Platão e Aristóteles na filosofia da matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conhecimento, arte e formação na República de Platão

Neste trabalho, investiga-se qual a relação entre arte, formação e política na obra República, de Platão, e estuda-se de que modo os pressupostos gnosiológicos platônicos esclarecem as tensões nessa relação. Busca-se reconstruir os argumentos centrais de Platão que sustentam a sua crítica à educação mitopoética. Defende-se a hipótese de que Platão, na República, reconhece o potencial formativo da arte, especialmente da poesia, embora, por razões de fundamentação ontológica e gnosiológica, tenha de subordiná- -lo à filosofia. A natureza dos questionamentos e os objetivos da pesquisa exigiram a consulta de fontes bibliográficas, sendo que para análise e interpretação foram utilizadas técnicas hermenêuticas de leitura de textos, com destaque para a apreensão dos sentidos dos conceitos essenciais na sua proveniência grega. Procedeu-se à explicação e ao comentário da obra República, mas também de Íon e Hípias Maior e da literatura crítica, que foram selecionadas como mais significativas entre as fontes levantadas, tendo em vista o problema de pesquisa. A análise conceitual e reflexiva mostrou ser a cultura mitopoética um componente indispensável à formação na obra platônica analisada, embora insuficiente, por si, para atingir o ideal de educação que se expressa pelos conceitos de verdade, bondade e beleza. Conclui-se que somente a filosofia, por superar os encantos da linguagem, da sensibilidade e do mundo sensível, poderá entender os limites e possibilidades da arte, especialmente daquela que usa a palavra. Assim como a cidade justa só seria possível pelo equacionamento do rei e do filósofo, não é admissível um verdadeiro poeta que não seja filósofo.

Platão e a matemática: uma questão de método

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The incorporeal order in Plato's Philebus

In this paper, I intend to analyze how Plato's Philebus takes up some specific topics of Platonic dialectic and employs them to understand how the cognitive soul can be affected by false pleasures, false opinions, and false images. This study aims to criticize certain modern readings of Platonism, chiefly esoteric theory based on Plato's unwritten doctrine, which stipulate a revision of the Platonic theory of forms and defend the emergence of a new ontology explained by two principles, the One and the unlimited Dyad of great and small, conceived both as formal principle and material principle.

Plato and Frankfurt: Two Theories of the Relations Between Love and Living Well

This thesis provides a comparison of the ideas of caring and love as they appear in the works of Plato and Frankfurt. Frankfurt, a contemporary philosopher, maintains that an individual arrives at the most meaningful life through understanding what it is that heor she cares about the most. Interestingly, the instances of eros in Plato's Symposium and Phaedrus resonate with this idea. We see throughout these erotic dialogues similarities to Frankfurt's notions of care and love.Throughout his many works, Frankfurt provides us with several distinct features of care and love. This thesis offers an in depth discussion of each of these features andalso provides commentary from other contemporary philosophers who are familiar with Frankfurt's work. In addition, this thesis applies these features of care and love to Plato's erotic dialogues, and emphasizes areas in which Plato and Frankfurt agree and those inwhich they disagree. In essence, it becomes apparent that while there are many similarities between the ideas of these two prominent thinkers, Plato and Frankfurt do not agree about what constitutes the best human life. Plato maintains that the best life is onespent dedicated to philosophy and in pursuit of the 'good'. Frankfurt, on the other hand,imposes no such limitations on what we should consider the best life because people are likely to have different life experiences that lead them to care about and love different things. Instead he suggests that the best or most meaningful human life is one in which a person spends his or her life caring about the things he or she does, indeed, care aboutand loving those things he or she does, indeed, love.

Plato's Doctrine Of Forms: Modern Misunderstandings

Among the philosophical ideas of Plato, perhaps the most famous is his doctrine of forms. This doctrine has faced harsh criticism due, in large part, to the interpretations of this position by modern philosophers such as René Descartes, John Locke, and Immanuel Kant. For example, Plato has been interpreted as presenting a ¿two-worlds¿ approach to form and thing and as advancing a rationalist approach to epistemology. His forms have often been interpreted as ideas and as perfect copies of the things of the visible world. In this thesis, I argue that these, along with other interpretations of Plato presented by the moderns, are based on misunderstandings of Plato¿s overall philosophy. In so doing, I attempt to show that the doctrine of forms cannot be directly interpreted into the language of Cartesian, Lockean, and Kantian metaphysics and epistemology, and thus should not be prematurely dismissed because of these modern Platonic interpretations. By analyzing the Platonic dialogues beside the writings of the modern philosophers, I conclude that three of the most prominent modern philosophers, as representatives of their respective philosophical frameworks, have fundamentally misunderstood the nature of Plato¿s famous doctrine of forms. This could have significant implications for the future of metaphysics and epistemology by providing an interpretation of Plato which adds to, instead of contradicts, the developments of modern philosophy.

Stent thrombosis with ticagrelor versus clopidogrel in patients with acute coronary syndromes: an analysis from the prospective, randomized PLATO trial

BACKGROUND We aimed to describe the effects of ticagrelor versus clopidogrel on stent thrombosis in the Platelet Inhibition and Patient Outcomes (PLATO) trial. METHODS AND RESULTS Of 18 624 patients hospitalized for acute coronary syndromes, 11 289 (61%) had at least 1 intracoronary stent. Ticagrelor reduced stent thrombosis compared with clopidogrel across all definitions: definite, 1.37% (n=71) versus 1.93% (n=105; hazard ratio [HR], 0.67; 95% confidence interval [CI], 0.50-0.90; P=0.0091); definite or probable, 2.21% (n=118) versus 2.87% (n=157; HR, 0.75; 95% CI, 0.59-0.95; P=0.017); and definite, probable, and possible, 2.94% (n=154) versus 3.77 (n=201; HR, 0.77; 95% CI, 0.62-0.95). The reduction in definite stent thrombosis was consistent regardless of acute coronary syndrome type, presence of diabetes mellitus, stent type (drug-eluting or bare metal stent), CYP2C19 genetic status, loading dose of aspirin, dose of clopidogrel before randomization, and use of glycoprotein IIb/IIIa inhibitors at randomization. The reduction in stent thrombosis with ticagrelor was numerically greater for late (>30 days; HR, 0.48; 95% CI, 0.24-0.96) and subacute (4 hours-30 days; HR, 0.60; 95% CI, 0.39-0.93) compared with acute (<24 hours; HR, 0.94; 95% CI, 0.43-2.05) stent thrombosis or for patients compliant to therapy (ie, taking blinded study treatment ≥80% of the time) compared with less compliant patients. Randomization to ticagrelor was a strong independent inverse predictor of definite stent thrombosis (HR, 0.65; 95% CI, 0.48-0.88). CONCLUSION Ticagrelor compared with clopidogrel reduces the incidence of stent thrombosis in patients with acute coronary syndromes, with consistent benefit across a broad range of patient, stent, and treatment characteristics.

Effect of ticagrelor on the outcomes of patients with prior coronary artery bypass graft surgery: insights from the PLATelet inhibition and patient outcomes (PLATO) trial

BACKGROUND Patients with prior coronary artery bypass graft surgery (CABG) who present with an acute coronary syndrome have a high risk for recurrent events. Whether intensive antiplatelet therapy with ticagrelor might be beneficial compared with clopidogrel is unknown. In this substudy of the PLATO trial, we studied the effects of randomized treatment dependent on history of CABG. METHODS Patients participating in PLATO were classified according to whether they had undergone prior CABG. The trial's primary and secondary end points were compared using Cox proportional hazards regression. RESULTS Of the 18,613 study patients, 1,133 (6.1%) had prior CABG. Prior-CABG patients had more high-risk characteristics at study entry and a 2-fold increase in clinical events during follow-up, but less major bleeding. The primary end point (composite of cardiovascular death, myocardial infarction, and stroke) was reduced to a similar extent by ticagrelor among patients with (19.6% vs 21.4%; adjusted hazard ratio [HR], 0.91 [0.67, 1.24]) and without (9.2% vs 11.0%; adjusted HR, 0.86 [0.77, 0.96]; P(interaction) = .73) prior CABG. Major bleeding was similar with ticagrelor versus clopidogrel among patients with (8.1% vs 8.7%; adjusted HR, 0.89 [0.55, 1.47]) and without (11.8% vs 11.4%; HR, 1.08 [0.98, 1.20]; P(interaction) = .46) prior CABG. CONCLUSIONS Prior-CABG patients presenting with acute coronary syndrome are a high-risk cohort for death and recurrent cardiovascular events but have a lower risk for major bleeding. Similar to the results in no-prior-CABG patients, ticagrelor was associated with a reduction in ischemic events without an increase in major bleeding.

The PLATO 2.0 mission

PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) and a large photometric magnitude range (4–16 mag). It focusses on bright (4–11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2 %, 4–10 % and 10 % for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2–3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50 % of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA’s Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science.