# Pierce's type-token distinction

There are only 26 letters in the English alphabet and yet there are more than 26 letters in this sentence. Moreover, every time a child writes the alphabet 26 new letters have been created.

The word ‘letter’ was used three times in the above paragraph, each time in a different meaning. The word 'letter' is one of many words having "type-token ambiguity". This article disambiguates 'letter' by separating the three senses using terminology standard in logic today. The key distinctions were first made by the great American logician-philosopher Charles Sanders Peirce in 1906 using terminology that he established.[1]

The letters that are created by writing are physical objects that can be destroyed by various means: these are letter TOKENS or letter INSCRIPTIONS. The 26 letters of the alphabet are letter TYPES or letter FORMS.

Peirce's type-token distinction, also applies to words, sentences, paragraphs, and so on: to anything in a universe of discourse of character-string theory, or concatenation theory.[2] There is only one word type spelled el-ee-tee-tee-ee-ar,[3] namely, ‘letter’; but every time that word type is written, a new word token has been created.

Some logicians consider a word type to be the class of its tokens. Other logicians counter that the word type has a permanence and constancy not found in the class of its tokens. The type remains the same while the class of its tokens is continually gaining new members and losing old members.

The word type ‘letter’ uses only four letter types: el, ee, tee, and ar. Nevertheless, it uses ee twice and tee twice. In standard terminology, the word type ‘letter’ has six letter OCCURRENCES and the letter type ee OCCURS twice in the word type ‘letter’. Whenever a word type is inscribed, the number of letter tokens created equals the number of letter occurrences in the word type.

Peirce's original words are the following. "A common mode of estimating the amount of matter in a … printed book is to count the number of words. There will ordinarily be about twenty ‘thes’ on a page, and, of course, they count as twenty words. In another sense of the word ‘word,’ however, there is but one word ‘the’ in the English language; and it is impossible that this word should lie visibly on a page, or be heard in any voice …. Such a … Form, I propose to term a Type. A Single … Object … such as this or that word on a single line of a single page of a single copy of a book, I will venture to call a Token. …. In order that a Type may be used, it has to be embodied in a Token which shall be a sign of the Type, and thereby of the object the Type signifies." – Peirce 1906, Ogden-Richards, 1923, 280-1.

These distinctions are subtle but solid and easy to master. Reflection on the simple case of occurrences of numerals is often helpful.[4] This article ends using the new terminology to disambiguate the first paragraph.

There are 26 letter types in the English alphabet and yet there are more than 26 letter occurrences in this sentence type. Moreover, every time a child writes the alphabet 26 new letter tokens have been created.

## References

1. ^ CHARLES SANDERS PEIRCE, Prolegomena to an apology for pragmaticism, Monist, vol.16 (1906), pp. 492–546.
2. ^ Concatenation theory
3. ^ Using a variant of Alfred Tarski's structural-descriptive naming found in John Corcoran , Schemata: the Concept of Schema in the History of Logic, Bulletin of Symbolic Logic, vol. 12 (2006), pp. 219–40.
4. ^ Occurrences of numerals