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A 'quantitative' attribute is one that exists in a range of magnitudes, and can therefore be measured. Measurements of any particular quantitative property are expressed as a specific quantity, referred to as a unit, multiplied by a number. Examples of physical quantities are distance, mass, and time. Many attributes in the social sciences, including abilities and personality traits, are also studied as quantitative properties and principles. In the classical definition of measurement, the structure quantitative property is such that different magnitudes of the quantity stand in relation to one another as ratios which, in turn, can be expressed as real numbers. Measurement is the determination or estimation of ratios of quantities. Quantity and measurement are therefore mutually defined quantitative attributes are those which it is possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton, and was foreshadowed in Euclid's Elements (Michell, 1993). In the representational theory, measurement is regarded as "the correlation of numbers with entities that are not numbers" (Nagel, 1932). In some forms of representational theory, numbers are assigned on the basis of correspondences or similarities between the structure of number systems and the structure of qualitative systems. A quantitative property is therefore one for which such structural similarities can be established. In other forms of representational theory, such as that implicit within the work of Stanley Smith Stevens, numbers need only be assigned according to a rule. Whether numbers obtained through an experimental procedure are considered measurements is, on the one hand, largely a matter of how measurement is defined. On the other hand, the nature of the measurement process has important implications for scientific research. Firstly, many arithmeitic operations are only justified for measurements either in the classical sense described above, or in the sense of interval and ratio-level measurements as defined by Stevens (which arguably describe the same thing). Secondly, quantitative relationships between different properties which feature in most natural theories and laws imply that the properties have a specific type of quantitative structure; namely, the structure of a continuous quantity. The reason for this is that such theories and laws display a multiplicative structure (for example Newton's second law).
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