Antipho ̄n of Athens (450 – 400 BCE)
The sophist, distinguished by Hermogene ̄s of Tarsos (De ideis 399.18–400.6 = DK 87 A 2)
from the homonymous Athenian politician and logographer Antipho ̄n of Rhamnous.
(Many, however, reject the distinction and identify the two.) Hermogene ̄s ascribes to the
sophist Antipho ̄n the treatises On Truth, On Concord, and Politicus, and a dream-book of no
fixed title. All the evidence bearing on Antipho ̄n’s scientific and mathematical interests is
plausibly ascribed to the two-volume treatise On Truth.
A and related sources describe Antipho ̄n’s contribution to the problem of the
quadrature of the circle (DK 87B13). Antipho ̄n (it is reported) inscribed a regular polygon
in a circle, then constructed isosceles triangles upon the sides of the polygon, and sub-
sequently repeated this process until an inscribed polygon was produced whose sides
coincided with the circumference of the circle. Here we find the first attested adumbration
of the notion of exhausting a curvilinear figure, an idea taken up and perfected later by
E K and which represents an important early contribution to the
development of calculus. Other fragments evidence Antipho ̄n’s interests in subjects ran-
ging from cosmology (DK 87B22–25) to the source of the moon’s illumination and the
cause of its eclipses (DK 87B27–28) and the nature and movements of the sun (DK
87B26). An important text transmitted in Arabic attests Antipho ̄n’s interest in medicine
and the humoral theory of disease (DK 87B29a=F29a Pendrick), while a papyrus frag-
ment suggests he espoused the theory of sight by visual rays (POxy 52 [1984] 3647,
col. III.6–8).
Taken together, the evidence shows Antipho ̄n’s thorough engagement in conventional
topics of Pre-Socratic natural inquiry. Whether he espoused a general theory of nature or
phusis is unknown. Aristotle (DK 87B14) reports a sort of thought experiment about a
buried bed, which he claims shows that Antipho ̄n defined nature generally as matter. But
the inference is suspect; and the larger import of Antipho ̄n’s views on nature, including its
relation to morality, remains uncertain.
DPA 1 (1989) 225–244 (#209), M. Narcy; Corpus dei papiri filosofici greci e latini I.1* (1989) 176–236,
F. Decleva Caizzi and G. Bastianini; M. Gagarin, Antiphon the Athenian: Oratory, Law and Justice in the Age
of the Sophists (2002); G.J. Pendrick, Antiphon the Sophist: The Fragments (2002).
G.J. Pendrick
Antisthene ̄s of Athens (ca 425 – ca 365 BCE)
Antisthene ̄s (born ca 445 BCE), one of the associates of So ̄crate ̄s, who praised his bravery at
the battle at Tanagra 424 BCE where both fought (D L 6.1) and whose
death he attended (P, Phaido ̄n 59b), became one of the most prominent Socratic
teachers in Athens and was later regarded as the founder of the Cynic tradition; he died
ca 365 BCE. The work titled Peri to ̄n sophisto ̄n phusiogno ̄monikos (D.L. 6.15.15) or Phusiogn-
o ̄monikos (Ath., Deipn. 14 [656f]) quite certainly is not a technical text on the art of physi-
ognomy, but rather an anti-Sophistic text in the same tradition as that of other Socratic
writers, making use of the art of physiognomy in much the same way as Plato in the
Sumposion 215a4–217a2 has Alkibiade ̄s compare So ̄crate ̄s’ features to that of satyrs, and
Phaido ̄n of E ̄lis in his treatise Zo ̄puros (cf. Z): to contrast the external appearance of
So ̄crate ̄s and his internal soul and character, and thus to refute the possibility of physio-
gnomical inferences from body to soul.
ANTISTHENE ̄S OF ATHENS