"Few" redirects here. For the basketball coach see Mark Few. It has been suggested that Quantitative property be merged into this article or section. (Discuss) Proposed since July 2009.

Quantity is a kind of property that can exist as magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal" or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality substance change and relation. Being a fundamental term quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number) while others are functioning as states (properties dimensions attributes) of things such as heavy and light long and short broad and narrow small and great or much and little. One form of much muchly is used to say that something is likely to happen. A small quantity is sometimes referred to as a quantulum.

Two basic divisions of quantity magnitude and multitude imply the principal distinction between continuity (continuum) and discontinuity.

Under the names of multitude come what is discontinuous and discrete and divisible into indivisibles all cases of collective nouns: army fleet flock government company party people chorus crowd mess and number. Under the names of magnitude come what is continuous and unified and divisible into divisibles all cases of non-collective nouns: the universe matter mass energy liquid material animal plant tree.

Along with analyzing its nature and classification the issues of quantity involve such closely related topics as the relation of magnitudes and multitudes dimensionality equality proportion the measurements of quantities the units of measurements number and numbering systems the types of numbers and their relations to each other as numerical ratios.

Thus quantity is a property that exists in a range of magnitudes or multitudes. Mass time distance heat and angular separation are among the familiar examples of quantitative properties. Two magnitudes of a continuous quantity stand in relation to one another as a ratio which is a real number. Contents 1 Background 2 Quantitative structure 3 Quantity in mathematics 4 Quantity in physical science 5 Quantity in logic and semantics 6 Quantity in natural language 7 Further examples 8 References Background

The concept of quantity is an ancient one which extends back to the time of Aristotle and earlier. Aristotle regarded quantity as a fundamental ontological and scientific category. In Aristotle's ontology quantity or quantum was classified into two different types which he characterized as follows: 'Quantum' means that which is divisible into two or more constituent parts of which each is by nature a 'one' and a 'this'. A quantum is a plurality if it is numerable a magnitude if it is measurable. 'Plurality' means that which is divisible potentially into non-continuous parts magnitude that which is divisible into continuous parts; of magnitude that which is continuous in one dimension is length; in two breadth in three depth. Of these limited plurality is number limited length is a line breadth a surface depth a solid. (Aristotle book v chapters 11-14 Metaphysics).

In his Elements Euclid developed the theory of ratios of magnitudes without studying the nature of magnitudes as Archimedes but giving the following significant definitions: A magnitude is a part of a magnitude the less of the greater when it measures the greater; A ratio is a sort of relation in respect of size between two magnitudes of the same kind.

For Aristotle and Euclid relations were conceived as whole numbers (Michell 1993). John Wallis later conceived of ratios of magnitudes as real numbers as reflected in the following: When a comparison in terms of ratio is made the resultant ratio often namely with the exception of the 'numerical genus' itself leaves the genus of quantities compared and passes into the numerical genus whatever the genus of quantities compared may have been. (John Wallis Mathesis Universalis)

That is the ratio of magnitudes of any quantity whether volume mass heat and so on is a number. Following this Newton then defined number and the relationship between quantity and number in the following terms: "By number we understand not so much a multitude of unities as the abstracted ratio of any quantity to another quantity of the same kind which we take for unity" (Newton 1728). Quantitative structure Continuous quantities possess a particular structure which was first explicitly characterized by Hlder (1901) as a set of axioms which 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 Hlder (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 which 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 ra". Quantity in mathematics This section may be confusing or unclear to readers. Please help clarify the section; suggestions may be found on the talk page. (July 2010) Being of two types magnitude and multitude (or number) quantities are further divided as mathematical and physical. Formally quantities (numbers and magnitudes) their ratios proportions order and formal relationships of equality and inequality are studied by mathematics. The essential part of mathematical quantities is made up with a collection variables each assuming a set of values and coming as scalar vectors or tensors and functioning as infinitesimal arguments independent or dependent variables or random and stochastic quantities. In mathematics magnitudes and multitudes are not only two kinds of quantity but they are also commensurable with each other. The topics of the discrete quantities as numbers number systems with their kinds and relations fall into the number theory. Geometry studies the issues of spatial magnitudes: straight lines (their length and relationships as parallels perpendiculars angles) and curved lines (kinds and number and degree) with their relationships (tangents secants and asymptotes). Also it encompasses surfaces and solids their transformations measurements and relationships. Quantity in physical science Establishing quantitative structure and relationships between different quantities is the cornerstone of modern physical sciences. Physics is fundamentally a quantitative science. Its progress is chiefly achieved due to rendering the abstract qualities of material entities into physical quantities by postulating that all material bodies marked by quantitative properties or physical dimensions which are subject to some measurements and observations. Setting the units of measurement physics covers such fundamental quantities as space (length breadth and depth) and time mass and force temperature energy and quantum. Traditionally a distinction has also been made between intensive quantity and extensive quantity as two types of quantitative property state or relation. The magnitude of an intensive quantity does not depend on the size or extent of the object or system of which the quantity is a property whereas magnitudes of an extensive quantity are additive for parts of an entity or subsystems. Thus magnitude does depend on the extent of the entity or system in the case of extensive quantity. Examples of intensive quantities are density and pressure while examples of extensive quantities are energy volume and mass. Quantity in logic and semantics In respect to quantity propositions are grouped as universal and particular applying to the whole subject or a part of the subject to be predicated. Accordingly there are existential and universal quantifiers. In relation to the meaning of a construct quantity involves two semantic dimensions: 1. extension or extent (determining the specific classes or individual instances indicated by the construct) 2. intension (content or comprehension or definition) measuring all the implications (relationships and associations involved in a construct its intrinsic inherent internal built-in and constitutional implicit meanings and relations). Quantity in natural language In human languages including English number is a syntactic category along with person and gender. The quantity is expressed by identifiers definite and indefinite and quantifiers definite and indefinite as well as by three types of nouns: 1. count unit nouns or countables; 2. mass nouns uncountables referring to the indefinite unidentified amounts; 3. nouns of multitude (collective nouns). The word number belongs to a noun of multitude standing either for a single entity or for the individuals making the whole. An amount in general is expressed by a special class of words called identifiers indefinite and definite and quantifiers definite and indefinite. The amount may be expressed by: singular form and plural from ordinal numbers before a count noun singular (first second third) the demonstratives; definite and indefinite numbers and measurements (hundred/hundreds million/millions) or cardinal numbers before count nouns. The set of language quantifiers covers "a few a great number many several (for count names); a bit of a little less a great deal (amount) of much (for mass names); all plenty of a lot of enough more most some any both each either neither every no". For the complex case of unidentified amounts the parts and examples of a mass are indicated with respect to the following: a measure of a mass (two kilos of rice and twenty bottles of milk or ten pieces of paper); a piece or part of a mass (part element atom item article drop); or a shape of a container (a basket box case cup bottle vessel jar). Further examples Look up quantity or few in Wiktionary the free dictionary. Some further examples of quantities are: 1.76 litres (liters) of milk a continuous quantity 2r metres where r is the length of a radius of a circle expressed in metres (or meters) also a continuous quantity one apple two apples three apples where the number is an integer representing the count of a denumerable collection of objects (apples) 500 people (also a count) a couple conventionally refers to two objects References This article includes a list of references related reading or external links but its sources remain unclear because it lacks inline citations. Please improve this article by introducing more precise citations where appropriate. (July 2010) Aristotle Logic (Organon): Categories in Great Books of the Western World V.1. ed. by Adler M.J. Encyclopaedia Britannica Inc. Chicago (1990) Aristotle Physical Treatises: Physics in Great Books of the Western World V.1 ed. by Adler M.J. Encyclopaedia Britannica Inc. Chicago (1990) Aristotle Metaphysics in Great Books of the Western World V.1 ed. by Adler M.J. Encyclopaedia Britannica Inc. Chicago (1990) Hlder O. (1901). Die Axiome der Quantitt und die Lehre vom Mass. Berichte ber die Verhandlungen der Kniglich Sachsischen Gesellschaft der Wissenschaften zu Leipzig Mathematische-Physicke Klasse 53 1-64. Klein J. (1968). Greek Mathematical Thought and the Origin of Algebra. Cambridge. Mass: MIT Press. Laycock H. (2006). Words without Objects: Oxford Clarendon Press. Oxfordscholarship.com Michell J. (1993). The origins of the representational theory of measurement: Helmholtz Hlder and Russell. Studies in History and Philosophy of Science 24 185-206. Michell J. (1999). Measurement in Psychology. Cambridge: Cambridge University Press. Michell J. & Ernst C. (1996). The axioms of quantity and the theory of measurement: translated from Part I of Otto Hlders German text "Die Axiome der Quantitt und die Lehre vom Mass". Journal of Mathematical Psychology 40 235-252. Newton I. (1728/1967). Universal Arithmetic: Or a Treatise of Arithmetical Composition and Resolution. In D.T. Whiteside (Ed.) The mathematical Works of Isaac Newton Vol. 2 (pp. 3134). New York: Johnson Reprint Corp. Wallis J. Mathesis universalis (as quoted in Klein 1968).