Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...

Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...

Because Bertrand Russell adopted much of the logical symbolism of Peano, because Russell always had a high regard for the great Italian mathematician, and because Russell held the logicist thesis so strongly, many English-speaking mathematicians have been led to classify Peano as a logicist, or at least as a forerunner of the logicist school. An attempt is made here to deny this by showing that Peano's primary interest was in axiomatics, that he never used the mathematical (...) logic developed by him for the reduction of mathematical concepts to logical concepts, and that, instead, he denied the validity of such a reduction. (shrink)

Among the numerous influences and reciprocal interactions between France and Italy at the beginning of the 20th century, it is interesting to investigate the complex case of Louis Rougier’s reception of Italian mathematical logic (including in particular the contributions by some members of the Peano school: Giuseppe Peano, Giovanni Vailati, Alessandro Padoa, and Mario Pieri). This paper aims to investigate the role and the influence of the Peano school on the inversion of this French (...) tendency of philosophers to ignore logic and mathematics. My claim is that Rougier was not only personally interested in Italian mathematics and logic, and in particular in the innovations made by Peano and his school, but used it to support a project of renewal of French logic and scientific philosophy. Rougier recalls the contributions of the school to axiomatics and to mathematical logic, in order to criticize the standard teaching of logic in France, mainly based on syllogistic theory, as well as the view, still defended by his teacher Goblot in 1907, that mathematical proofs are largely based on intuition. For this purpose, any reference to Hilbert’s axiomatics would have sufficed. The reason why Rougier refers also to Peano and his entourage is related to a common interest in linguistics and in epistemology. (shrink)

The physical activity and sport are key elements for a healthy lifestyle. However, a little-investigated element is the presence of a possible relationship between school or academic performance an...

In the first part of this paper I critically examine some of the main interpretations of “classical” Yogācāra philosophy of Maitreya, Asaṅga and Vasubandhu. Among these interpretations, based on extant textual and contextual data, I consider philologically unlikely both metaphysical-idealistic readings, which ascribe to these authors the view that ultimate reality is a mental or subjective stuff, and epistemological-idealistic readings which advocate that either Yogācāra suspends judgment on the existence of the extramental or that it maintains that the extramental exists (...) in itself and ultimately. Instead, I consider more likely the thesis that classical Yogācāra upholds an epistemological idealism that, while admitting epistemological priority of the mental over the extramental, rules out the ultimate existence of both the former and the latter. This exclusion, however, does not amount to the exclusion of every metaphysics, but rather to the adoption of a metaphysics of emptiness conceived, in fact, as absence of the mental/extramental dichotomy. In the second part of the paper this reading of classical Yogācāra is compared with the interpretation of Nāgārjuna’s philosophy that I elsewhere called “realistic antimetaphysical”, and I reach the conclusion that, while with respect to epistemology between early Madhyamaka and classical Yogācāra there is continuity, regarding metaphysics these two schools are deeply distinct and discontinuous: while Nāgārjuna conceives of emptiness as an extinction of any metaphysical view, Yogācāra emptiness actually presents itself as a metaphysical point of view. (shrink)

In the introduction to the Normal and the Pathological, Canguilhem’s doctoral dissertation in medicine, defended in 1943, he claimed, “philosophy is a reflection for which all unknown material [matière étrangère] is good.” In this case the “unknown material” was precisely medicine; “a technique or art at the crossroads of several sciences” which was supposed to provide “an introduction to concrete human problems.” Canguilhem had started studying medicine six years before, while he was a high-school professor in Toulouse. At the (...) time he was distancing himself from the philosophical framework that had marked his studies and writings during the previous decade. This framework implied an anti-vitalist, Kantian and Cartesian approach to man, strongly influenced by his mentor Emile Chartier, also known as Alain. In this chapter, I try to provide concrete explanations concerning his decision to study medicine. I will not rely on those proposed by the existent scholarship, which frequently relate his decision to his interest in technology and technique. On the contrary, by examining unpublished material, such as a series of lectures given between 1933 and 1935, I claim that the motivation of his turn has to be related to the readings of works in psychology and ethology undertaken during this period. (shrink)

What is the truth of the unconscious? _Truth and the Unconscious in Psychoanalysis _explores the intersection of these two concepts within a Bionian framework. Giuseppe Civitarese maps out the unconscious in psychoanalysis, and focuses on the differences between the Freudian, Kleinian, Bionian and Lacanian schools of thought on this topic, as well as drawing on findings from neuroscience. The book explores topics including the inaccessibility of the unconscious, dreams, body issues, issues of personality, the influence of field theory and (...) the clinical implications of this theorising. It contains innovative comparison between Freudian metapsychology and the Bionian theory on thinking, and novel use of Bion's hallucinosis as an important new technical tool. An internationally recognised author, Civitarese provides fresh ideas throughout on a challenging subject, supported with vivid clinical material. _Truth and the Unconscious in Psychoanalysis _will be of interest to anyone following the growing post-Bionian movement within contemporary psychoanalysis, enabling them to familiarize themselves with some of the most important current issues in psychoanalytic research. _Truth and the Unconscious in Psychoanalysis _will appeal to psychotherapists, psychologists and psychoanalysts, as well as undergraduate and postgraduate students studying in the field. (shrink)

This paper examines the contribution of Gabrio Piola to continuum mechanics.Though he was undoubtably a skilled mathematician and a good mechanician, little is commonly known about his papers within the international scientific community, principally because a large part of the Italian school of mechanics was isolated in the first half of the XIXth century.We examine and comment on Piola’s most important papers, and compare them with those of his contemporaries Cauchy, Poisson and Kirchhoff.

With regards the crucial issue of the existence of the self, within canonical texts of the Buddhist Abhidharma schools we find passages that are frequently at odds with one another. Sometimes the Buddha defends or respects the belief in the self and in personal continuity; at other times he seems to deny that beyond the psycho-physical factors to which our existential experience can be reduced there is an ātman that contains, owns or controls these same factors; in further cases still, (...) he states that the use of the metaphysical categories of “being” and “non-being” must be avoided – thus, about the self (or everything else), it is inappropriate to say that it exists or that it does not exist. Faced with these divergences (or contradictions) within contemporary Buddhist studies, we can detect two main tendencies. Some scholars start from the assumption that the Buddha’s teaching is or should be coherent and univocal, and, therefore, propose readings of his original message that are supposed to iron out or conciliate any inconsistencies. Others believe that the inconsistencies are actually irreconcilable and, therefore, maintain that the Abhidharma canons are a composite and stratified redaction in which the opposite views of different writers overlap and intersect. Against these historiographical approaches, the purpose of the present paper is to show that the three aforementioned modes of the Buddha’s teaching are, in fact, both alternative and irreconcilable. This, however, far from presenting a puzzle to be solved or explained (by resorting to suppositions of which, in the canons, we have no explicit confirmation), is nothing more than a feature of the Buddha’s Dharma, which appears to be a teaching that develops different pedagogical/soteriological modes for different purposes, and which is conceived for the spiritual growth of followers with different intellectual and psychological profiles. (shrink)

This book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in (...) the sciences. The scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School. (shrink)

This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics (...) as classes, functions, meaning and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both. (shrink)

The subject of bullying has received widespread academic attention, going back to pioneering studies in the 1970s. However, work in this area has tended to take a gender-neutral/male perspective that does not distinguish between male and female bullying. While retaining a dialogue with generalist literature on the subject, this article seeks to highlight the theoretical and political-social relevance of gender-specific and intersectional approaches when exploring the question of bullying between adolescent girls. Based on the study _Il bullismo femminile a scuola. (...) Un’indagine intersezionale mixed-method_ (Female bullying at school, an intersectional, mixed-method study) – conducted in medium-sized and large cities in northern, central and southern Italy – it proposes a theoretical-analytical framework in which to consider the phenomenon of female bullying in Italian schools. (shrink)

The Decision Regret Scale was assessed for its psychometric qualities in measuring decision regret in ordinary life scenarios. Although the scale has typically been used with patients and in the context of medical decision-making in earlier studies, this contribution shows that the instrument may have a variety of uses, retaining excellent metric properties even in non-medical contexts. The tool showed good fits with both the CFA and the gender Measurement Invariance. A non-probabilistic selection of 2,534 Italian university students was conducted. (...) The internal consistency measures were found to be completely appropriate. Correlations with the General Decision-Making Style and Scale of Regulatory Modes were used to check for convergent validity. Convergence analysis showed that participants with higher regret scores were those who favored a rational decision-making style, while lower regret scores correlated with avoidant and spontaneous styles. With regard to the regulatory modes, the relationship between regret and locomotion was positive. Overall, the directions of association point to an interesting predictive measure of a person’s decision-making and self-regulatory orientation through the evaluation of regret using the DRS. The excellent psychometric properties found foreshadow a reliable use in various contexts where knowledge of post-decisional attitude becomes important: school, university, professional orientation, marketing studies, relationship choices, as well as for use in research. (shrink)

Experiences of contact with nature in school education might be beneficial for promoting ecological lifestyles and the wellbeing of children, families, and teachers. Many theories and empirical evidence on restorative environments, as well as on the foundations of classical pedagogical approaches, recognize the value of the direct experience with natural elements, and the related psychological and educational outcomes. In this work we present two studies focusing on the contact with nature in outdoor education interventions with primary and secondary (...) class='Hi'>school students in Italy. A questionnaire measuring connectedness to nature, psycho-physical wellbeing, pro-environmental attitudes, students’ life satisfaction, pro-social behavior, empathy and anxiety was completed before and after the education program by the participants to the intervention group and by students of a control group. The students in the intervention groups participated in environmental education programs consisting in guided activities in contact with the nature during four visits in one of two natural protected areas. The students in the control groups attended the same schools as the intervention group but they were not involved in the environmental education program. The students in both the groups completed the questionnaire in the same weeks of the year. Findings show that taking part to the outdoor education program has positive outcomes on psycho-physical wellbeing, on connectedness to nature and on pro-social behavior of students in the intervention group, compared to the control group. The implications related to the effectiveness of outdoor education interventions and future directions of research and practice in environmental psychology and education are discussed. (shrink)

One 1120 pages volume, with 4000 entries covering - Western philosophy: authors, schools, concepts and terminology; - religions, cultural anthropology, eastern philosophies; - Psychology and psychoanalysis; - linguistics and semiotics; - sociology and political theory.

Narcolepsy type 1 deeply impacts on quality of life, especially during adolescence, with NT1 children and adolescents that frequently report difficulties in integration with peers and decreased participation in after-school activities. Here we describe the case of NT1 teenager girl presenting with severe physical and social withdrawal, fulfilling the proposed diagnostic criteria for hikikomori, together with the classic NT1 symptoms. Social withdrawal is an overlooked phenomenon among NT1 children and adolescents that, if present, require a multidisciplinary approach and personalized (...) interventions, but patients can benefit from NT1 pharmacological treatment. (shrink)

The notion of loop seems to be ubiquitous in the study of organisms, the human mind and symbolic systems. With the possible exception of quantum-mechanical approaches, the treatments of consciousness we are acquainted with crucially appeal to the concept of loop. The uses of loops in this context fall within two broad classes. In the first one, loops are used to express the control of the organism’s interaction with the environment; in the second one, they are used to express self-reference. (...) Both classes are tied with investigations which aim at accounting for symbolic capabilities, and ultimately for subjectivity. Neurophysiological research detects loops in the animal nervous system since its very inception (e.g., all the work on the reflex arc). Recently, Gray proposed a model purporting to explain the mechanism supporting the contents of consciousness in the human CNS, in ways that are practically indistinguishable from models formulated within the cybernetical point of view. Both types of models apply loops in strikingly similar ways. While there is no conclusive evidence that loops are necessary to support consciousness, they are nonetheless as good a candidate as today can be found for inclusion in the list of essential ingredients for subjectivity to arise. In the first two sections we discuss the above mentioned uses by means of significant examples. In the third section, we compare Gray’s recent model to MacKay’s early cybernetical model of a selfobserving system, in the setting of a broader discussion on loops for consciousness. (shrink)

The mathematical description of the three distinct fundamental notions of “individual sample” of “preparing procedure,” and of “Piron's state” of a physical entity are precisely introduced in the framework of the Piron's “preparation-question structure” (without specific axioms C, P, A) based on Ludwig's “selection structure.” We compare our realization of the above notions with a similar use of the standard terminology of the “Geneva School” adopted by Pykacz and Santos in a recent paper.

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind (...) of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind (...) of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)

The paper advocates an epistemological interpretation of the Peano School axiomatics. The construction of axiom systems is presented as a cognitive enterprise unveiling the internal dynamics, evolution, and architecture of axiomatic systems as well as connections to applications. This approach reveals that the study of the relation between axioms and theorems not only serves to reduce a theory to a minimum number of principles and increase the certainty or justification of the latter, but also to study alternative settings (...) of a given mathematical theory. The paper explains why the Peanian conception of axiomatics differs from axiomatic deductivism, if-thenism and scientific deductivism, and analyzes Peano’s conception of rigor. The paper also postulates that Peano had a set-theoretic but also an algorithmic conception of function, and prioritized functions over relations. Two seemingly contradictory aspects of Peano’s axiomatics, global and local reasoning, are illustrated through the examples of rigor and simplicity. Finally, the paper claims that Peano’s axiomatics was a dynamic mathematical enterprise rather than an a priori axiomatization grounded on logical principles, which explains the difference with respect to Frege’s project. (shrink)

The book is a collection of the author¿s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:russell: the Journal of Bertrand Russell Studies n.s. 33 (winter 2013–14): 173–90 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\kenneth\documents\type3302\rj 33,2 114 red.docx 2014-01-31 8:29 PM oeviews MODES AND LEVELS OF PERPLEXITY I. Grattan-Guinness Middlesex U. Business School Hendon, London nw4 4bt, uk [email protected] John Ongley and Rosalind Carey. Russell: a Guide for the Perplexed. London: Bloomsbury, 2013. Pp. ix, 212. isbn: 978-0-8264-9753-6. £45 (...) (hb), £14.99 (pb); us$80 (hb), us$24.95 (pb). i his book is the 41st in a series of guides to the work of various philosophers and philosopher groups, written at a level of readability for students. The authors survey the course of Bertrand Russell’s philosophical career, starting out with his work on logic and mathematics. The main philosophical tools are presented: in logic, they are term, proposition, proposition function, relation, paradox, and first- vis-à-vis higher-order logic. Then, moving on to epistemology, the principal philosophical notions are presented, such as sense-data, facts related to language, Russell’s overriding preference for positivistic philosophies and suspicions of metaphysics, knowledge by acquaintance and by description, theories of truth, logical atomism, percept, events, meaning, and inference in the context of scientific theories. It is nice to have many of the principal components of Russell’s philosophy exhibited together, including the later works An Inquiry into Meaning and Truth and Human Knowledge. The perplexed reader would like to be given precise references for Russell’s assertions on various points, especially when he was so prolific. A cited short item does not need more precision; but the two main chapters that cover the logic and epistemology story often seem to invoke The Principles of Mathematics or Principia Mathematica and yet contain only one precise citation of a longer text in their 64 pages (p. 85). The other chapters of the book are somewhat better in this respect. The index is excellent, though W. V. Quine was missed at pp. 29–30. The table of contents would have benefited from including the titles of the sections. q= 174 Reviews c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 ii Much ground is covered; however, the account is mitigated by the failure to provide a biographical factual survey that should have constituted the opening chapter. Little or no description or explanation is given of, among others, Cambridge University, its mathematical tripos, Russell’s research fellowship in 1895, the philosophical journals Mind and The Monist, Russell’s conversion from neo-Hegelian to positivistic philosophy following G. E. Moore around 1899, the start of personal contacts with Giuseppe Peano in 1900, the gradual involvement of A. N. Whitehead from around 1902, the financial rescue of Principia Mathematica by the grant from the Royal Society in 1909, the serious mistake in Volume 2 detected by Whitehead in 1911 while it was in press, the initial contact with Ludwig Wittgenstein from 1911, Russell’s switch from logic to epistemology in the early 1910s, Whitehead’s intentions for the fourth volume of Principia that was abandoned in 1918, the circumstances of the second edition published in the mid-1920s, Russell’s partial return to serious philosophical writings from the mid-1930s onwards, or the Trinity fellowship from 1944. Presumably the authors have made most of these omissions intentionally ; but the target audience is the loser. The opening “introduction” does mention some of these events and publications ; but its purpose is to provide a preliminary look at some of the main features of Russell’s logic, including the comprehension axiom “that every predicate defines a class” (p. 3), type theory, definite descriptions, “the noclass theory of classes” (p. 10), and the status and role of “analysis”. Why do these features need prologues when the others do not? When they are re-discussed in the later chapters on logic and epistemology, several near-repetitions occur. Furthermore, quantification does not receive sufficient consideration in the book; and the logical connectives and rules of inference none at... (shrink)

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

Between Giuseppe Peano and Camillo Berneri, a foremost protagonist of the Italian anarchist movement, an interesting correspondence was exchanged in the years 1925-1929. Along with a presentation of the correspondence, Peano's political attitude and the role of his international language projects in early 20th century Italian left are discussed.