Type–token distinction

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Although this flock is made of the same type of bird, each individual bird is a different token. (50 MB video of a flock of birds in Rome)

The type–token distinction is the difference between a word referring to a class of objects and the same word referring to an individual instance of an object. For example, the sentence "A rose is a rose is a rose" could be said to contain three words, the word types "a", "rose", and "is"; or to contain eight words, the word tokens "a", "rose", "is", "a", "rose", "is", "a", "rose". The distinction is important in disciplines such as logic, linguistics, metalogic, typography, and computer programming.

Logic the systematic study of the form of arguments

Logic is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on.

Linguistics is the scientific study of language. It involves analysing language form, language meaning, and language in context. The earliest activities in the documentation and description of language have been attributed to the 6th-century-BC Indian grammarian Pāṇini who wrote a formal description of the Sanskrit language in his Aṣṭādhyāyī.

Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

Contents

Overview

The sentence "they drive the same car" is ambiguous. Do they drive the same type of car (the same model) or the same instance of a car type (a single vehicle)? Clarity requires us to distinguish words that represent abstract types from words that represent objects that embody or exemplify types. The type–token distinction separates types (abstract descriptive concepts) from tokens (objects that instantiate concepts).

For example: "bicycle" represents a type: the concept of a bicycle; whereas "my bicycle" represents a token of that type: an object that instantiates that type. In the sentence "the bicycle is becoming more popular" the word "bicycle" represents a type that is a concept; whereas in the sentence "the bicycle is in the garage" the word "bicycle" represents a token: a particular object.

(The distinction in computer programming between classes and objects is related, though in this context, "class" sometimes refers to a set of objects (with class-level attribute or operations) rather than a description of an object in the set, as "type" would.)

Computer programming Process that leads from an original formulation of a computing problem to executable computer programs

Computer programming is the process of designing and building an executable computer program for accomplishing a specific computing task. Programming involves tasks such as: analysis, generating algorithms, profiling algorithms' accuracy and resource consumption, and the implementation of algorithms in a chosen programming language. The source code of a program is written in one or more languages that are intelligible to programmers, rather than machine code, which is directly executed by the central processing unit. The purpose of programming is to find a sequence of instructions that will automate the performance of a task on a computer, often for solving a given problem. The process of programming thus often requires expertise in several different subjects, including knowledge of the application domain, specialized algorithms, and formal logic.

In computer science, an object can be a variable, a data structure, a function, or a method, and as such, is a value in memory referenced by an identifier.

The words type, concept, property, quality, feature and attribute (all used in describing things) tend to be used with different verbs. E.g. Suppose a rose bush is defined as a plant that is "thorny", "flowering" and "bushy". You might say a rose bush instantiates these three types, or embodies these three concepts, or exhibits these three properties, or possesses these three qualities, features or attributes.

Property types (e.g. "height in metres" or "thorny") are often understood ontologically as concepts. Property instances (e.g. height = 1.74) are sometimes understood as measured values, and sometimes understood as sensations or observations of reality.

Ontology study of the nature of being, becoming, existence or reality, as well as the basic categories of being and their relations

Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences.

Some types exist as descriptions of objects, but not as tangible physical objects. One can show someone a particular bicycle, but cannot show someone, explicitly, the type "bicycle", as in "the bicycle is popular.". Such use of typologically similar yet different semantic properties appear in mental and documented models, and are often referenced in every day conversation.

In common usage, a physical object or physical body is a collection of matter within a defined contiguous boundary in 3-dimensional space. The boundary must be defined and identified by the properties of the material. The boundary may change over time. The boundary is usually the visible or tangible surface of the object. The matter in the object is constrained to move as one object. The boundary may move in space relative to other objects that it is not attached to. An object's boundary may also deform and change over time in other ways.

Some say tokens are objects that are tangible, exist in space and time as physical matter and/or energy. However, tokens can be intangible objects of types such as "thought", "tennis match", "government" and "act of kindness".

Occurrences

There is a related distinction very closely connected with the type-token distinction. This distinction is the distinction between an object, or type of object, and an occurrence of it. In this sense, an occurrence is not necessarily a token. Considering the sentence: "A rose is a rose is a rose". We may equally correctly state that there are eight or three words in the sentence. There are, in fact, three word types in the sentence: "rose", "is" and "a". There are eight word tokens in a token copy of the line. The line itself is a type. There are not eight word types in the line. It contains (as stated) only the three word types, 'a', 'is' and 'rose', each of which is unique. So what do we call what there are eight of? They are occurrences of words. There are three occurrences of the word type 'a', two of 'is' and three of 'rose'.

The need to distinguish tokens of types from occurrences of types arises, not just in linguistics, but whenever types of things have other types of things occurring in them. [1] Reflection on the simple case of occurrences of numerals is often helpful.[ citation needed ]

Numeral system Writing system for expressing numbers

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

Typography

In typography, the type–token distinction is used to determine the presence of a text printed by movable type: [2]

The defining criteria which a typographic print has to fulfill is that of the type identity of the various letter forms which make up the printed text. In other words: each letter form which appears in the text has to be shown as a particular instance ("token") of one and the same type which contains a reverse image of the printed letter.

Charles Sanders Peirce

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 'letters' was used three times in the above paragraph, each time in a different meaning. The word 'letters' is one of many words having "type–token ambiguity". This section disambiguates 'letters' by separating the three senses using terminology standard in logic today. The key distinctions were first made by the American logician-philosopher Charles Sanders Peirce in 1906 using terminology that he established. [3]

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. There is only one word type spelled el-ee-tee-tee-ee-ar, [4] 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. This section 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.

See also

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References

  1. Stanford Encyclopedia of Philosophy, Types and Tokens
  2. Brekle, Herbert E.: Die Prüfeninger Weiheinschrift von 1119. Eine paläographisch-typographische Untersuchung, Scriptorium Verlag für Kultur und Wissenschaft, Regensburg 2005, ISBN   3-937527-06-0, p. 23
  3. Charles Sanders Peirce, Prolegomena to an apology for pragmaticism, Monist, vol.16 (1906), pp. 492–546.
  4. 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.

Sources