Apeiron

A Journal for Ancient Philosophy and Science

ISSN: 2156-7093

First published: March 1, 1967

Edited by: Christian Wildberg, Benjamin Morison

About this journal

Objective
Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on a double-blind basis.

Topics

ancient philosophy
ancient science
reception of ancient philosophical and scientific ideas in the later western tradition

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Original Articles

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Volume 54 Issue 2

April 2021

Frontmatter

April 13, 2020 Page range: i-iii

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Free access PDF PDF

Research Articles

The Stoic Appeal to Expertise: Platonic Echoes in the Reply to Indistinguishability

Simon Shogry August 21, 2019 Page range: 129-159

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Abstract

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. I argue that this claim is reflected in the Stoic definition of the kataleptic appearance, and that it respects their more general account of mental representation. I further suggest that, in attributing some activity to the mind in creating each kataleptic appearance, and in claiming that the expert’s mind allows her to form more kataleptic appearances than the amateur, the Stoics draw inspiration from the wax tablet model in Plato’s Theaetetus (190e–196d), where Socrates distinguishes the wise from the ignorant on the basis of how well they match sensory input with its appropriate mental ‘seal’ (σφραγίς).

The Physics of Stoic Cosmogony

Ian Hensley August 21, 2019 Page range: 161-187

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Abstract

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 is not necessary to posit the existence of proto-elements. Third, while scholars such as Salles and David Hahm have argued that Cleanthes held a distinct theory of cosmogony from Zeno and Chrysippus, I argue that each of these Stoics endorse the same cosmogonic theory.

Seneca on Human Rights in De Beneficiis 3

Alex Long August 21, 2019 Page range: 189-201

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Abstract

The paper discusses Seneca’s phrase ‘human rights’ (ius humanum) 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 other people, and yet it does, if exercised through benefactions, create a duty in others. By contrast, the relation between right and duty is usually expected to be unconditional.

Aristotle on the Authority of the Many: Politics III 11, 1281a40–b21

Antony Hatzistavrou September 17, 2019 Page range: 203-232

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Abstract

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 arguments do not possess complete political excellence but rather the highest degree of military excellence among their fellow citizens in a polity. Third, the members of that multitude are collectively superior to the best citizens in making decisions about political particulars, for example, decisions about specific policies. Fourth, their superiority can be explained by reference to the fact that they collectively possess superior experience than the best citizens, though they have individually and collectively inferior political understanding. Finally, their collective superiority in making political decisions is the outcome of the aggregation of their individual political judgements that are based on experience rather than the outcome of some form of public deliberation that enables them to grasp the political reasons which support their decisions.

Gapless Lines and Gapless Proofs: Intersections and Continuity in Euclid’s Elements

Vincenzo De Risi November 7, 2019 Page range: 233-259

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Abstract

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 (two circles, for instance) is regarded as the actual meeting of such lines, it being simply assumed that the point of their intersection exists. Such assumptions are labelled, today, as implicit claims about the continuity of the lines, or about the continuity of the underlying space. Euclid’s proofs, therefore, would seem to have some demonstrative gaps that need to be filled by a set of continuity axioms (as we do, in fact, find in modern axiomatizations). I show that Euclid’s theory of intersections was not in fact based on any notion of continuity at all. This is not only because Greek concepts of continuity (such as the Aristotelian ones) were largely insufficient to ground a geometrical theory of intersections, but also, at a deeper level, because continuity was simply not regarded as a notion that had any role to play in the latter theory. Had Euclid been asked to explain why the points of intersections of lines and circles should exist, it would have never occurred to him to mention continuity in this connection. Ancient geometry was very different from ours, and it is only our modern views on continuity that tend to give rise to the expectation that this latter must be included in the foundations of elementary mathematics. We may hope to reconstruct Euclid’s views on intersections if we undertake a critical examination both of the extension and of the limits of ancient diagrammatic practices. This is tantamount to attempting to understand to what extent the existence of an intersection point may be inferred just from the inspection of a diagram, and in which cases we need rather to supplement such inference by propositional rules. This leads us to discuss Euclid’s definition of a point, and to work out the details of the complex interaction between diagrams and text in ancient geometry. We will see, then, that Euclid may have possessed a theory of intersections that was sufficiently rigorous to dispel the main objections that could be advanced in antiquity.

Ahead of Print / Just Accepted

Ahead of Print / Just Accepted

Volume 54 (2021)

Volume 53 (2020)

Volume 52 (2019)

Volume 51 (2018)

Volume 50 (2017)

Volume 49 (2016)

Volume 48 (2015)

Volume 47 (2014)

Volume 46 (2013)

Volume 45 (2012)

Volume 44 (2011)

Volume 43 (2010)

Volume 42 (2009)

Volume 41 (2008)

Volume 40 (2007)

Volume 39 (2006)

Volume 38 (2005)

Volume 37 (2004)

Volume 36 (2003)

Volume 35 (2002)

Volume 34 (2001)

Volume 33 (2000)

Volume 32 (1999)

Volume 31 (1998)

Volume 30 (1997)

Volume 29 (1996)

Volume 28 (1995)

Volume 27 (1994)

Volume 26 (1993)

Volume 25 (1992)

Volume 24 (1991)

Volume 23 (1990)

Volume 22 (1989)

Volume 21 (1988)

Volume 20 (1987)

Volume 19 (1985)

Volume 18 (1984)

Volume 17 (1983)

Volume 16 (1982)

Volume 15 (1981)

Volume 14 (1980)

Volume 13 (1979)

Volume 12 (1978)

Volume 11 (1977)

Volume 10 (1976)

Volume 9 (1975)

Volume 8 (1974)

Volume 7 (1973)

Volume 6 (1972)

Volume 5 (1971)

Volume 4 (1970)

Volume 3 (1969)

Volume 2 (1968)

Volume 1 (1967)

European Reference Index for the Humanities

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All submissions should be prepared for blind review, which means that no internal references, bibliographic information, or acknowledgements that could be used to identify the author should appear in the paper, bibliography, or notes. Where such information would appear, authors should cite their published work as they would the work of any other author. In other cases, authors are encouraged to include lacunae such as "[reference omitted for blind review]". Manuscripts that do not conform to this requirement may be returned to the authors for correction. Submission of a paper to Apeiron will be taken to imply that the paper is not under editorial consideration elsewhere.

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Editorial

Editors
Christian Wildberg (University of Pittsburgh)
Benjamin Morison (Princeton University)

Associate Editor
Luis Alejandro Salas (Washington University in St. Louis)

Editorial Office
APEIRON: a journal for ancient philosophy and science
Department of Classics
Washington University
1 Brookings Drive, Campus Box 1050
Saint Louis, MO 63130
apeiron.editorial@degruyter.com

Editorial Board
Marquis Berrey (Classics, University of Iowa)
Richard Bett (Philosophy, Johns Hopkins University)
Alan C. Bowen (Institute for Research in Classical Philosophy and Science)
Eric Brown (Philosophy, Washington University in St. Louis)
Klaus Corcilius (Philosophy, University of Tübingen)
Patricia Curd (Philosophy, Purdue University)
Lesley Dean-Jones (Classics, University of Texas at Austin)
Michael T. Ferejohn (Philosophy, Duke University)
Jyl Gentzler (Philosophy, Amherst College)
Daniel Graham (Philosophy, Brigham Young University)
Brad Inwood (Classics, Yale University)
David Konstan (Classics, New York University)
Timothy O'Keefe (Philosophy, Georgia State University)
Mariska Leunissen (Philosophy, University of North Carolina at Chapel Hill)
Richard McKirahan (Classics and Philosophy, Pomona College)
Mark McPherran (Philosophy, University of Maine at Farmington)
Phillip Mitsis (Classics, New York University)
Deborah Modrak (Philosophy, University of Rochester)
Naomi Reshotko (Philosophy, University of Denver)
Ricardo Salles (Philosophy, National University of Mexico)
Mark Schiefsky (Classics, Harvard University)
Janet Sisson (Philosophy, University of Calgary)
Nicholas Smith (Philosophy, Lewis and Clark College)
Martin Tweedale (Philosophy, University of Alberta)
Katja Vogt (Philosophy, Columbia University)
Michael J. White (Philosophy, Arizona State University)
Stephen White (Classics, University of Texas at Austin)
Paul Woodruff (Philosophy, University of Texas at Austin)
Marco Zingano (Philosophy, University of São Paolo)

Former Editors
Markus Asper (Classics, Humboldt Universität zu Berlin)
Peter Bicknell (Classics, Monash University) †
Robert W. Hall (Philosophy, University of Vermont) †
R.J. Hankinson (Philosophy, University of Texas at Austin)
John King-Farlow (Philosophy, University of Alberta)
David Rankin (Classics, University of Southampton)
Roger Shiner (Philosophy, Okanagan University College)

(Deutsch)

Apeiron

A Journal for Ancient Philosophy and Science

The Stoic Appeal to Expertise: Platonic Echoes in the Reply to Indistinguishability

Abstract

The Physics of Stoic Cosmogony

Abstract

Seneca on Human Rights in De Beneficiis 3

Abstract

Aristotle on the Authority of the Many: Politics III 11, 1281a40–b21

Abstract

Gapless Lines and Gapless Proofs: Intersections and Continuity in Euclid’s Elements

Abstract

Details