# Dictionary Definition

fewness n : the quality of being small in
number

# User Contributed Dictionary

## English

### Noun

- The state, quality, or condition of being few.

#### Translations

state of being few

- Finnish: vähyys

# Extensive Definition

Quantity is a kind of property which exists as
magnitude or multitude. It is among the basic classes of things
along with quality,
substance, change, and relation. Quantity was first
introduced as quantum,
an entity having
quantity. 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 (or number), 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.

## 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 Hölder (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 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 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

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

Some further examples of quantities are:- 1.76 litres (liters) of milk, a continuous quantity
- 2πr 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

- 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)
- Hölder, O. (1901). Die Axiome der Quantität und die Lehre vom Mass. Berichte über die Verhandlungen der Königlich 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. http://www.oxfordscholarship.com/oso/public/content/philosophy/0199281718/toc.html#
- Michell, J. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, 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 Hölder’s German text "Die Axiome der Quantität 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. 3-134). New York: Johnson Reprint Corp.
- Wallis, J. Mathesis universalis (as quoted in Klein, 1968).

fewness in Arabic: كمية

fewness in Czech: Kvantita

fewness in German: Quantität

fewness in Modern Greek (1453-): Ποσότητα

fewness in Spanish: Cantidad

fewness in Esperanto: Kvanto

fewness in Persian: کمیت

fewness in French: Quantité

fewness in Korean: 양 (크기)

fewness in Italian: Quantità vocalica

fewness in Hungarian: Mennyiség

fewness in Macedonian: Количество

fewness in Dutch: Kwantiteit

fewness in Japanese: 量

fewness in Norwegian Nynorsk: Storleik

fewness in Portuguese: Quantidade

fewness in Russian: Количество

fewness in Sicilian: Quantitati

fewness in Simple English: Quantity

fewness in Slovak: Kvantita

fewness in Finnish: Määrä

fewness in Swedish: Kvantitet

fewness in Ukrainian: Кількість

fewness in Chinese: 数量