An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the (...) authors knowledge, this is the first account of resolution for mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing. (shrink)

The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity ( ISCI ); a syntactically motivated \(\mathsf {ND}^1_{\mathsf {ISCI}}\) and a semantically motivated \(\mathsf {ND}^2_{\mathsf {ISCI}}\). The formulation of \(\mathsf {ND}^1_{\mathsf {ISCI}}\) is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI -specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due (...) to the normalization procedure non-subformulas can label only leaves of proofs. In \(\mathsf {ND}^2_{\mathsf {ISCI}}\), we propose only two general identity-related rules, in reference to the treatment of the identity connective in First-Order Logic. (shrink)

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved in full generality.

The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.

We introduce a notion of ideal type such that any two ideals with the same ideal type are isomorphic. From this we infer, under the axiom t = h, that each ideal which consists of all nowhere Ramsey sets contained in some family of infinite subsets of natural numbers is isomorphic with the ideal of all nowhere Ramsey sets.

p-consequence (plausible consequence; see [2]) allows for a formulation of non-deductive reasonings, i.e., such where the conclusion has weaker justification then assumptions and thus when added to the set of assumptions results in its extension. But theoretical modesty of p-consequence operation does not tell the difference between “good” and “worse” conclusions. Therefore the bisconsequence is introduced.

This paper aims to present how logic may undermine a parliamentary assault on democratic institutions based on the analysis conducted with reference to the so-called Polish constitutional crisis. I analyse whether a law can be reviewed on the basis of this law itself. The Polish Constitutional Tribunal faced such a problem while passing the verdict of 9th March, 2016, regarding the constitutionality of the amendment to the Statute on the Constitutional Tribunal from 22nd December, 2015. This problem, called a ‘verdict (...) paradox’, was claimed to be a type of the Liar paradox. I argue that, contrary to the common view, the problem of the verdict paradox is not based on the Liar paradox; for this purpose, a logical analysis is applied to four variants of a reasoning with regard to the constitutionality of the said amendment. The distinction between two levels of analysis concerning emerging reasonings, namely an abstract level and a concrete level placed in the context of the legal system, is also introduced. This paper demonstrates that although only two variants of the reasoning concerning a law’s judicial review based on the law itself involve logical contradiction, the possibility of employing reasonings from other variants must be excluded, albeit due to alternative reasons. Therefore, the Constitutional Tribunal’s decision to avoid the verdict paradox by passing over the reviewed provisions in the review process was correct and might be perceived as an example of how logic and reason can defend the institutional guarantees of political freedom. (shrink)

In my paper I present David Hume's philosophy from the perspective of Charles Sanders Peirce's theory of signs. I argue that by interpreting impressions and ideas as iconic signs it is possible to avoid many inconsistencies in Hume's philosophy. Apart from that it makes possible to avoid Hume's scepticism about the existence of the external world by introducing Peirce's concept of the dynamic and immediate object. What is more, the generative structure of signs helps us to deal with the "gmissing (...) shade of blue" problem. (shrink)

Wittgenstein introduced his claim about colour incompatibility originally in the Tractatus Logico-Philosophicus , where he stated that there could be only one colour in one place and time. It is commonly believed that Wittgenstein abandoned his conception of logical atomism when he realized the consequences of this claim. The aim of this article is to provide an interpretation of the colour incompatibility claim in terms of Wittgenstein’s phenomenology. I will focus on two works of great significance for the claim: Some (...) Remarks on Logical Form and Philosophical Remarks . These two works were written between 1929 and 1930, which is the beginning of the “middle period” in Wittgenstein’s philosophy. I will focus not only on Wittgenstein’s formulation of the colour incompatibility claim, but also on how this claim was justified. The explanation of Wittgenstein’s justification of this claim will help to understand his phenomenology and theory of philosophical grammar. (shrink)

Dharmakīrti argues that there is no pramāṇa (valid means of cognition or source of knowledge) for a thesis that is a self-contradiction (svavacanavirodha). That is, self-contradictions such as ‘everything said is false’ and ‘my mother is barren’ cannot be known to be true or false. The contemporary scholar Tillemans challenges Dharmakīrti by arguing that we can know that self-contradictions are false by means of a formal logical inference. The aims of the paper are to answer Tillemans’ challenge from what we (...) take to be Dharmakīrti’s or Dharmakīrtian (someone who is like Dharmakīrti) perspective and to demonstrate the unique features of Dharmakīrti’s view of inference. By so doing, we show that the epistemology in relation to the formal conception of logic that underlies Tillemans’ challenge is problematic from Dharmakīrti’s or Dharmakīrtian perspective. The paper, thus, presents Dharmakīrti’s view of inference and logical reasoning as well as a Dharmakīrtian challenge to the formal conception of logic that is the dominant contemporary conception. (shrink)

Assume that there is no quasi-measurable cardinal not greater than 2ω. We show that for a c. c. c. σ -ideal [MATHEMATICAL DOUBLE-STRUCK CAPITAL I] with a Borel base of subsets of an uncountable Polish space, if [MATHEMATICAL SCRIPT CAPITAL A] is a point-finite family of subsets from [MATHEMATICAL DOUBLE-STRUCK CAPITAL I], then there is a subfamily of [MATHEMATICAL SCRIPT CAPITAL A] whose union is completely nonmeasurable, i.e. its intersection with every non-small Borel set does not belong to the σ (...) -field generated by Borel sets and the ideal [MATHEMATICAL DOUBLE-STRUCK CAPITAL I]. This result is a generalization of the Four Poles Theorem and a result from [3]. (shrink)

The COVID-19 pandemic caused university education to transition from face-to-face contacts to virtual learning environments. Young adults were forced to live an entirely new life online, without valuable and enjoyable social interaction. We examined subjective perspectives towards life online during the pandemic. We identified four viewpoints about life mediated by computers. Two viewpoints express “struggling”: Viewpoint 1 (Angry, Depressed and Overwhelmed), and Viewpoint 3 (Restricted to and Overwhelmed by Virtuality). A third feeling-state conveys experiences of “surviving”: Viewpoint 4 (Isolated and (...) Powerless in Convenience). Surprisingly, Viewpoint 2 is about “thriving” (Comfortable and Convenient Routine with Computers). The research shows that virtualization, confinement, and anxiety are taking a toll on the mental health of some members of the younger generation, while at the same time other members feel they are thriving in a situation of limited resources, virtuality, and reduced face-to-face human interaction. (shrink)

We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity. We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.

The article aims to present issues arising out of differences in the way that the terms chimera and hybrid are defined in legal systems and by natural sciences in the context of mixing human and animal DNA. The author analyses the different approaches to defining these terms used in various legal systems, dividing them into groups in light of conclusions reached from examining definitions used in natural sciences. The distinction is used to answer the question of which approach to definitions (...) applied by legislators is the best way to handle the subject of human-animal organisms, given the need to balance their impact on medicine and the ethical concerns that arise. (shrink)

Faces of liberalism: formation of a Christian liberal community in Krakow: The aim of the essay is to show the birth of the Kraków liberal community in the years 1977–1980. An attempt is made to reconstruct the main ideological assumptions of the liberal entourage in the context of the opposition activities of Robert Kaczmarek and Mirosław Dzielski. The author refers to the main events occurring in this period, such as the establishment of the Prywatna Inicjatywa Krakowska and the magazine Merkuryusz (...) Krakowski i Światowy, as well as paying special attention to the program texts that were published in it. The article also contains a reconstruction of the debate aimed at classifying the views presented by Mirosław Dzielski. (shrink)

E. T. A. Hoffmann is one of the most famous representatives of early German horror literature. He has been both, inspired by its predecessors, as well as having influenced the work of many of his successors, and hence the development of the whole genre. The present article examines a story by E. T. A. Hoffmann, “Vampirismus” from the collection of short stories “Serapions Brüder”. Emphases are, on the one hand, on the mechanisms that cause readers’ fear and uncertainty and, on (...) the other hand, the peculiarity of the vampire or Nachzehrer figure and their function in the story. Firstly, it will be shown that the vampire depicted in the work is not actually a vampire. We find here a ghoul; that is a demon from Arab culture. However, the ghoul has more to do with the monster outlined by Antoine Galland in his translation of the “One Thousand and One Nights” than with traditional folk beliefs. Secondly, the author comes to the conclusion that Hoffmann has functionalized the Horrible. This element does not work by itself, but serves the author as the background of the action. And he is using this background to let the characters reveal all their weaknesses and dark sides. The violation of the order ruling in the world as it is represented engages the reader and at the same time raises his fear. The resulting excited feelings and general alienation are further reinforced for the figure of the Nachzehrer that occurs instead of a formerly innocent, graceful girl. The emergence of the supernatural – the final confirmation of the breach of order – is responsible for the effect just described. (shrink)

p-consequence is intended as a formalization of non-deductive reasoning. So far semantical or general properties have been presented more thoroughly ([2]–[5]). In the present paper we would like to focus on its syntactic properties.

The aim of the paper is to compare the role played by logical analysis in Wittgenstein’s Tractatus logico-philosophicus and Russell’s On Denoting. Whereas in Russell’s work it is an important element of his argument in support of description theory, in his pupil’s it does not function this way. Russell, while analysing various propositions, including descriptions translates them into formal language, indicating that those propositions, despite the appearances, in fact do not denote. Logical analysis shall be a tool decisive in favour (...) of Russell’s thesis. Wittgenstein similarly analyses some troublesome propositions and claims that they are meaningless. The difference is that Russell’s final conclusion is derived from logical analysis, whereas Wittgenstein’s from pure speculation. In Tractatus logico-philosophicus logical analysis is not a method thanks to which the author gets certain result, just as it was the case with his teacher and his On Denoting. In Wittgenstein’s early philosophy logical analysis concerns just a few technical problems connected only to some ideas from Principia mathematica, and not to the main subject of his work, which is the analysis of philosophical theses. (shrink)

The liar paradox is still an open philosophical problem. Most contemporary answers to the paradox target the logical principles underlying the reasoning from the liar sentence to the paradoxical conclusion that the liar sentence is both true and false. In contrast to these answers, Buddhist epistemology offers resources to devise a distinctively epistemological approach to the liar paradox. In this paper, I mobilise these resources and argue that the liar sentence is what Buddhist epistemologists call a contradiction with one’s own (...) words. I situate my argument in the works of Dignāga and Dharmakīrti and show how Buddhist epistemology answers the paradox. (shrink)

Using “big data” from sensors worn continuously outside the lab, researchers have observed patterns of objective physiology that challenge some of the long-standing theoretical concepts of emotion and its measurement. One challenge is that emotional arousal, when measured as sympathetic nervous system activation through electrodermal activity, can sometimes differ significantly across the two halves of the upper body. We show that traditional measures on only one side may lead to misjudgment of arousal. This article presents daily life and controlled study (...) data, as well as existing evidence from neuroscience, supporting the influence of multiple emotional substrates in the brain causing innervation on different sides of the body. We describe how a theory of multiple arousals explains the asymmetric EDA findings. (shrink)

Our main inspiration is the work in paper (Gitik and Shelah in Isr J Math 124(1):221–242, 2001). We will prove that for a partition \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document} of the real line into meager sets and for any sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}_n}$$\end{document} of subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}}$$\end{document} one can find a sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{B}_n}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{B}_{n}}$$\end{document}’s are pairwise disjoint and have the same “outer measure with respect to the ideal of meager sets”. We get also generalization of this result to a class of σ-ideals posessing Suslin property. However, in that case we use additional set-theoretical assumption about non-existing of quasi-measurable cardinal below continuum. (shrink)