Diels–Kranz numbering

From Wikipedia, the free encyclopedia
Hermann Alexander Diels

Diels–Kranz (DK) numbering is the standard system for referencing the works of the ancient Greek pre-Socratic philosophers, based on the collection of quotations from and reports of their work, Die Fragmente der Vorsokratiker (The Fragments of the Pre-Socratics), by Hermann Alexander Diels. The Fragmente was first published in 1903, was later revised and expanded three times by Diels, and was finally revised in a fifth edition (1934–7) by Walther Kranz and again in a sixth edition (1952). In Diels–Kranz, each passage, or item, is assigned a number which is used to uniquely identify the ancient personality with which it is concerned, and the type of item given. Diels–Kranz is used in academia to cite pre-Socratic philosophers, and the system also encompasses Sophists and pre-Homeric poets such as Orpheus.

Stephanus pagination is the comparable system for referring to Plato, and Bekker numbering is the comparable system for referring to Aristotle.


The works of the pre-Socratics have not survived extant to the present day. Our knowledge of them exists only through references in the works of later philosophers (known as doxography) in the form of quotations and paraphrases. For example, our knowledge of Thales of Miletus comes largely from the works of Aristotle, who lived centuries after him. Another interesting example of such a source is Hippolytus of Rome, whose polemic Refutation of All Heresies is a source of many direct quotations of Heraclitus as well as of other philosophers, thereby perpetuating the work of those he was refuting.

These quotations, paraphrases and other references to pre-Socratic philosophers were collected by Diels and Kranz in their book, which became a standard text in modern pre-Socratic education and scholarship. Because of its influence, Diels–Kranz numbering became the standard way of referencing the material: in literature, conferences, and even in conversation.

Numbering system[edit]

The number corresponding to an item was made up of three parts:

  1. a number representing the personality the item is concerned with - this number is also the chapter number in the Fragmente. For example, "11", also the eleventh chapter of the Fragmente, refers to Thales.
  2. the letter A, B, or C, corresponding to the type of item given, respectively:
    A: Testimonia: These are accounts of the authors' life and doctrines. Testimonia include commentaries on the works of the pre-Socratics and accounts of their lives and of their philosophical views.
    B: Ipsissima Verba: Literally translated to "exact words", and sometimes also termed "fragments", these are items containing exact words of the author in the form of quotations in later works.
    C: Imitations: Works which take the author as a model.[1]
  3. a number representing the position of the particular item in its chapter. For example:

Why, take the case of Thales, Theodorus. While he was studying the stars and looking upwards, he fell into a pit, and a neat, witty Thracian servant girl jeered at him, they say, because he was so eager to know the things in the sky that he could not see what was there before him at his very feet.[2]

The above text has a DK number of 11A9, since it refers to Thales who is, as mentioned above, chapter 11's subject. The source is Theaetetus (one of Plato's dialogues), and gives an account of Thales' life, hence it is a testimonium, represented by the letter A. Finally, it is the ninth item in its chapter, giving it the overall number of DK 11A9.

Sometimes, the chapter (personality) number may simply be replaced by the name, which can be helpful in cases where the former is the same as the passage number, to avoid ambiguity. For example:

Those who seek for gold dig up much earth and find a little.[3]

Rather than "22B22" the above may also instead be referred to as "Heraclitus B22" as it is a direct transmission of the words of Heraclitus (thus, B) and is the 22nd item in the chapter about Heraclitus (whose chapter number is 22) in the Fragmente.[4]


The following table gives the Diels–Kranz numbering of Pre-Socratic philosophers.[5][6][7][8][a] Note that the numbering scheme presented is that of the fifth edition of Die Fragmente der Vorsokratiker, the first to be revised by Kranz. The fifth edition's numbering is the scheme which has since gained the most traction in modern Pre-Socratic scholarship, and it is the one used consistently throughout this article. It should not be confused with the numberings given in other versions, which changed frequently depending on the particular edition of the Fragmente.[b][9]

Most entries (78) are concerned with a single, named individual, while the remaining minority of entries (12) have more complex context. Of these latter, eight (10, 19, 39, 46, 53-56) are each concerned with groups of named personalities, who typically have a clear relationship of some kind to justify their association in each entry. Two entries (58, 79) are devoted not to individuals, but to schools of thought (Pythagoreanism and Sophism), and the last two (89, 90) reproduce contemporaneous anonymous texts. Although "the Seven Sages of Greece" implies a clearly defined set of seven people, historical disagreement renders intractable the problem of exactly who they were, with multiple sources suggesting several different candidates. If one takes the Seven Sages as a group of seven and includes the later Iamblichus, Diels–Kranz encompasses 106 named personalities and two anonymous authors. The chapter on Sophism is concerned with the named sophists who take up most of the rest of the scheme, and per Freeman with regard to the chapter on Pythagoreanism, a catalogue due to Iamblichus lists 218 named men and 17 named women as Pythagoreans, along with other probable, anonymous adherents.[10]

In several cases, the personalities listed are so obscure that they are merely mentioned by name in other sources, commonly with hints as to their geographical and philosophical associations, and without even surviving paraphrases of any of their ideas, or what they might have written. That is, these more obscure personalities survive in the historical record only as names cited by others, and so came to be included in Diels–Kranz for the sake of scholarly completeness.

1 Orpheus 31 Empedocles 61 Metrodorus
2 Musaeus 32 Menestor 62 Cleidemus
3 Epimenides 33 Xuthus 63 Idaeus
4 Hesiod 34 Boidas 64 Diogenes
5 Phocus 35 Thrasyalces 65 Cratylus
6 Cleostratus 36 Ion 66 Antisthenes
7 Pherecydes 37 Damon 67 Leucippus
8 Theagenes 38 Hippon 68 Democritus
9 Acusilaus 39 Phaleas and Hippodamus 69 Nessas
10 The Seven Sages of Greece:
Bias, Chilon, Cleobulus,
Periander, Pittacus, Solon, and Thales
40 Polycleitus 70 Metrodorus
11 Thales 41 Oenopides 71 Diogenes
12 Anaximander 42 Hippocrates 72 Anaxarchus
13 Anaximenes 43 Theodorus 73 Hecataeus
14 Pythagoras 44 Philolaus 74 Apollodorus
15 Cercops 45 Eurytus 75 Nausiphanes
16 Petron 46 Archippus, Lysis, and Opsimus 76 Diotimus
17 Brontinus 47 Archytas 77 Bion
18 Hippasos 48 Ocellus 78 Bolus
19 Calliphon and Democedes 49 Timaeus 79 'Sophist': Name and Concept
20 Parmeniscus 50 Hicetas 80 Protagoras
21 Xenophanes 51 Ecphantus 81 Xeniades
22 Heraclitus 52 Xenophilus 82 Gorgias
23 Epicharmus 53 Diocles, Echecrates,
Polymnastus, Phanton, and Arion
83 Licophron
24 Alcmaeon 54 Prorus, Amyclas, and Cleinias 84 Prodicus
25 Iccus 55 Damon and Phintias 85 Thrasymachus
26 Paron 56 Simus, Myonides, and Euphranor 86 Hippias
27 Ameinias 57 Lycon 87 Antiphon
28 Parmenides 58 The Pythagorean School 88 Critias
29 Zeno 59 Anaxagoras 89 The Anonymous Writer
quoted by Iamblichus
30 Melissus 60 Archelaus 90 Twofold Arguments

See also[edit]


  1. ^ Kathleen Freeman adopted the fifth edition's numberings for both her Companion and Ancilla, while also reproducing the fourth edition's numberings in parentheses. A matching online version of the Ancilla's table of contents is available at Sacred Texts, for reference. Later, Robin Waterfield prepared a new Pre-Socratic reader, which uses an entirely different scheme unrelated to Diels–Kranz. Nevertheless, Waterfield gives a partial concordance of his own scheme with that of Diels–Kranz, and the partial DK numbering given by Waterfield matches the fifth-edition Fragmente numbering used by Freeman, so far as it is taken in Waterfield's case.
  2. ^ For one example of a variant edition and numbering scheme, see ix-x in the following link.


  1. ^ "IEP: "Diels–Kranz Numbering System"". www.iep.utm.edu. Retrieved 2017-08-30.
  2. ^ "Plato, Theaetetus, page 174". www.perseus.tufts.edu. Retrieved 2017-08-30.
  3. ^ Fragments of Heraclitus  – via Wikisource.
  4. ^ "Heraclitus". www.iep.utm.edu. Retrieved 2017-08-30.
  5. ^ Freeman, Kathleen (1959). The Pre-Socratic Philosophers: A Companion to Diels, Fragmente der Vorsokratiker (Second Ed.). Cambridge, MA: Harvard University Press. p. v-vii.
  6. ^ Freeman, Kathleen (1971). Ancilla to the Pre-Socratic Philosophers: A complete translation of the Fragments in Diels, Fragmente der Vorsokratiker. Cambridge, MA: Harvard University Press. p. vii-ix. 1971 Importation, SBN 674-03500-3
  7. ^ "Ancilla to the Pre-Socratic Philosophers: Contents". Sacred Texts.
  8. ^ Waterfield, Robin (2000). The First Philosophers: The Presocratics and the Sophists. Oxford: Oxford University Press. p. 345-349. ISBN 9780199539093.
  9. ^ "Die Fragmente der Vorsokratiker". archive.org. 1903.
  10. ^ Freeman's Companion, 244-245

External links[edit]