RESUMO A alimentação é o fator que mais onera um sistema de produção animal. Assim, a utilização de diferentes estratégias de alimentação dos animais ainda é o grande desafio da nutrição animal, principalmente, levando em consideração as exigências nutricionais de diferentes categorias de ruminantes, em especial bovinos em regiões tropicais, haja vista que a sazonalidade na produção de forragens afeta diretamente a produção bovina, promovendo inadequação no atendimento das exigências nutricionais dos animais principalmente em minerais e vitaminas. Uma alimentação que (...) não atenda as exigências nutricionais dos ruminantes gera prejuízos no sistema de produção, além de, em casos mais graves, ocasionar a perda do animal. Estudos que abordam o efeito e a importância de vitaminas e minerais na nutrição bovina são escassos e necessários. Recentemente a National Research Council (NRC) apresentou novos registros das exigências nutricionais das vitaminas e minerais. Essas alterações proporcionam um impacto econômico significativo em relação à nutrição animal. Nesse sentido, objetivou-se com esta revisão trazer informações acerca de vitaminas e minerais na nutrição de bovinos em pastejo. -/- Palavras-chave: Alimentação animal; forragem; pastagem; requerimentos nutricionais; ruminantes; vitaminas lipossolúveis (Source: AGROVOC). -/- ABSTRACT Animal feed is the factor that most burdens a production system. Thus, the use of different animal feeding strategies is still the great challenge of animal nutrition, taking into account the nutritional requirements of different categories of ruminants, especially cattle in tropical regions, given that seasonality in forage production directly affects cattle production, promoting inadequacy in meeting the nutritional requirements of animals, mainly in minerals and vitamins. A diet that does not meet the nutritional requirements of ruminants generates losses in the production system, in addition to, in more serious cases, causing the loss of the animal. Studies that address the effect and importance of vitamins and minerals in bovine nutrition are scarce and necessary. Recently the National Research Council (NRC) presented new records of the nutritional requirements of vitamins and minerals. These changes provide a significant economic impact on animal nutrition. In this sense, the objective of this review was to bring information about vitamins and minerals in the nutrition of grazing cattle. -/- Keywords: Animal feeding; fat soluble vitamins; forage; nutritional requirements; pasture feeding; ruminants (Source: AGROVOC). -/- REFERÊNCIAS BIBLIOGRÁFICAS -/- 1. Cavalcanti CPL, Silva e Macedo TJ, Gois GC, Menezes VG, Monte APO, Silva AD, Silva DJM, Silva EO, Araújo GGL, Rodrigues RTS, Wischral A, Matos MHT, Queiroz MAA. Licuri oil improves feedlot performance and modifies ruminal fauna of Santa Inês ewes. Liv Sci. 2022; 265:e105093. 2. Busato KC, Chizzotti ML, Rodrigues RTS, Silva TS, Silva IF, Queiroz MAA, Silva KT, Borges JC, Gois GC. Ingestive behavior and growth performance of boer crossbred and indigenous goat kids under different feeding levels in Semiarid Region in Brazil. Trop Agric Res. 2022; 33:299-309. 3. Patton J, Dineen M, Keady TWJ, McGee M, Waters S. Developments in nutrition for pasture-based cattle and sheep systems in Ireland. Irish J Agric Food Res. 2022; 61(1):12-37. 4. McAllister TA, Stanford K, Chaves AV, Evans PR, Figueiredo, EES, Ribeiro G. Nutrition, feeding and management of beef cattle in intensive and extensive production systems. Chapter 5. In: Bazer FW, Lamb GC, Wu G, editors. Animal Agriculture. Sustainability, Challenges and Innovations. 1st ed. Elsevier Inc.: Academic Press; 2020. 5. Byrne L, Murphy RA. Relative bioavailability of trace minerals in production animal nutrition: A review. Anim. 2022; 12:e1981. 6. Arthington JD, Ranches J. Trace mineral nutrition of grazing beef cattle. Anim. 2021; 11:e2767. 7. Silva NCD, Martins TLT, Borges I. Efeito dos microminerais na alimentação de ruminantes. Ci Anim. 2017; 27:75-98. 8. Tufarelli V, Ragni M, Laudadio V. Feeding forage in poultry: A promising alternative for the future of production systems. Agric. 2018; 8:1-10. 9. Elgersma A, Søegaard K, Jensen SK. Fatty acids, α-tocopherol, β-carotene, and lutein contents in forage legumes, forbs, and a grass–clover mixture. J Agric Food Chem. 2013; 61:11913–11920. 10. Collet SG, Demeda MA, Taffarel GV, Taffarel L, Girardini LK, Nesi CNH, et al. Efeito de um suplemento mineral traço e vitaminas A e E injetáveis sobre a produção e composição de leite em vacas Holandesas. Rev Ci Agrovet. 2017; 16:463-472. 11. Silva NCD, Martins TLT, Borges I. Macrominerais: Deficiências E Interações Com A Produção E Nutrição De Ruminantes. Scient Agr Paranaensis. 2018; 17:263-271. 12. Danieli B, Schogor ALB. Uso de aditivos na nutrição de ruminantes: revisão. Vet Zootec. 2020; 27:1-13. 13. Goff JP. Invited review: Mineral absorption mechanisms, mineral interactions that affect acid–base and antioxidant status, and diet considerations to improve mineral status. J Dairy Sci. 2018; 101:2763–2813. 14. NRC. National Research Council. Nutrient requirements of beef cattle. 8th ed.Washington, DC.: The National Academy Press; 2016. 15. Silva LFC, Valadares Filho SC, Engle TE, Rotta PP, Marcondes MI, Silva FAZ, et al. Macrominerals and trace element requirements for beef cattle. Plus One. 2015; 10:e0144464. 16. Miranda MMF, Ferrarezi Junior E, Cavichioli FA. Boas práticas agropecuárias: Os benefícios da suplementação alimentar em ruminantes. Int Tec. 2021; 18:455-465. 17. Bhanderi BM, Goswami A, Garg MR, Samanta S. Study on minerals status of dairy cows and their supplementation through área specific mineral mixture in the state of Jharkhand. J Anim Sci Techn. 2016; 58:1-8. 18. Rezende FV, Silva NCD, Florentino LA, Rezende AV. Minerais: fatores que interferem na biodisponibilidade de macro e microminerais para fêmeas ruminantes durante o período de gestação. Nucleus Anim. 2019; 11:123-136. 19. NRC. National Research Council. Nutrient requeriments of dairy cattle. 7th rev.ed. Washinton, DC.: The National Academy Press; 2001. 20. Marku A, Galli A, Marciani P, Dule N, Perego C, Castagna M. Iron metabolism in pancreatic beta-cell function and dysfunction. Cells. 2021; 10:e2841. 21. DA SILVA, Emanuel Isaque Cordeiro. Nutrição e Suplementação Mineral de Bovinos de Corte. Emanuel Isaque Cordeiro da Silva, 2021. 22. Suganya A, Saravanan A, Manivannan N. Role of zinc nutrition for increasing zinc availability, uptake, yield, and quality of maize (Zea mays L.) grains: An overview. Commun Soil Sci Plant An. 2020; 51:2001-2021. 23. Byrne L, Murphy RA. Relative bioavailability of trace minerals in production animal nutrition: A review. Anim. 2022. 12:e1981. 24. Valentim JK, Mendes JP, Przybulinski BB, Serpa FC, Barbosa DK, Castilho VAR, et al. Fatores nutricionais aplicados à reprodução de ruminantes. Rev Uniciên. 2019; 23:77-82. 25. Martins KPF, Fonseca TRS, Silva ES, Munhoz TCP, Dias, GHS, Glauco JN, et al. Bócio em bovino. Pesq Vet Bras. 2018; 38:1030-1037. 26. González-Montaña JR, Escalera-Valente F, Alonso AJ, Lomillos JM, Robles R, Alonso ME. Relationship between vitamin B12 and cobalt metabolism in domestic ruminant: An update. Anim. 2020; 10:e1855; 27. Ventura RA, Cuzzuol GD, Silva TB, Malegoni ACS, Roque LZ, OLiveira SFC, et al. Deficiência de cobalto em bovinos: Revisão. Pubvet. 2021; 15:1-4. 28. Lopes HOS. Suplementação de Baixo Custo para Bovinos Mineral e Alimentar. 1st ed. Brasília, DF: Embrapa Cerrados; 1998. 29. Paul SH, Usman AA, Gana IN, Manase A, Adeniyi OD, Olutoye MA. Comparative study of mineral and nutritional composition of a multifunctional flora composite formulated from seven medicinal plants and their applications to human health. Eng Techn Open Access J. 2018; 1:137-150. 30. Zhou J, Zhang J, Xue B, Yue S, Yang C, Xue B. Effects of premating calcium and phosphorus supplementation on reproduction efficiency of grazing yak heifers. Anim. 2021; 11:1-9. 31. Harder H, Khol-Parisini A, Metzler-Zebeli BU, Klevenhusen F, Zebeli Q. Treatment of grain with organic acids at 2 different dietary phosphorus levels modulates ruminal microbial community structure and fermentation patterns in vitro. J Dairy Sci. 2015; 98:8107–8120. 32. Jain RK, Mudgal V. Phosphorus deficiency influences rumen microbial activity: Review. Int J Zoo Anim Biol. 2021; 4:1-9. 33. Barreto JC, Branco AF, Santos GT, Magalhães VJA, Coneglian SMC, Teixeira S. Avaliação dos efeitos de fontes de fósforo na dieta sobre parâmetros do meio ruminal e eficiência de síntese microbiana, digestibilidade dos nutrientes e fósforo plasmático em bovinos. Rev Bras Zootec. 2009; 38:760-769. 34. Yamada S, Inaba M. Potassium metabolism and management in patients with CKD. Nutr. 2021; 13:1-19. 35. Martinsen TC, Fossmark R, Waldum HL. The phylogeny and biological function of gastric juice—Microbiological consequences of removing gastric acid. Int J Mol Sci. 2019; 20:1-22. 36. González FHD, Silva SC. Minerais e vitaminas no metabolismo animal. 1st ed. Porto Alegre: Universidade Federal do Rio Grande do Sul; 2019. 37. Melo RR, Gonçalves SLS, Baccarin FJB, Vasconcelos WA, Miranda SC. Influência de altas dosagens de cloreto de potássio no desenvolvimento de espécies em cultivo hidropônico. Pubvet. 2020; 14:1-9. 38. Araújo WAG, Rostagno HS, Albino LFT, Carvalho TA, Ribeiro Neto AC. Potássio na nutrição animal. Rev Eletr Nutr. 2010; 7:1280-1291. 39. NRC. National Research Council. Nutrient requeriments of dairy cattle. 8th ed. Washinton, DC.: The National Academy Press; 2021. 40. Palomares RA. Trace Minerals Supplementation with Great Impact on Beef Cattle Immunity and Health. Anim. 2022; 12:e2839. 41. Tariq M, Abbas G, Ahmad S, Mustafa R, Sultan H, Abdullah M, Hussain I, Arshad M, Cheema UB, Hassan SU. Effect of supplementation of minerals on the productive and reproductive performance of lactating cattle and buffalo. Pakistan J Sci. 2022; 74:e425. 42. Pagno KCA Barbosa JD, Salvarani FM, Bomjardim HA, Faial KCF, Souza RS, Gava A, Perotta JH, Barros Filho IR. Micromineral concentrations (copper, cobalt, iron, molybdenum and zinc) in the liver of dairy cows from Campos Gerais Region, Paraná state, Brazil. Pesq Vet Bras. 2023; 43:e07137. 43. Jeong H, Vacanti NM. Systemic vitamin intake impacting tissue proteomes. Nut Met. 2020; 17:1-16. 44. Spears JW, Weiss WP. Invited Review: Mineral and vitamin nutrition in ruminants. Appl Anim Sci. 2014; 30:180-191. 45. Erickson PS, Kalscheur KF. Nutrition and feeding of dairy cattle. Chapter 9. (pp. 157-180). In: Bazer FW, Lamb GC, Wu G, editors. Animal Agriculture. Sustainability, Challenges and Innovations. 1st ed. Elsevier Inc.: Academic Press; 2020. 46. Kareem MM, Jabir MS. Vitamins. Chapter 3. In: Imran M, Imran A, editors. Malnutrition. 1st ed. London, UK.: IntechOpen; 2020. 47. Akram M, Munir N, Daniyal M, Egbuna C, Găman MA, Onyekere PF, et al. Vitamins and minerals: Types, sources and their functions. Chapter 9. (pp 149–172). In: Egbuna C, Tupas GD, editors. Functional foods and nutraceuticals. Switzerland, AG.: Springer, Cham; 2020. 48. Marino CT, Medeiros SR. Minerais e vitaminas na nutrição de bovinos de corte. Chapter 6. (pp. 79-93). In. Medeiros SR, Gomes RC, Bungenstab DJ, editors. Nutrição de bovinos de corte: fundamentos e aplicações. Brasília, DF: Embrapa; 2015. 49. Hodnik JJ, Ježek J, Starič J. A review of vitamin D and its importance to the health of dairy cattle. J Dairy Res. 2020; 87:84–87. 50. Alves EM, Pedreira MS, Santana CA, Silva FF. Nutrição vitamínica de vacas leiteiras. Pubvet. 2008; 2:1-17. 51. Jiang Q, Lin L, Xie F, Jin W, Zhu W, Wang M, et al. Metagenomic insights into the microbe-mediated B and K2 vitamin biosynthesis in the gastrointestinal microbiome of ruminants. Microb. 2022; 10:1-16. 52. Magan JB, O’Callaghan TF, Zheng J, Zhang L, Mandal R, Hennessy D, et al. Effect of diet on the vitamin B profile of bovine milk-based protein ingredients. Foods. 2020; 9:1-17. 53. Pinedo LA, Berenchtein B, Selem ASMA. Estudo dos processos bioquímicos da fermentação, degradação e absorção de nutrientes dos alimentos em ruminantes. Pubvet. 2008; 2:1-10. 54. DA SILVA, Emanuel Isaque Cordeiro. Formulação e Avaliação de Suplemento Mineral Para Caprinos. Instrução Técnica Para o Produtor Rural de Pernambuco, v. 3, n. 1, p. 1-4, 2023. 55. DA SILVA, Emanuel Isaque Cordeiro. Nutrição Sobre a Reprodução e Fertilidade dos Bovinos. Emanuel Isaque Cordeiro da Silva, 2021. 56. DA SILVA, Emanuel Isaque Cordeiro. Suplementação e formulação de sal mineral e mistura múltipla para bovinos. Revista Universitária Brasileira, v. 2, n. 1, 2024. (shrink)

A Crítica de Hume ao Argumento do Desígnio José Oscar de Almeida Marques Dep. de Filosofia – UNICAMP -/- RESUMO: É comum considerar que o chamado “argumento do desígnio” (o argumento a posteriori para provar a existência de Deus a partir da ordem e funcionalidade do mundo) teria sido refutado ou seriamente abalado por Hume. Mas a natureza e o alcance dessa alegada refutação são problemáticos, pois Hume muitas vezes expressou suas críticas através de seus personagens e evitou assumi-las (...) diretamente enquanto autor. Em vez de supor que Hume procedeu dessa forma apenas para disfarçar suas verdadeiras convicções e evitar um conflito com as autoridades eclesiásticas, proponho que sua posição nesse assunto não é tão categórica como às vezes se supõe, e que os famosos argumentos de Filo nos Diálogos mostram apenas que é possível que a ordem e funcionalidade do mundo tenham surgido sem a intervenção de um desígnio consciente, mas não podem por si sós dar a essa hipótese o mínimo grau de plausibilidade necessário para torná-la digna de uma séria consideração. De fato, antes da revolução explicativa operada por Darwin um século depois, ninguém estava realmente em condições de vislumbrar uma alternativa plausível à atuação de algum tipo de inteligência na geração da ordem e funcionalidade do mundo. ------------ Some Remarks on Hume’s Critique of the Argument from Design José Oscar of Almeida Marques Dep. of Philosophy - UNICAMP -/- ABSTRACT: The so-called “argument from design” (the a posteriori argument to prove the existence of God from the order and functionality of the world) is commonly considered to have been refuted or seriously impaired by Hume. But the nature and scope of this alleged refutation is problematic because Hume often expressed his critics through other characters’ mouth and avoided to assume them directly as author. Contrarily to the supposition that Hume proceeded in this way only to disguise his true convictions and to avoid a confrontation with the ecclesiastical authorities, I propose that his stance on the matter is not, in fact, as clear-cut as it is sometimes supposed, and that Philo’s famous arguments in the Dialogues show only that it is possible for the order and functionality of the world to have arisen without the intervention of an intelligent design, but cannot by themselves lend to this hypothesis the least degree of plausibility needed to make it worthy of serious consideration. In fact, before the explanatory revolution inaugurated by Darwin a century later, nobody was in position to envisage a plausible alternative to the operation of some sort or other of intelligence in the generation of the order and functionality of the world. (shrink)

I examine the difficulties involved in the Aristotelian proposal to identify the knowledge of “what it is” and “why it is”, in order to better understand the outlines that delimit it. I propose that the connections by which Aristotle links definition and explanation, and hence essence and cause, depend on the mutual convertibility between nominal expressions and predicative sentences.

A tese central deste trabalho consiste em reconstruir em bases filosóficas as linhas gerais da teoria aristotélica da verdade mostrando, a partir da análise do Livro IV da Metafísica, que esta teoria está fundada naquilo que é chamado nesta investigação de princípio transcendental de verdade, o qual é constituído pela bi- implicação modal dos princípios de não-contradição, do terceiro excluído e de identidade.

This dissertation critically examines the writings of Max Stirner, especially his masterpiece The Ego and Its Own, as a discourse of resistance against modern forms of domination and, in particular, against the modern political State. I begin by examining Stirner's inversion of the Hegelian concept of the State, from the “actualization of freedom”to an instance of domination. The State appears, to Stirner as to Hegel, as the guardian of order and cohesion in modern societies. While both recognize the genesis of (...) sovereign power as violent, Hegel sustains that, with the progress of civilization, force is eradicated from the public order and private interests and common interest are reconciled. Stirner, on the contrary, insists that force is the other face of right, as the hidden pillar of the norm, which only reveals itself in moments of crisis. Stirner’s focus on the extreme case, largely anticipated and devalued by Hegel as unilateral and equivocal, seems to be anchored on the conviction that conflict is ineradicable, that between my own will and the (political, social) representation of that will there is always a gap, which cannot be filled by any collective arrangement. From this follows that, if conflict is scarcely manifest in modern societies, it is not because it was truly solved, but because it is effectively masked, due to the dissymmetry of power and the internalization of authority. The “unique one” appears, in this environment of great suspicion, as the one who cannot be represented, who surpasses every representation, threatening the authority of every representative. Accordingly, the “unique one” reclaims his own power, without allowing the satisfaction of his will to be mediated by obedience to collective institutions, affirming himself instead as sovereign over himself. Stirner suggests that the self-affirmation of the “unique one” inevitably leads to confrontation with the external powers that organize his existence. Stirner, nonetheless, chooses to think this confrontation in terms of a “revolt”, of a reflexive and individual act by which the individual emerges from the situation in which he finds himself, rather than as a “revolution”, a political or social act directed towards the systemic transformation of the status quo. Even if we admit the validity of the Stirnerian critique of the legitimizing discourses of modernity, the problem remains if this critique can be sustained on the “unique one”, “a thoughtless word”, an openly self-contradictory and self-destructive name, subject or principle (?). The possibility of founding a discourse of resistance on the egoism of Max Stirner seems to depend upon the answer that we choose to give to two intimately connected questions: what remains after the destructive vortex of the “unique one” that may sustain the resistance against a state that Max Stirner deems oppressive? Can this resistance be realized in the revolt of a unique one without the recognition of another one with whom to build the conditions of freedom? (shrink)

To try to understand Nietzsche’s conception of Christianity is to try to understand his conception of morality, or to try to analyze, dissect, and diagnose the forces and the relation of forces that underly it, or permeate it. These forces characterize not only the reality as Nietzsche considers it, but also the dynamic of his own writing, thought, and perspective. This is the reason why we can affirm that Nietzsche’s thought and writing are essentially, intrinsically, paradoxical. Indeed, the Nietzschean text (...) unfolds as what constantly resists and escapes the order of discourse as such, which means that it would be a frustrating undertaking to seek a key that discloses and explicates the plurality of meanings that engender and determine the development of his writing. Paradoxically, Nietzschean thought reveals itself only to the extent that it is masked, reread, repeated, rewritten, and stripped of all attempts to master it. In other words, it progresses through a continuous intermingling of forces and, consequently, of values, interpretations, and significations that are unceasingly overcoming and surpassing each other. (shrink)

My aim is to show that, in Posterior Analytics B 8, the conception of lunar eclipse brought about by pre-demonstrative knowledge (hoti) is deeply vague and radically different from the one obtained by demonstrative knowledge (dioti).

On assiste, depuis les années 70, à une interminable littérature sur la vie et la pensée de Nietzsche. Ce foisonnement d’études prend des proportions telles, que même des interprétations relativement récentes (Deleuze, Derrida, Klossowski, Sarah Kofman) se voient déjà élevées au rang des classiques. Les thèmes anciens, mêlés à d’autres plus actuels, sont repris, répétés, relus et réécrits dans des perspectives diverses. Ainsi se noue le dialogue d’une philosophie avec de larges pans de culture : Nietzsche et la métaphysique, Nietzsche (...) et la science, Nietzsche et la politique, Nietzsche et la musique, Nietzsche et la religion, Nietzsche et l’antisémitisme, Nietzsche et les Nazis, Nietzsche et le féminin, Nietzsche et la psychanalyse. (shrink)

The themes addressed by this paper intersect the industrial heritage and its main components, from industrial archeology to the technical landscapes of production. From this point of view, the historic center of São Luís, Brazil as case study has an intrinsic relationship with the Bacanga River. It is the main landscape that is to the surroundings of the historical center tilted by the Unesco. The historic center of São Luís with the sea and the river dialogue between colonial urban occupation (...) and water as a landscape that embraces this urbanization. (shrink)

In his Lectures on Fine Art (1835), Hegel emphasizes the grotesque character of Indian art. Grotesqueness results, in his view, from a contradiction between meaning and shape due to the incongruous combination of spiritual and material elements. Since Hegel's history of art is teeming with examples of inadequacy between meaning and shape, this paper aims to distinguish the grotesque from other types of artistic dissonance and to problematize Hegel's ascriptions of grotesqueness to ancient Indian art. In the first part of (...) the paper, I characterize the grotesque by the unnatural distortion of natural shapes with the purpose of achieving a direct sensuous manifestation of an indeterminate and impersonal divinity, Brahman. Such an attempt is, in Hegel's view, self-contradictory and self-defeating, leading to an exaggeration of the conflict between nature and spirit instead of the intended reconciliation between the two parts. In the second part of the paper, I compare Hegel's account of Indian art to the ‘monstrous myths’ of early modern Europe. Unlike his predecessors, Hegel legitimizes the grotesque representations of Hindu gods as endowed with profound meaning and the result of a universal human need, yet he describes them as ultimately irrational and repulsive based on a prejudiced view of the Indian people(s). In this sense, Hegel's assessment of Indian art functions as a reflection of modern European culture, its fascination and horror in the face of what Enlightenment could not entirely purge, rather than as a truthful and objective account of Indian art and culture. By questioning Hegel's characterization of Hindu iconography and mythology, this paper contributes to underexplored areas of Hegelian aesthetics, namely Hegel's account of symbolic art, especially Indian art, as well as his views on negative aesthetic experiences and values. (shrink)

In this paper I will discuss Dummett’s interpretation of Frege’s “On sense and reference” that takes place in his Frege: Philosophy of Language, where he attributes a notion of meaning to Frege that is not explicit on the text of “On sense and reference”. I believe that this attribution is incompatible with what Frege is really saying in the article and with the partition of the notion that Dummett himself exposes.

Despite pervasive variation in the content of laws, legal theorists and anthropologists have argued that laws share certain abstract features and even speculated that law may be a human universal. In the present report, we evaluate this thesis through an experiment administered in 11 different countries. Are there cross‐cultural principles of law? In a between‐subjects design, participants (N = 3,054) were asked whether there could be laws that violate certain procedural principles (e.g., laws applied retrospectively or unintelligible laws), and also (...) whether there are any such laws. Confirming our preregistered prediction, people reported that such laws cannot exist, but also (paradoxically) that there are such laws. These results document cross‐culturally and –linguistically robust beliefs about the concept of law which defy people's grasp of how legal systems function in practice. (shrink)

This is a Review of Tópicos em Ontologia Analítica by Décio Krause. Both the review and the book are in Portuguese.

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 (...) propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices. (shrink)

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 (...) address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

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 (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

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 (...) must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs. (shrink)

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 (...) of propositional justification, intersubjective propositional justification, that is neither entirely apsychological nor idiosyncratic. To do so, I argue that to be able to attribute propositional justification to a subject, we have to consider her social context as well as broad features of our human cognitive architecture. (shrink)

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 (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

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 (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

This paper has a twofold aim. On the one hand, we will discuss the much debated question of the source of normativity (which traditionally has nature and practical reason as the two main contenders to this role) and propose a new answer to it. Second, in answering this question, we will present a new account of practical wisdom, which conceives of the ethical virtues as ultimately unified in the chief virtue of phronesis, understood as ethical expertise. To do so, we (...) will first criticize the main current view of phronesis and its bearer (the phronimos), then offer another view of the nature of phronesis and of its relation to the other ethical virtues. Our proposal should not be intended as an interpretation of Aristotle’s own view; rather, it should be seen as a broadly Aristotelian theoretical proposal, which we believe can satisfyingly address most of the problems that afflict the more traditional accounts of practical wisdom. In section 2 of this paper, after criticizing first-nature naturalistic views of moral virtue, we take practical reason to be the cornerstone of second-nature naturalistic views; in section 3, we will outline criticisms to which, in our view, the traditional views of phronesis are ill-suited to respond, and, in section 4, we will outline our view of phronesis as ethical expertise – a view which in our view is immune to the above-mentioned criticisms – by spelling out the three main tenets of phronesis as ethical expertise: a conceptual thesis, an epistemic thesis, and the educational implications of the two. Finally, we will support our proposal with some empirical evidence taken from cognitive science. (shrink)

Estas reflexões têm como principal objetivo mostrar como a concepção do belo em Agostinho de Hipona é tributária da tradição platônico-aristotélica e das Escrituras. No que tange à primeira influência, a ênfase é colocada nas noções de simetria, de proporção, de forma, de unidade e, portanto, de belo. No que diz respeito às Escrituras, Agostinho considera em primeiro lugar o papel da criação e a ação de Deus no universo como o Ser a partir do qual todas as coisas se (...) mantêm harmônica e proporcionalmente vinculadas entre si. Neste universo, ao pôr o acento sobre o homem como a imagem e semelhança de Deus, o teólogo explora igualmente o conceito de participação, que também remete a Platão e às Escrituras. O texto termina apontando para o paradoxo, tipicamente estoico, do apesar de, isto é, apesar do mal, existe o bem, apesar do feio e do desgracioso, existe o belo. (shrink)

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 (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

RESUMO A inseminação artificial (IA) é a biotecnologia mais empregada com vantagens superiores em relação a utilização da monta natural, cuja eficácia se dá na larga escala de reprodução entre os bovinos. Associando essa biotécnica com hormônios pode-se estabelecer manipulações do sistema reprodutivo da fêmea, levando a manejos de inúmeras cabeças de gado para inseminar a um tempo fixo. Portanto, foram realizados 5 protocolos de IATF, tendo 2 categorias de animais: nulíparas e multíparas. No protocolo 1 foram submetidas 81 multíparas, (...) resultando em 47 animais prenhes; No protocolo 2 foram protocoladas 103 animais multíparas, no qual resultou em 51 prenhes; já o protocolo 5 foram submetidas 77 animais multíparas, no qual resultou em 36 animais prenhes. Cada serviço realizado foi matematicamente calculado, sendo o ponto de partida o escore corporal, bem estar animal e a técnica bem exercida. Desta forma obteve bons resultados na (IATF) , no qual destaca-se o percentual : o protocolo 1 obteve 58,02%, o protocolo 2 obteve 49,51% na taxa de prenhez, No protocolo 3 obteve 55,67% na taxa de prenhez, o protocolo 4 obteve 53,33% de prenhes, já o protocolo 5 resultou em 46,75% de prenhez. O uso das biotecnologias da reprodução, realizadas em bovinos de corte, obteve resultado dentro do descrito pela literatura consultada. A boa taxa de prenhes apresentada na IATF deveu-se ao bom controle hormonal do ciclo estral e da qualidade do sêmen utilizado. A taxa de prenhez dos animais que foram submetidos à monta natural foi baixa pelo fato de que os reprodutores não conseguiram cobrir todas as fêmeas. ABSTRACT The artificial insemination (AI) is the most used biotechnology with superior advantages in relation to the use of natural mounting, whose effectiveness is given in the large scale of reproduction among cattle. Associating this biotechnique with hormones it is possible to establish manipulations of the reproductive system of the female, leading to managements of numerous heads of cattle to inseminate at a fixed time. Therefore, 5 IATF protocols were performed, having 2 categories of animals: nulliparous and multiparous. In protocol 1, 81 multiparous animals were submitted, resulting in 47 pregnant animals; in protocol 2, 103 multiparous animals were submitted, resulting in 51 pregnancies; and in protocol 5, 77 multiparous animals were submitted, resulting in 36 pregnant animals. Each service performed was mathematically calculated, with the starting point being the body score, animal welfare and the well exercised technique. Thus obtained good results in the (IATF), which highlights the percentage: protocol 1 obtained 58.02%, protocol 2 obtained 49.51% in pregnancy rate, in protocol 3 obtained 55.67% in pregnancy rate, protocol 4 obtained 53.33% pregnant, and protocol 5 resulted in 46.75% pregnant. The use of the reproduction biotechnologies, performed in beef cattle, obtained results within the described by the consulted literature. The good pregnancy rate presented in the IATF was due to the good hormonal control of the estrous cycle and the quality of the semen used. The pregnancy rate of animals that were subjected to natural mating was low due to the fact that the sires could not cover all the females. Keywords: Hormones. Cattle Pregnancy Rate. Artificial Insemination in Cattle. Hormones in Cattle Reproduction. -/- REFERÊNCIAS BIBLIOGRÁFICAS AMBRÓSIO, P. H. et al. Ressincronização da ovulação em programas de IATF: novas estratégias. 2018. BARUSELLI, P. S.; GIMENES, L. U.; SALES, J. N. de S. Fisiologia reprodutiva de fêmeas taurinas e zebuínas. Revista Brasileira de Reprodução Animal, v. 31, n. 2, p. 205-211, 2007. BARUSELLI, P. S. et al. Evolução e perspectivas da inseminação artificial em bovinos. Revista Brasileira de Reprodução Animal, v. 43, n. 2, p. 308-314, 2019. BÓ, G. A. et al. Alternative programs for synchronizing and resynchronizing ovulation in beef cattle. Theriogenology, v. 86, n. 1, p. 388-396, 2016. BOTTINO, M. P. et al. Effects of eCG and FSH in timed artificial insemination treatment regimens on estrous expression and pregnancy rates in primiparous and multiparous Bos indicus cows. Animal Reproduction Science, v. 228, p. 106751, 2021. DA SILVA, Emanuel Isaque Cordeiro. Técnica da Inseminação Artificial em Bovinos: Manejo Passo a Passo. 2020. DA SILVA, Emanuel Isaque Cordeiro. Reprodução Animal: Inseminação Artificial. 2020. DA SILVA, Emanuel Isaque Cordeiro. Fisiologia da Reprodução Animal: Ovulação, Controle e Sincronização do Cio. 2020. DA SILVA, Emanuel Isaque Cordeiro. Fisiologia da Reprodução de Bovinos Leiteiros: Aspectos Básicos e Clínicos. Emanuel Isaque Cordeiro da Silva, 2022. KRAUS, Beth M.; PARENTE, Eric J.; TULLENERS, Eric P. Laryngoplasty with ventriculectomy or ventriculocordectomy in 104 draft horses (1992–2000). Veterinary Surgery, v. 32, n. 6, p. 530-538, 2003. MONGELLI, Melissa Sanches; TAVARES, Izabel Cristina; FERRANTE, Marcos. Evolução e premissas dos protocolos hormonais de inseminação artificial em tempo fixo na pecuária. Ciência Animal, v. 31, n. 1, p. 119-133, 2021. VILELA, G. C. Protocolos de IATF em novilhas precoce e super precoce. 2021. (shrink)

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 (...) diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

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 (...) develop a specific form of enhanced manipulative imagination, in order to draw inferences from knot diagrams by performing epistemic actions. Moreover, it will be argued that knot diagrams not only can promote discovery, but also provide evidence. This case study is an experimentation ground to evaluate the role of space and action in making inferences by reasoning diagrammatically. (shrink)

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; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

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 (...) in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology. (shrink)

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 (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

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 (...) that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them. (shrink)

É comumente aceito, atualmente, que Aristóteles não teria enfrentado ou tentado seriamente resolver o famoso paradoxo do mentiroso, embora ele tenha sido formulado por Eubúlides de Mileto, membro da escola megárica e rival filosófico de Aristóteles. No máximo, assim reza a visão tradicional, ele parece apenas fazer uma menção desse paradoxo nas Refutações sofísticas, Capítulo 25, talvez esboçando a sua solução. O meu intento, no presente artigo, é desafiar essa opinião geral mostrando que o Estagirita fornece uma explicação implícita para (...) duas versões do paradoxo do mentiroso, a saber, a versão autorreferencial (que pode ser apresentada pela declaração: “esta declaração é falsa”), e a versão anafórica (que pode ser apresentada por meio de duas declarações mutuamente referentes como estas: “a próxima declaração é verdadeira” e “a declaração anterior é falsa”). A minha alegação é que a solução aristotélica para essas duas versões do paradoxo encontra-se no núcleo de sua refutação de duas teses, as quais denominei como tese da synalethia (que defende que toda declaração é verdadeira) e como tese da sympseudia (que defende que toda declaração é falsa). Tal refutação é realizada no oitavo capítulo do quarto Livro da Metafísica, um texto até agora subestimado pelos intérpretes modernos, mesmo sendo a parte final de um dos mais importantes escritos de Aristóteles. A solução aristotélica, assim defendo, é levada a cabo por meio dos seguintes princípios: (i) toda declaração é sempre precedida por um operador de verdade da forma ‘é verdade que...’, ou seja, toda declaração, qualquer que seja o que ela possa declarar a mais, primariamente assevera a sua própria verdade; e, em conformidade com o princípio anterior, (ii) toda declaração que assevera a sua própria falsidade ou acarreta a verdade de sua contraditória é necessariamente falsa. Através desses princípios, a refutação de Aristóteles da synalethia e da sympseudia é bem-sucedida. Mostrarei que obtemos uma boa solução para as versões do mentiroso acima mencionadas (e implicitamente presentes nas posições refutadas), apenas aplicando esses mesmos princípios a elas. Esse tipo de solução ao mentiroso tanto quanto para as teses antes citadas é muito parecido com aquele explicitamente encontrado nas obras de diversos filósofos, a saber, Guilherme de Sherwood, Tomás Bradwardine, João Buridano, Alberto da Saxônia, Paulo Venetus, Charles S. Peirce e Arthur Prior. Assim, também defendo que essa linhagem tem as suas raízes na solução de Aristóteles. (shrink)

Despite the importance of human blood to clinical practice and research, hematology and blood transfusion data remain scattered throughout a range of disparate sources. This lack of systematization concerning the use and definition of terms poses problems for physicians and biomedical professionals. We are introducing here the Blood Ontology, an ongoing initiative designed to serve as a controlled vocabulary for use in organizing information about blood. The paper describes the scope of the Blood Ontology, its stage of development and some (...) of its anticipated uses. (shrink)

In this chapter, we will offer a sketch of the state of the art as concerns existing accounts of virtue acquisition in relation to automaticity. In particular, we will focus on the so-called “skill model,” which we aim to improve by questioning its rather common underlying dualistic picture of the mind. Then we will propose an account of skillful emotions by identifying the features that make them both automatic and embedded in an intelligent practice. Finally, we will show how this (...) view can help the skill model by offering a better description of emotion shaping in virtue acquisition. By doing so, we will contend that emotions contribute autonomously and actively to the skillfulness of the habits in which they are embedded. (shrink)

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 (...) his literary writings, such as Dialogue between Nature and an Islander (1824)—an invective against nature and the suffering of creatures within it. In his last lyric, Broom, or the flower of the desert (1836), Leopardi points to the redeeming power of poetry and to human solidarity as placing at least temporary limits on the scope of evil. (shrink)

The Eleventh Aporia results from the breakup of the entire Greek philosophy previous to Aristotle in two manners of conceiving and proposing the first principles (archai), specially the One (to hen): (i) the manner by which Physiologoi conceived the One as a principle, namely, assuming an underlying nature, different from the One in itself, not adequately characterized by the simple fact of being one and which is denoted by the concept of One, and (ii) the manner inaugurated by the Pythagoreans (...) and later endorsed by Plato, marked by the abandonment of the appeal to an underlying nature and by conceiving the One in itself (auto to hen) as a principle, depriving it of any connection with some reality not strictly characterized by being one. Aristotle faces this aporia in Metaphysics Iota 2 and, according to the interpretation I propose: (a) refuses the Pythagorean-Platonic manner of conceiving and proposing principles, (b) endorses the course of action of the Physiologoi, and, in doing so, (c) steps back and retakes the “project” of the Physiologoi at the point where it was interrupted, namely, during the search for a principle of motion. From this scenario, I will try to show that the final outcome of the Eleventh Aporia can be the introduction of the Prime Mover as the properly Aristotelian (and cosmological) candidate to the title of One between the principles. (shrink)

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, (...) 5th ed., Cambridge University Press, 2007), Fixing Frege (Princeton University Press, 2005), Mathematics, Models, and Modality (Cambridge University Press, 2007), Philosophical Logic (Princeton University Press, 2009), Truth (with A. G. Burgess, Princeton University Press, 2011), Saul Kripke: Puzzles & Mysteries (Polity Press, 2012), Rigor & Structure (Oxford University Press, 2015), and Set Theory (Cambridge Elements, Forthcoming). In this interview, Professor Burgess talks about how his interests in mathematics and philosophy developed and relate to each other. He then answers questions about specific themes of his philosophical work, with a focus on issues pertaining to philosophy of mathematics. (shrink)

In the following pages, the reader will find a detailed study of what Aristotle considered the most difficult aporia formulated in Metaphysics III (Beta), which is answered in chapter 2 of Book X (Iota): the Eleventh Aporia. In such aporia, Aristotle rivals: (i) the conception assumed by the ancient Physiologoi, which takes the One to be an underlying nature whose being is not exhausted by being One, and (ii) the Platonic-Pythagorean view, which prefers to conceive the One in itself, according (...) to its own determinations and apart from any connection with some reality outside it. (shrink)

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.