El artículo trata sobre el proceso por el que el hombre llegó a ser un modelo para la metodología patrística. Presenta algunas articulaciones esenciales de la antropología filosófica, implícitas en toda la teología patrística. Afirma que la antropología como hermenéutica de la teología patrística, debe entenderse como un intento de presentar la importancia de las enseñanzas patrísticas y su interpretación específica, desde la importancia de las enseñanzas patrísticas y su interpretación específica, desde la perspectiva antropológica de los Padres de la (...) Iglesia. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

In the following paper sources of a constitution are put in question in general, and more specifically, the constitutional culture of the European Union Law is being investigated in-depth with regard to principles of deliberative democracy and rulings of the Court of Justice of the European Union. The change of a law application paradigm as well as the change of a legal systems’ nature are taken into account.

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a group scheme action.

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofinal structure of local bases in the groups C(X, R) of continuous real-valued functions on complete metric spaces X, with respect to the compact-open topology.

Presenting state-of-the-art work on the conscious and unconscious processes involved in emotion, this integrative volume brings together leading psychologists, ...

Children who experience parentification may have trouble performing developmental tasks due to being overwhelmed by their family caregiving roles and responsibilities. Past studies have found that parentification is negatively associated with academic achievement. However, most of these studies are limited in that they are retrospective and examine the association but not the mechanisms shaping them. The aim of the study was to explore to what extent diverse types of parentification relate to academic achievement and to what extent these relations are (...) mediated by self-reported quality of life among adolescents. The study sample was composed of Polish early adolescents. Types of parentification were measured with the Parentification Questionnaire for Youth, and quality of life was assessed with KidScreen27. School achievement was measured based on mean semester grade. We explored the associations among study variables and performed six mediation models in the planned analyses. Overall, bivariate relations were significant in a theoretically expected way, although the effect sizes for these associations were rather small. In the mediation analyses, the results showed that four of the six models were not significant. Different from previous studies, instrumental parentification was positively related to school achievement. Additionally, this positive association was mediated by adolescents’ general quality of life. Taken together, the findings were similar and different from the empirical literature base on types of parentification and select outcomes. (shrink)

The article presents the question of understanding divine causality and its analogical character in the context of Thomas Aquinas’s teaching on Divine Providence. Analyzing Aquinas’s texts concerning the relation of God’s action towards nature and its activities it is necessary to emphasize the proper understanding of mutual relations between secondary causes and the primary cause which are not on the same level. Influenced by the reflection of M. Dodds and I Silva, the author of the article refers to Aquinas’s biblical (...) commentaries which have not been discussed so far from the perspective of the character of God’s action. In the final part of the article, metaphors used by Thomas in reference to the relation of God towards the world will be presented. (shrink)

Maria Kokoszyńska-Lutmanowa (1906-1981) was a Polish philosopher and student of Kazimierz Twardowski, the founder of the Lvov-Warsaw School. In 1938 she went to the University of Cambridge (Newnham College) on a Sarah Smitton Fellowship. There she attended George Edward Moore’s lectures as well as one of Ludwig Wittgenstein’s Lectures on the Foundations of Mathematics in 1939. In this interview which was conducted with Alois Eder she talks about her encounter with Wittgenstein. It was published in 1978 in the Polish art (...) and culture magazine Odra and is her only published memoir about Wittgenstein. The interview is republished here both in English translation and as facsimile of the original publication with the kind permission of the Odra magazine. (shrink)

Recenzja książek: M. Heller, Wierzę, żeby rozumieć: w osobistej rozmowie o życiowych wyborach; rozmawiają Wojciech Bonowicz, Bartosz Brożek, Zbigniew Liana, Znak, Kraków 2016 oraz Heller M. Brotti G., Bóg i nauka: moje dwie drogi do jednego celu; Michał Heller w rozmowie z Giulio Brottim, tłum. Ewa Nicewicz-Staszowska, Copernicus Center Press, Kraków 2013.

Recenzja książek: M. Heller, Wierzę, żeby rozumieć: w osobistej rozmowie o życiowych wyborach; rozmawiają Wojciech Bonowicz, Bartosz Brożek, Zbigniew Liana, Znak, Kraków 2016 oraz Heller M. Brotti G., Bóg i nauka: moje dwie drogi do jednego celu; Michał Heller w rozmowie z Giulio Brottim, tłum. Ewa Nicewicz-Staszowska, Copernicus Center Press, Kraków 2013.

On the example of a workload dispute (a version of a ‘border dispute’) I present the general problem of two persons – M and P – with equal entitlements to one commodity, which is equally desired by both of them. They are both moderately altruistic; they are not angels untempted by a selfish willingness to get their own way, nor are they devils, who want to destroy others even if it leads to self-destruction. As human beings operating in a world (...) of limited goods, they are so physically and intellectually feeble that neither of them is able to permanently enslave the other and submit him to the second person’s will. Such being the case, each solution to the problem means that the profit of one person is the loss of the second. The question, whether justice is possible at all, suggests itself whether in a situation when people are more or less equal, or with limited altruism and/or selfishness and scarce resources. (shrink)

The article offers an analysis of Józef Bocheński's studies of the concept of nation. Bocheński acknowledges that there are difficulties in defining a nation. After that he claims that he will attempt to propose a definition of the Polish nation. Nation is a social group centered around some cultural ideal. The analysis shows that Bocheński did not avoid serious logical problems. First of all, he constantly falls into a circular reasoning. Furthermore, it is called into question if it makes sense (...) to refer to a cultural ideal or ideology while defining a nation. Is not such an attempt essentially bound to become circular? A doubt is also raised whether nowadays, in the face of constant migration of people and cultural ideals, one can continue to reasonably talk about nations. (shrink)

In my paper I'm going to present and evaluate position that science and religion (Christianity) do not contradict each other and that they rather answer different kinds of questions and solve different problems. Even if they both claim anything about the origin of Universe or human their claims are made from various, independent perspectives. Advocates of complementarity of science and religion state that science is a search for empirical data while religion refers to the domain of values and meaning. In (...) effect they are complementary to each other and their connection gives richer and consistent picture of reality. I agree that there are many problems and questions that are not common to scientific and religious domains, but I'm also going to show that meaning of many religious claims - also the crucial ones - is dependent upon existence of some facts in empirical world included to realm of science. I will also argue that the thesis of complementarity of science and religion is based on discredited neopositivistic picture of science as free from any philosophical commitments. (shrink)

Choice reaction times to visual stimuli may be influenced by preceding subliminal stimuli . Some authors reported a straight priming effect i.e., responses were faster when primes and targets called for the same response than when they called for different responses. Others found the reversed pattern of results. Eimer and Schlaghecken [Eimer, M. & Schlaghecken, F. . Links between conscious awareness and response inhibition: evidence from masked priming. Psychonomic Bulletin & Review, 9, 514–520.] showed recently that straight priming occurs whenever (...) a prime is not efficiently masked thereby the information provided by the prime is accessible for consciousness. In the present study, a hypothesis is tested that straight priming is due to mediation of consciousness. To test this hypothesis, prime validity was manipulated. We showed that even when no mask was used so that participants could fully and consciously perceive the prime and participants were informed that primes were mostly invalid, for the short prime–target ISI interval straight priming occurred. The priming was inverse when the ISI was 800 ms. This indicates that participants were able to use the information provided by the prime to prepare the response opposite to that cued by the prime but only if the time between the prime and the target was long enough. (shrink)

Stein’s theory of empathy lies at the intersection of the phenomenological findings of E. Husserl and M. Scheler. By presenting the issue of “empathy” in a broader framework, including intentionality, the originality of experience, the issue of personality and the individual identity, as well as the so-called world of values, namely the culture, I argue for a dynamic, process-oriented concept of dealing with feelings, namely diapathy. -/- Koncepcja Edyty Stein rozumienia drugiego człowieka jest znana z jej dysertacji O zagadnieniu wczucia. (...) Niemniej, gruntowne przebadanie struktury osobowości ludzkiej, jakie podjęła w Filozofii psychologii i humanistyki, rzuca nowe światło na tę kwestię. Stein dokonuje swoistej syntezy Husserlowskiego prymatu prawdy i Schelerowskiej koncepcji miłości, unikając przy tym idealizmu i woluntaryzmu, którym obarczone są te stanowiska. Steinowska koncepcja znajduje kontynuację w fenomenologii M. Merleau-Ponty’ego i R. Barbarasa. (shrink)

The aim of this paper is to shed light on the changes in perceiving the sacred which have appeared in the history of pilgrimage. These are linked with different theological approaches to space and subsequent periods of desacralisation, secularization and re-sacralisation. Relying on a modern theology of pilgrimage and research into the philosophy of religion by M. Eliade the paper offers a new interpretation of the message of the Camino de Santiago which overcomes previous reductionisms based on seeing the sacred (...) solely in the destination (the shrine). The relationship with the Camino and the content of pilgrim blessings indicate the role of experiencing order, beauty and these virtues which shape the relational order (corresponding with the virtue of _religio_). The effort of pilgrims is linked to this, however, it is no longer described in terms of ‘sacrifice’ although it is related to the same content which is perceived in a new post-secular cultural context. (shrink)

Artykuł poświęcony jest koncepcjom estetycznym polskiego filozofa i teoretyka pedagogiki, Stefana Szumana. Jego zainteresowanie twórczością dziecka i sztuką ludową wpisuje się w szeroki w kulturze europejskiej początków XX w. zwrot ku „prymitywowi”, będący pochodną tyleż krytycznej oceny procesów modernizacyjnych i regeneracyjnych tęsknot, co ówczesnych badań antropologicznych nad strukturą społeczeństw pierwotnych i ich twórczością. Podobnie jak Franz Boas, który w swej teorii sztuki prymitywnej odrzucił model ewolucjonistyczny i utożsamienie „prymitywu” z niższym stadium rozwoju, Szuman podkreślał swoistość twórczości dziecięcej i sztuki ludowej. (...) Nawiązując do etnologa neoewolucjonisty Maxa Richarda Verworna i do psychologicznych hipotez Jeana Piageta, w sztuce dziecka widział związek z organicznym rozwojem zdolności poznawczych i potrzebą ich uzewnętrzniania. Proponowana przez Szumana koncepcja wychowania przez sztukę, zakładająca nie tyle gotowy program kształcenia, co wspomaganie indywidualnego rozwoju uczniów, stała się częścią silnego w polskiej tradycji nurtu pedagogiki personalistycznej, reprezentowanej m.in. przez Henryka Rowida, Janusza Korczaka czy Antoniego Kenara. (shrink)

We propose to model spacetime by a differential space rather than by a differential manifold. A differential space is the pair (M, C), where M is any set, and C a family of real functions on M, satisfying certain axioms; C is called a differential structure of a corresponding differential space. This concept suitably generalizes the manifold concept. We show that C can be chosen in such a way that it contains all information about the causal structure of spacetime. This (...) information can be read out of C with the help of only one postulate, namely that physical signals travel along piecewise smooth curves in (M, C). We effectively construct the Minkowski spacetime, with its cone structure, in this way. Some comments are made. (shrink)

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic based on boolean (...) algebra. (shrink)

The paper seeks to give an ontological account of idea as mental content in the philosophy of John Locke. The foundation on which to place and polarise philosophical standpoints with regard to this issue is the 17th- century controversy between J. Locke and N. Malebranche with respect to the genesis of human knowledge. Showing the foundation of this controversy, as expressed in the polemic work of Locke entitled An Examination of P. Malebranche\'s Opinion of Seeing All Things in God, I (...) shall outline two possible approaches to our mental contents, namely the psychologistic and anti-psychologistic ones. In this perspective Locke is a representative of the first standpoint, whereas Malebranche of the second. In the psychologistic approach, the content of our conscious acts (or according to 17th-century Cartesian philosophy ideas) is exclusively an internalelement of this consciousness. On the contrary – in the case of the anti- psychologistic characteristation, the content of our consciousness is described as ontologically antonomous, i.e. as independent from thr knowing subject. Following the analyses of An Examination, I obtain additional arguments on behalf of the psychologistic interpretation of Locke\'s conception of idea (expressed, among others, by J. Yolton and M. Ayers), contrary to the anti-psychologistic approaches (claimed by, among others, T. Reid, R. McRae, and N. Jolley). (shrink)

The paper is an introductory essay to the Polish translation of M.E. Bratman's paper The Fecundity of Planning Agency. Instead of summarizing the main drifts of Bratman's work, the author tries to show a few important parallels between his approach to action theory and the so-called praxiology proposed by Tadeusz Kotarbinski. It occurs that there are important similarities between their approaches both to specific problems in action theory and to the general question how to understood agency. A brief presentation of (...) these similarities gives two central results. Firstly, it allows to interpret Bratman as a kind of praxiologist, and, secondly, it shows that praxiological thinking proposed by Kotarbinski is still a vital perspective in contemporary action theory. (shrink)

Philippa Foot once said: I'm not clever at all. I have a certain insight into philosophy, cost I think. But I'm not clever, I don't find complicated arguments easy to follow. Foot's cleverness enticed many thinkers to take these Gombrowiczian lines seriously.

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.

The paper concerns the origin and early stage of development of the Center for Interdisciplinary Studies at the Pontifical Academy of Theology in Kraków. Center for Interdisciplinary Studies was founded by Michał Heller and Józef Życiński in the late 1970s. It was an informal institution which focused on conducting scientific activity in the area of philosophy of nature, relationship between mathematical & natural sciences and philosophy, history of science, as well as relationships between science and religion. In this paper I (...) would like to present how this institution developed, I will discuss various forms of its activity and discuss—very generally—what kind of philosophy was promoted by M. Heller, J. Życiński as well as their pupils and close associates. An important part of the paper will also concern the Center for Interdisciplinary Studies as a unique institution, which has developed—in difficult historical period in Poland—philosophical research in the spirit of freedom and respect for the new achievements of science, and also promoted interdisciplinary dialogue between scientists and philosophers. (shrink)

The aim of this paper is to describe and assess the energetic-metabolic activity of selected muscles of upper and lower extremities during Rotational Training (RT). The influence of RT on temperature changes in the biceps and triceps brachii muscles as well as the quadriceps and biceps femoris muscles of healthy university students were verified, in addition to temperature differences between the left and right side before and after RT. The study was conducted on 18 subjects. RT was conducted in accordance (...) with accepted forms of training methodology of collective fitness. An important part of RT was the performance of circular and rotational movements. Thermograms taken before and immediately after RT focused on 4 regions of selected agonists and synergists in the upper and lower body. The camera used was the infrared hand-held CEDIP Titanium 560M IR (USA), located at a distance of 10 m from the subject. After RT, median Tsk (skin temperature) decreased in almost all of the examined ROIs, except for the left and right Qf (the quadriceps femoris, rectus femoris, and sartorius muscles) as well as the left Tb (triceps brachii) in female subjects. In male subjects, left and right Tsk of Qf increased both for the left and right Tb. Left-Right ΔTsk (temperature difference) was statistically significant (p <0.05) for Of, Bf, Bb, Tb in female as well as male subjects. It was concluded that thermography is a non-invasive, safe, and low-cost method for the recording of physiological response of the skin to RT. (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)