Wholistic reference is reference to the whole—with respect to the context. In its strongest, unqualified form, the principle of wholistic reference is the

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

that each and every proposition, regardless how limited the referents of its non-logical or content terms, refers to the whole of its

universe of discourse In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The doma ...

. According to this principle every proposition of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

, even an equational proposition such as 5 + 7 = 12, refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. The relation verb ‘refers’ is being used in its broad sense (loosely “is about”) and not as a synonym for ‘names’ in the sense of “is a name of”.

George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ...

(1815–1864) introduced this principle into modern logic: Even though he changed from a monistic fixed-universe framework in his 1840s writings to a pluralistic multiple-universe framework in 1854, he never wavered in his frank avowal of the principle of wholistic reference. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. For Boole, the essential first step in the process of conceiving of a proposition preliminary to making a judgement of its truth or falsity – or even using it in a deduction, however hypothetically – was to conceive of the universe of discourse. See Boole 1854/2003, xxi, 27, 42, 43. One statement of his principle is in the sentence immediately following his definition of universe of discourse, which is his first use of the expression 'universe of discourse' and probably the first in the history of the English language. See the next section. Similar views, perhaps not similarly motivated, are found in later logicians, including

Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic ph ...

(1848–1925). Some recent formulations of standard one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. Corcoran, John. Principle of Wholistic Reference. ''Manuscrito'' 27 (2004): 155–166.

References

Concepts in logic Holism Philosophy of logic Philosophy of language Semantics {{semantics-stub