Concept formation is a functional domain which comprises linguistic operations for the formation and modification of concepts.

Fundamental operations of concept formation

At the lowest and the highest level of structural complexity, the introductory definition is meant to exclude two limiting cases from the functional domain of concept formation:

1. A concept may be available as the meaning of a lexeme. In this case, the process of lexicalization is already presupposed; and no other specific linguistic operation (apart from the selection and combination of the unit in question) is required for the formation and use of the concept.
2. A concept may be formed at the textual level, for instance by an explicit definition. The operations achieving this are not part of the language system, either.

There are general cognitive operations of concept formation, including at least the following (Cassirer 1953, ch. IV):

1. the delimitation of a percept against its environment
2. the selection of a percept as something to be developed into a concept
3. the abstraction from features considered accidental and the concentration on features shared by different percepts and considered as essential for the concept to be formed.

Of these, only #3 has a manifestation as a specifically linguistic operation, viz. as nominalization. #1 and 2 are pre-linguistic in the sense that they do not take the form of a grammatical operation. They may, however, determine the ways in which mental representations and ad-hoc concepts are lexicalized in a language. Whenever a concept is coded as the meaning of a lexeme, the first two steps have already been taken.

Categories of concepts

Concepts are here categorized according to the function they have in a proposition. A proposition consists at least of a referential expression and a predicate. While the referential expression may or may not be based on a concept, the predicate generally is (certain equations are exceptions). Accordingly, the main subdivision is into referential and predicable notions (using the terms of formal ontology):

• A referential notion is a concept which can form the semantic core of a referential expression without any change to the concept.
• A predicable notion is a concept which can form the semantic core of a predicate without any change to the concept.

Natural languages categorize elementary concepts in word classes. The two basic word classes are noun and verb. The meaning of a noun is a referential notion; the meaning of a verb is a predicable notion. Without taking up the typological debate concerning the universality or otherwise of the noun-verb distinction, it suffices to look at the English pair in to understand the idea.

The core of the meaning of the subject of .a is a referential notion; the semantic core of its predicate is a predicable notion. As shown by #b, it cannot be the other way around. The primary categorization of ‘grow’ can be changed into the referential notion designated by growth, while nothing of the kind is available for apple. The point here, however, is not about distributional properties of English word classes, but about the way in which what is designated by a noun differs categorially from what is designated by a verb: A referential notion has a set of (concrete or abstract) objects in its extension, so that the application of some referential operation to it (proximate deixis in the case of .a) enables it to refer. A predicable notion applies intensionally to referents.

As it may be seen, this semantic distinction is based on a grammatical distinction and is therefore commonly taken to be irrelevant to predicate calculus. Natural language grammar, however, tends to respect this distinction, though – depending on the language – at different levels of grammatical structure. Operations that change the (primary) categorization of concepts are dealt with in the next section. There, a third conceptual category, the modifier, will be introduced, too.

Linguistic operations on concepts

The domain of concept formation includes those categories and operations which the grammar and the lexicon make available for the formation and modification of concepts. These operations include at least the following:

Formation of a concept

Abstraction from a proposition

The designatum of a predication or proposition is converted into a concept. To an incipient extent, it is treated as an entity; and to this extent, abstraction involves reification. This is the presupposition for the concept to function as a referential notion. The main grammatical operation involved is nominalization, more specifically, substantivization.

Orientation

Both referential and predicable notions may be oriented. It is here assumed that orientation is an operation on a proposition, not on a concept. In other words, the sequence of operations in forming an oriented concept on the basis of a proposition is: first orient the proposition, then convert it into a concept. As discussed in the section on internal-head relative clauses, orientation may be performed, at the semantic level, on a closed clause. As an operation recognizable in linguistic structure, orientation presupposes an open clause.

Modification of a concept

A concept is used as the core of the concept to be formed, and this core is enriched by other concepts or specifiers so that a changed concept emerges.

Modification

Modification is the enrichment of a concept by additional features. It is a secondary-level predication, a kind of predication that subordinates itself to an operation of reference or predication. To this end, modification combines a modifier – a kind of downgraded predicate – with a modificatum – a concept that forms the core of a referent or of a predicate.

The product of the operation is the modificatum as modified by the modifier. In the simplest case, the semantic effect is restriction. From a structural point of view, the product is endocentric. I.o.w., modification does not change the category of the modificatum.

Both referential and predicable notions may be modified. Modification of a predicable notion is an operation of the functional domain of participation. The main grammatical operation achieving modification of a referential notion is attribution.

Modification by another concept: characterization¹

A core concept is combined in such a way with another concept that the latter modifies the former. The modified concept has a richer intension. This is typically achieved by some form of characterizing attribution.

• Modification by a property:
  A subtype of the core concept is formed which is distinct by a certain property. The principal grammatical operation involved is adjectival attribution.
• Other modification:
  The core concept may also be enriched by other concepts like material or provenience. One of the grammatical operations to achieve this is compounding.

A language may provide one or more word classes whose primary function is to serve as characterizing modifiers. The adjective and the adverb are such word classes.

Modification by one or more referents: anchorage

A core concept is combined with semantic components to which a subset of the elements in its extension bears some relation. In this way, the extension of the concept is restricted to this particular subset.

• Anchorage of a concept by a relation to some reference point:
  The extension of a concept may be limited to that subset of its elements which bear a certain relation to some reference point. The standard grammatical operation to achieve this is nominal and adverbial attribution, including possessive attribution.
• Anchorage of a concept by the role of its referent in a proposition:
  The extension of a concept may be restricted to that subset of elements falling under it which bears a certain participant function in a proposition. The operation dedicated to this concept anchoring by participation is relative clause formation.

For #1, the underlying predication or proposition may or may not be oriented by the nominalization. The modifiers and specifiers of #2 are, in any, case oriented.

Functional domain of concept formation

A concept, however much it is restricted and specified, can serve either as a predicate or as the basis of a referential expression. The distinction between characterization and anchoring of a concept is meant to be gradual. In the prototypical case, characterization forms a more specific concept with a referential potential like that of the core concept, while anchoring prepares the selection of a particular set of objects. However, on the one hand, even an unmodified concept (i.e. the meaning of a simple lexeme) may be sufficient, in a given context, to select a certain entity. And on the other hand, even the relation to some reference point or some particular situation may still characterize a concept rather than a specific set of objects; and such a concept may be used as a predicate rather than as the basis of a referential expression.

At any rate, if a concept is to be used as the basis of a referential expression, then its purpose is the selection of entities. To this purpose, concept anchoring is more efficient than concept characterization, since it selects those elements in the extension of the core concept which bear the relation in question to the referents appearing in the specifier.

The functional domain of concept formation is to be delimited against neighboring functional domains:

• The functional domain of apprehension is concerned with the classification of concepts and individuals and with the individuation of entities on the basis of a concept.
• The functional domain of reference is concerned with the identification of a referent, both for the first time in a discourse and at subsequent resumptions.

¹ Some awkward-seeming formulations here are due to respect for traditional terminology. Traditionally, all the adnominal dependents except determiners are considered as modifiers, viz. attributes. One might consider restricting the term ‘modification’ to what is here called characterization.