We begin by introducing our readers to the Extended Mind Thesis and briefly discuss a series of arguments in its favour. We continue by showing of such a theory can be resisted and go on to demonstrate that a more conservative account of cognition can be developed. We acknowledge a stalemate between these two different accounts of cognition and notice a couple of issues that we argue have prevented further progress in the field. To overcome the stalemate, we propose to (...) focus on the ethical implications of these theories. We link work conducted on the Extended Mind Thesis with contemporary transhumanist research and claim that extended may be ethically preferred over embedded because it is a more progressive and inclusive theory. (shrink)

Advances in artificial intelligence and robotics stand to change many aspects of our lives, including our values. If trends continue as expected, many industries will undergo automation in the near future, calling into question whether we can still value the sense of identity and security our occupations once provided us with. Likewise, the advent of social robots driven by AI, appears to be shifting the meaning of numerous, long-standing values associated with interpersonal relationships, like friendship. Furthermore, powerful actors’ and institutions’ (...) increasing reliance on AI to make decisions that may affect how people live their lives may have a significant impact on privacy while also raising issues about algorithmic transparency and human control. In this paper, building and expanding on previous works, we will look at how the deployment of Artificial Intelligence technology may lead to changes in identity, security, and other crucial values. We will discuss what challenges we may face in the process, while critically reflecting on whether such changes may be desirable. Finally, drawing on a series of considerations underlying virtue ethics, we will formulate a set of preliminary suggestions, which—we hope—can be used to more carefully guide the future roll out of AI technologies for human flourishing; that is, for social and moral good. (shrink)

En este trabajo se analiza la vigencia del pensamiento educativo de Félix Varela en Cartas a Elpidio. En particular se estudian sus ideas acerca del método científico en la enseñanza y de la subordinación del bien individual al bien común. Asimismo se toman en consideración las condiciones y el momento histórico en que fue escrita, su alcance local, nacional y latinoamericano en correspondencia con el actual ámbito de la Universidad de Ciencias Médicas y otras personalidades de la cultura. Mediante la (...) revisión bibliográfica de diversas fuentes utilizadas se obtuvieron datos favorables para este análisis. The validity of Felix Varela´s educative thought in Letters to Elpidio was analyzed in this work. His ideas about the scientific method in teaching and the subordination of individual good to common good were particularly studied. The conditions and the historical moment in which it was written, its local, national and Latin-American repercussion in regards to the updated field of the University of Medical Sciences and other personalities of the cultural field were taken into consideration. Favorable data for this analysis were obtained through bibliographic revision of different sources. (shrink)

Las características de la enseñanza universitaria actual hacen necesaria una constante búsqueda de innovaciones que permitan introducir mejoras en la misma. Este artículo pretende dar a conocer las principales metodologías y herramientas empleadas durante el curso 2021-2022 para mejorar el proceso de enseñanza-aprendizaje en la asignatura de Historia Económica, del Grado en Administración y Dirección de Empresas, en la Universidad de Jaén. Se ha constatado que el empleo de nuevas metodologías alternativas a las tradicionales ha contribuido a mejorar significativamente la (...) comprensión de los contenidos, la adquisición y la evaluación de competencias relacionadas con la asignatura, obteniéndose resultados bastante satisfactorios. (shrink)

In Section 1, I introduce three views that explain human cognitive development from different standpoints: Marcus’s neo-nativism, standard neuroconstructivism, and neo-neuroconstructivism. In Section 2, I assess Marcus’s attempt to reconcile nativism with developmental flexibility. In Section 3, I argue that in structurally reconfiguring nativism, Marcus ends up transforming it into an unrecognizable form, and I claim that his view could be accommodated within the more general framework provided by standard neuroconstructivism. In Section 4, I focus on recent empirical findings in (...) neuropsychology and cultural/social neuroscience, and propose a friendly revision to standard neuroconstructivism, thus developing the neo-neuroconstructivist view. I conclude the article in Section 5 by analysing the implications of the results discussed in Section 4 for both neo-nativism and standard neuroconstructivism. 1 Introduction2 Marcus’s Neo-nativism3 Is Marcus’s Neo-nativism Really a Form of Nativism?4 Neo-neuroconstructivism and Dynamic Enskillment5 Conclusion. (shrink)

Block (Trends Cogn Sci 7:285–286, 2003) and Prinz (PSYCHE 12:1–19, 2006) have defended the idea that SSD perception remains in the substituting modality (auditory or tactile). Hurley and Noë (Biol Philos 18:131–168, 2003) instead argued that after substantial training with the device, the perceptual experience that the SSD user enjoys undergoes a change, switching from tactile/auditory to visual. This debate has unfolded in something like a stalemate where, I will argue, it has become difficult to determine whether the perception acquired (...) through the coupling with an SSD remains in the substituting or the substituted modality. Within this puzzling deadlock two new approaches have been recently suggested. Ward and Meijer (Conscious Cogn 19:492–500, 2010) describe SSD perception as visual-like but characterize it as a kind of artificially induced synaesthesia. Auvray et al. (Perception 36:416–430, 2007) and Auvray and Myin (Cogn Sci 33:1036–1058, 2009) suggest that SSDs let their users experience a new kind of perception. Deroy and Auvray (forthcoming) refine this position, and argue that this new kind of perception depends on pre-existing senses without entirely aligning with any of them. So, they have talked about perceptual experience in SSDs as going "beyond vision". In a similar vein, MacPherson (Oxford University Press, New York, 2011a) claims that “if the subjects (SSD users) have experiences with both vision-like and touch-like representational characteristics then perhaps they have a sense that ordinary humans do not” (MacPherson in Oxford University Press, New York, 2011a, p. 139). (shrink)

This paper examines an argument by Schaffer (2017) that aims to prove how, contrary to what many philosophers hold, there is no special explanatory gap occurring in the connection between the physical and the phenomenal. This is because a gap of the same kind can be found in every connection between a more fundamental and a less fundamental level of reality. These gaps lurk everywhere in nature. For Schaffer, they can be bridged by means of substantive metaphysical principles such as (...) grounding principles. He thus puts forward a version of grounding-based physicalism, which is supposed to provide this kind of substantive bridge principle. My main contention is as follows: even if Schaffer’s argument indeed proves the existence of a gap in every connection between fundamental and derivative entities, and such gaps can be bridged by means of grounding principles, a different gap remains open in the psycho-physical connection. (shrink)

This book provides an introduction to the study of words, their main properties and how we use them to create meaning. It offers a detailed description of the organizational principles of the lexicon, and of the categories used to classify various lexical phenomena, including polysemy, meaning variation, behaviour in composition, and the interface with pragmatics. Elisabetta Ježek uses empirical data from digitalized corpora and speakers' judgements, combined with the formalisms developed in the field of general and theoretical linguistics, to (...) propose representations for each of these phenomena. The book's clear structure and accessible approach make it an ideal textbook for all students of linguistics and a valuable resource for scholars and students of language in the fields of cognitive science and philosophy. (shrink)

This critical essay evaluates the potential integration of distinct kinds of expertise in policymaking, especially during situations of critical emergencies, such as the COVID-19 pandemic. This article relies on two case studies: herd immunity and restricted access to ventilators for disabled people. These case studies are discussed as examples of experts’ recommendations that have not been widely accepted, though they were made within the boundaries of expert epistemic authority. While the fundamental contribution of biomedical experts in devising public health policies (...) during the COVID-19 pandemic is fully recognized, this paper intends to discuss potential issues and limitations that may arise when adopting a strict expert-based approach. By drawing attention to the interests of minorities, the paper also claims a broader notion of “relevant expertise.” This critical essay thus calls for the necessity of wider inclusiveness and representativeness in the process underlying public health policymaking. (shrink)

In this paper I focus on the emergence of the concept of the “historical a priori” at the origin of Foucault’s archeology. I emphasize the methodological function of this concept within Foucault’s archaeology, and I maintain that despite the different thesis it entails as compared to its philosophical sources, it pertains to one of the main issues of phenomenology, that is, the problematization of the relation between reality as it appears in its historicity, and transcendentality. I start from the interest (...) of the young Foucault in existential psychiatry, and I focus on the French philosophical context in which Foucault’s Introduction to Ludwig Binswanger’s “Dream and Existence” (1954) was conceived. My aim is to show that the first “phenomenological” phase of Foucault’s work is coherent, from a methodological point of view, with the development of archaeology intended as “historical epistemology.” I conclude by arguing that Foucault’s archaeology is methodologically linked to Canguilhem’s epistemology, in that the latter presents itself as an important attempt at linking together historicity and transcendentality. (shrink)

This paper investigates the claim that artificial Intelligence Systems cannot be held morally responsible because they do not have an ability for agential self-awareness e.g. they cannot be aware that they are the agents of an action. The main suggestion is that if agential self-awareness and related first person representations presuppose an awareness of a self, the possibility of responsible artificial intelligence systems cannot be evaluated independently of research conducted on the nature of the self. Focusing on a specific account (...) of the self from the phenomenological tradition, this paper suggests that a minimal necessary condition that artificial intelligence systems must satisfy so that they have a capability for self-awareness, is having a minimal self defined as ‘a sense of ownership’. As this sense of ownership is usually associated with having a living body, one suggestion is that artificial intelligence systems must have similar living bodies so they can have a sense of self. Discussing cases of robotic animals as examples of the possibility of artificial intelligence systems having a sense of self, the paper concludes that the possibility of artificial intelligence systems having a ‘sense of ownership’ or a sense of self may be a necessary condition for having responsibility. (shrink)

Philosophical Psychology is dedicating this issue on trust and trustworthiness to Katherine Hawley (1971–2021) for two reasons. First, she was an expert in the area. Hawley was one of the most rele...

An innovative examination of the ways in which dance and philosophy inform each other, Dance and Philosophy brings together authorities from a variety of disciplines to expand our understanding of dance and dance scholarship. Featuring an eclectic mix of materials from exposes to dance therapy sessions to demonstrations, Dance and Philosophy addresses centuries of scholarship, dance practice, the impacts of technological and social change, politics, cultural diversity and performance. Structured thematically to draw out the connection between different perspectives, this books (...) covers: - Philosophy practice and how it corresponds to dance - Movement, embodiment and temporality - Philosophy and dance traditions in everyday life - The intersection between dance and technology - Critical reflections on dance Offering important contributions to our understanding of dance as well as expanding the study of philosophy, this book is key to sparking new conversations concerning the philosophy of dance. (shrink)

L’autore si propone di investigare i rapporti tra retorica e tempo nel “Dialogo sui due massimi sistemi del mondo” di Galileo Galilei, giustificando l’analisi retorico-stilistica della prosa scientifica sintesi di ragione e immaginazione, stabilendo un parallelo tra l’abbattimento della discontinuità tra Cielo e Terra e alcune innovazioni retoriche della prosa galileiana che precede il Dialogo e prendendo in considerazione passi del “Dialogo” in cui Galileo manipola i concetti di ‘tempus’ e ‘aeternitas’ tramite metafore, similitudini e altre figure, che sono strumento (...) essenziale alla dimostrazione della tesi che interessa, cioè quella della fondamentale identità tra cielo e terra, dell’unità del tempo cosmico. (shrink)

The distinction between concept and conception has been widely debated in political philosophy, whereas in the philosophy of psychology is frequently used, but rarely focused on. This paper aims at filling in this lacuna. I claim that far from being explanatorily idle, the distinction makes it possible to provide an adequate description of phenomena such as genuine disagreement, and concept contestation, which would otherwise remain implausibly puzzling. I illustrate and assess three accounts of the concept-conception distinction. Finally I propose a (...) social externalist account, which relies on deference to experts, and builds on Tyler Burge’s ideas of many decades ago. The debate on concepts and conceptions thus shows a connection with the increasing research work on experts and expertise in psychology and social epistemology. (shrink)

Baccarini and Malatesti (2017) defend the idea that we must use coercively biomedical means to enhance the morality of a specific group of individuals: psychopaths, diagnosed through the Psychopathy Checklist-Revised (PCL-R) standards (Hare, 2003). Their argument is theoretical, thus it goes independently from the actual effectiveness of existent treatments, and it is based on a logical reasoning. Moral bioenhancement (MB) means include psychotropic drugs, brain stimulations, neurosurgeries, genetic editing, etc. -/- In short, the authors apply Gerald Gaus' account of open (...) justification (Gaus, 1996, 2011), according to which “a prescription addressed to an agent is a reasoning that includes premises that consider the system of reasons (such as beliefs, preferences, etc.) of that agent” (Baccarini and Malatesti, 2017, p. 1). In their view, coercive MB of psychopaths is morally sound and deducible by reasons within the psychopath's cognitive-affective system—even if the psychopath needs not to be able to consciously or sincerely endorse them. We believe that this argument is flawed. In sum, we argue that the psychopath's cognitive-affective system would consistently justify reasons against mandatory MB to herself, even if she wishes differently for others, and that the prescription cannot be extended. (shrink)

Numerous studies suggest that both emotion knowledge and language abilities are powerfully related to young children’s theory of mind. Nonetheless, the magnitude and direction of the associations between language, emotion knowledge, and theory-of-mind performance in the first years of life are still debated. Hence, the aim of this study was to assess the direct effects of emotion knowledge and language on theory-of-mind scores in 2- and 3-year-old children. A sample of 139 children, aged between 24 and 47 months (M = (...) 35.5 months; SD = 6.73), were directly administered measures of emotion knowledge, theory of mind, and language. We conducted structural equation modeling (SEM) to evaluate the effects of these variables within a single comprehensive framework, while also controlling for any effects of age and gender. The proposed structural equation model provided an excellent fit for the data, indicating that both children’s emotion knowledge and their language ability had direct positive effects on theory of mind scores. In addition, age was found to wield statistically significant effects on all the variables under study, whereas gender was not significantly associated with any of them. These findings suggest the importance of fostering young children’s emotion knowledge and language with a view to enhancing their comprehension of mental states. (shrink)

Queremos mostrar que ninguno de los argumentos conocidos a favor del externismo fenoménico es convincente. PE es la tesis de que las propiedades fenoménicas de nuestras experiencias se tienen que individuar en modo amplio en la medida en la que están constituidas por propiedades del mundo. Examinamos los que nos parecen los cinco mejores argumentos a favor de PE. Intentamos mostrar que ninguno de ellos puede establecer el resultado deseado. Mientras no aparezcan argumentos mejores en el debate, no tenemos razón (...) para renunciar a una idea que parece intuitiva y atractiva para muchos psicólogos cognitivos: que la fenomenología es estrecha, es decir, que las propiedades fenoménicas son propiedades intrínsecas de nuestras experiencias. Esta idea subyace a la posición filosófica opuesta, el internismo fenoménico. (shrink)

This book provides an introduction to the study of words, and how we use words to create meaning. It offers an accessible description of the main properties of words and the organizational principles of the lexicon, based on theoretical accounts and extensive empirical data.

This is the first book to explore the epistemology and ethics of advanced imaging tests, in order to improve the critical understanding of the nature of knowledge they provide and the practical consequences of their utilization in healthcare. Advanced medical imaging tests, such as PET and MRI, have gained center stage in medical research and in patients’ care. They also increasingly raise questions that pertain to philosophy: What is required to be an expert in reading images? How are standards for (...) interpretation to be fixed? Is there a problem of overutilization of such tests? How should uncertainty be communicated to patients? How to cope with incidental findings? This book is of interest and importance to scholars of philosophy of medicine at all levels, from undergraduates to researchers, to medical researchers and practitioners (radiologists and nuclear physicians) interested in a critical appraisal of the methodology of their discipline and in the ethical principles and consequences of their work. -/- . (shrink)

The quarantine model, recently proposed by Pereboom and Caruso, is one of the most influential models developed to date in the context of criminal justice. The quarantine model challenges the very idea of criminal punishment and asserts that nobody deserves punishment on a fundamental level. Instead, in order to deal with offenders, it proposes a series of incapacitation measures based on public safety concerns. In this article, we examine several objections to the quarantine model that demonstrate how, in our view, (...) it can be improved. These mainly pertain to (2.1) the difficulty of reliably identifying dangerous individuals and consequently the need to base confinement decisions on probability, and (2.2) the potential for the quarantine model not to properly deter certain crimes. Three additional objections are raised with respect to (3.1) the rights that are potentially suppressed in the quarantine model; (3.2) the role of “genetic justice”; and (3.3) the difficulty it faces accommodating reasons-responsiveness. Whereas these objections do not constitute knock-down arguments against the quarantine model, they highlight issues that invite closer scrutiny, at least if it is to be considered as a credible framework for the development of viable policies in criminal justice. (shrink)

Acoustic codes assure the intra and interspecific communication of vocal animals. They are composed by a sequence of nominal entities and by magnitude modulation confirming in such a way contemporarily a behavioural and ecological nature. The acoustic codes find evidence in the acoustic niche hypothesis by which species in order to reduce interspecific competition occupy a restricted portion of the available frequencies modulating very precise acoustic cues . Their evolution, like other aspect of biology, is under control of the environmental (...) conditions assuming the more favourable configurations. These nominal entities respond also to the amount of energy by which are emitted allowing to the eavesdropping individuals to range the distance at which a potential competitor is broadcasting a signal. Environmental alterations, especially if of anthropogenic origin, can produce severe consequence of the acoustic codes that in turn may affect the prey–predator balance and the complexity of communities. In fact acoustic codes under an environmental constraint like human noise intrusion can be modified in order to reduce a masking effect, demonstrating their phenological plasticity. The new ecological discipline of soundscape ecology offers the possibility to investigate the nature and the evolution of the acoustic codes in different environmental conditions. (shrink)

This commentary focuses on Machery's eliminativist claim, that ought to be eliminated from the theoretical vocabulary of psychology because it fails to denote a natural kind. I argue for the more traditional view that concepts are a functional kind, which provides the simplest account of the empirical evidence discussed by Machery.

How should human beings and robots interact with one another? Nyholm’s answer to this question is given below in the form of a conditional: If a robot looks or behaves like an animal or a human being then we should treat them with a degree of moral consideration (p. 201). Although this is not a novel claim in the literature on ai ethics, what is new is the reason Nyholm gives to support this claim; we should treat robots that look (...) like human or non-human animals with a certain degree of moral restraint out of respect for human beings or other beings with moral status. Although Danaher or Coeckelbergh also claim that we should treat robots with a degree of moral consideration, the reasons they give for making this claim focus on duties or rights attaching to the robot themselves (see J. Danaher, “Welcoming Robots into the Moral Circle: A Defence of Ethical Behaviourism,” Science and Engineering Ethics, (2019): 1–27 or M. Coeckelbergh, “Moral Appearances: Emotions, Robots and Human Morality,” Ethics and Information Technology, 12(3) (2010): 235–241.). Nyholm disagrees with this type of reasoning and claims that until robots develop a human or animal like inner life, we have no direct duties to the robots themselves. Rather, it is out of respect for human beings or other beings with moral status that we should treat some robots with moral restraint. Gerdes, similarly inspired by Kant, focuses on the human agent to argue that we should avoid treating robots in cruel ways because this may corrupt the human agent’s character (see A. Gerdes, “The Issue of Moral Consideration in Robot Ethics,” siggas Computers and Society, 45(3) (2015): 274–279.). Nyholm’s contribution here is to extend this view such that the corruption or harm being done is against the humanity in all of us. (shrink)

Advanced medical imaging, such as CT, fMRI and PET, has undergone enormous progress in recent years, both in accuracy and utilization. Such techniques often bring with them an illusion of immediacy, the idea that the body and its diseases can be directly inspected. In this paper we target this illusion and address the issue of the reliability of advanced imaging tests as knowledge procedures, taking positron emission tomography in oncology as paradigmatic case study. After individuating a suitable notion of reliability, (...) we argue that PET is a highly theory-laden and non-immediate knowledge procedure, in spite of the photographic-like quality of the images it delivers; the diagnostic conclusions based on the interpretation of PET images are population-dependent; PET images require interpretation, which is inherently observer-dependent and therefore variable. We conclude with a three-step methodological proposal for enhancing the reliability of advanced medical imaging. (shrink)

There is a lot of conceptual engineering going on in medical research. I substantiate this claim with two examples, the medical debate about cancer classification and about obesity as a disease I also argue that the proper target of conceptual engineering in medical research are experts’ conceptions. These are explicitly written down in documents and guidelines, and they bear on research and policies. In the second part of the chapter, I propose an externalist framework in which conceptions have both the (...) explanatory power of psychological concepts and that of semantic concepts. It is likely, however, that human activities and practices distinct from medical research, and regulated by different practices and epistemic rules, call for different targets for conceptual engineering. I conclude with indicating an open agenda of problems for philosophers of medicine interested in conceptual engineering. (shrink)

Sensory substitution devices are a type of sensory prosthesis that (typically) convert visual stimuli transduced by a camera into tactile or auditory stimulation. They are designed to be used by people with impaired vision so that they can recover some of the functions normally subserved by vision. In this chapter we will consider what philosophers might learn about the nature of the senses from the neuroscience of sensory substitution. We will show how sensory substitution devices work by exploiting the cross-modal (...) plasticity of sensory cortex: the ability of sensory cortex to pick up some types of information about the external environment irrespective of the nature of the sensory inputs it is processing. We explore the implications of cross-modal plasticity for theories of the senses that attempt to make distinctions between the senses on the basis of neurobiology. (shrink)

We maintain that no extant argument in favor of phenomenal external- ism is really convincing. PE is the thesis that the phenomenal properties of our experiences must be individuated widely insofar as they are constituted by worldly properties. We consider what we take to be the five best arguments for PE. We try to show that none of them really proves what it aims at proving. Unless better arguments in favor of phenomenal externalism show up in the debate, we see (...) no reason to relinquish an idea that seems intuitive and appeals to many cognitive sci- entists: that phenomenology is narrow, i.e., that phenomenal properties are intrinsic properties of our experiences. This idea grounds the opposite philosophical position, phenomenal internalism. (shrink)

Italy is in the forefront of forensic neuroscience practice among European nations. In recent years, the country presented two major criminal cases, the Trieste Case in 2009 and the Como Case in 2011, which were the first cases employing neurogenetic and functional neuroimaging methods in European courts. In this paper we will discuss the consequences that an understanding of the neural and genetic determinants of human (mis)behavior will have on law, especially on the Italian legal context. Some claim that such (...) consequences will actually be revolutionary, while others argue that legal doctrine assumptions won’t be undermined by neuroscientific findings. In the first section of the paper, we introduce the general debate and follow with a section devoted to the two Italian cases. In the third and final section, we discuss epistemological and ethical issues regarding Italian neurolaw. We defend a position which diverges from those prevailing in the debate. While negative outcomes and concerns were usually evidenced, we focus on positive changes coming with the new paradigm of interaction between neuroscience and the law. Our view is that these cases are clearly pioneering ones, anticipating what will happen in the courtrooms of the European Union in the whole, in the near future. (shrink)

A growing body of scholarship has documented the experiences of different groups of migrants involved in the maintenance and development of transnational families worldwide showing that proximity is not a prerequisite of family life and that families can successfully be done from a distance. While most work deals with the experiences of labour migrants less attention has been paid to forced migrants. Still little is known about families that fail to operate transnationally and are broken by the migration experience. For (...) instance, when can we say that this type of family cannot be sustained? This article, drawing on the transnational motherhood literature and on Zontini previous study on Filipino labour migrants in Southern Europe, highlights the factors that shape transnational parenting. The authors then use this framework to explore the experiences of a group of Zimbabwean asylum seeking mothers in the UK. In doing so, the authors point out some of the specificities of this particular group; highlighting the differentiated impact of transnationalism and contributing to refining the literature on transnational parenthood. (shrink)

In this work we will show the role of lexical resources in machine translation processes, giving several examples after a brief overview of Machine Translation studies. Then we will advocate the need for a richer lexicon in MT processes and sketch a methodology to obtain it through a mix of corpus-based and machine learning approaches.

The mathematical scenario in Italy during the Late Middle Ages and the Renaissance is mainly dominated by the treatises on the abacus, which developed together with the abacus schools. In that context, between approximately the last thirty years of the fourteenth century and the first twenty years of the sixteenth century, the manuscript and printed tradition tell us of queries and challenges, barely known or totally unknown, in which the protagonists were abacus masters. We report in this work on the (...) most significant examples and draw out interesting cues for thoughts and remarks of a scientific, historical and biographical nature. Five treatises, written in the fifteenth and sixteenth century, have been the main source of inspiration for this article: the Trattato di praticha d’arismetricha and the Tractato di praticha di geometria included in the codices Palat. 573 and Palat. 577 (c. 1460) kept in the Biblioteca Nazionale of Florence and written by an anonymous Florentine disciple of the abacist Domenico di Agostino Vaiaio; another Trattato di praticha d’arismetrica written by Benedetto di Antonio da Firenze in 1463 and included in the codex L.IV.21 kept in the Biblioteca Comunale of Siena; the Tractatus mathematicus ad discipulos perusinos written by Luca Pacioli between 1477 and 1480, manuscript Vat. Lat. 3129 of the Biblioteca Apostolica Vaticana; and Francesco Galigai’s Summa de arithmetica, published in Florence in 1521. (shrink)