G. Fichte, and Georg W. F. Hegel all employ transcendental argumentation to demonstrate the sovereignty of community and the existence of power. They do this in the attempt to conceptually ground the idea of freedom and reconcile it with the notion of coercion within the framework of the idea of positive law. This article focuses solely on the Kantian project, since the approaches of Fichte and Hegel take (...) on a more speculative turn in addition to their transcendental form. (shrink)

W artykule autor przedstawia dorobek o. Ziemiańskiego SJ na polu metafizyki. Okazją do tego był jubileusz 90. urodzin, z którego perspektywy można pełniej docenić wkład Jubilata w tę dziedzinę filozofii. Prezentację rozpoczyna przybliżenie kontekstu historycznego kształtowania się myśli filozoficznej o. Ziemiańskiego, gdzie podstawową rolę odegrała filozofia tomistyczna, skoncentrowana w ówczesnych polskich realiach na dyskusji z marksizmem. Dyskusja ta nie sprowadzała się wyłącznie do odkrywania ograniczeń i krytyki marksizmu. Przedstawiciele tomizmu proponowali własną interpretację rzeczywistości, odznaczającą się większym realizmem i bardziej przekonującą (...) racjonalnością. Kolejny punkt poświęcony został koncepcji metafizyki o. Ziemiańskiego, nawiązującej do tradycji arystotelesowsko-tomistycznej, wzbogaconej elementami zaczerpniętymi ze współczesnych kierunków filozoficznych oraz nauk szczegółowych. Pośród najbardziej charakterystycznych cech tego ujęcia wskazano oparcie na doświadczeniu i zorientowanie na byt realnie istniejący, metodę _abstractio totius_, poznawczy realizm i maksymalizm, jak też ukierunkowanie na poznanie bytu absolutnego. W dalszej kolejności omówiono wkład Ziemiańskiego w interpretację kluczowych zagadnień metafizycznych, takich jak transcendentalia, przygodność, celowość czy struktura bytu. Podkreślono, iż opowiadał się on za egzystencjalną naturą transcendentaliów, a przez to ich niesprowadzalnością do pojęć uniwersalnych. Ponadto, w ciekawy sposób przedstawił specyfikę relacji wiążącej byt przygodny z bytem koniecznym, jak również uzasadnienie konieczności istnienia przyczyny celowej oparte na analizie wewnętrznej struktury bytu. Ważnym jego wkładem do refleksji nad strukturą bytu było także opracowanie problematyki relacji w ujęciu F. Suareza oraz ukazanie funkcjonalnych aspektów złożenia bytu z istoty i istnienia. W zakończeniu odnotowano wnioski koncentrujące się na znaczeniu metafizyki jako bazowej dziedziny poznania filozoficznego. (shrink)

Sights of gothic cathedrals in Zygmunt Krasiński’s letters are proves of his great and deep fascination of medieval times. Following the examples of Goethe, Chateaubriand, and Friedrich he defines beauty of gothics churches. Such conact with a monumental architecture seems to be a pretext to estetic and philosophical reflections. Not only did he touch a matter of light in order to show the organic style of architecture, but also emphazised the importance of this case in creating a special style. View (...) of the church remains have got also some kind of a metaforic meaning fог the times that passed by and a symbol of previous generations. It makes us think about the significance of our life. (shrink)

We present the (Lascar) Galois group of any countable theory as a quotient of a compact Polish group by an F_σ normal subgroup: in general, as a topological group, and under NIP, also in terms of Borel cardinality. This allows us to obtain similar results for arbitrary strong types defined on a single complete type over ∅. As an easy conclusion of our main theorem, we get the main result of [K. Krupiński, A. Pillay and T. Rzepecki, Topological dynamics and (...) the complexity of strong types, Israel J. Math.228 (2018) 863–932] which says that for any strong type defined on a single complete type over ∅, smoothness is equivalent to type-definability. We also explain how similar results are obtained in the case of bounded quotients of type-definable groups. This gives us a generalization of a former result from the paper mentioned above about bounded quotients of type-definable subgroups of definable groups. (shrink)

In this paper we show that if the real line \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\Bbb R}$\end{document} is not a union of less than continuum many of its meager subsets then there exists an almost continuous Sierpiński–Zygmund function having a perfect road at each point. We also prove that it is consistent with ZFC that every Darboux function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $f\colon{\Bbb R}\to{\Bbb R}$\end{document} is continuous on some set (...) of cardinality continuum. In particular, both these results imply that the existence of a Sierpiński–Zygmund function which is either Darboux or almost continuous is independent of ZFC axioms. This gives a complete solution of a problem of Darji [4]. The paper contains also a construction (in ZFC) of an additive Sierpiński–Zygmund function with a perfect road at each point. (shrink)

Tomasz Ignacy Szpot Dunin SJ w swoim dziele poświęconym historii Chin nie ominął postaw znaczących chińskich dowódców w okresie przełomu historycznego jakim był upadek dynastii Ming i jej zastąpienie przez mandżurską dynastię Qing. Jednym z nich był Wu Sangui, który początkowo wspierał Mingów w walce z zewnętrznymi i wewnętrznymi wrogami, by w kluczowym momencie przyczynić się do powodzenia najazdu mandżurskiego, a po niemal trzech dekadach działania pod zwierzchnością nowej dynastii wypowiedzieć jej posłuszeństwo i stanąć na czele tzw. Rebelii Trzech (...) Lenników. Sprawa ta była znana w Europie i stała się nawet przedmiotem zainteresowania literackiego w XVIII w. Szpot Dunin nie poddaje się w swoim opisie skrajnym tendencjom, umiejętnie rozważa okoliczności decyzji i przedstawia zniuansowany, ale jednocześnie wyrazisty obraz postaci Wu Sangui, jego zamiarów i niepowodzeń. (shrink)

In 2006 Tomasz F. Bigaj published in English a book "Non-locality and the Possible Worlds. A Counterfactual Perspective on Quantum Entanglement". He considered the question whether a satisfactory interpretation of quantum mechanics in the standard form should include the assumption of a non-local, immediate influence of one part of a specific quantum system (like two electrons in the singlet state) on the other, spatially separated part of that system. Bigaj - following H. Stapp - chooses as conceptual instruments of (...) his analysis counterfactual conditional statements and possible-worlds semantics of such statements. After thorough examination of different Stapp's arguments, he reaches the conclusion "that no matter what available interpretation of counterfactuals we decide to follow, there is no need in standard quantum mechanics for measurement-included non-locality". My critique concerns mainly Bigaj's selection of conceptual tools: the counterfactuals and possible-worlds semantics. I point to the fact that such selection assumes the "necessitarian" interpretation of laws of nature in the domain of micro-objects (e.g. for systems like two electrons in the singlet state). The different, "regularist" interpretation of physical laws in that domain is possible as well, and counterfactual arguments are not valid for such interpretation. (shrink)

Science today is an international business, of course, and there has hardly ever been a partition wall between the logical work in Poland and Germany. However, apart from long lasting personal scientific contacts there are good reasons to further intensify the relations between the German and the Polish Community of Logic and Logical Philosophy. So it was only natural to think about bringing them together at a scientific event in a friendly environment. This idea was carried out as a common (...) initiative of the Polish Association for Logic and Theory of Science (PTL) and of the German based Society for Analytic Philosophy (GAP). The First German-Polish Workshop on Logic and Logical Philosophy was held in Bachotek/Poland from September 10.–13., 1995. It was organized by Kazimierz Świrydowicz (PTL), Heinrich Wansing (GAP) and Max Urchs (both). This part of the present volume of Logic and Logical Philosophy is not the proceedings of the workshop. On one hand, not all the papers presented at the workshop (see previous page for the programme) are attended to this volume. Due to their more technical character, the contributions of Gregory Restall, Tomasz Skura, Heinrich Wansing, Andrzej Wroński and others will appear in the next number of Reports on Mathematical Logic. Some papers included in this issue were changed considerably for publication. On the other hand, colleagues who intended to join the workshop but had to cancel for some reason were invited to submit their material, too. We would like to thank the editors of both journals very kindly for their suggestion to publish the submitted material. (shrink)

In this paper we study symmetric inference systems (that is, pairs of inference systems) as refutation systems characterizing maximal logics with certain properties. In particular, the method is applied to paraconsistent logics, which are natural examples of such logics.

In their insightful article, Brent Kious and Margaret Battin (2019) correctly identify an inconsistency between an involuntary psychiatric commitment for suicide prevention and physician aid in dying (PAD). They declare that it may be possible to resolve the problem by articulating “objective standards for evaluating the severity of others’ suffering,” but ultimately they admit that this task is beyond the scope of their article since the solution depends on “a deep and difficult” question about comparing the worseness of two possible (...) scenarios: letting someone die (who could have been helped) with not letting someone die (whose suffering could only be alleviated by death). In our commentary, we argue that creating such standards is more difficult than the authors assume because of the many types of deep uncertainties we have to deal with: (1) diagnostic, (2) motivational, and (3) existential. (shrink)

While agreeing with the main conclusion of Dominic Wilkinson and colleagues (Wilkinson, Butcherine, and Savulescu 2019), namely, that there is no moral difference between treatment withholding and withdrawal as such, we wish to criticize their approach on the basis that it treats the widespread acceptance of withdrawal aversion (WA) as a cognitive bias. Wilkinson and colleagues understand WA as “a nonrational preference for withholding (WH) treatment over withdrawal (WD) of treatment” (22). They treat WA as a manifestation of loss aversion (...) and refer to Kahneman and colleagues (1991), which defined this effect as follows: “the disutility of giving up an object is greater that the utility associated with acquiring it” (194). In a previous work, Wilkinson and Savulescu understood nonequivalence between treatment withholding and withdrawal as a reflection of slightly different, although related, phenomena: status quo bias or omission bias (Wilkinson and Savulescu 2012, 130–131). In neither of these two papers do they describe precisely the relation between these well-known psychological effects and WA, nor do they explain why they treat these effects as examples of nonrational preferences, despite the fact that these issues have been the subject of wide-ranging discussions on the intersection of psychology, economy, and philosophy. (shrink)

The attitude towards death and dying reflects the society’s view on a human being as a subject. Due to the progress in medical science a growing interest has been observed in the problem of death, including the right to dignified dying. One of the issues connected with the phenomenon of dying is the problem of euthanasia seen as one’s right to decide on one’s own death in extreme cases. The question of the legality of euthanasia is becoming a subject of (...) consideration more and more often, which is a result of a celebratory culture of death and the obsolescence of faith and religious practice. The aim of the following report is to show the attitude of major religions of the world towards euthanasia. What arguments of religious nature are against the legality of mercy killing? Both Christian and non-Christian religions rise to speak on the matter. All religions stress their veto over mercy killing, justifying their view in various ways. Christians claim that God is the donor and lord of life; a man cannot decide on ending human life as he or she is only the user, not the owner of it. Judaism assumes that human life has an absolute value, is sacred, untouchable, as God’s gift. Islam, quoting Koran, also preserves life as God’s gift. According to Buddhist ethics, the annihilation of both one’s own and someone else’s life is the worst of evil deeds. Will the arguments of religious nature mean enough to stop the legality of euthanasia? (shrink)

Juristic argumentation must in normal cases lead to a positive conclusion. The adoption of the rules of the burden of argumentation is, therefore, necessary. It is the task of the normative theory of juristic argumentation to formulate and to justify these rules., The rules of the burden of argumentation are constitutive rules. They do not impose duties or obligations to justify, but they state under what conditions a thesis counts as justified. The basic problem lies in the second‐order justification, that (...) is, in the justification of the rules of the burden of argumentation. Their rational justification is a precondition for rational juristic discourse. (shrink)