Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.

What are the evolutionary scenarios of academic capitalism, able to deliver an ever more strategic knowledge, with a high added value within the global society? Under the current system of knowledge economy, characterized, at the beginning of this third millennium, by strong hyper-complexity, the challenge for the society evolution toward a sustainable world, full of varieties and opportunities, is the development of a form of capitalism able to guide and facilitate the reshaping of society through self-organizing systems (Lazslo 2011) the (...) academic capitalism as a form of functional capitalism, the difference that makes the knowledge considered at a systemic level. (shrink)

The philosophy of arithmetic of Wittgenstein's Tractatus is outlined and the central role played in it by the general notion of operation is pointed out. Following which, the language, the axioms and the rules of a formal theory of operations, extracted from the Tractatus, are presented and a theorem of interpretability of the equational fragment of Peano's Arithmetic into such a formal theory is proven.

A conjecture on the metaphysical nature of Tractatus objects is put forward and its interpretative adequacy is tested. The clarification of the true import of the metaphor of logical space and the recognition of the theoretical role played by Wittgenstein's explicit claim that the emptiness of logical space is conceivable enable us to account for the thesis that objects are the substance of the world. Once objects are identified with those universal abstract entities which are qualia, and complexes or states (...) of affairs with their concrete instances, some statements of the Tractatus become liable to a consistent reading: that objects are colourless ; that space, time and colour are forms of objects ; that Leibniz's Principle of the Identity of Indiscernibles, though still holding for complexes, does not apply to objects . Lastly, it is shown how the interpretation of objects as qualia sheds a vivid light on the theme of the relation between objects and time. (shrink)

On the basis of an analysis of the relevant parts of Tractatus logico-philosophicus, a definition of the property of saying something, and of the obviously correlated property of saying nothing, is given. By applying that definition, both tautologies and contradictions are sanctioned as saying nothing, as lacking sense, in full agreement with Wittgenstein's explicit statements. On the other hand, a recent systematic attempt by A. Negro to extract from the Tractatus a criterion for sense containment and a criterion for saying (...) more, that is, for comparing the amount of sense of propositions, leads to the conclusion that the sense of any proposition is contained in the sense of a contradiction and that contradictions say more than any other propositions. The problem faced in this paper is that of restoring consistency between Negro's criteria, which on the whole give a correct interpretation of the text of the Tractatus, and Wittgenstein's thesis that, not only tautologies, but also contradictions say nothing. (shrink)

Philosophical Investigations, EarlyView.

Researching for the sources of the Ars geomantiae – the oldest divinatory handbook of Western geomancy, translated from Arabic into Latin by Hugo of Santalla in 12th-century northern Spain – led to a double outcome: on the one hand, it showed the nature of Hugo’s cultural competence, imbued with the texts and scientific knowledge of his time; on the other hand, it revealed a series of historico-philosophical and philological data relating to the appearance of his version. In particular, the analysis (...) of the three explicit sources of the Sayings attributed to Socrates, of the Centiloquium of pseudo-Ptolemy and of the Isagoge ad Techne Galieni of Iohannitius has allowed not only to give a direct insight into the fundamental contribution of Arabic culture in the 12th-century translation of scientific studies, but also to carry out a more certain clarification on the dating of the Ars geomantiae and its placement within the translating activity of the master of Santalla. Finally, the question of the hermeticity of the text, raised by the reference to Enoch, one of the three Hermes of Abu- Ma’šar’s legend, has specified to what extent the Ars geomantiae belongs to the Hermetic tradition. (shrink)

SCIENCE, PHILOSOPHY, COMMON SENSE: HOW THE EXTRAORDINARY COULD TURN INTO THE OBVIOUS The paper is devoted to an examination of some aspects of the relation between science, philosophy and common sense. By referring to crucial episodes of the history of astronomy and physics such as the Copernican Revolution and the birth of Relativity Theory, attention is paid to the process by which new scientific ideas contrasting with deeply entrenched intuitions and socially shared beliefs are gradually absorbed into the conceptual schema (...) underlying common sense. Some light is thrown on the role that philosophy can play in that process. (shrink)

1 Qualche considerazione preliminare È opportuno cominciare citando per intero la sezione 5.1362 del Tractatus, attorno alla quale ruoterà gran parte di ciò che andrò sostenendo: Il libero arbitrio consiste nell’impossibilità di conoscere ora azioni future. Noi le potremmo conoscere solo se la causalità fosse una necessità interiore, come quella della conclusione logica. — La connessione di conoscere e conosciuto è quella della necessità logica. (“A sa che p" è priva di senso, se p è una taut...

Understanding Wittgenstein's Tractatus provides an accessible and yet novel discussion of all the major themes of the Tractatus. The book starts by setting out the history and structure of the Tractatus. It then investigates the two main dimensions of the early Wittgenstein's thought, corresponding to the division between what language can say by means of its propositions and what language can only show. It goes on to discuss picture theory, logical atomism, extensionality, truth-functions and truth-operations, semantics, metalogic and mathematics, solipsism (...) and value, metaphysics, and finally, Wittgenstein's idea of the duty of maintaining silence. Frascolla also proposes a new interpretation of the ontology of the Tractatus. Based on the identification of objects with qualia, the argument put forward in the book challenges the currently prevalent ideas of the ‘New Wittgenstein'. The paradoxical nature of the Tractatus itself, and the theme of "throwing away the ladder", are thus revisited in a new key. _Understanding Wittgenstein's Tractatus_ is essential reading for anyone wishing to further their insight into one of the most influential works of twentieth-century philosophy. (shrink)

While many sociocultural, contextual, biological, behavioral, and psychological variables may contribute to the widespread under-representation of girls and women in the science, technology, engineering, and mathematics field, this study focused on STEM-gender stereotypes, school experiences, and adolescence as critical factors in driving students' interest and motivation in STEM. Based on this, the study investigated differences by gender and national context in adolescents' STEM-gender stereotypes, school empowerment, and school engagement in a preliminary step, and simultaneously examined how adolescents' STEM-gender stereotypes were (...) related to school empowerment and school engagement as well as to socioeconomic status. These latter relations were considered within the context of the potential moderating role of gender and national context. Participants included 213 Italian adolescents and 214 Nigerian adolescents, who completed measures of school empowerment and engagement, STEM-gender stereotypes, and SES. A multivariate analysis of covariance showed that Nigerian girls and boys reported significantly higher levels of school empowerment, school engagement, and STEM-gender stereotypes than their Italian peers. Moreover, regardless of the national context, boys scored significantly higher on school empowerment and STEM-gender stereotypes than girls. Furthermore, a multiple-group path analysis revealed how higher school empowerment was related to lower STEM-gender stereotypes in both Italian and Nigerian girls' groups, while higher school engagement was associated with lower STEM-gender stereotypes only in the Nigerian groups. Regardless of gender and nationality, higher SES was linked to lower STEM-gender stereotypes. These findings particularly suggest that school empowerment and school engagement can be relevant dimensions to be studied and to develop strategies to counteract STEM-gender stereotypes in adolescence. Nonetheless, gender and national context are key factors to be considered. Limitations, strengths, future research, and educational implications are discussed. (shrink)