Extension (semantics) in the context of Operationalism

In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the two ways he believed a singular term may have meaning.

The reference (or "referent"; Bedeutung) of a proper name is the object it means or indicates (bedeuten), whereas its sense (Sinn) is what the name expresses. The reference of a sentence is its extension, whereas its sense is the thought that it expresses. Frege justified the distinction in a number of ways.

A thoroughfare is a primary passage or way of transport, whether by road on dry land or, by extension, via watercraft or aircraft. Originally, the word referred to a main road or open street which was frequented thoroughly.

In research design, especially in psychology, social sciences, life sciences and physics, operationalization (or operationalisation) is a process of defining the measurement of a phenomenon which is not directly measurable, though its existence is inferred from other phenomena. Operationalization thus defines a fuzzy concept so as to make it clearly distinguishable, measurable, and understandable by empirical observation. In a broader sense, it defines the extension of a concept—describing what is and is not an instance of that concept. For example, in medicine, the phenomenon of health might be operationalized by one or more indicators like body mass index or tobacco smoking. As another example, in visual processing the presence of a certain object in the environment could be inferred by measuring specific features of the light it reflects. In these examples, the phenomena are difficult to directly observe and measure because they are general/abstract (as in the example of health) or they are latent (as in the example of the object). Operationalization helps infer the existence, and some elements of the extension, of the phenomena of interest by means of some observable and measurable effects they have.

Sometimes multiple or competing alternative operationalizations for the same phenomenon are available. Repeating the analysis with one operationalization after the other can determine whether the results are affected by different operationalizations. This is called checking robustness. If the results are (substantially) unchanged, the results are said to be robust against certain alternative operationalizations of the checked variables.

In mathematics, a setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional set.

Setoids are studied especially in proof theory and in type-theoretic foundations of mathematics. Often in mathematics, when one defines an equivalence relation on a set, one immediately forms the quotient set (turning equivalence into equality). In contrast, setoids may be used when a difference between identity and equivalence must be maintained, often with an interpretation of intensional equality (the equality on the original set) and extensional equality (the equivalence relation, or the equality on the quotient set).

In linguistics, semantic loan is a process (or an instance or result) of borrowing semantic meaning (rather than lexical items) from another language. It is very similar to the formation of calques, excepting that in this case the complete word in the borrowing language already exists; the change is that its meaning is extended to include another meaning that is already possessed by its counterpart in the lending language. Semantic loans are often grouped roughly together with calques and loanwords under the phrase borrowing.

Semantic loans often occur when two languages are in close contact, and they take various forms. The source and target word may be cognates, which may or may not share any contemporary meaning in common; they may be an existing loan translation or parallel construction (compound of corresponding words); or they may be unrelated words that share an existing meaning.