The origins of mathematics, a close connection and interpenetration of its parts, and uniform procedures of dealing with the mathematical matter - all of them speak in favour of the integrality of mathematics. It seems that a strong argument for such a view is a fundamental object of contemporary mathematics; namely a real line, which contains real numbers (so arithmetics as well) and constitutes a basis of geometry, mathematical analysis and all derivative branches. From the basic-structures perspective it is clear (...) that the real line is an exceptionally complex structure, for it contains the ordered structure (generated by the less-than relation), the algebraic structure (generated by addition and multiplication), the gemetrical structure (generated by translations and reflections) and the topological structure (generated by open intervals). This example explains, at least to some extent, the integrality and also the vivacity of mathematics. On the other hand, the integrality has not been confirmed by comprising the whole mathematics in one axiomatised, deductive theory. Moreover, the increasing „volume” of mathematics, unwillingness of mathematicians to cross the specialisation-barriers, emphasis on utility (models) and difficulties with axiomatisations of some parts of mathematics cast some doubts on the integrality in question. (shrink)

Primary object of interest of mathematicians can be identified as a „mathematical matter”, the concept analogous to „physical matter” or „biological matter”. The „mathematical matter” is the soil upon which mathematics grows. One can distinguish three levels of it: some abstract but not necessarily clear conceptions, operational notions (like number) but not necessarily openly defined, theories not necessarily axiomatic. The „mathematical matter” originates in the abstract reflection upon events and forms in time and space. Its important elements are notions formed (...) mostly in the process of idealization and/or abstraction. Once formed, notions usually evolve being, e.g., simplified or complexified. Mathematics is a mirror of the world, most abstract and therefore fundamental. Although it is a free activity of human mind, mathematics reflects some deep ideas (beauty, simplicity etc.) while most interesting notions come up in tension fields between pairs of poles: the notion of a function can be seen as a bridge connecting variability and immutability, while that of a limit – connecting finiteness and infinity. A fusion of freedom and internal restrictions leads to mathematics which is simple, beautiful and effective. (shrink)

The article recalls shortly the early story of cooperation between the already existing Lvov philosophical school, headed by Twardowski, and the just then establishing Warsaw mathematical school, headed by Sierpiski. After that recollection the article proceeds to contributions made by men influenced by the two schools. Most prominent of them was Alfred Tarski whose work in those times, concentrated mainly upon the theory of deduction, axiom of choice, cardinal arithmetic, and measure problem, has been described in some detail.

The vivacity of mathematics results (partly) from the fact that mathematics is stretched between several poles, not being committed to any one. The paper presents the following polarities: realism - idealism, the finite - the infinite, the discrete - the continuous, the approximate - the exact, certitute - probability, simplicity - complexity, unity - multiplicity.

la historia del escepticismo es oscura. Si bien se reconoce la existencia, misteriosa y discutida, de un escepticismo académico platónico, hay algunas dudas de la realidad inequívoca de una escuela pirrónica radical. En este artículo vamos a discutir, primero, hasta qué punto puede hablarse de escuela, secta o grupo filosófico pirrónico, y, segundo, si, como veremos, hay dudas del reconocimiento de este homogéneo grupo ¿por qué se habla de ella de ‘escuela’, ‘secta’ o ‘sistema’ pirrónico?

Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and ...

A primary issue in the field of business and society over the past 25 years has been the relationship between corporate social performance and corporate financial performance. Recently, Griffin and Mahon (1997) presented a table categorizing studies that have investigated this relationship. Motivated by concerns with this table, as well as a desire to account for progress in research in this area, the authors reconstructed it. The authors present a portrait of this relationship that is (a) substantially different from that (...) shown in the Griffin and Mahon table and (b) more consistent with the latest research on the topic. (shrink)

INTRODUCTION I have often asked myself why Husserl, really, headed in the direction of transcendental idealism from the time of his ...

The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

Introduction The starting point for our reflections upon the musical work will be the unsystematized convictions that we encounter in daily life in our communion with musical works before we succumb to one particular theory or another.

The purpose here is to give a thorough phenomenological account of the aesthetic experience. The difference between cognitive perception of a real object and the aesthetic experience of an esthetic object is discussed at length. Elements and phases of an esthetic experience are delineated; illustrations of a preliminary emotion of esthetic experience are given, All of which suggest a fundamental change of attitude. From normal perceiving to esthetic perceiving there is a change from categorical structures to qualitative harmony structures, Producing (...) pleasure in the presence of an esthetic object. (staff). (shrink)

”Rotu” mielletään usein pelkästään biologiseksi käsitteeksi. Niinpä rasismista syytetyt toisinaan puolustautuvat julkisuudessa sanomalla, että he eivät ole biologisten rotuoppien kannattajia, vaan esimerkiksi vain kannattavat kulttuurien oikeutta olla erilaisia. Historiallisissa yhteyksissä menneiden aikojen ajattelijoita saatetaan puolustaa sillä, että he eivät olleet ainakaan biologisia rasisteja. Erottelun taustalla on olettamus, että biologiaa koskevat ja kulttuuria koskevat käsitykset voidaan ongelmattomasti erottaa toisistaan. Tämän esityksen yhtenä pyrkimyksenä on pohtia biologia vs. kulttuuri -erottelun merkitystä rotua koskevissa käsityksissä, ja problematisoida sitä. Tarkastelun aineistona käytetään 1800-luvun lopun ja (...) 1900-luvun alun vaikutusvaltaisimpia ”klassisia” rotuteorioita. Näitä näkemyksiä luonnehditaan yleensä ”biologisiksi”. Vaikka rotuteorioiden juuria on etsitty antiikista saakka, ja vaikka eri vuosisatojen ajattelijoilta on helppo poimia rotuennakkoluuloja heijastavia kommentteja, tarkasteltuna ajanjaksona laskettiin se teoreettinen perusta, joille esimerkiksi 1930- ja 1940-lukujen rasistiset käytännöt rakennettiin. Harva enää vaivautuu lukemaan tuon aikakauden rotuteoreetikkoja tai edes tunnistaa heidän nimensä: rotuteoriat ovat tyypillistä pseudotiedettä, vailla itsenäistä älyllistä arvoa. Kuitenkin johtavien rotuteoreetikkojen kirjoitukset käännettiin aikanaan useimmille eurooppalaisille kielille, ja niitä myytiin satoja tuhansia kappaleita. Rotuajattelusta tuli liberalismin, sosialismin ja kommunismin kaltainen vaikuttava yhteiskunnallinen virtaus. Sen historiallisesti tunnetuin ilmaus oli Saksan kansallissosialismi, mutta lähes kaikissa Euroopan maissa – ja monissa Euroopan ulkopuolisissa maissa – syntyi paikallisesti värittyneitä versioita rotuopeista. Useimmissa maissa nämä opit syntyivät jo ennen kuin kansallissosialismista tuli Saksan hallitseva ideologia. Yhtäältä rotuopit sekoittuivat vanhempiin, kielellisesti ja kulttuurisesti muotoiltuihin nationalismin versioihin. Toisaalta ne kytkeytyivät usein biologisin käsittein muotoiltuihin ideoihin rodun parantelusta. Silti rotuopit erottuvat käsitteellisesti ja teoreettisesti sekä ”pelkästä” nationalismista että ”pelkästä” rotuhygieniasta. Tämän esityksen muina tavoitteina on pyrkiä muodostamaan historiallisesti ja filosofisesti täsmällisempi käsitys rasismia tukevasta ajattelusta. Samalla rotuopit toimivat kiinnostavana ja varoittavana esimerkkinä politiikan käyttöön valjastetun pseudotieteen argumentaatiotavoista. (shrink)

Der thematisch scharf umgrenzte Sammelband ist von grundlegender Bedeutung füuuml;r die Ästhetik der Gegenwart und vervollstäauml;ndigt Ingardens großen Entwurf einer philosophisch begründeten Theorie des Kunstwerks. Im Mittelpunkt der Eröouml;rterungen stehen das ästhetische Erlebnis, das Form-Inhalt-Problem im literarischen Kunstwerk und vor allem der Fragenkomplex des ästhetischen Wertes.

Enesidemo ha sido considerado, tradicionalmente, como figura mediadora entre el escepticismo pirroniano y el escepticismo académico. En el Códice 212 de su Bibliotheca, Focio proporciona alguna infonnación fundamental para reconocer a Enesidemo como figura clave del escepticismo entre Timón de Filunte y Sexto Empírico. Así, es corriente hablar de la pertenencia de Enesidemo a la academia platónica, y de su separación, cuando Filón de Larisa y su sucesor Clitx5maco empiezan a renunciar a los principios académicos y adoptan principios estoicos2, A (...) partir de aquí es corriente concluir que trabajaba por restaurar cierta originalidad de la especulación filosófica, basada en Pirrón, frente a todo el trabajo de reflexión y de análisis que él mismo había realizado en la academia en contra de los dogmáticos estoicos. La hipótesis de este artículo rompe esta ortodoxa interpretachin. Enesidemo es el primero en recuperar sistemáticamente los presupuestos del pensamiento pirroniano, generando un movimiento desconocido como tal hasta ese momento, el pirronismo shrink)

Parece que Platón enseñó en la Academia otras doctrinas diferentes de las expuestas por él en los diálogos. Además, parece también que voluntariamente se abstuvo de consignarlas por escrito al creer que la palabra, la enseñanza oral, era un medio más eficaz que la escritura para transmitir aquello que "tenía importancia". Dicho así, puede resultar una paradoja que el mejor prosista griego, sea un detractor, al menos en parte, de la prosa escrita. A partir de aquí, las interpretaciones novedosas que (...) han provocado las doctrinas no-escritas de Platón han generado debates a veces imposibles de resolver. Añadir unas breves notas a estas discusiones es la intención de este artículo. (shrink)

People have always tried to make predictions; they are necessary and useful, but very often they commit obvious errors, which have negative consequences on decision-making. Prediction errors are in some cases, not few, unavoidable, because the world itself is unpredictable, subject to chance (or randomness in mathematics). Chance is a property of nature. The causes of random events are physically determined, but so numerous and complex that they (the events) are unpredictable. Science is not about certainty. Human knowledge itself is (...) not certain. We can only have provisional truths. Therefore, we must manage to reach a state of accommodation with uncertainty and unpredictability. The complexity of natural phenomena generates events that we cannot control through theoretical modeling precisely because of the ignorance of the causal mechanisms, which exist in their privacy but have not (yet) been revealed by the data and observations at our disposal. We have, on the one hand, life experience taken over and assimilated and established in society and, on the other hand, experience gained from real life. Norm and chance follow each other rather chaotically. The duration of validity of a norm and the moment of occurrence of the random event are unpredictable. However, norms and events coexist in our consciousness. Order and predictability are born (formed and exist) from rules; chance and unpredictability are born from the lack of rules. The highest truths, recognized as such by society cannot be transposed into the life of society only by the force of reason. It is imperative that they are reinforced and embedded in the social behavior of all citizens. Rules are needed. Without rules there is no freedom. (shrink)