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.

This volume provides a comprehensive historico-doctrinal analysis of the transformation of the concept of time in the transition from the medieval debate to ...

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)

Early parental loss or trauma has been proposed by some as a significant factor in the adoption of atheist, non-theist, or irreligious worldviews. Relevant empirical data, however, have been limited, impressionistic, methodologically questionable, or limited to historically prominent figures. Survey data from the GSS and a study of affirmatively non-theistic and irreligious secular group affiliates in the U.S. do not provide evidence of disproportionately high rates of early parental loss among individuals who describe themselves as “atheist” or “anti-religious,” reject belief (...) in God, or express strong anger about religion. Loss of a parent or other loved may play a role in turns toward, as well as away from, God and religion for some. There is also evidence of comparatively high rates of parental loss in the lives of historically prominent figures, both religious and non-religious. Present results, however, do not support the hypothesis that early loss is a disproportionately frequent experience in the lives of atheistic or irreligious people. (shrink)

The official documents of the Parisian Faculty of Arts (starting from the Statute of March 1255) show a close identification between the philosophical sciences and the corresponding textbooks: to learn a particular science means essentially to read certain, prescribed books. The case of theology seems to be different, however. In spite of the fact that the Bible served as a paradigm for the ‘textualization’ of all kinds of knowledge, and even of the whole world, it did not fit perfectly the (...) epistemological criteria which Aristotle’s Posterior analytics established as necessary for every science. Already in the second half of the 13thcentury, both Thomas Aquinas and Henry of Ghent tried to construct theology as a science, in the Aristotelean sense, by appealing respectively to the theory of the subalternation of the sciences and to the doctrine of the lumen medium. The different reactions to these two models by Godfrey of Fontaines, Durandus of Saint-Pourçain and Peter Auriol seem to indicate a process in which theology can constitute itself as a true science only through a broadening of its textual basis, outside the scope of Sacred Scripture. (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)

In the U.S., ‘employee wellness’ programs are increasingly attached to employer-provided health insurance. These programs attempt to nudge employees, sometimes quite forcefully, into healthy behaviors such as smoking cessation and exercise routines. Despite being widely promoted as saving on healthcare costs, numerous studies undermine this rationale. After documenting the programs’ failure to deliver a positive return on investment, we analyze them as instead providing an opportunity for employers to exercise increasing control over their employees. Based on human capital theory and (...) neoliberal models of subjectivity that emphasize personal control and responsibility, these programs treat wellness as a lifestyle that employees must be cajoled into adopting, extending the workplace not just into the home but into the bodies of workers, and entrenching the view that one belongs to one’s workplace. At the same time, their selective endorsement of health programs (many scientifically unsupported) produce a social truth of wellness framed as fitness for work. We conclude by arguing that the public health initiatives occluded by the private sector’s promotion of wellness programs would be a much better investment of resources. (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)

This 44-chapter volume tackles a quickly-evolving field of inquiry, mapping the existing discourse as part of a general attempt to place current developments in historical context; at the same time, breaking new ground in taking on novel subjects and pursuing fresh approaches. The term "A.I." is used to refer to a broad range of phenomena, from machine learning and data mining to artificial general intelligence. The recent advent of more sophisticated AI systems, which function with partial or full autonomy and (...) are capable of tasks which require learning and 'intelligence', presents difficult ethical questions, and has drawn concerns from many quarters about individual and societal welfare, democratic decision-making, moral agency, and the prevention of harm. This work ranges from explorations of normative constraints on specific applications of machine learning algorithms today-in everyday medical practice, for instance-to reflections on the (potential) status of AI as a form of consciousness with attendant rights and duties and, more generally still, on the conceptual terms and frameworks necessarily to understand tasks requiring intelligence, whether "human" or "A.I.". (shrink)

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'.

J. Dudley, Aristotle’s Concept of Chance. Accidents, Cause, Necessity, and Determinism, State University of New York Press, Albany 2012.