We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We (...) focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...) that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain (...) ordering on ideals. (shrink)

We present several naturally defined σ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such σ-ideals.

We investigate several ideal versions of the pseudointersection number \(\mathfrak {p}\), ideal slalom numbers, and associated topological spaces with the focus on selection principles. However, it turns out that well-known pseudointersection invariant \(\mathtt {cov}^*({\mathcal I})\) has a crucial influence on the studied notions. For an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal J})\) introduced by Borodulin-Nadzieja and Farkas (Arch. Math. Logic 51:187–202, 2012), and an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal I},{\mathcal J})\) introduced by Repický (Real Anal. Exchange 46:367–394, 2021), we have $$\begin{aligned} (...) \min \{\mathfrak {p}_\mathrm {K}({\mathcal I}),\mathtt {cov}^*({\mathcal I})\}=\mathfrak {p},\qquad \min \{\mathfrak {p}_\mathrm {K}({\mathcal I},{\mathcal J}),\mathtt {cov}^*({\mathcal J})\}\le \mathtt {cov}^*({\mathcal I}), \end{aligned}$$ respectively. In addition to the first inequality, for a slalom invariant \(\mathfrak {sl_e}({\mathcal I},{\mathcal J})\) introduced in Šupina (J. Math. Anal. Appl. 434:477–491, 2016), we show that $$\begin{aligned} \min \{\mathfrak {p}_\mathrm {K}({\mathcal I}),\mathfrak {sl_e}({\mathcal I},{\mathcal J}),\mathtt {cov}^*({\mathcal J})\}=\mathfrak {p}. \end{aligned}$$ Finally, we obtain a consistency that ideal versions of the Fréchet–Urysohn property and the strictly Fréchet–Urysohn property are distinguished. (shrink)

We show that there exist uncountably many pairwise nonisomorphic density-like ideals on $\omega $ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80, pp. 1268–1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.

Mental imagery, a fascinating yet contentious phenomenon, has a rich research history. Kant, for instance, believed mental imagery was necessary for perception. However, since the early 20th centur...

The mainstream concept of death—the biological one—identifies death with the cessation of an organism. In this article, I challenge the mainstream position, showing that there is no single well-established concept of an organism and no universal concept of death in biological terms. Moreover, some of the biological views on death, if applied in the context of bedside decisions, might imply unacceptable consequences. I argue the moral concept of death—one similar to that of Robert Veatch—overcomes such difficulties. The moral view identifies (...) death with the irreversible cessation of a patient’s moral status, that is, a state when she can no longer be harmed or wronged. The death of a patient takes place when she is no longer capable of regaining her consciousness. In this regard, the proposal elaborated herein resembles that of Veatch yet differs from Veatch’s original project since it is universal. In essence, it is applicable in the case of other living beings such as animals and plants, provided that they have some moral status. (shrink)

Foundations of Science recently published a rebuttal to a portion of our essay it published 2 years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy’s use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning (...) the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy’s mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno’s flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz. (shrink)

Singer claims that there are two ways of challenging the fact that brain-dead patients, from whom organs are usually retrieved, are in fact biologically alive. By means of the first, the so called dead donor rule may be abandoned, opening the way to lethal organ donation. In the second, it might be posited that terms such as “life” and “death” do not have any primary biological meaning and are applicable to persons instead of organisms. This second possibility permits one to (...) acknowledge that brain-dead patients are deceased because they are irreversibly unconscious. In the commentary which follows, I will argue that Singer’s second option is preferable since it provides a higher amount of organs available for transplant, and is better suited to the meaning of “death” which occurs in ordinary language. I will also defend such a concept of death against the objections raised by Michael Nair-Collins in the article Can the brain-dead be harmed or wronged? On the moral status of brain death and its implications for organ transplantation. (shrink)

Two eight-century Jaina contemporaries, a Śvetāmbara philosopher Siddhasena Mahāmati and a Digambara Akalaṅka Bhaṭṭa revolutionised Jaina epistemology, by radically transforming basic epistemological concepts, which had been based on canonical tradition. The paper presents a brief historical outline of the developments of basic epistemological concepts in Jaina philolosophy such as the cognitive criterion and logical faculties as well as their fourteen typological models which serve as the backdrop of important innovations in epistemology introduced by Siddhasena, Pātrasvāmin and Akalaṅka. An important contribution (...) of these Jaina thinkers was to economize Indian logic and the rules of inference, first, by devising only one kind of logical reason called ‘inexplicability otherwise’, based on the single inseparable connection of the proving property with the inferable property, and, second, by limiting the necessary number of the members of the proof formula merely to two. These two innovations were related to the thinkers’ intention to devise a logic which would not primarily be based on empirical verification but its structural patterns would be valid irrespective of external observation. Further, the paper focuses on the nature of the epistemological shifts which Siddhasena and Akalaṅka introduced independently of each other and on the question how Siddhasena’s and Akalaṅka’s ideas were partly anchored in Buddhist concepts of the pramāṇa school of Diṅnāga and Dharmakīrti. With the Buddhist background, Siddhasena sought to define the criteria essential to distinguish true from false cognitions and to provide a novel classification of the pramāṇas. He can further be accredited with formulating the first Jaina descriptive definition of the cognitive criterion. The final section of the paper explains how Akalaṅka applies novel epistemological ideas, first, to construct realistic ontology and objectivity of both the external world and the cognising subject, and, secondly, to combat fundamental Buddhist concepts such as idealism and momentariness. (shrink)

In this paper, I discuss the interpretation of the method of deconstruction in David J. Gunkel’s Deconstruction (MIT Press 2021). I focus on the relationship between deconstruction and truth. I hold that the concept of truth is indispensable for deconstruction since truth introduces correctness conditions for the deconstructive method. However, I claim that truth, being essential and primitive for deconstruction, is fundamentally inaccessible for being analyzed by the latter. ------------------------- Received: 19/10/2022. Reviewed: 13/12/2022. Accepted: 20/12/2022.

In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false.

Planning organizes our actions and conditions our effective-ness. To understand this philosophical hint better, the author investigates and juxtaposes two important accounts in action theory. He discusses the concept of a plan proposed by Tadeusz Kotarbiński in his praxiology (theory of efcient action), and the so called “planning theory of intention” by Michael E. Bratman. The conceptual meeting of these two proposals helps to remove aws in Kotarbiński’s action theory, it also shows the way, in which we can enrich the (...) idea of plans in the frame-work of intentions. Generally, praxiology occurs to be still an important perspective in action theory, which particularly shows how we can improve our understanding of planning when confronted with infuentialcontemporary accounts. (shrink)

Despite its importance, the work is rather secondary in the sense that it relies, for the most part, on the Buddhist logical legacy. The first extant commentary is the Nyayavatara-vivrti of Siddharsigani.

The structure of this paper is as follows. My starting point is psychological flexibility (henceforth, PF) as it has been presented in psychology. Here I offer a synthetic view which embraces the most crucial aspects of flexibility, and describes its functional roles and underlying mechanisms. Secondly, I move my attention onto the field of current action theory and discuss two elementary concepts we commonly use when describing our actions: intention and desire. Of course, there are many “theories of desire” and (...) there is no point in trying (nor even the option) to discuss all of them under one heading. To show where the question of PF sneaks into the scene of action theory, I explore the idea of the resistance of desire, as proposed by Timo Airaksinen. The second concept to investigate at this stage is intention. As in the previous case, it is plain that there are plenty of accounts of intentions and there are many roles they play in the phenomenology of action. For the purposes of this paper, we need only something that can be interpreted as an approach to PF. Such an approach can be found in the idea of stability of intention or a plan, discussed famously by Michael Bratman. According to my interpretation, these two ideas, resistance of desire and stability of intention, allow to initially understand some important aspects of PF in action theory. To get a slightly more comprehensive view – and to supplement the outcomes gained on the grounds of the analyses of these two accounts – I introduce, in the third step, the concept of plasticity which comes from the so-called praxiology proposed by Tadeusz Kotarbiński (Lvov-Warsaw School). I try to show how this concept is still feasible and how it may enrich current philosophical accounts of agential flexibility. The strategy behind this stage of the paper is to enrich the Bratmanian approach to psychological stability. The last part of the paper contains some remarks on the philosophical outcome of the interdisciplinary approach to PF. (shrink)

This is an expository paper on the problem of independent axiomatization of any set of sentences. This subject was investigated in 50's and 60's, and was abandoned later on, though not all fundamental questions were settled then. Besides, some papers written at that time are hardly available today and there are mistakes and misunderstandings there. We would like to get back to that unfinished business to clarify the subject matter, correct mistakes and answer questions left open by others. We shall (...) deal with results of many authors. However, they will be exposed in a different manner, with complete proofs and, often, with refinements and supplements. Some questions will be brought up to date and related to other questions in logic. New results and questions will also be added. Stress will be laid on constructive aspects; that is, we will examine the problem of the possibility of independent axiomatization as well as algebraic means by use of which independent sets of axioms can be given. (shrink)

Przedmiotem artykułu jest rozważenie znaczenia zmian, jakie dla form działania podmiotowego (duchowości) mają zmiany technologicznie. Przyjmując, że pewne punkty zaczepienia takiej refleksji dostępne są w popkulturowych formach oswajania postępu, jako osiowe wybieram pojęcie „dżihadu buteriańskiego” z powieści Diuna Franka Herberta, scalające kilka istotnych aspektów tak rozwoju technicznego, jak i refleksji nad nim. W części pierwszej, koncentrując się na drugim składniku tego wyrażenia, omawiam pogląd Samuela Butlera oraz wskazuję na znaczenie wystąpienie luddystów w początkach XIX w. W części drugiej rozwijam ten (...) wątek, omawiając krytykę społeczeństwa technologicznego formułowaną przez współczesnych anarchoprymitywistów. W części trzeciej zwracam uwagę na pierwszy element wyrażenia Herberta by wskazać na podmiotowe aspekty zmian technologicznych. W konsekwencji wskazuję kierunki analizy, dzięki którym etyka cnót może wypracować adekwatną odpowiedź na zagrożenia płynące ze strony technologii przy akceptacji korzyści zeń płynących. (shrink)

Aristotle in Analytica Posteriora presented a notion of proof as a special case of syllogism. In the present paper the remarks of Aristotle on the subject are used as an inspiration for developing formal systems of demonstrative syllogistic, which are supposed to formalize syllogisms that are proofs. We build our systems in the style of J. Łukasiewicz as theories based on classical propositional logic. The difference between our systems and systems of syllogistic known from the literature lays in the interpretation (...) of general positive sentences in which the same name occurs twice (of the form SaS). As a basic assumption of demonstrative syllogistic we accept a negation of such a sentence. We present three systems which differ in the interpretation of specific positive sentences in which the same name occurs twice (of the form SiS). The theories are defined as axiomatic systems. For all of them rejected axiomatizations are also supplied. For two of them a set theoretical model is also defined. (shrink)

This paper analyzes selected issues related to the philosophy of the Krakow physicist Andrzej Fuliński. Since the 1970s, Fuliński has been strongly associated with the interdisciplinary milieu gathered around Heller and Życiński. His activity can therefore be considered within the context of the broader phenomenon known as the Krakow School of Philosophy in Science, which was founded by Heller and Życiński. This paper proposes the thesis that Fuliński’s style of philosophy is connected with the concept of philosophy in science and (...) tries to justify the thesis that Fuliński, due to his cooperation with the interdisciplinary milieu in Krakow and the specificity of his philosophical works, deserves to be regarded as a representative of the Krakow School of Philosophy in Science. (shrink)

This paper depicts my conception of the philosophy of religion. I think that there nothing like religion in general. The world of what is customarily called religion is a very different and analogous reality. I make Catholic Christianity the starting point of this philosophy of religion. I treat it as the main analogy to the world of religion. The objective aim of the philosophy of religion is threefold: 1) description of religion, 2) justification of religion, 3) epistemology of religious beliefs. (...) In the philosophy of religion understood in this manner I use methods proper to general metaphysics, philosophical anthropology, and theory of knowledge. (shrink)

We present a dynamical model of interaction between recognition memory and affect, focusing on the phenomenon of “warm glow of familiarity.” In our model, both familiarity and affect reflect quick monitoring of coherence in an attractor neural network. This model parsimoniously explains a variety of empirical phenomena, including mere-exposure and beauty-in-averages effects, and the speed of familiarity and affect judgments.

Pessoa (2013) makes an impressive case that emotion, motivation, and cognition are neurally intertwined. Our commentary broadens the discussion to the functional, “mind” level. We argue that philosophical and computational considerations justify some modern “separatist” views. We highlight several psychological phenomena that illustrate independence, including affective and motivational reactions to rudimentary inputs, and the guiding role of such reactions in cognition.

Important problems of justice are raised by a project according to which the sovereign gives to victims the right to pardon a wrongdoer orally or in a testament. The author supports such an individualization of the right to pardon, which would turn the state into a contractor who is hired by citizens exclusively to guarantee them security and self-possession.

THE PROBLEM OF BEING IN PLATONISM FROM THE PERSPECTIVE OF THOMAS AQUINAS. A META-SYSTEMATIC ESSAY In spite of the apparent opposition to Plato, Aristotle accepted a lot from the thought of his master. The intuition, which plays the key role in the system of Plato, was understood by Aristotle in terms of how we grasp the middle term of syllogism. It is not, therefore, the intuition of being, but the reasoning, departing from the experience (nature’s “intention”), which is the way (...) of the cognition of the ultimate. The teleology of being, which Plato was so keen on finding, was found by Aristotle in the physical world as a counterpart of motion. Alas, Aristotle lost sight of what is most valuable in Plato: the sense of being that transgresses the categories. According to Thomas, being is what is the most perfect in things; so, consequently, what is the proper effect of the Ultimate Cause, and what is Its primary aim. It is better to be, i.e. to exist. Each thing craves for being. Being, however, is, in the Dionysius’ sense, a problem; it might guide us to God, but veil Him before us as well. It is a perfection, but not the Perfection itself, Plato was right at this point. Keywords: BEING, PLATO, ARISTOTLE, THOMAS AQUINAS. (shrink)

The paper explores possible influences that recent developments in the field of a branch of AI called Automated Discovery Systems might have upon some aspects of the old debate between Francis Bacon’s inductivism and Karl Popper’s falsificationism. Francis Bacon advocates mechanical induction as the legitimate, infallible method of science, and Karl Popper proposes his famous falsificationist view, according to which science proceeds by subsequent conjectures and refutations, and the question about where scientific hypotheses come from neither needs, nor is capable (...) of, logical analysis. The traditional method of discussing such methodological debates relies on the analysis of various historical examples of discoveries in order to see how well the two models of scientific method account for them. (shrink)