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|Quantities (Physics)||I 140
Quantities/Duhem: According to Aristotle, a property that can be expressed numerically must be quantitative and not qualitative.
How do we recognize that the length of a straight line is a variable? By comparison. Addition is possible.
Quantity: Every quantity value of a quantity can always be formed by addition from smaller values of the same quantity. Each quantity exists because of a commutative and associative operation in the union of quantities which are less than the first, but of the same kind.
Definition Quantity/Duhem: it is what has parts, some of which are outside the others.
Any property that is not a quantity is a quality.
Aristotle: Quality is ambiguous. Some cannot be more or less (e.g. circular).
Quantity is not simply defined by an abstract number, but is only defined in conjunction with a unit of measure.
Likewise the intensity of a quality, not only by a numerical symbol, but also a specific method, which is suitable to specify the scale of the intensities. Only the knowledge of this scale allows the algebraic propositions to give physical sense. Scale of course quantitatively.
In the field of quality, the concept of addition cannot occur, but it is found on the quantitative scale which indicates the intensities of the quality.
Ziel und Struktur der physikalischen Theorien Hamburg 1998