September 30, 2012, by Stephen Mumford

Quantities and Qualities

At a recent philosophy conference in Porto the organizers treated the delegates to a tour of some famous port wine cellars. We were shown the vintage wine collection, of which the company was very proud. Perhaps not realising we were philosophers, the tour guide asked if we had any questions. I’ve never understood what defined a wine as vintage so took the opportunity to learn. To my pleasure, though slight surprise, I discovered that an expert panel tastes the wine and makes a qualitative judgement. There is not a litmus test, no report of chemical composition, no data analysis. Vintage wines just taste very good in the judgement of the experts.

The reason I was slightly surprised by this answer is how little is left to qualitative judgement these days, perhaps for fear that such assessments are considered subjective, lacking in transparency, and open to appeal. Instead, the drive is ever more towards the numbers, where a feature is quantified and the meeting of a magnitudinal threshold is a matter of clear mathematical certainty. The fastest growing world religion seems to be Pythagoreanism, central to which is the worship of numbers. But how compelling is such a view?

Properties or features of things can be divided into qualities and quantities. Qualities are those such as heat, redness, roughness, beauty and tastiness. Quantities are amounts or extents of something, such as 10cm of length or 37 degrees C. As we increasingly mathematize our world, the thought is that everything should be measurable. If something cannot be quantified, its status is regarded as dubious. Qualitative judgements are increasingly seen as illegitimate.

Such a view is undoubtedly a philosophical one but it is also pervasive. The idea seems to be that all qualities are, or should be, ultimately reducible to quantities. Australian materialist philosopher David Armstrong has said as much. All the real properties of things, he argues, will be quantities. If one takes the example of colour, for instance, redness will ultimately be reduced to a certain magnitude or range of magnitudes of some medium. Redness might be just a certain specifiable length of lightwave. A problem, however, is that last time I checked the colours had not yet been successfully reduced in this way. It seems it is a far more complex matter than wavelength and there is nothing in common to everything that is red other than that all such things appear red to ordinary perceivers in standard conditions. Nevertheless, the number worshipers often respond that once we have knowledge of the completed science, all the qualities will indeed be reduced to quantities. It is not always obvious why we should have faith in this outcome.

Examples of rampant Pythagoreanism are not hard to find. When I travel and stay in hotels the star-rating system often amuses me. To get stars, the hotel has to tick the right boxes – so the assessment is objective and quantifiable. A TV in the room, a kettle, an iron, and so on, all contribute towards the awarding of stars. But I have found that there is often only a loose connection between the star-rating and how good the hotel is. How pleasant the location is, how noisy, how polite the staff are, how good the view, the choice or décor, etc., are the things I think make a good or bad hotel. But these are all qualitative judgements that cannot be included in the star-rating. (I know that somewhere there will be a Pythagorean who claims we can ‘simply’ count how many times the staff say nice things to the guests – and this constitutes the measurement – but it’s surely more complicated than that). One reason I like my favourite hotel is that the rooms contain pictures of ships. The pictures are pleasant in themselves but I also like it because it ties in with the view of the harbour just outside, with breath-taking mountain scenery beyond. How could any of that be reduced to a number?

An example quite prescient to those of us who work in Higher Education is the dreaded university League Table, which typically is presented as some kind of objective measure of how good a university is. These tables are notorious for throwing up bizarre results, such as that University of Beeston is better than Cambridge. The example shows two irrevocable flaws in the view that everything is quantifiable. First, as above, some of the most important things seem the least easy to quantify, such as how intellectually brilliant your lecturer is or how beautiful the campus is, neither of which can ever be measured directly. Second, even if one could quantify everything accurately, such tables are based on a range of such measurements and it is always a matter of qualitative judgement which measurements are important.  We have various data for each university – typical entry score, degree class outcomes, library spend per student, employment rates after graduation, and so on – but  someone still has to make the qualitative decision what data should be included and how much weight should be given to each value in the final calculation. The objectivity of such a league table is thus only apparent.

The worship of numbers has potentially damaging effects (especially when brought to bear on a health care system, for example) but it is something we should be able to resist if we are willing. Numbers are a tool, and a very important one, but they are not all that is. And it is still open to debate whether everything is a quantity. The world might indeed contain irreducible qualities that resist mathematization. And when I think about it, the qualities are exactly what I enjoy most about the world, such as the taste of a good wine.

Posted in AestheticsMathematicsMetaphysicsPhilosophyTheology and Religious Studies