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My real position is that Quantitative vs. Qualitative is not quite the right way of posing the issue (see here).
However here's a great quote anyway:
"In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be."
Lord Kelvin, PLA, vol. 1, "Electrical Units of Measurement", 1883-05-03
Striking as this is, and however well it has proved to serve Physics, Kelvin was surely wrong, even about Science. The most central parts of Biology are:
Similarly, even Geology (surely as physical and concrete as a science can get) has at its heart strata and their sequence. This is about ordering and topology: perhaps maths, but not numbers. It is true that numbers are useful in Geology in making practical predictions about where strata will appear, but actually strata do not always have constant thickness nor slope. The heart of the science and of its birth when prediction became possible, does not rest on numbers.
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