Diels–Kranz numbering

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Diels–Kranz (DK) numbering is the standard system for referencing the works of the 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. It was first published in 1903, was later revised and expanded three times by Diels, and was finally revised in a 5th edition (1934–7) by Walther Kranz and again in a sixth edition (1952). In the system, each philosophical work is assigned a number which was used to uniquely identify the source and the author. This system is used in references in academia concerned with pre-Socratic philosophers.


Works of pre-Socratic philosophers have not survived 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 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 reader in pre-Socratic philosophy classes and academia. Because of its influence, the position of a source in the book became the standard way of referencing the source itself (in literature, conferences and even in conversation).

Numbering system[edit]

The number corresponding to a source was made up of three parts

  1. a number representing the philosopher it is about - the number is the chapter number in the book since the book has a separate chapter for each philosopher, for example chapter 11 is about Thales
  2. the letter A, B, or C, corresponding to the type of source it is, 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 sources 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 source in that 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 is talking about Thales who is, as mentioned above, contained in chapter 11. The source is paraphrased in Theaetetus (one of Plato's dialogues), hence it is a testimonium, represented by the character A. Finally, it is the 9th item in this chapter of the book, giving it the overall number of DK 11A9.

Sometimes, the chapter number is replaced by name of the philosopher for easier understanding, for example:

The things that can be seen, heard, and learned are what I prize the most.[3]

The above can be referred to as "Heraclitus B22" as it is a direct transmission of the words of Heraclitus (in this case, quoted by Hippolytus of Rome) and is the 22nd item in the chapter about Heraclitus in the book.[4]


  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. ^ Wikisource link to Fragments of Heraclitus. Wikisource. 
  4. ^ "Heraclitus". www.iep.utm.edu. Retrieved 2017-08-30. 

External links[edit]