Is the debate over the existence of numbers unsolvable? Mario Gómez-Torrente presents a novel proposal to unclog the old discussion between the realist and the anti-realist about numbers. In this paper, the strategy is outlined, highlighting its results and showing how they determine the desiderata for a satisfactory theory of the reference of Arabic numerals, which should lead to a satisfactory explanation about numbers. It is argued here that the theory almost achieves its goals, yet it does not (...) capture the relevant association between how a number can be split up and the morphological property of Arabic numerals to be positional. This property seems to play a substantial role in providing a complete theory of Arabic numerals and numbers. (shrink)

Many theories about human number representation stress the importance of a central semantic representation that includes the magnitude information of small integer numbers, and that is conceived as an abstract, compressed number line. However, thus far there has been little or no direct evidence that units and teens are represented on the same number line. In two masked priming experiments, we show that single-digit and two-digit Arabic numerals are equally well primed by an Arabic numeral with the (...) same number of digits as by an equally distant Arabic numeral with a different number of digits (e.g. the priming effect of 7 on the target 9 is the same as the priming effect of 11 on the target 9). The finding was obtained both with a number naming task and with a parity judgement task. This is in line with the hypothesis that units and teens are part of a continuous number line. (shrink)

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received (...) wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps. (shrink)

Melisa Vivanco objects to my theory of the Arabic numerals in Roads to Reference that the reference fixing procedure that I postulate doesn’t exploit the morphological structure of the Arabic numerals, but it should. Against Vivanco, I argue that the procedure in question does exploit the morphological structure of the numerals in an essential way.

Arabic literacy skills are essential for Muslim learners to comprehend religious texts; however, when trying to improve these skills, students face numerous obstacles that require immediate attention. This study aims to develop and evaluate an Arabic learning model designed to enhance the capability of students in Indonesian boarding schools to read religious books. The research follows a three-stage approach: introductory study, model development, and model validation. The study takes place in Al-Jawami and Al-Falah boarding schools in West Java (...) Province, Indonesia. These schools were selected due to the emphasis they place on the Arabic reading skills needed for comprehending religious scriptures. The research employs the research and development (R&D) method, involving 80 students. A three-time experimental test compared the learning outcomes of students in the experiment group (EG) using the new model with those in the control group (CG) using the existing model. Data analysis utilized both qualitative and quantitative approaches, employing t-test statistics. Results indicated significantly higher effectiveness in the treatment group, demonstrating that the Arabic learning model utilized in this study effectively enhances the reading capacity of students. Additionally, student perspectives on the developed model were sought, revealing a highly positive response. The majority of students expressed satisfaction with the model's impact on their reading skills and demonstrated enthusiasm for self-directed Arabic learning. Overall, the research contributes valuable insights into effective Arabic language education strategies, with the developed model proving to be a successful approach in enhancing students' reading proficiency in religious texts. (shrink)

Within the professional practice of psychology the code of ethics characterizes what is morally right or wrong, by means of a set of principles, values, and standards of conduct. While there are numerous international mental health organizations that incorporate ethical guidelines such as the APA and EFPA; these codes still fall short in providing guidelines for psychologists working in non-western cultures, especially when there are no universally adopted and valid cross-cultural ethics codes. This paper explores various challenges psychologists in the (...) Arab region face when using a western code which does not reflect the values and traditions of their culture. A comparison of several ethical codes from different Arab countries is presented, with a focus on challenging areas of interest such as confidentiality, informed consent and multiple relationships. (shrink)

El Tesoro de la lengua castellana o española of Covarrubias covers up another treasure: a basic grammar of Arabic spread over the two hundred Arabic etymologies provided by the prominent Arabist, contemporary of the lexicographer, Diego de Urrea.Such is the subject of our study that will be devoted, thanks to linguistic analysis, to highlight in this corpus the explicit and implicit presence of numerous grammatical data that refer to fundamental rules of Arabic grammar such as the derivation (...) system and the morphonology of the verb. The presentation of this data in the Tesoro is made by an original terminology that can only be understood in the context of Arabic grammar and which is a true innovation in the field of Arab grammars composed by contemporary European Arabists. On the other hand, Urrea’s etymologies support the new “verbal root theory” introduced by Erpenius in his Grammatica Arabica, and therefore suggest his involvement in contemporary arabism. This study shed new light on the place of the Arabic language in the Tesoro of Covarrubias, a place that had remained, since the first modern reissue of the Tesoro in 1943, completely unnoticed by the research. It invites to see in the Tesoro an innovative work in the context of the new scientific interests that, from the end of the 16th century, would be directed towards the emergence of a new science: Orientalism. (shrink)

Moshe ben Maimon, or Moses Maimonides, remains one of the most celebrated rabbis in this history of Judaism; his numerous writings include philosophical and medical treatises in Arabic, two of history's most important works on Jewish law, and, most notably, efforts to reconcile Aristotelian philosophy with biblical teaching. The _Complete Medical Works_, edited by Gerrit Bos of the Martin-Buber-Institut fur Judaistik at the University of Cologne, collects the entirety of Maimonides's medical writings. Notwithstanding its title, _On Asthma_ is in (...) fact a complete regimen of health, designed for the needs of a high-ranking patient whose identity is not stated. In true Galenic fashion, Maimonides stresses that a healthy lifestyle and diet are the most important preventative measures against chronic illness such as asthma. Good and bad foods are described in detail, and many recipes for beneficial dishes and drugs are included, with Maimonides adapting Galenic regimens to the needs of his Muslim patient. (shrink)

This book explores the reaction of tenth-century Arab philosopher Abu Nasr Alfarabi to the logical works of Aristotle. From numerous short treatises the author develops a systematic and comprehensive topical survey of Alfara bi's logical writings. The book is divided into two major parts: language as a tool of logic and logic as a tool with which to analyze language. The first five chapters deal with Alfarabi's analysis of the meanings of various terms as they are used in logic and (...) philosophy. Alfarabi refutes the Arab grammarians who claimed that Arab logicians were building a language within a language and shows that the philosophical meanings of terms are in fact their most original and essential meanings. The final chapter deals with Alfarabi's analysis of certain aspects of the Arabic language and demonstrates that Arabic, like any natural language, conforms to universal logical structures of which natural languages are only a concrete expression. (shrink)

Ever since the Arab Spring revolutions started, numerous journalists, academics and Middle East experts have been appearing on news channels, websites and radio talk shows warning of an impending and inevitable Islamist takeover should free elections be held in the post-Arab Spring Middle East. Their winning of free elections would almost certainly be followed with the implementation of the strictest interpretations of shariah. Was it so? The aim of this article is to answer the following question: Did the ‘Arab Spring’ (...) pave the way for shariah-based constitutions? At the time of this writing (mid-2013) certain reversals of the Arab Spring are obviously taking place, hence this article is restricted to the immediate post-Arab Spring period. (shrink)

Moshe ben Maimon, or Moses Maimonides (1135-1204), remains one of the most celebrated rabbis in this history of Judaism; his numerous writings include philosophical and medical treatises in Arabic, two of history's most important works on Jewish law, and, most notably, efforts to reconcile Aristotelian philosophy with biblical teaching. The Complete Medical Works, edited by Gerrit Bos of the Martin-Buber-Institut fur Judaistik at the University of Cologne, collects the entirety of Maimonides's medical writings. Notwithstanding its title, On Asthma is (...) in fact a complete regimen of health, designed for the needs of a high-ranking patient whose identity is not stated. In true Galenic fashion, Maimonides stresses that a healthy lifestyle and diet are the most important preventative measures against chronic illness such as asthma. Good and bad foods are described in detail, and many recipes for beneficial dishes and drugs are included, with Maimonides adapting Galenic regimens to the needs of his Muslim patient. Volume Two offers Gerrit Bos’s critical editions of all three surviving medieval Hebrew translations of Maimonides’ work: one allegedly prepared by the fourteenth-century physician Samuel Benveniste, who served Don Manuel, brother of King Pedro IV of Aragon; a second by Joshua Shatibi from Játiva (Xátiva) between the years 1379 and 1390, for the referendary Fernán Díaz of Toledo at the court of King Juan II of Castile; and a third by an anonymous translator, perhaps in the thirteenth century. The volume also contains critical editions by Michael R. McVaugh of the two medieval Latin translations of Maimonides’ treatise, one probably made by Giovanni da Capua at Rome c. 1300 and the other begun by Armengaud Blaise in Montpellier in 1294 but completed eight years later. It concludes with a section of addenda and corrigenda to the first volume. (shrink)

Les documents chinois, depuis le Iersiècle, indiens, depuis le Vesiècle, et arabes, depuis le IXesiècle, contiennent des procédures tabulaires similaires pour l'extraction de racines carrées et cubiques avec des systèmes de numération positionnels. Par ailleurs tant Jia Xian, astronome chinois du XIesiècle, qu'al-Samaw'al, mathématicien arabe du XIIesiècle, ont extrait des racines de degré plus élevé par la procédure dite de Ruffini-Horner. L'article tente de définir une méthode textuelle pour organiser ce corpus, en y distinguant des axes pertinents qui permettent de (...) dégager similarités et différences, d'un point de vue tant historique que conceptuel. Une première partie analyse trois états différents des descriptions d'algorithmes entre le Iersiècle et le XIesiècle en Chine, qui présentent chacun une stabilité historique certaine. La réécriture qui fait passer d'un état au suivant laisse émerger progressivement une uniformité dans les composantes de l'algorithme, laquelle culmine avec des procédures du type Ruffini-Horner. Des critères textuels font apparaître une affinité plus grande de certains algorithmes, tels ceux décrits par Kūshyār ibn Labbān (ca1000), avec les textes chinois qu'avec les textes indiens, plus proches, eux, des algorithmes décrits par al-Khwārizmī. Des critères de même nature lient, d'une part, les algorithmes de Jia Xian et d'al-Samaw'al, d'autre part les algorithmes de Kūshyār et d'al-Samaw'al. (shrink)

Summary As a divinatory device based on the numerical values of names, onomancy requires a system of letter-number equivalents. In Greek and the Semitic languages, a unique system is used, which consists of ascribing the first nine letters of the alphabet to the units (1–9), the following nine letters to the tens (10–90), and the remaining letters to the hundreds (100-). Given the structural similarities between those languages, the transfer of onomancy between Greek and Semitic cultures does not pose particular (...) problems. Difficulties arise when onomancy is translated into Latin, where there is no such system of letter-number equivalents. This article examines the various solutions put forward by the translators and authors of the earliest Latin onomantic texts of Arabic origin, the so-called Alchandreana. (shrink)

At a time when cooperation between Europe and the Arab World is getting more and more concrete, this article highlights the reciprocal influences between languages and legal culture both North and South of the Mediterranean for the redaction of a common discourse. Europe conceives and produces numerous pieces of legislation that have a significant impact on both Maghreb and Mashriq. It is thus necessary to look back at a few seminal studies on European legal discourse to focus on the various (...) types of corpus used, as well as how they are perceived abroad. This state of play underlines the linguistic and cultural interactions that will be faced by language studies in Europe in the fields of terminology, semantics and pragmatics. (shrink)

This study explores how Islamic business ethics and values impact the way in which Muslim women entrepreneurs conduct their business in the Arab world. Guided by institutional theory as a theoretical framework and social constructionism as a philosophical stance, this study uses a qualitative, interview-based methodology. Capitalizing on in-depth, face-to-face interviews with Muslim Arab women entrepreneurs across four countries in the Arab Middle East region, the results portray how Islamic work values and ethics are embedded in the entrepreneurial activities of (...) these Arab women. The results also illustrate how Muslim women entrepreneurs seek well-being in their life and excellence in their work while running their businesses. The Muslim women entrepreneurs adhered to the Islamic work-related values of good and hard work, honesty and truthfulness, fairness and justice, and benevolence and perceived them as instrumental to the survival and success of their enterprises. The agency of the Muslim Arab women allowed them to construct and navigate their entrepreneurial careers away from the traditional, doctrinaire interpretations of Islam. This study, therefore, contributes to theory development on the interrelationship between gender and business ethics within entrepreneurial contexts and in relation to Muslim values. It also contributes to studies on entrepreneurship and business ethics by showing how Arab women practice entrepreneurship and project their faith in their enterprises. The implications of the study for academics, multinational corporations, and globalization are numerous and important for understanding how business is conducted in Islamic countries. (shrink)

Avicenna’s _Physics_ is the very first volume that he wrote when he began his monumental encyclopedia of science and philosophy, _The_ _Healing_. Avicenna’s reasons for beginning with _Physics_ are numerous: it offers up the principles needed to understand such special natural sciences as psychology; it sets up many of the problems that take center stage in his _Metaphysics_; and it provides concrete examples of many of the abstract analytical tools that he would develop later in _Logic_. While Avicenna’s _Physics _roughly (...) follows the thought of Aristotle’s _Physics_, with its emphasis on natural causes, the nature of motion, and the conditions necessary for motion, the work is hardly derivative. It represents arguably the most brilliant mind of late antiquity grappling with and rethinking the entire tradition of natural philosophy inherited from the Greeks as well as the physical thought of Muslim speculative theologians. As such, _Physics_ is essential reading for anyone interested in understanding Avicenna’s complete philosophical system, the history of science, or the history of ideas. (shrink)

This source publication of ʿAlī b. ʿUbayda al-Rayḥānī ’s remaining works provides fascinating new material for the study of Arabic literature on proverbs, translations of classical Greek and Persian into Arabic, and clarification of numerous obscure titles in the Arabic bibliographical literature.

The tradition of Lughz and muʿammā in Arab poetry has an important place. Ibn al-Fāriḍ (d. 632/1235) is a divine love poet that lived in the Ayyubids period. He is an important point in the process of change and transformation of Arabic poetry language. This research aims to carry out a theoretical and anecdotal examination of the Lughzes in Ibn al-Fāriḍ’s Dīwān. The work explains, firstly, the concept of Lughz in terms of conceptual content and theoretical structure and summarizes (...) its own method to be applied in solving and evaluating Lughzes in ten articles. The paper indicates whether the Lughzes in Dīwānhave a theoretical structure or not. In this context, it distinguishes the Lughzes from the number of layers, simple and compound structure maintenance. It examines the theoretical and functional contributions of the tahsīl, takmīl, tashīland tazyīlmethods, the stages of the establishment and the solution of the Lughzes.Abstract: Abū Hafs Sharafuddīn Omar b. Ali al-Hamavī al-Mısrī (d. 632/1235) known as the king of lovers, and called Ibn al-Fārid, is a divine love poet that lived in Egypt during the Ayyubids period (1171-1462). He is an important figure in the process of change and transformation of poetry language in Arabic literature. The lughz and muʿammā (enigma, enigmetic speech, allusion, inversion riddle, poetry puzzle, synecdoche and metaphoric language) means a word pointing to a name or something by symbol and sign. Numerous books have been written about lughzes. These include Arabic poetry, Persian poetry, Classical Turkish poetry, Arabic grammar, Islamic law, hadith, mathematics and inheritance law. The lughz and muʿammā have some linguistic features related to phonetics, statistical linguistics, morphology, lexicology, grammar, syntax, semantics and prosody. This tradition has an important place in Arabic poetry. The research aims to carry out a theoretical and anecdotal examination of the lughzes and muʿammās in Ibn al-Fārız’s Dīwān. The paper explains, firstly, the concept of lughz in terms of conceptual content and theoretical structure. The article summarizes its own method to be applied in analyzing and evaluating lughzes within ten items. The research examines the series of lughzes in Dīwānand divides them into parts according to the original question in the riddles. This work examines the secondary lughzes given in the details of poems in solution parts. The paper indicates whether the lughzes in Dīwānhave a theoretical structure or not. In this context, the research examines lughzes in terms of language and structure, especially in terms of the processes of establishment and solution. This paper categorizes the lughzes according to the number of layers and to whether they have a simple or compound structure. This paper examines the theoretical and functional contributions of the amal al-tahsīlī, amal al-takmīlī, amal al-tashīlī and amal al-tazyīlī methods in the stages of the establishment and the solution of the lughzes. The work applies the theoretical perspectives of these methods to each lughz. The research also examines the contribution of these four methods to the lughzes.There are many lughzes in Ibn al-Fārid’s poems. In Ibn al-Fārid’s Dīwān, in general, fifty-four things are asked. Fifty-one of them are words. Three of them are verbs. One of the verbs is in the order structure and two in the past tense. His lughzes have a theoretical and methodical structure. In terms of organizational structure, lughzes are generally multi-layered, intricate, compound and integrated. Composite lughzes are multi-layered, simple poems are single-layered. Approximately twenty words are asked in the lughzes. These words are always in the first layer of lughz, whether simple or compound. Thirty-seven words in the lughz are secondary lughz with an auxiliary and complementary nature. They are located between the second and sixth layers. Seventeen of the lughzes asked in the auxiliary nature are located in the second layer, thirteen in the third layer, five in the fourth layer, one in the fifth layer and one in the sixth layer. One of the lughzes is six-layered, one of them are five-layered, four of them are four-layered, eight are three-layered, four are double-layered and three are single-layered. According to this, the majority of lughzes in Ibn al-Fārid’s poems are in the unified form and multilayered.The lughzes are formed in terms of word, composition, phrase, grammar and meaning levels. The lughzes have both lexical and semantic characteristics. Ibn al-Fārid uses the configuration (amal al-tahsīlī), completion (amal al-takmīlī), facilitation (amal al-tashīlī) and addition (amal al-tazyīlī) methods to design the lughzes. The structure in the lughzes is shaped by these methods. The words in his lughzes constitute eleven categories, consisting of names, acts and noun verbs. The answers of the questions asked in the poems consist in general of prophet names, surah names, tribal names, administrator’s surnames, letters, cities, animals, food and drink names, attributes and actions. Verbs are in the past time or order form. Some of the lughzes in Ibn al-Fārid’s poems are built in an extraordinary style beyond being interesting. Not all the sentences used in couplets are part of the lughzes. These elements are mentioned in order to complete the lughzes in terms of rhythm and meaning. To be able to solve the lughzes of Ibn al-Fārid, one must be knowledgeable about the language and narrative features of Arabic and Islamic culture, as well as subjects such as the Quran, Sufism, abjad calculation, mathematics, geometry, geography, biology, botany and zoology. His poems contributes to the development and transformation of Arabic poetry. (shrink)

This paper argues that, given a simple [DP VP] sentence, the availability of a collective interpretation crucially depends on the syntactic and semantic properties of the subject DP, specifically the presence versus absence of a pluralizing function that makes the collective interpretation available. In support of my claim, I present Lebanese Arabic and Western Armenian examples in which an indefinite DP contains a cardinal numeral and there is no overt distributivity operator but the interpretation of the sentence is nevertheless (...) obligatorily distributive, regardless of the predicate. I show that neither a distributivity operator within the DP nor one on the predicate can explain this strictly distributive interpretation. Instead, I argue that in order to allow a collective interpretation, an indefinite DP must denote a quantifier over pluralities, a condition that is not always met in numeral-containing indefinite DPs. While the claims in this paper are based primarily on observations from Lebanese Arabic and Western Armenian, because both are morphologically rich languages, the fact that this constraint is operative in these two unrelated languages, in addition to striking similarities to the Russian gender system, suggest that it is an inherent property of DPs crosslinguistically. (shrink)

Background Research ethics guidelines are essential for conducting medical research. Recently, numerous attempts have been made to establish national clinical research documents in the countries of the Middle East. This article analyzes these documents. Methods Thirteen Arab countries in the Middle East were explored for available national codes, regulations, and guidelines concerning research ethics, and 10 documents from eight countries were found. We studied these documents, considering the ethical principles stated in the Declaration of Helsinki, the Council for International Organizations (...) of Medical Sciences (CIOMS) guidelines, and the International Conference of Harmonization - Guidelines for Good Clinical Practice (ICH-GCP). Our paper comprises a complete list of protections, such as confidentiality, informed consent, ethics committees, and others. Results This study found different levels and kinds of research ethics regulations and guidelines in the countries examined. Two groups can be distinguished: the countries in the first group have one or more research ethics regulations or guidelines, while the countries in the second group have not yet established any. Most of the documents showed various degrees of deficiencies in regard to ethical protection. The majority of the documents that were examined refer to one or more international documents on biomedical research ethics. Conclusions Recently, a lot of efforts have been made in many countries in the Middle East. However, compared with international documents, most of the research ethics documents in use in this region demonstrate numerous deficiencies. As it relates to these documents, extensive differences could be observed in regard to development, structure, content, and reference to international guidelines. (shrink)

In order to find positive solutions for third-degree equations, which he did not know how to solve for roots, m proceeds by the intersections of conic sections. The representation of an algebraic equation by a geometrical curve is made possible by the choices of units of measure for lengths, surfaces, and volumes. These units allow a numerical quantity to be associated with a geometrical magnitude. Is there a trace of this unit in the mathematicians to whom al-Khayyām refers directly in (...) his Algebra? How does this unit enable the measurement of quantities and rational and irrational relations? We find answers to these questions in the commentaries to Books V and X of the Elements. (shrink)

The treatise on conic sections by the Hellenistic mathematician Apollonius from Perga is regarded as a supreme achievement of Greek mathematics and maintained its authority right up to the 18th century. This new edition is the first to consider all Greek and Arabic sources, with the Arabic texts being presented in the first ever critical edition. Both versions of the text are accompanied by a French translation, an extensive mathematical commentary, numerous philological notes and a complete glossary. The (...) four volumes of the edition are intended to be completed in 2009. (shrink)

Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The performance of 10- and 11-year-old children with DD characterised by a weakness in arithmetic facts retrieval and age-matched control children was compared on various number comparison tasks. Participants were asked to compare a (...) quantity presented in either a symbolic (Arabic numerals, number words, canonical dots patterns) or a nonsymbolic format (noncanonical dots patterns, and random sticks patterns) to the reference quantity 5. DD children showed a greater numerical distance effect than control children, irrespective of the number format. This favours a deficit in the specialised cognitive system underlying the processing of number magnitude in children with DD. Results are discussed in terms of access and representation deficit hypotheses. (shrink)

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To (...) do this, I summarize Clark’s notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited. (shrink)

This is the first edition to provide the complete text of both the fifth-century Calculus of Victorius of Aquitaine and Abbo of Fleury's Commentary on it. These two works shed light on the early history of mathematics, before the introduction of Arabic numerals. The wide range of Abbo's thought is reflected in the Commentary, covering the nature of wisdom, the philosophy of number, the relationship of unity and plurality, and the arithmetic of the Calculus - all of it (...) set in the broader context of his theology of Creation. This edition is crucial for our current reappraisal of Abbo of Fleury as a major figure of the tenth century, who had a profound impact on later medieval English thought. (shrink)

By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280–1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of (...) mathematical practices necessary for the development towards symbolic reasoning. It is shown how justification schemes compensated for the lack of symbolism in abbaco treatises and at the same time facilitated a process of abstraction. (shrink)

The ability to appropriately sequence a list of discrete items is an important facet in performing routine cognitive tasks and may play a significant role in the acquisition of early communication skills. Though the serial learning abilities of some species, such as chimpanzees and rhesus macaques are well documented, there is virtually no information on the extent of these skills with gorillas. In this study, a young female western lowland gorilla has demonstrated the ability to learn a list of seven (...) Arabic numerals by selecting them on a monitor behind an infrared touchframe. As list length increased, Rollie required fewer trials to reach the criterion, suggesting an acquisition of skills associated with serial learning. Rollie was most likely to correctly select the first item in the sequence and least likely to select the penultimate item in the sequence. Her performance suggests serial learning abilities in the range of other non-verbal species and provides preliminary evidence that supports the assertion that gorillas can succeed at this form of serial learning task. (shrink)

Summary In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of (...) commercial calculations. A method of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and in his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculation carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial (...) calculations. A method of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however, a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculations carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

This chapter discusses about the description of two manuscripts MS 139a and MS 139b. It explains about the typescript TS 207. The manuscript of MS 139a is held at the Wren Library of Trinity College, Cambridge. It comprises 12 loose sheets written in pencil, both in recto and in verso, with many corrections and marks. The content is oriented in landscape position with the original binding edge at the bottom. The manuscript of MS 139b is held at the Österreichische Nationalbibliothek, (...) Vienna. The manuscript comprises 10 loose sheets written in pencil, both in recto and verso, except for the last page, which is written solely in recto. The typescript TS 207 is held at the Wren Library of Trinity College, Cambridge. The text bears neither title nor date. They are numbered with Arabic numerals typed in the upper left corner and handwritten in the upper right corner. (shrink)

In this paper I present a picture of the social status of the Antwerp arithmetic teachers. This requires first a closer look at the Antwerp schoolmaster in general. Because no fewer than two-thirds of them were also reckoning masters most of the conclusions about teachers are also valid for reckoning masters. The consequences of the sack of Antwerp in 1585 provides us with a wealth of information about the social position of its inhabitants. The material about reckoning teachers is presented. (...) Especially important, in this period of religious turmoil and civil war, is the information concerning the religious convictions of reckoning masters. Finally, a closer look is given to the contents of the arithmetic books and the introduction of arabic numerals. (shrink)

Why is the number seven lucky--even holy--in almost every culture? Why do we speak of the four corners of the earth? Why do cats have nine lives? From literature to folklore to private superstitions, numbers play a conspicuous role in our daily lives. But in this fascinating book, Annemarie Schimmel shows that numbers have been filled with mystery and meaning since the earliest times, and across every society. In The Mystery of Numbers Annemarie Schimmel conducts an illuminating tour of the (...) mysteries attributed to numbers over the centuries. She begins with an informative and often surprising introduction to the origins of number systems: pre-Roman Europeans, for example, may have had one based on twenty, not ten, while the Mayans had a system more sophisticated than our own. Schimmel also reveals how our fascination with numbers has led to a rich cross-fertilization of mathematical knowledge: "Arabic" numerals, for instance, were picked up by Europe from the Arabs, who had earlier adopted them from Indian sources. But the heart of the book is an engrossing guide to the symbolism of numbers. Number symbolism, she shows, has deep roots in Western culture, from the philosophy of the Pythagoreans and Platonists, to the religious mysticism of the Cabala and the Islamic Brethren of Purity, to Kepler's belief that the laws of planetary motion should be mathematically elegant, to the unlucky thirteen. After exploring the sources of number symbolism, Schimmel examines individual numbers ranging from one to ten thousand, discussing the meanings they have had for Judaic, Christian, and Islamic traditions, with examples from Indian, Chinese, and Native American cultures as well. Two, for instance, has widely been seen as a number of contradiction and polarity, a number of discord and antithesis. And six, according to ancient and neo-platonic thinking, is the most perfect number because it is both the sum and the product of its parts. Using examples ranging from the Bible to the Mayans to Shakespeare, she shows how numbers have been considered feminine and masculine, holy and evil, lucky and unlucky. A highly respected scholar of Islamic culture, Annemarie Schimmel draws on her vast knowledge to paint a rich, cross-cultural portrait of the many meanings of numbers. Engaging and accessible, her account uncovers the roots of a phenomenon we all feel every Friday the thirteenth. (shrink)

It is a familiar fact that different systems of notation can function in radically different ways. Consider, to take a very simple example, the difference between the sign-designs ‘twenty-three’, ‘XXIII’, and ‘23’. The first is an expression of English tracing the sounds a speaker makes in uttering the words ‘twenty’ and ‘three’. The second is a Roman numeral that uses signs for collections of things—‘X’ for ten things and ‘I’ for one thing—to present by addition the idea of ten and (...) ten and one and one and one, that is, twenty-three, things. Instead of tracing the sounds a speaker makes in speaking in some natural language, the Roman numeral ‘XXIII’ directly represents a collection of things. The Arabic numeral ‘23’ is different again. Like the Roman numeral ‘XXIII’ it in some way represents a number directly; unlike the Roman numeral it is not immediately additive. The numeral ‘23’ is not to be read as designating two and three things. The Arabic numeration system functions as a notational system in a way that is different both from the notational system of a written natural language such as English and from that of the Roman numeration system. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:178 Reviews c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 THE EARLY MOORE AND RUSSELL Ray Perkins, Jr. Philosophy / Plymouth State U. Plymouth, nh 03264 1600, usa [email protected] G. E. Moore. Early Philosophical Writings. Edited and with an Introduction by Thomas Baldwin and Consuelo Preti. Cambridge and New York: Cambridge U. P., 2011. Pp. lxxxv, 251. isbn: 978-0521190145. £68.00; us$114.00. aldwin and Preti have put together a very nice book (...) which gives us G. E. Moore’s 1897 and 1898 Trinity College dissertations and an informative look at the historical context in which they were written. This story—including information about Moore’s early life, the philosophical influences at Cambridge and a critical commentary on his dissertations and readers’ reports— is clearly and carefully presented in their 78-page introduction.1 The book is a valuable addition to the history of analytic philosophy and will be of special interest to Moore (and Russell) scholars and to historians generally who wish to know more about the genesis of the ideas shaping the new analytic philosophy at the end of the century. Moore entered Trinity in 1892 to study classics. There he met Russell (who was in his third year) and took his advice to study philosophy in his last two years and take his final exams (Tripos, Part ii) in both disciplines, which he did successfully in 1896. And like Russell—who had won a Trinity prize fellowship in 1895 (with a dissertation on the foundations of geometry2 ) only one year after his graduation—he submitted a dissertation (1897) in hopes of winning a prize fellowship. Moore’s first attempt failed, but his 1898 version was successful. And not only did the success of the 1898 dissertation launch Moore’s career as a professional philosopher, it also paved the way for the new analytic philosophy of the next century. Moore’s dissertations and his Trinity examiners’ reports (by Caird, Sidgwick, Ward and Bosanquet3 ) are fascinating reading, and it’s a great convenience to have them handy in a single volume. But the editors deserve special 1 Hereafter I shall use the editors’ convention of referring to the pagination of their introduction with roman numerals and to Moore’s dissertations (plus examiners’ reports) with arabic numerals. 2 Russell’s dissertation was published in 1897 as An Essay on the Foundations of Geometry. 3 Edward Caird was an idealist and highly respected Kant scholar at Oxford. Henry Sidgwick was one of Moore’s teachers at Cambridge and author of the influential _= Reviews 179 c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 praise for not only giving the reader an astute critical summary of the dissertations, but also for their skillful reconstruction of Moore’s surviving, but incomplete, 1898 manuscript from which parts of the early chapters had been removed. The editors make a good case (pp. lxxv–lxxix) that those pages became the basis of Moore’s 1899 Mind article, “The Nature of Judgment”. (Those familiar with Russell’s early work may recall it as an article that Russell claimed as of paramount importance for his own early work.4 I’ll return to the question of Russell and Moore and this article’s significance.) the dissertations, 1897 and 1898 Moore’s dissertations reveal a young Moore with remarkable powers of analysis and more than a hint of the careful, courageous scepticism and intellectual honesty for which he later became known. But as the editors make clear, their main importance is the record they reveal of the transition away from Kant and Hegel to the new philosophy, which put a premium on conceptual analysis and metaphysics without Kantian or neo-Hegelian idealism. The 1897 dissertation (“The Metaphysical Basis of Ethics”) is an analysis of the basic concepts of ethics with considerable critical discussion of Kant, especially concerning freedom and reason, and Moore’s attempt to fashion his own good-based ethics utilizing a little from Kant and much from Bradley (p. l). At this time both Moore and Russell were still under the influence of Kant... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Locke on the Knowledge of Material Things ROBERT FENDEL ANDERSON IT IS nOT John Locke's intention, in his Essay Concerning Human Understanding, to deal with matter and material substance nor with how these are able to affect the mind. These are considerations for natural philosophy; Locke counts himself rather among the moral philosophers. He does not propose, therefore, to meddle with the physical aspects of the mind, nor with (...) the physical production of sensations through the organs, nor with the production of ideas in the understanding, nor even with whether ideas depend upon matter for their source. He defers to the wisdom of such men as Boyle, Sydenham, Huygens and Newton in these considerations, and finds it "... ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge....,, 1 It is true that Locke's Essay is characterized chiefly not by an interest in matter and the mechanics of perception but rather by an interest in epistemology and in the ordering and assessment of our knowledge. Because of the very nature and emphasis of this epistemology, however, Locke finds that he must, from time to time, at least mention the nature of matter and how it affects us. Finally, it becomes apparent, certain changes or ambiguities in his point of view regarding the mode of our knowledge and its certainty are consequences of his understanding of matter. It is a demonstration of these elements of his doctrine, which seem not to have obtained the full attention of such scholars as Aaron, Fraser, and Gibson, that I shall attempt in this paper. Fundamentally, Locke's theory of matter appears to be that of Democritus and Epicurus. Like the Greek atomists, he conceives of matter as consisting of particles or corpuscles infinite in number. At least some of these are so minute as to be individually insensible, and probably he intends that all are, although, to my knowledge, he never states that this is so. In the aggregate, in any case, particles do constitute perceptible bodies. As for the Greeks, so also for Locke, the particles arc all extended, having size and shape. They are said also to possess motion or rest, although he takes care to say that matter cannot produce motion in itself,e Locke frequently mentions other properties as being "primary" or "really in" material things. Some of these are solidity, texture, cohesion of parts, situation, and number. Apparently some of these may be ranked under others since, as he 1"Epistle to the Reader," Vol. I, p. 14. All footnotes refer to passages in John Locke's An Essay Concerning Human Understanding, collated and annotated, with prolegomena, biographical, critical, and historical by Alexander Campbell Fraser, in two volumes (New York, Dover Publications, Inc., 1959). Large Roman numerals refer to books of the Essay; small Roman numerals refer to chapters of the books; Arabic numerals refer to sections of the chapters. 2 IV, x, 10. [205] 206 HISTORY OF PHILOSOPHY remarks, figure presupposes extension, and receiving or communicating motion through impact presupposes solidity. The influences of these particles upon one another are treated by Locke under the topic of "powers," a notion which includes in it some kind of "secret relation of parts." 3 The capacities in any substance to give alterations of primary qualities are active powers; the capacities to receive such alterations are passive powers. This alteration must be accomplished by impact or impulse since this, Locke says, is the only way in which bodies can be conceived to operate. Sensation in the percipient being then is to be understood as a special case of this impact of particles upon others. It is evident to Locke that from external obiects some motion must be conveyed by some parts of our bodies to the brain or seat of sensation to produce in our minds the particular ideas we have of these external objects. We are able by sight to perceive at a distance the primary qualities of bodies of observable size. Locke reasons that therefore "... some singly imperceptible bodies must come from them to the eyes, and thereby convey to... (shrink)

Scientific knowledge is acquired according to some paradigm. Galileo wrote that the “book of nature” was written in mathematical language and could not be understood unless one first understood the language and recognized the characters with which it was written. It is argued that Turing planted the seeds of a new paradigm. According to the Turing Paradigm, the “book of nature” is written in algorithmic language, and science aims to learn how the algorithms change the physical, social, and human universe. (...) Some sources of the Turing Paradigm are pointed out, and a few examples of the application of the Turing Paradigm are discussed. (shrink)

This book is an expanded catalogue of an exhibit of mid‐fifteenth‐ through seventeenth‐century drawings, woodcuts, engravings, and etchings emphasizing hands as objects of study, as teaching tools, and as reflections of the human being. In addition, it contains an extended introduction by the curator of the exhibit, Claire Richter Sherman, and four essays by other contributors on pertinent topics: the hand as an instrument of the intellect, manual reckoning, music, and chiromancy . These essays, which precede the catalogue itself, are (...) only loosely connected to the exhibit, but each deals with its subject clearly and crisply.In his composition on the hand as a means of expression, Martin Kemp traces the legacy of ancient thought as reflected in the various anatomical drawings from Leonardo through the detailed Bidloo prints. Kemp concludes that the hand remains “a prime mechanism for personal expression—for the manifestation of individual character and identity.” In the following essay Sachiko Kusukawa provides a succinct sketch of finger numeration, noting that a system alluded to by ancient authors was fully described by the Venerable Bede in the eighth century. Bede also wrote of a method of using the hand as a mnemonic aid in determining the proper date for Easter and other movable feasts. Finger counting remained popular throughout the Middle Ages but gradually fell into disuse in the West by the sixteenth century and was merely quaint by the eighteenth. Kusukawa does not, unfortunately, suggest a reason for the decline, but the spread of computation with Arabic numerals was surely a major factor.Next, Susan Forscher Weiss discusses the use of the hand in teaching music theory and scales. Although there are some indications of this practice in antiquity, variations on a system developed in the eleventh century by Guido of Arezzo were used to teach music through the sixteenth century. Finally, Brain P. Copenhaver discusses the history of the pseudoscience chiromancy . Already in existence in antiquity, palmistry, and other forms of divination, flourished despite the prohibitions of the church. Copenhaver concludes with a witty discussion of the hard times on which palmistry has fallen recently in California.As for the catalogue, it consists of eighty‐three monochrome illustrations, each with an extensive commentary about the artist, the subject, and the reason the item was included in the exhibit. These descriptions are frequently fascinating short essays in themselves, enticing the reader to investigate further. The organization is thematic rather than chronological, with six divisions : “Reading the Writing on Hands,” “Handiwork of the Creator,” “Messengers of the World,” “Knowledge on Hand,” “Whole World in the Hand,” and “Guiding Hands.” The faults are minor. Although the themes of the divisions themselves are clearly described in Sherman's introduction, several of the illustrations seem to have only a general association with the stated theme. A few are filled with details too small to be legible in the necessary reduction of plates to fit the book. Most of the illustrations, however, are excellent examples of the main subject of the exhibit and are fascinating studies in their own right.Generally, this volume is a valuable work for anyone interested in the history of the hand in science and the arts. The four prefatory essays are particularly instructive, and the prints are reproduced clearly, with elaborate descriptions of their historical context and their meaning. Accordingly, this book is much more than merely a catalogue; it is an important work in its own right. Throughout, the substantial references to other works indicate directions for further study. One only regrets that the exhibit itself was shown in only two venues. (shrink)

I first focus on Gomez-Torrente’s defense of a neo-Kripkean treatment of theoretical identification statements like “Water is H2O” against objections that ‘water’ is vague and that ‘H2O’ does not designate a genuine explanatory kind. On my reading, Gomez-Torrente accepts and while interpreting the identity statement as correctly attributing vague identity to the pair consisting of the vague natural kind water and the related kind H2O. My discussion sketches a framework for making sense talk of vague objects, properties, and identities that (...) seems to fit his discussion. Next I focus on his treatment of a problem posed by seemingly conflicting perceptual reports of secondary qualities, like being hot, or red, made by equally competent observers. Since the observers are equally competent, it is hard to explain the apparent inconsistency. Whereas Gomez-Torrente treats the reports as so fine-grained as not to conflict, I suggest dispensing with ultrafine-grained semantic contextual parameters in favor of richer pragmatic parameters determining negotiated asserted contents. Next I question whether his plausible individually sufficient but not disjunctively necessary rules for uses of names and demonstratives should be understood as providing speaker referents versus contributions to illocutionary contents of uses of sentences containing those terms. Finally, I explain why I take the crowning jewel of the book to be the account in chapter 4 of natural numbers as plural cardinality properties, and of verbal, and Arabic, numerals as Millian names of those properties, the referents of which are fixed by genuinely semantic reference-fixing expressions. (shrink)