## Quantitative structure::Quantity

### ::concepts

**Quantity**::number Which::numbers Between::relation Theory::property Length::**quantity** Count::michell**Quantitative structure**
Continuous quantities possess a particular structure that was first explicitly characterized by Hölder (1901) as a set of axioms that define such features as *identities* and *relations* between magnitudes. In science, quantitative structure is the subject of empirical investigation and cannot be assumed to exist *a priori* for any given property. The linear continuum represents the prototype of continuous quantitative structure as characterized by Hölder (1901) (translated in Michell & Ernst, 1996). A fundamental feature of any type of quantity is that the relationships of equality or inequality can in principle be stated in comparisons between particular magnitudes, unlike quality, which is marked by likeness, similarity and difference, diversity. Another fundamental feature is additivity. Additivity may involve concatenation, such as adding two lengths A and B to obtain a third A + B. Additivity is not, however, restricted to extensive quantities but may also entail relations between magnitudes that can be established through experiments that permit tests of hypothesized observable manifestations of the additive relations of magnitudes. Another feature is continuity, on which Michell (1999, p. 51) says of length, as a type of quantitative attribute, "what continuity means is that if any arbitrary length, a, is selected as a unit, then for every positive real number, *r*, there is a length b such that b = *r*a".

**Quantity sections**

Intro Background Quantitative structure Quantity in mathematics Quantity in physical science Quantity in logic and semantics Quantity in natural language Further examples References External links

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