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Encyclopedia > Quantity

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. A small quantity is sometimes referred to as a quantulum. For the Talib Kweli album Quality (album) Quality can refer to a. ... Look up substance in Wiktionary, the free dictionary. ... This article does not cite any references or sources. ... Look up Relation in Wiktionary, the free dictionary In mathematics, a relation is a generalization of arithmetic relations, such as = and <, which occur in statements, such as 5 < 6 or 2 + 2 = 4. See relation (mathematics), binary relation (of set theory and logic) and relational algebra. ... In physics, a quantum (plural: quanta) is an indivisible entity of energy. ... An entity is something that has a distinct, separate existence, though it need not be a material existence. ...


Two basic divisions of quantity, magnitude and multitude (or number), imply the principal distinction between continuity (continuum) and discontinuity. The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ... For other uses, see Number (disambiguation). ... Look up continuum in Wiktionary, the free dictionary. ... In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ...


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. This article or section is in need of attention from an expert on the subject. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... A scale for measuring mass A quantitative property is one that exists in a range of magnitudes, and can therefore be measured. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...

Contents

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: Aristotle (Greek: Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... In philosophy, ontology (from the Greek , genitive : of being (part. ... In physics, a quantum (plural: quanta) is an indivisible entity of energy. ...

'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: The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Euclid (Greek: ), also known as Euclid of Alexandria, was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323 BC-283 BC). ...

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: The integers consist of the positive natural numbers (1, 2, 3, &#8230;) the negative natural numbers (&#8722;1, &#8722;2, &#8722;3, ...) and the number zero. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... Please refer to Real vs. ...

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). Sir Isaac Newton in Knellers portrait of 1689. ...


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". The terms a priori and a posteriori are used in philosophy to distinguish between two different types of propositional knowledge. ... In mathematics, the word continuum sometimes denotes the real line. ...


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. In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector. ... A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ...


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 the primary quantities of physical things, 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. It has been suggested that this article or section be merged into intensive and extensive properties. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... This article or section is in need of attention from an expert on the subject. ...


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). In linguistics, grammatical number is a morphological category characterized by the expression of quantity through inflection or agreement. ...


Further examples

Look up quantity, few in Wiktionary, the free dictionary.

Some further examples of quantities are: Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ...

  • 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).

  Results from FactBites:
 
CATHOLIC ENCYCLOPEDIA: Quantity (667 words)
quantity is that which consists of parts having position in reference to each other, so that the limit of the one is the limit of the next.
quantity, as the first subject of colour is said to be the superficies".
Aristotle's own argument lies in the consideration that length, breadth, and depth are quantities, but are not substances.
Online Etymology Dictionary (1935 words)
Meaning "small quantity (of something) from which the general quality (of the whole) may be inferred" (usually in a commercial sense) is recorded from 1428; sense of "specimen for scientific sampling" is from 1878.
Extended sense of "a quantity adopted as a standard of measure" is from 1738.
Meaning "quantity of liquor served to a company at one time" is from 1633; that of "single bout in a fight or boxing match" is from 1812; "single discharge of a firearm" is from 1725.
  More results at FactBites »

 
 

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