Results for 'Luisa Toffoli'

35 found
Order:
  1. Groundwork for a Fallibilist Account of Mathematics.Silvia De Toffoli - 2021 - Philosophical Quarterly 7 (4):823-844.
    According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  2. Forms and Roles of Diagrams in Knot Theory.Silvia De Toffoli & Valeria Giardino - 2014 - Erkenntnis 79 (4):829-842.
    The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...)
    Download  
     
    Export citation  
     
    Bookmark   30 citations  
  3. An Inquiry into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: Springer International Publishing. pp. 315-336.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  4. ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  5. Intersubjective Propositional Justification.Silvia De Toffoli - 2022 - In Paul Silva & Luis R. G. Oliveira (eds.), Propositional and Doxastic Justification: New Essays on their Nature and Significance. New York: Routledge. pp. 241-262.
    The distinction between propositional and doxastic justification is well-known among epistemologists. Propositional justification is often conceived as fundamental and characterized in an entirely apsychological way. In this chapter, I focus on beliefs based on deductive arguments. I argue that such an apsychological notion of propositional justification can hardly be reconciled with the idea that justification is a central component of knowledge. In order to propose an alternative notion, I start with the analysis of doxastic justification. I then offer a notion (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  6. Reconciling Rigor and Intuition.Silvia De Toffoli - 2020 - Erkenntnis 86 (6):1783-1802.
    Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  7. Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  8. What are mathematical diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
    Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  9. (1 other version)Recalcitrant Disagreement in Mathematics: An “Endless and Depressing Controversy” in the History of Italian Algebraic Geometry.Silvia De Toffoli & Claudio Fontanari - 2023 - Global Philosophy 33 (38):1-29.
    If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  10. Objectivity and Rigor in Classical Italian Algebraic Geometry.Silvia De Toffoli & Claudio Fontanari - 2022 - Noesis 38:195-212.
    The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  11. Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  12. Proofs for a price: Tomorrow’s ultra-rigorous mathematical culture.Silvia De Toffoli - 2024 - Bulletin (New Series) of the American Mathematical Society 61 (3):395–410.
    Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...)
    Download  
     
    Export citation  
     
    Bookmark  
  13. Leopardi “Everything Is Evil”.Silvia De Toffoli - 2019 - In Andrew Chignell (ed.), Evil: A History (Oxford Philosophical Concepts). New York: Oxford University Press. pp. 351-357.
    Giacomo Leopardi, a major Italian poet of the nineteenth century, was also an expert in evil to whom Schopenhauer referred as a “spiritual brother.” Leopardi wrote: “Everything is evil. That is to say, everything that is, is evil; that each thing exists is an evil; each thing exists only for an evil end; existence is an evil.” These and other thoughts are collected in the Zibaldone, a massive collage of heterogeneous writings published posthumously. Leopardi’s pessimism assumes a polished form in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  14. The Epistemic Roles of Diagrams.Silvia De Toffoli - forthcoming - In Kurt Sylvan, Ernest Sosa, Jonathan Dancy & Matthias Steup (eds.), The Blackwell Companion to Epistemology, 3rd edition. Wiley Blackwell.
    Download  
     
    Export citation  
     
    Bookmark  
  15. The Epistemological Subject(s) of Mathematics.Silvia De Toffoli - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2880-2904.
    Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...)
    Download  
     
    Export citation  
     
    Bookmark  
  16. Mathematical Justification without Proof.Silvia De Toffoli - forthcoming - In Giovanni Merlo, Giacomo Melis & Crispin Wright (eds.), Self-knowledge and Knowledge A Priori. Oxford University Press.
    According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit justification an argument (...)
    Download  
     
    Export citation  
     
    Bookmark  
  17. What is Mathematical Rigor?John Burgess & Silvia De Toffoli - 2022 - Aphex 25:1-17.
    Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  18. Conversation with John P. Burgess.Silvia De Toffoli - 2022 - Aphex 25.
    John P. Burgess is the John N. Woodhull Professor of Philosophy at Princeton University. He obtained his Ph.D. from the Logic and Methodology program at the University of California at Berkeley under the supervision of Jack H. Silver with a thesis on descriptive set theory. He is a very distinguished and influential philosopher of mathematics. He has written several books: A Subject with No Object (with G. Rosen, Oxford University Press, 1997), Computability and Logic (with G. Boolos and R. Jeffrey, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  19. Tools of Reason: The Practice of Scientific Diagramming from Antiquity to the Present.Greg Priest, Silvia De Toffoli & Paula Findlen - 2018 - Endeavour 42 (2-3):49-59.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  20. Mindset and Levels of Conceptual Understanding in the Problem-Solving of Preservice Mathematics Teachers in an Online Learning Environment.Ma Luisa Mariano-Dolesh, Leila Collantes, Edwin Ibañez & Jupeth Pentang - 2022 - International Journal of Learning, Teaching and Educational Research 21 (6):18-33.
    Mindset plays a vital role in tackling the barriers to improving the preservice mathematics teachers’ (PMTs) conceptual understanding of problem-solving. As the COVID-19 pandemic has continued to pose a challenge, online learning has been adopted. This led this study to determining the PMTs’ mindset and level of conceptual understanding in problem-solving in an online learning environment utilising Google Classroom and the Khan Academy. A quantitative research design was employed specifically utilising a descriptive, comparative, and correlational design. Forty-five PMTs were chosen (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  21. El fracking y el principio de precaución.Luisa Fernanda Martínez Cabra - manuscript
    El presente artículo analiza la técnica del fracking como una solución a la problemática que en materia hidrocarburos se había dado en las últimas dos décadas, y los impactos negativos que conlleva para la salud y el ambiente. Se plantea como solución la aplicación del principio de precaución que le permite al Estado actuar ante una situación de riesgo e incertidumbre. La metodología escogida fue de corte analítico-deductivo a partir de la normatividad vigente y de los postulados teóricos de algunos (...)
    Download  
     
    Export citation  
     
    Bookmark  
  22. Uma leitura no escuro: o tempo em Finnegans wake e a hospitalidade da literatura.Luísa Leite S. De Freitas - 2019 - Dissertation, Universidade de Brasília
    Download  
     
    Export citation  
     
    Bookmark  
  23. Strategies to Overcome Collaborative Innovation Barriers: The Role of Training to Foster Skills to Navigate Quadruple Helix Innovations.Luisa Barbosa-Gomez & Vincent Blok - 2023 - Journal of the Knowledge Economy.
    Quadruple Helix Collaborations (QHCs) is a cooperation model in which industry, government, academia, and the public interact to innovate. This paper analyses the impact of a training intervention to provide specific knowledge, skills, and attitudes to deal with barriers commonly found in the progress of QHCs. We designed, implemented, and evaluated three training programs in Austrian, Colombian, Danish, and Spanish institutions. We analysed trainees’ (n = 66) and trainers’ (n = 9) perceptions to identify the competencies acquired with the intervention (...)
    Download  
     
    Export citation  
     
    Bookmark  
  24. Jardins Integrados na Paisagem: A Ecologia aliada à Estética.Maria Luisa Jardim Malheiro Garcia - 2021 - Dissertation, Universidade de Lisboa
    Download  
     
    Export citation  
     
    Bookmark  
  25. Time and Space in Manic Episodes.Maria Luìsa Figueira & Luìs Madeira - 2011 - Dialogues in Philosophy, Mental and Neuro Sciences 4 (2):22-26.
    Temporality and Spatiality have been extensively addressed in philosophy, and their disturbances have been extensively studied in psychopathology (e.g. Wyllie 2005). Mental health patients: (1) describe pathological experiences of Time and Space (Gallagher and Varela 2003); (2) show disturbed timing (Tysk 1984); (3) experience psychopathological phenomena that could be the cause of changes in temporality and spatiality. These topics will be discussed in the case of mood disorders, in particular euphoric and dysphoric mania episodes. Any phenomenological study in mood disorders (...)
    Download  
     
    Export citation  
     
    Bookmark  
  26. Artificial Intelligence and Legal Disruption: A New Model for Analysis.John Danaher, Hin-Yan Liu, Matthijs Maas, Luisa Scarcella, Michaela Lexer & Leonard Van Rompaey - forthcoming - Law, Innovation and Technology.
    Artificial intelligence (AI) is increasingly expected to disrupt the ordinary functioning of society. From how we fight wars or govern society, to how we work and play, and from how we create to how we teach and learn, there is almost no field of human activity which is believed to be entirely immune from the impact of this emerging technology. This poses a multifaceted problem when it comes to designing and understanding regulatory responses to AI. This article aims to: (i) (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  27. Theories of Consciousness From the Perspective of an Embedded Processes View.Nelson Cowan, Nick I. Ahmed, Chenye Bao, Mackenzie N. Cissne, Ronald D. Flores, Roman M. Gutierrez, Hayse Braden, Madison L. Musich, Hamid Nourbakhshi, Nanan Nuraini, Emily E. Schroeder, Neyla Sfeir, Emilie Sparrow & Luísa Superbia-Guimarães - manuscript
    Considerable recent research in neurosciences has dealt with the topic of consciousness, even though there is still disagreement about how to identify and classify conscious states. Recent behavioral work on the topic also exists. We survey recent behavioral and neuroscientific literature with the aims of commenting on strengths and weaknesses of the literature and mapping new directions and recommendations for experimental psychologists. We reconcile this literature with a view of human information processing (Cowan, 1988; Cowan et al., 2024) in which (...)
    Download  
     
    Export citation  
     
    Bookmark  
  28. Un llamado ético a la inclusión de mujeres embarazadas en investigación: Reflexiones del Foro Global de Bioética en Investigación.Carla Saenz, Jackeline Alger, Juan Pablo Beca, José Belizán, María Luisa Cafferata, Julio Arturo Canario Guzman, Jesica Candanedo, Lissette Duque, Lester Figueroa, Ana Garcés, Lionel Gresh, Ida Cristina Gubert, Dirce Guilhem, Gabriela Guz, Gustavo Kaltwasser, Roxana Lescano, Florencia Luna, Alexandrina Cardelli, Ignacio Mastroleo, Irene Melamed, Agueda Muñoz del Carpio Toia, Ricardo Palacios, Gloria Palma, Sofía Salas, Xochitl Sandoval, Sergio Surugi de Siqueira, Hans Vásquez & Bertha Villela de Vega - 2017 - Revista Panamericana de Salud Pública 41 (e13):1-2.
    El Foro Global de Bioética en Investigación (GFBR por sus siglas en inglés) se reunió el 3 y 4 de noviembre en Buenos Aires, Argentina, con el objetivo de discutir la ética de la investigación con mujeres embarazadas. El GFBR es una plataforma mundial que congrega a actores clave con el objetivo de promover la investigación realizada de manera ética, fortalecer la ética de la investigación en salud, particularmente en países de ingresos bajos y medios, y promover colaboración entre países (...)
    Download  
     
    Export citation  
     
    Bookmark  
  29. Pertinencia de la metodología de enfoque de Sistemas Socio-Ecológicos (SSE) para determinar los actores y sistema de gobernanza en un conflicto ambiental: Estudio de caso del Arroyo de San Basilio de Palenque.Mauricio Luna-Galvan, Iván Vargas-Chaves & Luisa Guerra - 2019 - In Gloria Amparo Rodriguez & Adolfo Ibañez-Elam (eds.), Las disputas ambientales en Colombia. Grupo Editorial Ibáñez.
    El presente texto presenta los resultados de un estudio exploratorio de las interacciones entre el sistema de gobernanza y de los actores como causa de la contaminación del arroyo de San Basilio de Palenque en Colombia. Lo anterior, a partir de la validación de la metodología de enfoque de sistemas socio-ecológicos como método de caracterización de conflictos ambientales con impactos culturales.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  30. Book Review: Maria Luisa Ardizzone, Reading as the Angels Read: Speculation and Politics in Dante's Banquet. [REVIEW]Jason Aleksander - 2017 - Renaissance Quarterly 70 (4):1625.
    A review of Maria Luisa Ardizzone's Reading as the Angels Read: Speculation and Politics in Dante’s Banquet. Toronto: University of Toronto Press, 2016. xii 1 454 pp. $95.
    Download  
     
    Export citation  
     
    Bookmark  
  31. Enseñanza de la Literatura española en contextos universitarios peruanos. Entrevista a María Luisa Roel Mendizabal.Jesús Miguel Delgado Del Aguila - 2022 - Estudios Λambda. Teoría y Práctica de la Didáctica En Lengua y Literatura 7 (1):1-5.
    Esta entrevista retoma la experiencia de enseñanza de la profesora María Luisa Roel en función de la producción literaria de España. El objetivo es interiorizar sobre cómo esta se ha transferido en el ámbito de educación universitaria. A partir de la trayectoria de la docente, se brinda un panorama de cómo los estudiantes de la carrera profesional de Literatura acatan el conocimiento y la lectura de autores españoles, como Miguel de Cervantes. De igual forma, se mencionan dos momentos históricos (...)
    Download  
     
    Export citation  
     
    Bookmark  
  32. Analisi del discorso politico. Dalla dittatura alla pace. Review of Analisi del discorso politico. Dalla dittatura alla pace of Luisa Messina Fajardo. Dialogi Recensioni. [REVIEW]Ruth Castillo - 2019 - Dialogi 6:170-171.
    Download  
     
    Export citation  
     
    Bookmark  
  33.  43
    Neke slabe tačke Luisove teorije o tvrđenjima kojima se pripisuje znanje subjektu.Aleksandra Davidović - 2023 - Theoria 66 (3):21-37.
    Predmet ovog rada je istraživanje i kritika nekih aspekata teorije Dejvida Luisa o tvrđenjima kojima se pripisuje znanje subjektu. U prvom odeljku izlažem skeptički paradoks i osnovne postavke epistemičkog kontekstualizma. U drugom odeljku objašnjavam na koji način Luis kombinuje teoriju relevantnih alternativa i epistemički kontekstualizam prlikom formulisanja svoje teorije o tvrđenjima kojima se pripisuje znanje subjektu. U trećem odeljku pokazujem da ova teorija dopušta postojanje znanja koje je zasnovano samo na ignorisanju i argumentujem da ova nepovoljna posledica proističe iz (...)
    Download  
     
    Export citation  
     
    Bookmark  
  34. La recepción por Leibniz del concepto spinoziano de potentia agendi et patiendi.Cabañas Leticia - 2014 - In Mesquita Antonio Pedro (ed.), A paixão da razão. Homenagem a Maria Luísa Ribeiro Ferreira. Centro de Filosofia da Universidade de Lisboa,. pp. 171-180.
    Download  
     
    Export citation  
     
    Bookmark  
  35. É o Género uma Construção Social?Teresa Marques - 2014 - In Mesquita Antonio Pedro (ed.), A paixão da razão. Homenagem a Maria Luísa Ribeiro Ferreira. Centro de Filosofia da Universidade de Lisboa,. pp. 561-578.
    É muitas vezes aceite que certas categorias, tipicamente as de género, raça, orientação sexual ou doença mental, são construções sociais e não divisões naturais no mundo. A distinção entre categorias naturais e categorias sociais, como pretende ser a distinção entre o sexo e o género, tem servido no âmbito da crítica e ciência social para advogar a abolição de certas normas sociais, e para a implementação de políticas mais equitativas. Contudo, há aspectos centrais do construtivismo que são pouco claros. O (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation