We show that it is consistent with MA + ¬CH that the Forcing Axiom fails for all forcing notions in the class of ωω–bounding forcing notions with norms of [17].

This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

Singh asserts that the parent–child relationship engenders a moral responsibility for the newborn. Simultaneously, he contends, drawing on the argument from potentiality, that the fetal stage of human development does not establish the parent–child relationship. Consequently, within Singh’s proposed relational framework, moral responsibility for the developing fetus does not manifest. Thus, Singh advocates for abortion, citing the absence of moral responsibilities arising for the pregnant woman for the fetus. In this article, I critique Singh’s argument from potentiality, identifying flaws and (...) highlight the incoherence of the argument pertaining to the parent–child relationship. (shrink)

In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We (...) formulate an axiomatization of mereological structures, different from Tarski’s axiomatization aspresented in [10] . We prove that these axiomatizations are equivalent . Of course, these axiomatizations are definitionally equivalent to thevery first axiomatization of mereology from [5], where the relation of being aproper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology”from [9] is essentially weaker than Leśniewski’s mereology. (shrink)

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

The paper contains an exposition of some non standard approach to gentzenization of modal logics. The first section is devoted to short discussion of desirable properties of Gentzen systems and the short review of various sequential systems for modal logics. Two non standard, cut-free sequent systems are then presented, both based on the idea of using special modal sequents, in addition to usual ones. First of them, GSC I is well suited for nonsymmetric modal logics The second one, GSC II (...) is devised specially for symmetric, i.e. Blogics. GSC I and GSC II are not different formalizations, from the theoretical point of view GSC I may be seen as a simplification of the more general approach present in GSC II. They are considered separately, mainly because Blogics demand different, and more complicated, strategy in completeness proof, whereas non symmetric logics are easily and uniformly characterised by means of Fitting's Consistency Properties. The weakest modal logic captured by this formalization is minimal regular logic C, but many stronger logics are obtainable by addition of suitable structural rules, which conforms to Do en's methodology. Both variants of GSC satisfy also other, besides cut-freedom, desirable properties. (shrink)

Provability, Computability and Reflection.

This book introduces the English-speaking reader to the thought of Stanislaw Brzozowski (1878-1911), the outstanding Polish philosopher and literary critic. Although practically unknown in the West, Brzozowski is an important but neglected forerunner of the intellectual tradition of `Western Marxism', most commonly associated with Georg Lukács and Antonio Gramsci. -/- Concentrating first on the early phase of Brzozowski's thought, Professor Walicki goes on to analyse his ideas on the working class and its relation to the intelligentsia and contemporary working-class ideologies. (...) Finally he deals with aspects of his thought which go beyond the Marxian problematic and round off the intellectual portrait of the man. -/- Brzozowski's anti-naturalistic approach resulted in a radical reinterpretation of Marxism which dealt with many of the problems of the revolt against positivism in European philosophy. Professor Walicki argues that the retrieval of the philosophical and humanist aspect of Marxism, and its separation from the Engels-inspired `scientific Marxism', was the achievement of Brzozowski and not, as frequently assumed, of Lukács, who came to similar conclusions only some ten years later. -/- By placing Brzozowski within the cross-currents of the various philosophical, sociological, literary, and political streams of Western and Eastern European thought in which Marxism was situated, Professor Walicki produces a fascinating study of an early East European challenge to orthodox Marxism. (shrink)

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

By and large, Inferential Erotetic Logic (IEL, for short) is an approach to the logic of questions which puts in the centre of attention inferential aspects of questioning. IEL is not an enterprise of the last few years only. The idea originates from the late 1980s. It evolved through time. Initially, the stress was put on the phenomenon of question raising. This changed gradually, as some forms of reasoning that involve questions have appeared to be analyzable by means of the (...) conceptual apparatus developed. In this essay I present the basics of IEL and comment on them. Most, though not all, of the ideas discussed here have been scattered across my earlier publications. The invitation from the organizers of the Asking and Answering workshop (Greifswald, September 2020) resulted in an attempt of presenting the themes of IEL in a concise but, as I hope, also comprehensible way. (shrink)

This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ + (for a strongly inaccessible cardinal λ).

Using two distinct membership symbols makes possible to base set theory on one general axiom schema of comprehension. Is the resulting system consistent? Can set theory and mathematics be based on a single axiom schema of comprehension?

Among issues considered in contemporary ethics, apart from concepts such as good, value and justice, there is also the concept of care, discussed extensively in feminism. The article presents and analyses this ethical concept. It shows some problems with the translation of the English word ‘care’ into the Polish equivalent ‘troska’. The focus here, however, is mainly on the way of understanding the concept of care among feminist ethicists, such as Virginia Held, Nel Noddings, Joan Tronto, Diemut Bubeck, and Sara (...) Ruddick. For all of them, care is a relation, though they differ in their account of the specificity and meaning of this relation. (shrink)

This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.

The epidemiological situation resulting from the SARS-CoV-2 pandemic caused the Polish universities to fully switch to distance education in March 2020. Medical e-learning has not yet been broadly implemented into the education process. Therefore, examples of successful e-learning implementations or the organization of the process of medical e-learning offer a valuable source of knowledge today, which is needed immediately. The article presents e-learning practices at the Polish medical universities during the SARS-CoV-2 epidemic during the period from March to September 2020, (...) covering seven universities in Poland that offer medical and health studies. The organization and implementation of e-learning classes is presented, including knowledge evaluation practices, providing example decisions issued by university rectors, on which the teaching process was based. A detailed presentation of the schools’ organizational units or workgroups that played an important role in the process of coordination of measures supporting e-education is also included. The article also presents a description of the software applications, utilities, and services used at the schools in the course of the process of online education. Below are some examples of specific such implementations in selected university courses. (shrink)

This is a summary of a talk delivered at the Winter School of Logic held in Rabka, 24.02 – 04.03.1986 by the Department of Logic of the Jagiellonian University. We wish to announce here several results on embeddability of quotient algebras of certain kind into algebras of some varieties related to the class of Heyting algebras. A “by product” is the deduction theorem for a large family of intermediate consequence operations.

We prove that the Sacks forcing collapses the continuum onto ${\frak d}$ , answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses $\omega_2$ then it forces $\diamondsuit_{\omega_{1}}$.

In this article, the author notes that Thomas Aquinas, in his brief work entitled De Ente et Essentia, proved that at the base of understanding the world, the human being, and God in particular, there is our understanding of being and its essence. When we make a small mistake at the beginning in our understanding of being and its essence, it will turn to be a big one in the end. And what is “at the end” of our knowledge is (...) the discovery of the First and Ultimate Cause of all things, known as: Ipsum Esse, God, the Absolute, The Most Perfect Substance, on whom everything depends, and who depends not on anything else. These present inquiries about the proper understanding of being and its essence are aimed at formulating proof of the necessity of existence of a Being that is the First Cause, and which, existing as Ipsum Esse, is the source and reason of existence of all beings. Without these inquiries, the proof itself would be incomprehensible, and more importantly it would be a purely a priori one. Furthermore, without the existential conception of being, which Thomas first formulated, one could not discover the First Cause which, as Ipsum Esse, is the source of the existence of every being. This issue seems to have escaped the attention of the author of the book Aquinas’s Way to God. The Proof in “De Ente et Essentia.”. (shrink)

A lattice L is split by a pair ha; bi, a; g 2 L i b is the smallest element of the set fx 2 L : x 6 sg or equivalently i = ; and = L. The concept of splitting is due to R. N. McKenzie [2] who characterized splittings of the lattice of all varieties of lattices. In a more general setting the concept was studied by A. Day in [1]. Our aim is to investigate splittings of (...) the lattice of subquasivarieties of a quasivariety. (shrink)

The concepta question is reducible to a non-empty set of questions is defined and examined. The basic results are: (1) each question which is sound relative to some of its presuppositions is reducible to some set of binary (i.e. having exactly two direct answers) questions; (b) each question which has a finite number of direct answers is reducible to some finite set of binary questions; (c) if entailment is compact, then each normal question (i.e. sound relative to its presuppositions) is (...) reducible to some finite set of binary questions. (shrink)

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 23 Heft: 1 Seiten: 179-203.

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's (...) second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

True Darwinian Ethics -/- Darwin’s model for the evolution of morality as presented in Descent of Man (1871) is shown to comprise three major stages that are here referred to as empathic premorality, tribal morality, and universalizing morality. Empathy, the key component of Darwin’s “social instincts” that started moral evolution, is here recognized as the principal cognitive device that conveys epistemic credibility to moral agency. The two constitutive elements of the tribal morality are conscience that Darwin conceived of as a (...) conflict between a lasting social motive and an immediate selfish impulse, and true altruism that evolved as a result of group (community) selection. Darwin’s genius recognized the uniqueness of group selection in human evolution as being dependent on mental faculties and speech that facilitated habit formation through praise and blame form other group members, with empathy as a gauge of others’ emotional reactions. Contrary to repeated claims, Darwin did not derive morality from reciprocity that he (and his contemporaries) considered to be “a low motive”, and adduced it only as a mechanism of habit formation. The universalizing morality was brought about by the increasing powers of intellect that led to respecting individual lives (rather than group interests only) and extending humane concerns beyond one’s group, ultimately to all sentient beings, which places Darwin among the spiritual fathers of modern humanitarianism. In terms of substantive ethics, Darwin’s views support moral individualism that requires to treat each subject according to his/her individual characteristics rather than any group membership. Darwin’s moral individualism and universalism have been elaborated by Peter Singer as the principle of equal consideration of interests and the expanding circle of ethics, respectively. Darwin’s model of moral evolution, which starts with intuitive but epistemically reliable moral agency and then allows for its rational improvement, provides a way out of the moral subjectivism of evolutionary ethics that reduces morality to an adaptation to social life. The primary or core morality that relies on empathy and implements reciprocity supports welfare (wellbeing) of a group and its members. Welfare (which has been defined by Darwin) is a basic “terminal” (ultimate) value that constitutes an objective, measurable fact. Since the primary morality supports welfare, it is objectively good, which justifies an ethical reasoning that such morality ought to be extended (with appropriate adjustments) to all sentient beings. Confusion over the status of morality is largely due to the lack of appreciation of its complexity: not only had its motivational apparatus (known as the moral agency) evolved by superposition of many emotional and pure cognitive mechanisms, but it has subsequently been co-opted to implement prudential, religious and possibly other norms that are accidental and sometimes contrary to its original social function. Those secondary morality norms are now enforced by the moral agency but lack moral objectivity and thus may support the perception of moral subjectivism and relativism. In short, true Darwinian ethics is based on the scientific axiology that recognizes evolutionary origins of all values, requires respecting all values that are experienced by each and every subject according to its individual characteristics, and calls for a critical assessment of each and every received morality. (shrink)

DARWIN’s (1859, 1871) discoveries have profound ethical implications that continue to be misrepresented and/or ignored. In contrast to socialdarwinistic misuses of his theory, Darwin was a great humanitarian who paved the way for an integrated scientific and ethical world view. As an ethical doctrine, socialdarwinism is long dead ever since its defeat by E. G. Moore although the socialdarwinistic thought is a hard-die in the biological community. The accusations of sociobiology for being socialdarwinistic are unfounded and stem from the moralistic (...) fallacy that is, a false assumption that morality is good by definition. Both social and developmental psychology demonstrate that the moral agency is a motivational device for executing reciprocity that remains at the core of any morality across all studied societies and throughout the ontogeny of moral judgment. The level of true universalizing ethical reflection (KOHLBERG’s postconvential stages or GIBBS’s existential phase) is achieved by a small minority of humans, thus showing that Homo sapiens is a moral but not an ethical animal. While the origin of reciprocity has been perfectly explained by sociobiology, the evolutionary assembly of affective and cognitive elements that make up the moral agency is being successfully studied by the social/personality/developmental psychology as extended to non-human primates. As DARWIN (1871) expected, the key innovation for the evolution of moral agency was the emergence of empathy that evolved independently at least three times: in elephants, dolphins and primates. Empathy has a motivational power of its own; it is also necessary for moral agency that requires two cognitive abilities: reflective self-consciousness and understanding of causality; the two make possible the attribution of responsibility. All these requirements are met by the chimpanzees whose moral agency operates in dyads. In contrast, the human moral agency allows for a third party intervention that opens up vast opportunities for ideologies, especially religions, to use and misuse the moral agency to enforce a reciprocation that may be harmful to both individuals and the entire group. Also, the moral agency is known to enforce enhanced intragroup cohesion and loyalty in response to conflict and war, which suggests that the two prima facie opposed human universals, morality and warfare, may have coevolved. The most important ethical consequence that follows from the increasing understanding of the primate moral agency is that every received morality is ethically flawed, none can be taken as a paragon of goodness, and each needs corrections by science-informed ethics. In fact, Darwin pioneered the integration of science and ethics, an approach that has come to be appreciated only recently under the heading of consilience. (shrink)

The evolutionary function of love is to create a strong bond between the partners with reproduction in view. In order to achieve this goal, humans use various sexual/reproductive strategies, which have evolved due to specific reproductive benefits. The use of particular strategies depends on many factors but one of the most important is early childhood experiences, on which life history theory focuses. John Lee identified 6 basic love styles: eros, ludus, storge, pragma, agape, and mania. Our goal was to check (...) whether love styles may be treated as sexual/reproductive strategies in the context of LHT - slow or fast strategy. In our study we found that people who prefer the slow reproductive strategy are inclined to show passionate, pragmatic and friendly love, and those who prefer the fast strategy, treated love as a game. A low level of environmental stress in childhood results in preferring eros, storge and agape love styles, belonging to the slow strategy, and a high one results in preferring ludus, which belongs to the fast strategy. People representing eros, storge or pragma styles have restricted sociosexual orientation so they prefer long-term relationships, whereas those with the ludus style are people with unrestricted orientation, preferring short-term relationships. Besides, storge, agape and pragma seem to determine preferring qualities connected with parental effort in one’s partner, mania - with mating effort, and eros - with both kinds of effort. No correlation was found between the love style and the number of children. (shrink)