Greco Roman Antiquity Questions

1
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Introduction
Today, if we wish to write or read about science or mathematics, we have
many choices: in addition to traditional formats, such as journal articles
and textbooks, we have the strikingly modern media of blogs and tweets.
Each of these formats has particular formal characteristics: for example,
contributors of research articles to the leading journal Science are limited
to 4,500 words, while reports can only be 2,500 words long; the listing of
‘keywords’ is often required by journals.
Ancient Greek and Roman authors writing on scientific and mathematical subjects also had a range of choices available for conveying ideas
and information. For example, writers on astronomy employed a number
of different formats: Aratus of Soli composed poetry, Plutarch adopted the
dialogue form, Claudius Ptolemy wrote extended, systematic prose works,
Cleomedes circulated lectures, Geminus offered an introductory teaching
text and Theon of Alexandria produced commentaries. All of these different textual formats were used to convey astronomical ideas and methods.
This diversity of literary formats used for the presentation of information
and ideas is, for modern readers, one of the surprising, yet seldom studied, features of ancient scientific writing. Each of these different formats
entailed specific formal requirements for the author as well as expectations
for readers.
Form matters, and it informs our understanding of the cultural contexts in which texts were produced and used. This book considers several important textual formats used by ancient Greek and Roman writers
to convey scientific and mathematical information. This Introduction is
meant to be an entrée to an approach to ancient scientific and technical
texts.
By concentrating attention on the choice of medium used to convey the
message, I consider the effects of literary conventions associated with particular literary forms on the presentation of scientific, mathematical and
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2
Introduction
technical material. That scientific, mathematical and technical (including
medical) information and ideas were communicated in a range of formats
typically used for others purposes –​including the literary –​indicates that
writing and reading about scientific matters was a part of broader Greco-​
Roman culture. Indeed, many of the texts considered here were not likely
to have been written for specialists, but rather for a wider reading public,
including students.
That said, it is important not to regard Greco-​Roman antiquity as one
homogeneous time or place: generalisations will always be of limited
value. The authors considered here range in date from about 700 BCE
to the sixth century CE. Their texts were composed in Greek or Latin,
languages which had various dialects and changed during the course of
antiquity. Furthermore, the various literary formats employed different
registers and conventions, reflected in the language.
From looking at the different ways in which scientific ideas were communicated amongst the ancient Greeks and Romans, it is clear that the
formats in which scientific work circulated were also not static: over time,
new literary forms –​such as the commentary and the ­encyclopaedia –​
emerged. At different points historically, certain forms dominated the
scientific literature. Today, some ancient formats, including introductory texts and question-​and-​answer texts, continue to be used, while
others, such as poetry, have been largely discarded in scientific contexts.1
Intriguingly, some formats –​such as the dialogue –​were seldom used
for scientific topics in antiquity but gained special prominence in the
early modern period, with later authors looking back towards what they
regarded as significant ancient models.2
By opting to write in a specific format, authors may have hoped to
reach certain audiences: some types of texts are more appropriate to students, others to specialists. In addition to providing insights into how
Erasmus Darwin’s The Botanic Garden (1791), consisting of two poems (The Economy of Vegetation
and The Loves of the Plants), is a modern example of a work of natural history presented as poetry; it
was a publishing success.
2
In the early modern period, two authors interested in promoting Copernican cosmology turned to
the dialogue form. Galileo Galilei wrote two important works in the form of dialogues: Concerning
the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo, 1632) and Two New
Sciences (Discorsi e dimostrazioni matematiche intorno a due nuove scienze, 1638). In 1608, Johannes
Kepler produced a Latin translation of Plutarch’s (born before 50 CE, died after 120 CE) Dialogue
on the Face on the Moon, which he appended to his own work, the Somnium (Dream, published
1634); he explained that this latter work was, to some extent, an imitation of part of Plutarch’s
(Kepler (1870) Opera Omnia 8: 25).
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3
Historiographical Context
3
specific authors sought to engage their audiences, the consideration of the
choice of textual format also indicates how authors regarded their work
in relation to that of others. By choosing to write a poem, an author may
have sought to place himself within a particular tradition, for example,
that of the archaic epic poetry of Homer and Hesiod, which brought
with it great authority; in deciding to present ideas in a dialogue, authors
may have intended to have their work read against the background of
the philosophical milieu depicted in Plato’s dialogues (Taub 2008a: 36–​37;
76–​77). Furthermore, the choice of format also reveals something about
the community of authors and readers interested in scientific topics. Some
authors (and readers) were specialist experts in particular fields; others
were working from the standpoint of a less technical background, presumably appealing to readers with a general interest in their subject. So,
for example, Aratus’ astronomical poem the Phaenomena and the several
Latin translations of that work composed in antiquity were not directed
to specialist practitioners, but to a wider readership (Taub 2010). Given
the range of options available to ancient authors, their choices reflected
some authorial intentions, including a desire to reach particular audiences. Other aims might be to collect and share information, put forward
a theory, argue against the ideas of others, gratify a patron, amuse friends
or educate others, to name a few possibilities. The significance of such
authorial choices in communicating scientific material in Greco-​Roman
antiquity is a central theme here.
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Historiographical Context
Traditionally, historians interested in ancient Greek and Roman writings
on nature and mathematics have tended to concentrate on the content
conveyed in those works, relying primarily on the methods of intellectual
history, often mining texts for the ideas contained there. This approach
has borne substantial fruit, useful to classicists and ancient historians and
also of great value to historians of philosophy, science and mathematics
working in later periods; yet, it has its limitations, some of which have
been hinted at earlier.
In recent years, historians have been increasingly concerned with issues
relating to the presentation and reception of ideas, looking at rhetorical
strategies and reading practices. Most of the scholarship to date has studied scientific texts from the early modern period and later (e.g. Blair 1999
on medieval and early-​modern problem texts; Moss 1993 on sixteenth-​and
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4
Introduction
seventeenth-​century texts; Rheinberger 2003 on the nineteenth and twentieth centuries). This research has demonstrated the desirability of looking
beyond just the ideas contained in a written work to the modes of discourse adopted and the implications for understanding authorial intention and reception by readers.
Classicists have, for the most part, tended not to concentrate on those
texts which convey scientific, mathematical and technical information and ideas, choosing instead to concentrate on more ‘literary’ texts.
Technical texts –​with few exceptions –​are generally not regarded as ‘literary’ and –​in the hierarchy of literary style –​are often overlooked. In order
to understand the place of these texts within the cultures in which they
were produced and read, we need to think in terms of discourse, not just
content.
The way in which technical texts are studied has begun to change.
A few scholars working on ancient scientific texts have considered issues
relating to literary form and authorial choice; much of their work to
date has been published in German. In recent years, there has been a
growing interest in studying ancient scientific and technical writings
as texts, with scholars bringing to their study the same sorts of questions that classicists and literary scholars typically apply to more literary, non-​scientific works.3 Technical texts often become more accessible
when approached in this way, being revealed as even more interesting
and richly layered than they might seem at first reading. The study of
scientific, mathematical and technical texts as texts (and not simply a
concatenation of ideas) reveals crucial links to other aspects of Greco-​
Roman culture.
Literary Formats, Genres and Types of Texts
Before going further, it is important to clarify a few of the terms used
here, as well as some of the working assumptions. The term ‘genre’ is
an abstraction –​a classificatory tool –​used to describe different sorts of
things, including films, paintings and forms of discourse (Paltridge 1997).
The term is applied variously, as we might expect, by scholars in different
disciplines.4
3
4
See Doody, Föllinger and Taub 2012: 233–​236 for a discussion of developments in the study of
technical texts.
Some historians refer to mathematics itself as a ‘genre’; this usage of the term (to refer to an intellectual discipline) differs from the way it is typically used in literary and linguistic studies.
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Literary Formats, Genres and Types of Texts
5
The medievalist Irma Taavitsainen, who works on medical linguistic
corpora, has offered a useful definition of genres as ‘inherently dynamic
cultural schemata used to organise knowledge and experience through
language’. Genres are based on conventions, and are realised in texts for
specific purposes in certain cultural contexts. As Taavitsainen explains,
genres ‘become institutionalized so that they can function at the same
time as “horizons of expectation” for readers’, giving clues as to what to
expect in a text, while providing models for authors. While genres are conventional, they are also fluid and dynamic, influenced by various factors
culturally and historically. Indeed, some scholars regard genres as culture-​
specific. Genre is sometimes seen as being defined by ‘external’ cultural
features, while another abstraction, the ‘text type’, is used to classify texts
on the basis of ‘internal’ linguistic and structural features. Egon Werlich
famously identified five ‘types of texts’: narrative, instructive, expository,
argumentative and descriptive. But, as Taavitsainen points out, the terms
‘genre’ and ‘text type’ are often used vaguely –​and even interchangeably –​
in the scholarly literature (Taavitsainen 2001: 139–​140; Werlich 1976: 39–​
41). This is not a problem that can be solved here, but it is worth noting
to highlight some of the difficulties –​and lack of unanimity –​involved in
using these abstract categorisations.
Two classicists interested in questions relating to literary styles, Gian
Biagio Conte and Glenn Most, use the term ‘genre’ to refer to ‘a grouping
of texts related within the system of literature by their sharing recognizably
functionalized features of form and content’. They emphasise that genre is
‘not only a descriptive grid devised by philological research, but also a system of literary projection inscribed within the texts, serving to communicate
certain expectations to readers and to guide their understanding’ (Conte and
Most 2012). This view of genre points to choices made by authors (and compilers and editors) who have a number of options open to them as they craft
their texts, and recognises also that readers have expectations that are shaped
and served in different ways by different styles. Christopher Carey has noted
that recent scholars have come to regard genres ‘as flexible modes of communication with permeable boundaries’, rather than as fixed (Carey 2007: 250;
see also Most 2000: 17–​18).
The aim here is not to try to un-​pick the scholarship devoted to the
study of such categorisations, but rather to adopt some of the tools –​however problematic –​used by literary and linguistic scholars, and others, to
talk about texts. Nevertheless, it is important to note that the terminology employed by scholars is not applied uniformly; furthermore, terms
like ‘genre’ are fluid and cannot always be easily pinned down. For our
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6
Introduction
purposes here, David Duff has offered another good working definition
of the term ‘genre’ as ‘a recurring type or category of text, as defined by
structural, thematic, and/​or functional criteria’.5
Once we adopt the notion of genre, it may help to provide clues to
the various aims of authors and to expectations of audiences of ‘scientific’
writings. For example, some scholars use the category of ‘didactic poetry’
to describe poems that were presumably intended to educate, or at least
teach, while attracting the reader with the cultural values associated with
metre; issues related to the use of the term ‘didatic poetry’ are discussed
in Chapter 1. However, individual authors may have pursued a number
of aims simultaneously: conveying specialist information, self-​promotion,
exerting intellectual and moral influence, entertaining readers and demonstrating allegiance to a particular point of view or social group are some
examples (Doody, Föllinger and Taub 2012). In attempting to associate
particular genres with specific authorial ambitions, we must guard against
adopting some genre distinctions too enthusiastically: the reliance on a
limited and particular group of categories (including ‘didactic poetry’ and
‘treatise’, to name two widely used terms applied to scientific and technical texts) suggests a degree of homogeneity which may result in the loss
of finer-​grained understanding of particular texts. A consideration of the
formal features of texts often displays a greater and more interesting variety than we might otherwise expect, and in some cases reveals intriguing
ambiguity. Some texts are genre-​combining or -​crossing, and may even be
regarded as hybrids.
If we think further about terminology, it is important to note that
text ‘traditions’ are also an abstraction in which one text builds on or is
linked to another (Taavitsainen 2001: 150); this connection can be seen
to be achieved in a number of ways, for example through subject matter
or formal features, such as metre. At least one genre, that of commentary,
involves deliberate crafting in relationship to earlier texts. The tradition
of producing and using commentaries, begun in the Hellenistic period
and often targeting literary as well as philosophical texts, served also as
a conduit communicating earlier Greco-​Roman ideas to other cultures,
allowing later ‘traditions’ (for example, those of the medieval Jewish,
Christian and Muslim scholarly communities) to engage with another,
earlier one.
5
Duff 2000: xiii; as he notes, the term is increasingly used to classify non-​literary texts. Today, even
Web pages are classified by genre; see Rosso 2008.
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7
‘Science’, ‘Scientific’, ‘Scientist’
7
Defining ‘Greco-​Roman’
The term ‘Greco-​Roman’ is intended to signal that intellectual work was
undertaken across cultural and linguistic communities in the ancient
Mediterranean world; many individuals, for example Marcus Tullius
Cicero (106–​43 BCE), had a working knowledge of both Greek and
Latin. In many instances, activities pursued by those writing in Latin were
closely related to work undertaken by Greek authors. This is not to say
that some Romans, who had their own interests, agendas and approaches,
did not on some occasions deliberately contrast what they regarded as
‘Greek’ ideas with Roman values. Nevertheless, Latin authors were often
very self-​conscious about their Greek predecessors and contemporaries.
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‘Science’, ‘Scientific’, ‘Scientist’
Literary and cultural terms –​such as ‘genre’, ‘tradition’, ‘Greco-​Roman’ –​
are not the only ones which present challenges: using the terms ‘science’
and ‘scientific’ to describe activities and texts in the ancient world is itself
somewhat problematic. In part, the problem is due to the changing understanding –​by modern practitioners, historians and philosophers –​of what
constitutes science. Indeed, the term ‘scientist’ is itself modern, said to
have been coined by the polymath, historian and philosopher of science
William Whewell (1794–​1866) in 1840, in The Philosophy of the Inductive
Sciences founded upon their history (Whewell 1840, vol. I, Introduction
cxiii, cited in the OED); arguably, there is no exact analogue in other
periods to that professional label. Historians, philosophers, sociologists
and others who study the scientific enterprise have sometimes been much
occupied by issues of definition, and although such issues cannot be
addressed in detail here, they must be acknowledged (see Cunningham
1988). Nevertheless, there are numerous ancient authors and texts whose
presence in any study of the history of science few, if any, historians would
question.
What is labelled ‘scientific’ is often a matter of taste. There are some
scholars, for example, who claim that the ideas of the Presocratic philosophers were not scientific, while there are numerous others who would
counter that they represent the beginning of a ‘proto-​scientific’ or ‘scientific’ enterprise; these positions cannot be argued here. Nevertheless,
it must be acknowledged that the status of various human activities as
scientific, non-​scientific or even pseudo-​scientific is not always clear-​cut.
While the ancient Greeks were themselves interested in classifying human
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8
Introduction
activities, there was no one term, either in Greek or in Latin, equivalent to
the meaning of the modern word ‘scientific’. While some have suggested
that the Greek word epistēmē is equivalent to the Latin scientia, this is
debatable; furthermore, neither conveyed the same meanings as our modern word ‘science’.
In the treatment of ‘scientific’ writings which follows, I have chosen
to include works by authors –​many of whom are usually considered to
have been philosophers –​who sought to explain nature (physis) and the
physical world. I have also included mathematical writers, since many
in antiquity who thought about such matters –​including such diverse
thinkers as Aristotle and Claudius Ptolemy –​considered mathematics
(mathematikē), like philosophy (philosophia), to be a branch of theoretical knowledge (theoretikē epistēmē). However, readers should be aware that
ancient understandings of what constituted mathematics and philosophy
do not map onto modern conceptions in a straightforward manner. Just as
today there is not exact unanimity regarding what constitutes science and
scientific practice, with some things being labelled as ‘pseudo-​science’ or
‘crank science’, so in antiquity people were not unanimous about the categories in which they placed those pursuits which might today fall under
the historian’s rubric of ‘scientific’.6 As G.E.R. Lloyd has noted, ‘a distinction between “philosophers” and “scientists” is in general hard to draw in
Greco-​Roman antiquity. Natural science is a domain that straddles both
those disciplines as we perceive them’.7 My working definition of ‘science’
is: ‘an attempt to understand and explain physical phenomena’.8 As with
‘scientific’, no one term, either in ancient Greek or in Latin, carried the
same meaning of the modern English word ‘science’, with its primary reference to knowledge of the physical world. The Greek word philosophia
means ‘love of wisdom’; ‘natural philosophy’ can be understood as ‘love of
wisdom about nature (physis)’.
While amongst the ancient authors concerned with physical phenomena the meaning of epistēmē (‘knowledge’) could be variously understood
and interpreted, Aristotle’s view that epistēmē depended on knowledge of
causes was very influential, not only in antiquity, but in later periods as
well. According to Aristotle (Metaphysics 1025b25–​6), epistēmē comprises
On the topic of the classification of knowledge and expertise, see Tatarkiewicz 1963; Kühnert 1961.
Lloyd 1991: 301, emphasis in the original. He goes on to distinguish (on p. 302) ‘between those who
engaged in detailed empirical work, and those who did not’.
8
I use this working definition with the recognition that the meaning of ‘natural’ is, like that of ‘science’, not unproblematic and varies in different contexts.
6
7
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9
Describing Texts
9
three types of knowledge: the practical, productive and theoretical.
Theoretical epistēmē can be further divided into three areas (Metaph.
1026a6–​
23): mathematics, physics and theology (metaphysics). Some
types of epistēmē, as defined by Aristotle, have correspondences with what
is understood as ‘science’ in later periods. With this in mind, I sometimes
use the term ‘natural philosophy’ to refer to efforts to explain physical phenomena. Because ancient Greek philosophers used the word physis to refer
to nature, and physikoi to refer to people who studied nature, I sometimes
use the word ‘physics’ as an equivalent of the term ‘natural philosophy’.
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Describing Texts
There are many issues involved in the identification and description of
different textual formats, types or genres. As has already been noted,
these are large topics which cannot be dealt with fully here; nor can all
the controversial questions be easily resolved. Nevertheless, it is important to recognise that the categories invoked are not entirely clear-​cut
and unproblematic. There are also issues encountered in identifying
and describing texts as ‘scientific’ and/​or ‘mathematical’, as it cannot
be assumed that there is unanimity in understanding these descriptors
as they are applied to modes of thinking, practice and texts. There is a
danger of applying such terms ahistorically by suggesting that the modern usages map onto those of ancient authors and practitioners. Modern
readers do not always agree as to what characterises a mathematical text;
ancient authors who wrote about mathematics did not always agree on
its definition either.
A certain style of presentation, with a systematic format, is often
regarded by modern readers as the paradigm of ancient Greek scientific
and mathematical texts. As Morris R. Cohen and I.E. Drabkin noted on
the first page of their Source Book in Greek Science, ‘the evidence indicates
that the ideal of rigorously deductive proof, the method of developing a
subject by a chain of theorems based on definitions, axioms, and postulates, and the constant striving for complete generality and abstraction are
the specific contributions of the Greeks’.9 This view of the characteristic
style of Greek scientific explanation and mathematical thought has deep
roots, going back to Aristotle in the Posterior Analytics, and to Plato before
him. The influence of the ‘axiomatic-​deductive system’ was powerful;
9
Cohen and Drabkin 1948: 1. Of course, they are focusing on textual evidence; not much archaeological or material evidence survives.
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10
Introduction
significantly, Isaac Newton adopted an axiomatic-​deductive style of presentation for his Principia Mathematica.10
The ideas and practices of ancient Greek scientific and mathematical
work were presented in a wide variety of types of texts, for the most part
in prose formats, but occasionally –​as we will see in what follows –​in
poems. Some of these texts were written by physikoi and mathematikoi,
men who presented themselves and were recognised by others as ‘physicists’ (or ‘natural philosophers’) and ‘mathematicians’. However, many of
the texts that we would identify as ‘scientific’ or ‘mathematical’ were written by individuals who were not themselves experts, some of whom might
have been described (in a different time and place) as ‘popularisers’.11
Even though there are numerous texts whose forms would today be
regarded as appropriate and usual for scientific work, such as teaching
texts and manuals, many ancient writings that are thought to be ‘scientific’ look very different from modern presentations of science and mathematics. Examples of Greco-​Roman writing on scientific and mathematical
topics are more rich and varied than we may have expected. This diversity
demonstrates that a ‘scientific’ text is not always the same sort of thing,
and identifying what characterises a ‘scientific’, mathematical or technical text may not be entirely straightforward. The formal diversity of these
texts points to a more nuanced understanding of the place of scientific
thinking in Greco-​Roman antiquity, suggesting that it is not always simple to identify ‘science’, nor is it easy to pigeon-​hole particular written
works. Ultimately, broad generalisations may prove of very limited use.
The aims of the author of a text and its intended function will often be
best understood by investigating its specific historical context; this is an
important undercurrent throughout this volume.
In the chapters that follow, several significant genres or types of scientific texts are treated in some detail. Here it seems appropriate to examine
some examples of Greek terminology and their relationship to modern
descriptions.
For example, many ancient scientific and technical texts are referred
to as ‘treatises’ by modern scholars, yet it is not always clear exactly what
this term means. In the modern period, prose is the dominant –​even
expected –​form of scientific communication. Greek and Roman authors
used prose as an important format for many scientific, medical and technical writings, even though it was not their only option. Some fifty years
10
11
See Clarke 2011: 266, on Newton’s Principia and axiomatic-​deductive presentation.
See, for example, Cuomo 2001: 73–​79 on non-​specialist authors writing about mathematics.
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Describing Texts
11
ago, Charles Kahn argued that the first Greek prose treatise was written
in the sixth century BCE by Anaximander (Kahn 1960: 6–​7 and 240). He
regards Anaximander’s Peri physeōs (On nature) as having been the first
example of ‘a new genre: the treatise peri physeōs’ (Kahn 2003: 145; see also
Graham 2010: 45, who agrees with Kahn). However, the question of what
constitutes a ‘treatise’ remains to be addressed.
Prose texts had various formats; the dialogue was particularly
favoured by Plato, but relatively few ‘scientific’ dialogues were composed in ancient Greece and Rome.12 Other prose formats important in
Greco-​Roman antiquity are discussed in this volume, including the letter, commentary and encyclopaedia. Considering formal features, Philip
van der Eijk has pointed to a ‘less well defined species of text’ that is
‘sometimes referred to in modern terms as “treatise” ’. The formal structure implied here does not fit into recognised ancient categories such
as dialogue (dialogos), letter (epistolē), handbooks (technai), introductions (eisagōgai) or commentaries (referred to as hupomnēmata, by some
ancient authors); as van der Eijk notes, the style of ‘treatises’ may be
regarded as ‘less elaborate’ (van der Eijk 1997: 89). If we accept the lack
of a distinct form which is attributable to ‘treatises’, it may make sense
to read ‘treatise’ in these contexts as referring simply to a written ‘work’
rather than to a particular genre.
Kahn has posited that there was a tradition of technical prose writing,
dating back to the invention of writing in Greece and the East, which
included notes and memoranda used for the practice, improvement and
teaching of technical work, such as astronomy, geometry, music, architecture and sculpture (Kahn 2003: 151); much of this writing would have
been very specialised, probably incomprehensible to those not in the
appropriate field. Acknowledging that there is not much evidence of such
prose works, Kahn nevertheless advised readers ‘to take into account the
importance of what happens not to have been preserved’, cautioning that
the unknown and absent should not be mistaken for what never existed
(Kahn 2003: 151).13 Such notes may have been the first prose writings on
technical topics in Greco-​Roman antiquity, and would have included
various sorts of hupomnēmata (here, to be understood as ‘notes’ or memoranda), including –​perhaps –​those that were aphoristic and memorable,
useful to practitioners and specialists in a particular technical field.
As was noted earlier, the dialogue was an important vehicle for presenting scientific explanations in
the early modern period, as attested by the writings of Galileo Galilei.
13
Nevertheless, in the absence of evidence, Kahn’s suggestion remains speculative.
12
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12
Introduction
Portions of the medical writings found in the so-​called Hippocratic corpus are amongst the earliest prose works in ancient Greece (Dean-​Jones
2003: 112).14 The works attributed to Hippocrates (most of which were not
actually composed by him) show a capacity for accurate and concise statement, and are often ‘aphoristic’ (as, for example, recipes), that is, short,
concise and often memorable statements. The first example in the book
known as the Aphorisms in the Hippocratic Corpus is indicative of this
type of text: ‘Life is short, the Art long, opportunity fleeting, experiment
treacherous, judgment difficult. The physician must be ready, not only to
do his duty himself, but also to secure the co-​operation of the patient, of
the attendants and of externals’.15
Elizabeth Craik has drawn attention to the compilations of aphorisms
within the Hippocratic corpus, noting that they are of the type designated
by ancient commentators as hupomnēmata (‘notes’) in contrast to another
type of text, the sungramma or suntagma (terms often translated as ‘treatise’) (Craik 2006: 335).16 The term hupomnēmata can refer to notes that
may serve as aides-​mémoire.17
Kahn argued that a new form of technical literature, the ‘Ionian prose
treatise’ –​associated with the ‘new’ science undertaken by the Ionian
philosophers –​emerged from the assumed, older tradition of technical
memoranda (Kahn 2003: 152). A new type of work, which we today sometimes refer to as the treatise, may have reached a wider audience than the
hupomnēmata would have done, through the extended presentation of the
topics covered.18
Given the power of poetry in the ancient Greco-​Roman world, and
the authority it conveyed, as exemplified by the canonical status of the
Homeric and Hesiodic poems, the use of prose –​that is, doing without metre and rhythm –​begs for explanation. While it may have been
assumed in the archaic period that metre was most appropriate for anything worthy of preservation, from the middle of the sixth century prose
These texts, while regarded by modern scholars as being anonymously authored, were associated
with Hippocrates in antiquity; this association may be regarded as a sort of ‘branding’ or ‘badging’.
See also Totelin 2004.
15
[Hippocrates of Cos] Aphorisms 1.1, trans. Jones 1931: 98–​99.
16
Craik 2006: 342–​344 also discusses the metre of some aphorisms, their mnemonic value, and relation to temple and to ‘scientific’ medicine.
17
However, the use of the term hupomnēmata is not uniform across authors and periods.
18
Furthermore, early ‘treatises’ –​or more extended treatments –​may have been read aloud. Kahn
2003: 152; see also Thomas 2003: 173–​180. The oral presentation of written texts is a recurring
feature of Greek and Roman culture; a number of scholars have suggested that Aristotle’s ‘treatises’
began life as lectures; see Taub 2008a: 18.
14
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Describing Texts
13
literature began to be produced, breaking free from any assumption of
the greater value and utility of poetic forms.19 Indeed, the presentation
of a text in a prose format which is meant to be shared with others has
been understood by some as signalling a particularly significant cultural
shift. The written preservation and transmission of some poems may have
been secondary to their oral composition and performance; significantly,
the archaic Homeric poems are understood to have been part of an oral
‘tradition’.20 In contrast, prose is normally regarded as being closely linked
to literacy and to the culture of writing texts. Simon Goldhill has argued
that in the fifth century BCE prose becomes ‘the medium for authoritative expression, the expression of power’ (Goldhill 2002: 5; cf. Kurke
2010: for example, 15, 47–​48, on experiments and ‘generic mixtures’). Of
course, poetry did not suddenly disappear; on the contrary, it continued
to wield great force. Yet, from a relatively early period, prose formats were
important for the communication of scientific ideas and methods. And
from the fifth century, prose was in the ascendancy as the primary mode
of discourse conveying authority, particularly in certain fields.
Some of the earliest writers of Greek prose may have been living in
Ionia during the sixth century BCE. Thales of Miletus is traditionally
regarded as the first to have philosophised about nature, but it is not clear
whether or not he wrote any works, or in what form they may have been
presented. Even Diogenes Laertius, in his lengthy work on the Lives of
Eminent Philosophers, expresses some scepticism regarding Thales’ authorship of any work (1: 23). Anaximander of Miletus is traditionally regarded
as a ‘student’ of Thales; only fragments of his work Peri physeōs (On nature)
survive. As noted earlier, Kahn argued that Anaximander’s writing is the
earliest example of a new genre: the treatise Peri physeōs was characterised both by its subject matter (on ‘nature’) and the order of topics discussed, beginning with first principles and the origin of heaven and earth,
and ending with a discussion of human beings (Kahn 1960: 6–​7 and 240;
Kahn 2003: 145).21 But is the term ‘treatise’ helpful in understanding the
character of Anaximander’s writing?
Thomas 1992: 64–​65; also Andersen 1987. Thomas 1992: 57–​61 depicted the diverse uses of writing
in the eighth and seventh centuries, including examples of graffiti to mark ownership and protect
objects.
20
The scholarship on traditional oral poetry is vast. A good starting point is with the Parry-​Lord
thesis: see Parry 1971, Lord 1960, and Thomas 1992: 29–​51.
21
By this definition, the monologic section offered by Timaeus in Plato’s dialogue of that name
might qualify as a treatise peri physeōs.
19
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14
Introduction
The attraction of the term ‘treatise’ may be partly motivated by the fact
that the prose treatise is an important form of modern scientific communication, and one with which modern readers are very familiar. The
English word ‘treatise’ refers to a written work dealing formally and systematically with a subject.22 However, ‘treatise’ is a modern term, and it
is not entirely clear that there was an entirely equivalent term used by
ancient Greek and Latin authors. Even a brief foray into the scholarly literature on scientific, medical and technical texts reveals references to a
wide range of writings with different specific formats as ‘treatises’, suggesting that there is no characteristic form which defines the category ‘treatise’; nor is the term applied in a homogeneous way. In actual usage, the
word ‘treatise’ does not seem to relate to particular formal features, but
often seems to be understood as a general term for a piece of writing dealing with a specified subject (such as physis).
Can the term ‘treatise’ be used to refer to a genre of text recognised in
antiquity? While the term ‘treatise’ is often used to refer to a ‘work’ or
‘text’ in a general sense, the term also has a particular historical resonance
and set of connotations in English, some of which are bound up with the
history of philosophy and scientific discourse.23 The Greek terms which
are often translated as ‘treatise’ –​such as logos, pragmateia, sungramma,
sungraphē, suntagma –​cannot be precisely translated by that term, because
the English word ‘treatise’ conveys historically influenced meanings and
expectations which do not neatly map onto the ancient Greek and Roman
contexts in which the ancient works were written. Perhaps surprisingly
to modern sensibilities –​and further complicating the matter –​the
idea that a treatise need not be a prose work was voiced by Kahn, who
described both poetical and prose examples of treatises peri physeōs (On
nature), pointing to Parmenides, Empedocles and Xenophanes as having
used verse as their medium (Kahn 2003: 145; Palmer 2009: 350 refers to
Parmenides’ poem as a ‘treatise’). The character of such ‘treatises’ did not
rely on the ‘in metre’ (emmetros) versus ‘without metre’ (aneu metrou) distinction, but was exemplified by the subject (physis) and the order of topics
The first definition for ‘treatise’ in the OED is: ‘A book or writing which treats of some particular
subject; commonly (in mod. use always), one containing a formal or methodical discussion or
exposition of the principles of the subject; formerly more widely used for a literary work in general’. Intriguingly, the online version notes that ‘This entry has not yet been fully updated (first
published 1914)’. Accessed 18 May 2015: www.oed.com/​view/​Entry/​205390?rskey=9b3QH3&result
=1#eid.
23
David Hume (1711–​1776), for instance, used both treatise and dialogue in titles of his own works,
such as A Treatise of Human Nature (1739–1740) and Dialogues concerning Natural Religion (1779,
published posthumously).
22
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Describing Texts
15
discussed. Kahn cites Hesiod’s Theogony as sharing, in part, the same order
as a treatise peri physeōs, crediting Anaximander with having produced a
work which he describes as ‘the prototype for a long-​lived literary genre,
the prose treatise peri physeōs’ (Kahn 2003: 145–​146). For Kahn, it is the
content that defines the peri physeōs treatise, rather than formal features
such as metre or prose.24
It may have been the case that ancient writers (and their readers) recognised a category of discourse concerned with a particular topic –​namely
peri physeōs –​that included what are in our terms very disparate formats: prose and poetry. However, it is not clear that the modern English
term ‘treatise’ can stretch to include poetry; certainly, the modern expectation of ‘treatise’ valorises prose formats. Although it may be important to
note that different types of texts were recognisable as peri physeōs, it may
not be helpful to label them all ‘treatises’, in our terms. The application
of the term ‘genre’ to ‘treatise’ implies that treatises share some formal
features, not only subject matter. Otherwise, we might well ask the question: Is Lucretius’ De rerum natura a treatise?
A functional definition of a treatise peri physeōs as attempting an ordered
account of a physical subject sets aside questions relating to formal and
stylistic features of texts and embraces the possibility that such ‘treatises’
may have been presented in metrical or in dialogic formats, as well as in
less elegantly crafted prose forms. While a possible genre of ‘treatise’ will
not be discussed in further detail here, there are a number of Greek works,
including those by Aristotle and Theophrastus, which can serve as examples of an ambition to provide a systematic discussion of a particular topic.
The usefulness of referring to ancient types of texts (including poems and
dialogues) concerned with the physical world as ‘treatises’ remains unclear,
even while we may acknowledge that such works may have shared some
features with other writings peri physeōs.
In the fifth and fourth centuries BCE, and later, a wide variety of prose
texts were written on a broad range of subjects by various authors; many
of these were rather technical. Franz Dirlmeier has suggested that the
Greek word pragmateia refers to a written ‘work’; his understanding of
what constitutes a ‘work’ seems to coincide largely with common modern
24
In the modern period there is an expectation that ‘treatise’ refers to a work in prose; cf., however, C.S. Lewis’ self-​claimed invention of the term ‘treatise poem’, cited in the OED, which also
cites another example from the Times Literary Supplement in 1980 (www.oed.com/​view/​Entry/​
205390?rskey=06o8p4&result=1&isAdvanced=false#eid; accessed 31 August 2015). Kahn 2003: 142
accepts the ancient view that Pherecydes’ (fl. 544–​541 BCE) work on theogony is the oldest Greek
prose ‘book’.
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16
Introduction
English usage of the term ‘treatise’.25 Dirlmeier was interested in issues
related to oral and written discourse, and argued that the appearance of
the systematic, thorough written work marked a development in styles of
presenting philosophy via written texts. In his view, the term pragmateia
signals work conveyed through a written text; he sees a shift from the
dialogues of Plato, with their sense of oral exchange, to the pragmateiai of
Aristotle.26
However, it is not clear that the term pragmateia refers to a particular
text type,27 format, or genre (if we understand that term to encompass
form as well as content). Dirlmeier suggests that the term is a synonym
for the written logos, indicating in particular serious, painstaking, almost
professional mental activity,28 but the word has other meanings as well,
sometimes referring to a field of study or a practical endeavour.29 In fact,
the term pragmateia may refer to an activity as well as to a (written) product resulting from that activity. Dirlmeier suggested that the term ‘work’
(German Arbeit) reflects the meaning of pragmateia (Dirlmeier 1962: 10).
In both English and German, work (Arbeit) can refer to an activity or
occupation (even a profession), and also to the products –​be they material or intellectual –​of that activity (cf. Immerwahr 1960 on the use of the
word ergon in Homer, Herodotus and Thucydides). We refer to the ‘works’
of an author, recognising that intellectual and other work was required
for its production. We also refer to an author’s ‘treatment’ of a subject;
the word ‘treatment’ may indicate a finished product (such as a written
‘work’), and also the process of treating the topic or question which is the
subject of that treatment, or work. This duality of connotation, referring
to both a product and the activity which results in that product, may be
significant in understanding some uses of pragmateia (see Fischer 2013).
Dirlmeier 1962: 10, where ‘Arbeit’ can refer to a ‘written work’. Kahn 2003: 148 has suggested that
syngraphē was the ‘normal term for a prose treatise’; cf. Dover 1997: 183–​184, who does not use the
term ‘treatise’ as one of many possible definitions he offers of sungraphē. LSJ suggests that the term
refers simply to what is written (for example, a narrative or a history).
26
However, in this context it is worth noting that some scholars, including Föllinger 2012, see dialogical elements in Aristotle’s extant writings.
27
Using Werlich’s term (1976: 39–​41); see also Taatsavinen 2001: 140.
28
Dirlmeier 1962: 10 ‘πραγματεíα ein Synonym für den geschriebenen Logos ist und im besonderen
die ernsthafte, mühevolle, ja geradezu berufliche geistige Betätigung anzeigt’. Lengen 2002 argues
that Aristotelian pragmateiai do not all have same structure; see, for example, pp. 176–​187 and
223–​231.
29
LSJ offers as definitions ‘occupation’ and ‘business’, citing Plato Theaetetus 161e referring to ‘the
business of dialectic’ and Aristotle Rhetoric 1354b24 to ‘the business of oratory’. See also Fischer
2013: 96–​97.
25
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Chapter 1: Poetry
17
Aristotle associates the term pragmateia with its purpose at the same time
as referring to the text as a product (as at Topics 1.1 101a26, cf. 100a18).
While other terms, including sungraphē, sungramma and suntagma,
refer to written texts, the word pragmateia is often used in scientific contexts (for example, referring to works on medicine, geography and music),
and suggests a preoccupation with a specific branch of theory or practice.
The term pragmateia does not seem to connote a particular style or format
of writing, but rather a specialist and intellectualised approach concerned
with a particular subject and related to specialised activities and practices,
which may be conducted in a context of research and/​or teaching (Fischer
2013: esp. 111–​112; cf. Dirlmeier 1962: 9–​11).
The term pragmateia can be applied to works in different literary formats, but formal characteristics are not the only features that define a
genre. Indeed, as was noted earlier, ‘genre’ can be understood as ‘a recurring type or category of text, as defined by structural, thematic and/​or
functional criteria’ (Duff 2000: xiii; cf. Swales 1990: 45–​58). The term
pragmateia can be translated by the word ‘work’ to refer to the sort of written discourse that has the function to provide an account concerned with
a particular subject, without the text adhering strictly to specific structural
features. Significantly for us, some ancient pragmateiai dealt with topics
understood by modern readers to be ‘scientific’.
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Chapter Outline
Each of the following chapters treats a particular genre, concentrating on
a small number of target texts providing ‘case studies’. Sub-​themes which
appear throughout the volume include the interplay between oral and literary culture reflected in many of the genres under consideration, and
the ways in which particular genres offer information about intellectual
communities in the Greco-​Roman world, particularly those concerned
with mathematics and explaining the physical world. For example, letters often give specific evidence of the relationships between the author
and intended readers, including patrons, followers and members of correspondence networks; in particular, letters survive between members of
the Greek mathematical community.
Chapter 1: Poetry
Poetry comported a special authority within the Greco-​Roman world,
even in texts devoted to scientific topics. Chapter 1 considers poems which
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18
Introduction
explain physical phenomena or present mathematical problems. Scientific
and technical writings were by no means confined to prose formats in
Greco-​Roman antiquity; in fact, a number of poems that reached very
wide audiences in antiquity were on technical, scientific subjects. The oldest surviving Greek texts are epic poems; some of the earliest extant philosophical texts are also poetry.
The earliest ancient Greek writings –​the Homeric and Hesiodic
poems –​were in metre, and, in the later Greco-​Roman world, poetry
was a particularly authoritative and respected format, adopted for a range
of subjects and audiences. Poetry was an especially powerful format for
ancient Greek and Latin philosophical and scientific texts.
Today, no scientist would choose to convey authority and expertise
through publishing work in poetry: prose formats are the genres of choice
for modern scientific communication. In sharp contrast to this, poetry must
be included as an important form of scientific discourse in antiquity. Certain
poems, for example Aratus’ Phaenomena and Lucretius’ De rerum natura,
would surely be on everyone’s top ten list of important poems written about
the physical world in antiquity. Perhaps surprisingly, a number of poems
presenting mathematical problems survive; I particularly consider these.
While the poems of Lucretius and Aratus are relatively well known,
mathematical epigrams (for example, those preserved in the Greek
Anthology) have been little studied and remain to be explained, from the
mathematical as well as literary and more broadly cultural vantage points.
Many of these poems display intriguing intertextualities with canonical
authors (including Hesiod and Plato), and they require further attention
in order for us to begin to understand their place in the history of Greek
mathematics. Since these mathematical problem-​poems preserved in the
Greek Anthology are epigrams, we should consider the significance of that
particular form. Significantly, ‘poetry’ was not a homogeneous category in
antiquity. The ancient authors who wrote on literary texts differentiated
between those composed in metre and those that were not; poetry was
not a genre itself, but a category comprising different genres of poetry,
including, for example, epic, elegy and epigram. As we will see, the distinctive features of epigram are particularly well-​suited to the presentation
of mathematical problems.
Chapter 2: Letter
Various sorts of letters were written and circulated in antiquity; not
all letters were intended for private purposes. Some, like the letters
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Chapter 3: Encyclopaedia
19
published today in newspapers, were clearly meant for a wider readership. Some were not ‘real’ letters, but were attributed to fictitious
authors, or spuriously credited to famous individuals, such as Plato.
Letters were used for various purposes, including for giving philosophical advice and instruction; examples include the three letters of
Epicurus (341–​270 BCE) preserved much later in the ‘Life of Epicurus’
by Diogenes Laertius (probably first half of the third century CE).
Other letters contained technical or scholarly work on mathematical,
mechanical and medical topics. A number of letters written by ancient
Greek mathematicians survive, indicating that letter writing was a useful mode of communication for them; for example, Eratosthenes of
Cyrene (ca. 285–​194 BCE), who worked in Alexandria, was the recipient
of letters from Archimedes (ca. 287–​212 or 211 BCE), living in Syracuse.
Some of the letters are clearly communications between friends and colleagues, and have almost the flavour of a conversation; others, particularly the letters of Epicurus, were intended to be instructional, serving
as brief summaries of his views for his students and followers. During
the early modern period, dedicatory letters were often used to advertise
patronage, but the practice dates to antiquity. In a letter attributed to
Eratosthenes, directed to his royal patron Ptolemy III, the solution to a
geometrical problem is announced. This particularly rich text is a focal
point of this chapter.
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Chapter 3: Encyclopaedia
Gaius Plinius Secundus (known to us as Pliny the Elder) was the author
of a remarkable work, the thirty-​seven-​book Historia Naturalis or Natural
History (=‘Enquiry into Nature’), which holds an important place in several fields of intellectual history, not least in history of science. The Natural
History is usually referred to as an ‘encyclopaedia’. It is the only one of
Pliny’s works that survives, and is a particularly interesting case, because,
while other encyclopaedic writings may have been produced in antiquity
(depending on how we define ‘encyclopaedia’), the Natural History is the
only one to have survived in its entirety. The Natural History stands at the
beginning of a tradition that developed and flourished primarily in later
periods. This chapter considers what it means to be an ‘encyclopaedia’,
as well as looking at links between Pliny’s work and Roman imperialism,
concentrating on Pliny’s treatment of ‘scientific’ material, arguing that his
approach is both ‘encyclopaedic’ and imperial, whilst being characteristically ‘Roman’.
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20
Introduction
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Chapter 4: Commentary
As part of the developing literary culture of the ‘book’,30 those working
within didactic and scholarly traditions produced a variety of handbooks,
epitomes and commentaries. Prose works and poetry (especially the
Homeric poems) were both the subjects of commentaries; philosophical
as well as mathematical texts were often the topic of such treatments. The
works of Aristotle particularly attracted commentators, perhaps partly
because of difficulties in understanding them (due in some degree to the
nature of the corpus in which they were transmitted (see, e.g., Bodéüs
1993: 10–​11).
While commentaries on various types of texts were important from the
third century BCE, the commentary was a particularly significant genre
for writing about scientific topics in the later period. The sixth century
CE was an especially important period for the production and use of
commentaries, and Alexandria was an important site for this tradition.
The commentary continued to be a key genre for the medieval period,
and flourished in Arabic, Hebrew and Latin.
Typically, a passage from the ancient source is quoted and then a comment appended, which may be of any length, from one sentence to several (modern) pages. And, the commentator may refer to other works,
by the author of the target text or other writers. Even as commentaries
encouraged a close engagement with particular texts, they often served as
vehicles for the presentation of the commentator’s own ideas. The commentary in some ways represents the culmination of the movement from
oral forms of discourse to the establishment of new written traditions,
which are in themselves text-​focused. However, commentaries were not
simply silent texts: they often were used within teaching contexts in which
lectures and discussion took place; Porphyry, in his account of the life of
his teacher Plotinus, reports that ‘in the meetings of the school he used
to have the commentaries read’ (14.11–​12; trans. Armstrong 1966: 41). A
significant number of important ancient commentaries on scientific and
mathematical works survive, including several on Aristotle’s writings, as
well as others on mathematical works, such as Proclus’ commentary on
Euclid. Three ancient commentaries on Aristotle’s Meteorology survive, at
least in part; these will be discussed in some detail here, as exemplars of
the genre.
30
See Knox 1989, Easterling 1989.
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Chapter 5: Biography
21
Chapter 5: Biography
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Biography was not a clearly demarcated genre for ancient Greeks and
Romans. The boundaries with other genres, including the eulogies or
encomia used to praise heroes and important citizens, are not distinct and
may be somewhat artificial. The bios (‘life’; plural = bioi) as an account or
celebration of a particular life can be found in a range of ancient writings
and may also include a discussion of an individual’s opinions (or doxai);
such accounts often carried an ethical or religious message. While biography itself was not a rigidly defined genre for the Greeks and Romans, the
bioi are linked by the desire to celebrate individuals.
Numerous bioi of ancient philosophers survive. One prominent subject
is Pythagoras, who holds a special place in the history of science, since
many later natural philosophers, mathematicians and scientists claimed
descent from his intellectual line. In the twentieth century, Einstein
argued that a scientist may even appear ‘Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research’.31 Three ancient accounts of the life
of Pythagoras survive from late antiquity; they can all be loosely dated
to about the third century CE, and were written by Diogenes Laertius,
Porphyry and Iamblichus. Taken together, these ‘lives’ allow us to explore
various strands of the ancient portrayals of the lives of individuals significant in histories of science, displaying formal resemblances to other
important ancient texts, notably the Christian gospels.
31
For the complete passage, see ‘Reply to Criticisms’, in Einstein 1949: 684; cited by Kahn 2001: 172.
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