Aceasta nu este o carte de matematică, ci una despre matematică, care se adresează elevului sau studentului, dar şi dascălului său, cu un scop cât se poate de practic, anume acela de a iniţia şi netezi calea către înţelegerea completă a matematicii predate în şcoală. Tradiţia predării matematicii într-o abordare preponderent procedural-formală a avut ca efect o viziune deformată a elevilor asupra matematicii, ca fiind ceva strict formal, instrumental şi calculatoriu. Pierzând contactul cu baza conceptuală a matematicii, elevii dezvoltă pe (...) parcurs o "anxietate matematică" şi renunţă la a mai căuta înţelegerea matematicii, care devine "duşmanul tradiţional" din şcoală. Această lucrare şi-a propus materializarea rezultatelor cercetărilor inter- şi trans-disciplinare având ca obiect înţelegerea matematicii, care au concluzionat că domeniile care au potenţialul de a contribui în acest fel la educaţia matematicii, unificând abordările procedurală şi conceptuală, sunt epistemologia şi filosofia matematicii şi ştiinţei, precum şi fundamentele şi istoria matematicii. Aceste rezultate susţin teza că teama de matematică poate fi înlăturată prin abordarea conceptuală, iar un elev cu o bună înţelegere conceptuală va fi un rezolvitor de probleme mai bun. Autorul a identificat acele zone şi concepte aparţinând acestor discipline, care pot fi adaptate şi prelucrate în vederea familiarizării elevului sau studentului cu acest tip de cunoştinţe, care să însoţească conţinutul tradiţional al matematicii şcolare. Lucrarea a fost astfel organizată încât să contureze cititorului o imagine unificatoare asupra complexităţii naturii matematicii, precum şi o perspectivă conceptuală necesară, în final, înţelegerii de tip holistic a matematicii şcolare. Autorul vorbeşte despre matematică, pentru a convinge că a înţelege matematica înseamnă mai întâi să o înţelegem ca întreg, dar şi ca parte a unui întreg. Natura matematicii, conceptele sale primare (cum ar fi numerele şi mulţimile), structurile, limbajul, metodele, rolurile şi aplicabilitatea matematicii, sunt prezentate în conţinutul lor esenţial, iar explicarea conceptelor non-matematice este făcută într-un limbaj accesibil, însoţită de multe exemple relevante. Cartea este o unitate didactică concepută să reprezinte punctul de plecare şi un ghid de orientare către dobândirea înţelegerii de tip holistic a matematicii (pentru elev sau student) şi (pentru dascăl) către o predare de tip epistemic-conceptual, în care înţelegerea conceptuală este la fel de importantă ca antrenarea abilităţilor procedural-aplicative. (shrink)

Discussions related to the detection of objective reality, the truth and lie are still a heated topic in the domain of philosophical epistemology. While certain philosophical contexts and theories suggest that the notion "reality as an independent category" should not be engaged, instead, interpretations, including reciprocal, should be used, others hold it that philosophical discussion cannot continue without reference to the said notion. Different philosophers and scolars approach this problem from different angles. When discussing these topics, philosophers often resort to (...) certain thought experiments, engaging an important concept, which can broadly be identified as "the global observer." This concept has something in common with such concepts as the God's Eye, Omniscient Interpreter, Ultimate Observer (quantum physics), Agent of Logical omniscience (game theories), Ideal Observer (ethics and meta-ethics), God (analytic theology). Despite the abundance of works on the topic and scrupulosity of arguments, there still remain many uncertainties in such discussions, mostly related to a great number of logical paradoxes, associated with the problem. Therefore, in view of the current situation, the focus of the research paper is on the deliberation of consistency of the notion "global observer" from the standpoint of logic and philosophy. The results of the analysis of the issue at stake are expected to clarify the notion and to enrich current discussions on the topic. I examine certain difficulties in the philosophical assumptions concerning one of the philosophical concepts, which could be collectively named as the "global observer." The article below explores the notion of the global observer as the guarantor of the determinability and configuration of events in the world. There is explained the meaning of this concept and attempt to show that, despite variations in the wording, it is used in many philosophical contexts related to epistemology. The core issue of the present research paper is the analysis of the consistency of the notion "global observer" from the standpoint of logic and philosophy. The paper discusses why application of this notion in some contexts poses challenges and appears to be paradoxical. (shrink)

As the popularity of the concept of ideology has waned, its ordinary or everyday usage has mirrored the plight of its scolarly usage, with the postulate of a “negative” and a “positive” sense of the term, and the opposition between an “ideological” and a “pragmatic” perspective, albeit with a recognition that ideology does involve a pragmatic dimension. The underlying anti-Marxism of this approach is evidence of a successful polemical strategy. This is an indication that its polemical thrust is an essential (...) aspect of the concept, and that one of the difficulties of “ideology” is that it is the site of the very struggles for whose analysis it provides a conceptual instrument. (shrink)

Discussions related to the detection of objective reality, the truth and lie are still a heated topic in the domain of philosophical epistemology. While certain philosophical contexts and theories suggest that the notion "reality as an independent category" should not be engaged, instead, interpretations, including reciprocal, should be used, others hold it that philosophical discussion cannot continue without reference to the said notion. Different philosophers and scolars approach this problem from different angles. When discussing these topics, philosophers often resort to (...) certain thought experiments, engaging an important concept, which can broadly be identified as "the global observer." This concept has something in common with such concepts as the God's Eye, Omniscient Interpreter, Ultimate Observer (quantum physics), Agent of Logical omniscience (game theories), Ideal Observer (ethics and meta-ethics), God (analytic theology). Despite the abundance of works on the topic and scrupulosity of arguments, there still remain many uncertainties in such discussions, mostly related to a great number of logical paradoxes, associated with the problem. Therefore, in view of the current situation, the focus of the research paper is on the deliberation of consistency of the notion "global observer" from the standpoint of logic and philosophy. The results of the analysis of the issue at stake are expected to clarify the notion and to enrich current discussions on the topic. I examine certain difficulties in the philosophical assumptions concerning one of the philosophical concepts, which could be collectively named as the "global observer." The article below explores the notion of the global observer as the guarantor of the determinability and configuration of events in the world. There is explained the meaning of this concept and attempt to show that, despite variations in the wording, it is used in many philosophical contexts related to epistemology. The core issue of the present research paper is the analysis of the consistency of the notion "global observer" from the standpoint of logic and philosophy. The paper discusses why application of this notion in some contexts poses challenges and appears to be paradoxical. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Before Science: The Invention of the Friars’ Natural Philosophy by Roger French, Andrew CunninghamIrven M. ResnickRoger French and Andrew Cunningham. Before Science: The Invention of the Friars’ Natural Philosophy. Hants, UK: Scolar Press, 1996. Pp. x + 298. Cloth, $68.95.This is a peculiar book that depicts thirteenth-century natural philosophy as wholly dependent on the theological interests of the mendicant orders. For the Friars, “Natural philosophy was a (...) study in which the central concerns were the detection, admiration and appreciation of God’s existence, goodness, providence, munificence, forethought and provision for His creation” (4). Although conceived as “a positive contribution to the discipline of the history of science” (3), the work begins and ends with the claim that medieval natural philosophers were not engaged in science.One difficulty is that the authors never make clear what they mean by science, although they evidently understand that it entails a repudiation of metaphysics and a doctrine of nature’s radical autonomy. Consequently, for French and Cunningham medieval “science” is a mythic construct of modern historians, since “[t]here was no scientific tradition (in the modern sense of the term ‘scientific’) of looking at nature in the thirteenth century, only a religio-political way of doing so” (273).Thus, when summarizing the accomplishments of Roger Bacon, they note that “[Bacon] has been credited, along with Grosseteste, with creating early ‘experimental science’. Bacon could not of course have been a ‘scientist’ because he lived in the wrong [End Page 623] age for this” (238). This seemingly casual conclusion is rather stunning not only in its own right, but also as a revelation of the authors’ own effort to disenfranchise medieval ‘scientists’ for having had the misfortune of living too soon.French and Cunningham propose that polemical or apologetical interests urged the Friars to study nature as a response to various heretics and especially the Cathars who, seemingly like moderns, sought to disengage the natural world from the Christian God, while using the vocabulary of Aristotle’s libri naturales. However this central argument demands better support. Since the authors can cite only one surviving Cathar text—De duobus principiis (ca. 1230)—almost everything known of this group is derived from anti-Cathar polemics. Based on this single text the authors can say no more than that it used “what looks very much like a commentary on Aristotle’s Physics or Metaphysics,” (134) but fail to identify more precisely its sources. It is clear that thirteenth-century orthodox polemics increasingly relied on Aristotelian materials, but the conclusion that natural philosophers did so only in response to heretics who beat them to the Aristotelian punch seems tendentious. The historian will likely remain unconvinced that the unparalleled translating activity of the late eleventh and twelfth centuries—the rendering into Latin of Arabic scientific knowledge (as in Constantine the African’s Pantegni or Adelard of Bath’s Quaestiones naturales), Greek medical literature (e.g. Galen’s Methodus medendi translated by Gerard of Cremona and Burgundio of Pisa) and mathematics (e.g. Euclid’s Optics, Theodosius’s Spherics, Archimedes’ On the Quadrature of the Circle, and Ptolemy’s Tetrabiblos and Almagest) culminating with thirteenth-century translations of Aristotle’s biological works—should all have stemmed from a preoccupation with heresy.A further shortcoming of this book is the limited attention given to works on natural philosophy by the Friars themselves. The book’s first seven of eleven chapters explore the educational establishments in which natural philosophy arose: first monastic and cathedral schools, and then the universities. The works of individual Friars receive only the briefest summary. Among the Dominican natural philosophers Albertus Magnus—the patron saint of scientists and one of a very few scholastics to have commented on all of Aristotle’s biological works—is awarded only five pages. For his mastery of Aristotle’s libri naturales Albertus has been called “the dominant figure in Latin learning and natural science of the thirteenth century.” (Cf. Lynn Thorndike, History of Magic and Experimental Science [New York: Macmillan, 1929], 2:521) Albertus described not only the natural world but also explored the philosophical foundations for scientific knowledge. Yet curiously French and Cunningham give much more attention... (shrink)