5 found

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  1. Gapless Lines and Gapless Proofs: Intersections and Continuity in Euclid’s Elements.Vincenzo De Risi - 2021 - Apeiron 54 (2):233-259.
    In this paper, I attempt a reconstruction of the theory of intersections in the geometry of Euclid. It has been well known, at least since the time of Pasch onward, that in the Elements there are no explicit principles governing the existence of the points of intersections between lines, so that in several propositions of Euclid the simple crossing of two lines is regarded as the actual meeting of such lines, it being simply assumed that the point of their intersection (...)
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  2. Aristotle on the Authority of the Many: Politics III 11, 1281a40–B21.Antony Hatzistavrou - 2021 - Apeiron 54 (2):203-232.
    In this article I propose a new interpretation of Aristotle’s arguments about the authority of the many at Politics III 11, 1281a40–b21. It consists of the following main tenets. First, the multitude that Aristotle refers to in his arguments should be understood on the model of the multitude which rules in polities and the members of which are accomplished in only a part of political excellence, namely, military excellence. Second, the best citizens with whom he compares that multitude in his (...)
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  3. The Physics of Stoic Cosmogony.Ian Hensley - 2021 - Apeiron 54 (2):161-187.
    According to the ancient Greek Stoics, the cosmos regularly transitions between periods of conflagration, during which only fire exists, and periods of cosmic order, during which the four elements exist. This paper examines the cosmogonic process by which conflagrations are extinguished and cosmic orders are restored, and it defends three main conclusions. First, I argue that not all the conflagration’s fire is extinguished during the cosmogony, against recent arguments by Ricardo Salles. Second, at least with respect to the cosmogony, it (...)
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  4. Seneca on Human Rights in De Beneficiis 3.Alex Long - 2021 - Apeiron 54 (2):189-201.
    The paper discusses Seneca’s phrase ‘human rights’ in On Benefits 3 and relates the passage to recent debates about human rights in Stoicism and ancient philosophy. I argue that the Latin phrase refers either to rights or to a law conferring rights. The difference between the passage and a common expectation for human rights lies in the kind of relation between right and duty. In Seneca’s passage the right does not in itself have a correlative duty on the part of (...)
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    The Stoic Appeal to Expertise: Platonic Echoes in the Reply to Indistinguishability.Simon Shogry - 2021 - Apeiron 54 (2):129-159.
    One Stoic response to the skeptical indistinguishability argument is that it fails to account for expertise: the Stoics allow that while two similar objects create indistinguishable appearances in the amateur, this is not true of the expert, whose appearances succeed in discriminating the pair. This paper re-examines the motivations for this Stoic response, and argues that it reveals the Stoic claim that, in generating a kataleptic appearance, the perceiver’s mind is active, insofar as it applies concepts matching the perceptual stimulus. (...)
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