We study Fermat's last theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions of models of arithmetical theories (in the language ) by a binary (partial or total) function e intended as an exponential. We provide a general construction of such expansions and prove that it is universal for the class of all exponentials e which satisfy a certain natural set of axioms. We construct a model and a substructure with e total and (...) (Presburger arithmetic) such that in both and Fermat's last theorem for e is violated by cofinally many exponents n and (in all coordinates) cofinally many pairwise linearly independent triples. On the other hand, under the assumption of ABC conjecture (in the standard model), we show that Catalan's conjecture for e is provable in (even in a weaker theory) and thus holds in and. Finally, we also show that Fermat's last theorem for e is provable (again, under the assumption of ABC in ) in “coprimality for e”. (shrink)

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations of (...) ZI are presented. The proofs of the validity of the axioms of ZI in arithmetical interpretations use some strengthening of Solovay's result about interpretability in Godel-Bernays set theory. (shrink)

Steve Fuller has argued that a scientific discovery will not be recognized unless it can be justified within the history of the relevant science. He cites Mendel's work on genetics, which was not recognized until thirty-five years after its publication, as an example. This essay argues that Mendel's work comes out of the tradition of work by both agricultural breeders and academics in nineteenth century Austria. Thus, Fuller is mistaken, and one must look elsewhere for the neglect of Mendel's work. (...) This essay also places Mendel's work within the philosophy of Jan Comenius, whose work was very likely known to Mendel.--------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- -----------------------------------------------. (shrink)

This book focuses on Stanislaw Ignacy Witkiewicz, philosopher and controversial artist. It expresses the opinions of philosophers, museologists and artists, for whom Stanislaw Ignacy Witkacy's 130th birthday anniversary became an opportunity to view his works from the perspective of postmodernity. The authors concentrate on Stanislaw Ignacy Witkiewicz as eminent and prophetic philosopher concerned about Western culture with its waning metaphysical feelings, master of gesture and poses, anticipating the postmodern theatricalization of life.

A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.

We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.

Recently there has been a debate on whether Pyrrho’s philosophy could be influenced by Indian Buddhist philosophy. Discussions revealing striking similarities between them often point out Pyrrho’s complicated sentence, referred to as tetralemma, as one of the most striking similarities. The central question of this paper is whether Pyrrho’s sentence is of the tetralemmatic kind. Authors argue that if Pyrrho’s sentence is not fourfold in structure it could scarcely be classified as similar to the Buddhist tetralemma. A careful analysis of (...) the question is provided, arguing that the approach to the problem of tetralemmatic structure cannot be carried out solely on syntactic grounds. An aspect of a deeper philosophical meaning of the formula is applied, which alone enables us (if at all) to link Pyrrho’s philosophy to Buddhism. (shrink)

The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.

The difference in formulation of the question of heredity on a different level of knowledge in Brno in the 1830s and after 1850 is discussed in this article. In order to solve the problem the most important source is forshown in the new philosophy of plant physiology and in physics. Mendel was pleased to have met excellent teachers of both these fields. This explanation is an example of Mirko Grmek's thesis: 'l'histoire des sciences est le laboratoire de l'épistomologie'.

Bilder gehören zu den ältesten Zeugnissen der menschlichen Kultur. Sie sind, soweit bekannt, wesentlich älter als jede Form des sprachlich vermittelten diskursiven Denkens. Bereits dieser historische Umstand markiert die Bilder als etwas Vortheoretisches. Philosophische Theorien über Bilder stützen von Beginn an diese geschichtliche Kontingenz. Die Bildtheorie verdankt Platon die bis in unsere Tage überaus wirksame Denkposition, dass sich Bilder primär an die Sinnlichkeit wenden und nicht an den Verstand. Eine alte Feindschaft - die zwischen Sprache und Bild, dem Diskursiven und (...) Nicht-Diskursiven oder dem Propositionalen und Nicht-Propositionalen - wurde im Laufe der Zeit von disparat bestehenden philosophischen Traditionen erhärtet. Die seit Anfang der 90er Jahre des 20. Jh. s immer intensiver betriebene Bildtheorie konzentriert sich ebenfalls auf das, was Bilder von der Sprache trennt. Im folgenden wird dagegen jener Aspekt hervorgehoben, den Bilder mit der Sprache gemeinsam haben. Bilder sind wie sprachliche Äußerungen in erster Linie äußerst flexible und vielseitig einsetzbare Werkzeuge. Die Frage nach ihrer Bedeutung gleicht der Frage nach ihrem Gebrauch durch die Menschen. (shrink)

Efforts to bring science into early 19th century breeding practices in Central Europe, organised from Brno, the Hapsburg city in which Mendel would later turn breeding experiments into a body of timeless theory, are here considered as a significant prelude to the great discovery. During those years prior to Mendel's arrival in Brno, enlightened breeders were seeking ways to regulate the process of heredity, which they viewed as a force to be controlled. Many were specialising in sheep breeding for the (...) benefit of the local wool industry while others were showing an interest in commercial plants, especially fruit trees and vines, and later cereals. Breeders explained their problems in regulating heredity in terms of climatic influences disruption due to crossing sports or saltations. Practical experience led them to the concepts of 'inheritance capacity' and the 'mutual elective affinity' of parents. The former was seen to differ among individuals and also among traits; the latter was proposed as a means of adding strength to heredity. The breeders came to recognise that traits might be hidden and yet transmitted as a 'potential' to future generations. They also grew to understand that heredity would be strengthened when a quality was 'fixed' within a lineage by 'pure blood relations.' Continued selection of the desired quality might then lead to 'a higher perfection.' But the ultimate 'physiological' question about breeding, 'what is inherited and how?,' found no answer. Major figures in this development included Abbot Napp, the one who asked this question and who was due to receive Mendel into the monastery in 1843, and Professor Diebl whose lectures on agriculture and natural science at the Brno Philosophical Institute Mendel would attend in 1846. Here we analyse their progress in theorizing about breeding up until about 1840. In discussing this development, we refer to certain international contacts, especially with respect to information transfer and scientific education, within the wider context of the late Enlightenment. (shrink)

The paper attempts to introduce the Stoic concept of a deterministic universe and the centrality of the Stoic sage in it, using selected parts of Stoic philosophy (physics of the elements, psychology, causality and hierarchization of causes). The basic line of interpretation is to prove the thesis that the freedom of the sage is based on the autonomy of his manifestations justified by the sovereignly rational disposition of his soul. The author of the paper argues in support of the thesis (...) that akrasia as acting against the order of reason and nature is not possible in the Stoic sage. (shrink)

The paper deals with the role of assent and instinct in the process of cognition. The author shows, that the Stoic instinct is a dynamic aspect in the processes of cognition, decision making and action, its consequence being at the same time the assent, i. e. the approval of a given descriptive or prescriptive proposition as a true one. Tha paper wants to stress e remarcable rationalistic character of the Stoic epistemology - the only constitutive elemnent of the instinct is, (...) at least in early Stoicism, the rational capacity of the soul. The three Stoic levels of cognition: opinion, understanding and cognition are intoruced as related to various intensities of assent given to the particual meanings of the proposition. (shrink)

PurposeThe purpose of this paper is to review critical emancipatory literature to identify a discourse that could be used to successfully customise generic Enterprise Resource Planning systems to particular user‐needs. The customisation exercise is posited in the context of contemporary society, which has to try to become more sustainable amidst uncertainty about the complex interrelationships between elements of the ecosystem. It raises new challenges for the customisation exercise, that of fostering the precautionary ethos and engaging realistically with complexity and uncertainty (...) inherent in emergent knowledge about ecological resilience.Design/methodology/approachThis is a conceptual paper that draws on published research papers to tease out political constructs which are vital for facilitating sustainable decisions.FindingsThis paper argues that the critical emancipatory influence on systems design has generated attempts to formulate socio‐ethical information systems. However, these systems are limited by their inability to engage with the politics of asymmetrical distribution of power, even though these systems rely on bottom‐up participation to change the status quo. Hence, it is suggested that systems design should learn from Gandhi's experiences in mobilising social reform to instil a precautionary ethos in the context of asymmetrical power relations. The discourse used to customise ERP should facilitate social learning about ecological resilience as it affects the capacity to reform in the interest of sustainable outcomes. It is proposed that the discourse be socially constructed on the vocabulary of integrated risk because it would enable management to take advantage of lived experiences and enhance the organisation's capacity to learn about formulating sustainable business practices.Practical implicationsThe recommended approach to identifying user‐needs is based on Gandhi's tried‐and‐tested approaches of mobilising bottom‐up participation in social reform.Originality/valueThis paper brings in Eastern philosophy into the predominately Western‐dominated systems design arena. Its value lies in its practical applicability to real‐world design challenges. (shrink)

Seminar papers; Study with special reference to Advaita philosophy of Śaṅkarācārya.

The aim of the paper is to shed light on the concept of cataleptic phantasy, which in Stoic fhiilosophy has been the kriterion of true knowledge. On the basis of original texts of Stoic fragments the author points out specific subjective and objective symptoms of its cataleptical chracter, distinguishing at the same time strictly between sensory ane non-sensory kind of Stoic phantasies. The author shows, that the way from a cataleptic phantasy to a cognitive content is not a straightforward one (...) and that it is the logical menaning that makes it possible. Thus the author inclines clearly to the rationalist interpretation of Stoic epistemology, which, contrary to sensualistic approaches, puts the stress on the importance of non-sensory cataleptic phantasy as the kriterion of true knowledge in Stoic Philosophy. (shrink)

The paper gives an outline of the Socratic Cynic school and its influence on Stoicism. In its first part the author gives a general characteristics of Cynicism of the 4th century B. C., showing, that the Cynic movment was based on the presupposition of an absolute incompatibility of virtue with the laws of polis. From the doxographical materials available it shows the basic characteristics of the Cynic virtue, such as self-sufficiency, the importance of physical work, stressing the poverty, a new (...) approach to women and an ascetic way of life. The second part of the paper is devoted to the relationship between Cynicism and Stoicism itself. It tries to highlight the consequences of the stoic merging of physics and ethics for a new understanding of life according to nature. The author argues, that the theory of appropriation - allowing for a value differentiation of the sphere of the indifferent in Stoa - introduced by the stoics was decisive for a new understanding of this Cynical philosophers' challenge. In conclusion an interesting personality of a cynicizing Stoic-apostate Ariston of Chia is presented, whose coming back to Cynicism in the frame of Stoa could not bring about a consequent revival of the original - often radical and exhibitionist - views an practices of old Cynics. (shrink)

Cieľom článku je nanovo reflektovať činnosť jednej z najslávnejších ženských filozofiek, Hip­parchie z Maróneie. Naším zámerom je ukázať, prečo sa stala v porovnaní s inými ženami antiky taká významná a v mnohom signifikantná pre ďalší vývoj procesu ženskej eman­cipácie. Hlavným svedectvom je pre nás fragment SSR V I 1 od Diogena Laertského, ktorý kladieme do súvislosti s ďalšími antickými správami o Antisthenovi a raných kynikoch. Dve hlavné témy Diogenovho svedectva sú Kratétova svadba s Hipparchiou a spor Hipparchie s Theodórom. Vo (...) výklade poukazujeme na momenty, v ktorých je filozofická osobnosť Hip­parchie nadčasová a inšpiratívna aj pre súčasnosť. (shrink)

Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.

Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form n.

The aim of our paper is to broaden the international discussion on environmentally friendly lifestyles. In most of the previous research, via a survey technique involving the self-nomination of participants, voluntary simplifiers are presented as part of a social movement typically connected with an urban environment. Our paper follows the third wave of longitudinal research conducted in the post-socialist Czech Republic in the years 1992, 2002 and 2015. The data were collected using in-depth interviews combined with observations in 20 voluntary (...) modest households. The biographical style of interview enables us to interpret the sources of the participants’ motivation for relocating to the countryside or staying in the urban environment as they interpret it retrospectively. Four dominant narratives emerged: 1) narrative of distaste for city life, 2) narrative of a nice life, 3) narrative about living in freedom, 4) narrative of a return to roots. (shrink)

The persisting controversial interpretation of constant hybrids and of the term Entwicklungsgeschichte, mentioned by Mendel in the Pisum paper, is elucidated in the context of his experiments with other plant species and of the growth of knowledge in scientific animal and plant breeding in Moravia.

Die Philosophie wurde von so unterschiedlichen Philosophen wie Wolff und Russell als Moglichkeitswissenschaft bezeichnet. Doch erwiesen sich die modalen Konzepte von Moglichkeit und Notwendigkeit als sperrig und vieldeutig, und ihr Verhaltnis zum Wirklichkeitsbegriff bleibt problematisch. Die vorliegende Sammlung beleuchtet die Metaphysik und Logik von Moglichkeit und Wirklichkeit aufs Neue und betrachtet sie aus unterschiedlichsten Perspektiven jenseits der Dichotomie von analytischer und kontinentaler Philosophie. Die Philosophiegeschichte (von der griechischen Antike bis zu David Lewis) kommt ebenso zu Wort wie die Semantik moglicher (...) Welten; Logik, Mathematik und Computerwissenschaft ebenso wie Literatur und Neue Medien; Formen des wissenschaftlichen ebenso wie des fiktionalen Diskurses. Philosophy has been called the science of the possible by philosophers as diverse as Christian Wolff and Bertrand Russell. The modal concepts of possibility and necessity, however, have proved to be ambiguous and recalcitrant to analysis, and their relation to the concept of reality have remained problematic up to the present day. Transcending the worn-out dichotomy between analytic and continental philosophy, this collection of papers takes a fresh look at the metaphysics and logic of possibility and reality, and illuminates them from a great variety of perspectives. Topics include the history of philosophy (from Greek antiquity to David Lewis) as well as the semantics of possible worlds; logic, mathematics and computer science as well as literature and the new media; forms of scientific as well as fictional discourse.". (shrink)

On the religious aspects of consumption (economics) in Islam.

Recently there has been a debate on whether Pyrrho’s philosophy could be influenced by Indian Buddhist philosophy. Discussions revealing striking similarities between them often point out Pyrrho’s complicated sentence, referred to as tetralemma, as one of the most striking similarities. The central question of this paper is whether Pyrrho’s sentence is of the tetralemmatic kind. Authors argue that if Pyrrho’s sentence is not fourfold in structure it could scarcely be classified as similar to the Buddhist tetralemma. A careful analysis of (...) the question is provided, arguing that the approach to the problem of tetralemmatic structure cannot be carried out solely on syntactic grounds. An aspect of a deeper philosophical meaning of the formula is applied, which alone enables us (if at all) to link Pyrrho’s philosophy to Buddhism. (shrink)

The paper tries to represent the polemic between the Stoics and the sceptically oriented Academy, concerning the abilities of human knowledge. It gives a brief account of the stoic epistemology on the basis of the characteristics of its criterion of knowledge – cataleptic fantasy. The description of the external and internal features of the latter is the ground of its criticism from Academy’s side. In its core this criticism tries to prove, that there is no fantasy meeting the strict claims (...) of the Stoics criterion on the truth. The author shows the stoic response to the Academy criticism, which initiated the revision of the original stoic attitudes. (shrink)

Efforts to bring science into early 19th century breeding practices in Central Europe, organised from Brno, the Hapsburg city in which Mendel would later turn breeding experiments into a body of timeless theory, are here considered as a significant prelude to the great discovery. During those years prior to Mendel's arrival in Brno, enlightened breeders were seeking ways to regulate the process of heredity, which they viewed as a force to be controlled. Many were specialising in sheep breeding for the (...) benefit of the local wool industry while others were showing an interest in commercial plants, especially fruit trees and vines, and later cereals. Breeders explained their problems in regulating heredity in terms of (1) climatic influences (2) disruption due to crossing (3) sports or saltations. Practical experience led them to the concepts of 'inheritance capacity' and the 'mutual elective affinity' of parents. The former was seen to differ among individuals and also among traits; the latter was proposed as a means of adding strength to heredity. The breeders came to recognise that traits might be hidden and yet transmitted as a 'potential' to future generations. They also grew to understand that heredity would be strengthened when a quality was 'fixed' within a lineage by 'pure blood relations.' Continued selection of the desired quality might then lead to 'a higher perfection.' But the ultimate 'physiological' question about breeding, 'what is inherited and how?,' found no answer. Major figures in this development included Abbot Napp, the one who asked this question and who was due to receive Mendel into the monastery in 1843, and Professor Diebl whose lectures on agriculture and natural science at the Brno Philosophical Institute Mendel would attend in 1846. Here we analyse their progress in theorizing about breeding up until about 1840. In discussing this development, we refer to certain international contacts, especially with respect to information transfer and scientific education, within the wider context of the late Enlightenment. (shrink)