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.
I think i agree but I’m confused about the relationship between objective/subjective and quantities/qualities. These cut across each other? So is the idea that some things can’t be quantified, or that some things must be subjective?
What, if anything, is the difference between the quantifiable and subjective, and the qualitative and objective? Which is the target of the argument?
What a gentle, incisive way to put it.
Let’s assume the Pythagorean is right, how are we to explain qualities? No doubt the answer would be very complicated, and I’m dubious the result would adequately recover our intuitions, if that matters.
The quality-quantity distinction, imho, is partly constituted by the ‘explicit computation – intuitive grasp’ distinction. By the latter I mean the difference between, say, number crunching and e.g. a mathematician regarding a proof. An enormous class of algorithm’s could parse the former; only a mind educated for some time (and poss of a certain inclination) could grasp the latter – importantly, no explicit calculation need be performed. Interestingly, infants frequently outperform the most advanced AI’s in spotting when something in an image is ‘odd’ or out of place – possibly the infants are performing vast swathes of calculations, but no one I’ve heard of could recreate them algorithmically.
In some ways the Pythagorean viewpoint is quite perverse. Rather than assuming that which doesn’t fit into any category that is computationally tractable is somehow ephemeral or dubious, isn’t this just a result of how few successful quantitative methods we actually have at our disposal? Unpacking that: I once heard a physicist remark that there are only about five basic mathematical methods in the physical sciences, everything else is a matter of approximating them. Now that is hyperbole, but she has a point – when scientists generate new formalisms to encompass new situations they very often adopt a ‘conservative’ stance, i.e. how can we adapt the old formalisms? Or sometimes problems are too hard to solve explicitly or ‘in practice’ and so some old faithful model might be rolled out and an approximation scheme adopted. Perhaps these are signs that our quantitative explorations are in fact quite limited. To take an extremely speculative example, if the Everettians are right in their interpretation(s) of quantum theory, and certain orthogonal states in Hilbert space are classical worlds, then what’s all the other stuff? Now the other stuff is certainly quantitative, but it doesn’t ‘do’ anything in our physical theories, at least that I know of. Perhaps, by brittle analogy, our entire quantitative grasp of the world is like those degrees of freedom that (might) represent classical worlds in quantum theory, and the ‘other stuff’ are those degrees of freedom that represent qualities?
What’s all that got to do with e.g. poetry? Well, just to say that endlessly cramming experience into discrete units is, quite frankly, barbaric, and doesn’t even represent what mathematicians and physicists do, never mind poets!
(On a different note, that’s not to say there’s nothing to a kind of Pythagorean metaphysic. One doesn’t have to believe in ‘impact’ as a good funding criterion to believe in e.g. ante rem structuralism, etc.)
[…] Stephen Mumford: 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. […]
I completely agree: the attempt to turn everything into numbers would be just plain nuts. But much of the way we use quantitative methods has nothing to do with strange metaphysics. It might seem to me that certain things are typically so or rarely so or overwhelmingly so, but I can be quite wrong about that and it’s only by counting carefully that we can be sure. If the numbers don’t reflect anything independently worth caring about, the numbers are empty. But nothing like the world we live in would be remotely possible if we haven’t learned how to use numbers and, more generally, mathematical techniques in powerful ways.
I’d venture to suggest that even in your wine example there’s something implicitly numeric going on. At the very least we don’t apply the vintage designation unless the experts mainly agree. And if it turned out the different panels of experts gave very different judgments, we would find the designation ‘vintage’ a lot less meaningful. In fact appealing to numbers (in particular using statistical methods) sometimes tells us exactly this sort of thing: that distinctions we’re inclined to believe we can make and designations we take to make sense aren’t so robust after all — or that, conversely, there’s a real phenomenon where we never expected it.
So no: the world isn’t made of numbers. And yes: life without the qualitative is unimaginable. But that leaves a lot for numbers to do without turning us into Pythagoreans.
[…] Stephen Mumford: 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. […]