# Does Science Require Metaphysics? – The Case of Vagueness

Ilkka Pättiniemi

Some time ago, Ilmari made a general case against the metaphysicians’ claim that science requires metaphysics. I agree with what was said there, but wish to make a more piecemeal case against such claims. To that end, I will look at vagueness, and see whether a metaphysical (or a merely philosophical) solution to the problems vagueness gives rise to is needed.

The problem of vagueness is an age old problem in philosophy, starting with the sorites paradox first known to be formulated in the 4th century BCE by – who else? – the Greeks. What is the paradox? It is a problem concerning concepts, namely vague concepts. Take the concept ‘heap’ as an example. One can derive the following inference:

Assume you have a heap of sand totalling n grains of sand, then

1. if you have a heap of sand (n grains), then after removing one grain of sand you will still have a heap of sand  (n – 1 grains).
2. If you have a heap of sand (n – 1 grains), then after removing one grain of sand you will still have a heap of sand  (n – 2 grains).
3. If you have a heap of sand (n – 2 grains), then after removing one grain of sand you will still have a heap of sand  (n – 3 grains).
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k. If you have a heap of sand (n – k grains), then after removing one grain of sand you will still have a heap of sand  (n – k – 1 grains).
Therefore no matter how many grains of sand you remove from a heap of sand, you will still have a heap of sand!

This can also be done the other way around with the conclusion that, no matter how many grains you add to a non-heap, you will never get a heap. But all this is manifestly silly! Clearly at some point we will stop (start) having a heap. There is, however, a problem here: it seems we cannot determine a clear dividing line between heaps and non-heaps (say 15 grains of sand). But so what? What do heaps have to do with science? Simply put, this has to do with logic

One property of vague concepts like ‘heap’, is that they do not jibe well with bivalence (which implies the law of excluded middle). And bivalence in turn is needed to keep the logic we use simple and fruitful – in a word classical. And such a logic is needed, in turn so that we are able to formalise and mathematise our scientific theories. (This is not strictly so, but it at least helps us to keep our formalisations simple.) Still, if the problem were only with concepts like ‘heap’, ‘tall’, ‘small’ and so on, this would not be a problem, as one rarely needs such terms in (formalised) science.

However, it turns out that a lot of concepts in ordinary language share this property of vagueness. And some of these concepts are used in science – concepts like species, mountain, cloud, gender, mammal to name a few. Here we can see problems beginning to rise: atmospheric sciences need terms like ‘cloud’ to be bivalent, as do biologists terms like ‘species’ and ‘mammal’. So, how to make such terms non-vague?

A (metaphysical) solution might be to say that there is indeed a well-defined dividing line between heaps and non-heaps, a proper definition of what constitutes a biological species, and so on. We simply are ignorant of these things. This line of thinking is championed by Timothy Williamson (1994). But this will be of little help to the working scientist. It will do nothing to settle the dispute between and advocate of the biological species conception and the ecological species conception. Nor will it tell the geologist what criteria to demand of a mountain. And so on.

A second (also metaphysical) solution is to say that vague terms do not track anything. There are no heaps, so there is no question of a dividing line between heaps and non-heaps. The same with clouds, genders, mountains, species and what-have-you. This nihilistic view was championed by Peter Unger (1979). But again, this is of no help to the working scientist, who might at this point begin to wonder the very point of this discussion.

I will offer a third possibility (though there are many more to be had), a solution I share with the great Willard Van Orman Quine (1981). This way of doing things leaves things as they were for the scientist, while (hopefully) putting at ease the worries raised by philosophers. Simply put, we accept that terms might not have any clear conditions of application, but nevertheless we make a precisification, that is we stipulate a dividing line between mountains and non-mountains, or a definition for biological species, and so on. Such a stipulation allows us to enjoy the benefits of bivalence while freeing us from additional metaphysical assumptions.

But there is a price for such a pragmatic move: we might have made a bad precisification! Bad in which way? Bad in a way that the stipulation made ends up going against the goals we were trying to accomplish. Say that we are convinced that the biological species concept, which is based on sexual reproduction, is the one to use in biological classification. If we are then confronted with an asexually reproducing organism (like bacteria) we will be thwarted in our efforts to classify such beings. Another example comes from the 2006 decision of the International Astronomical Union (IAU) to ‘downgrade’ the (until then) planet Pluto to the status of a dwarf planet. It had turned out that our solar system contains a great many objects that share their properties with Pluto and, crucially, that Pluto does not share certain important properties of the other planets. So, the IAU faced a conundrum: either accept a large group of celestial objects as planets, or remove from Pluto the status of a ‘planet’. So, a new definition for planets was developed along with a brand new definition for dwarf planets.

Therefore, the price for bivalence is that we have to both be cognisant of the fact that we have made a (somewhat arbitrary) stipulation and willing to change our precisifications and definitions when practical needs require. Such is the way of things, and is the way the sciences are already being practiced. So, at least this time around, there was no need for metaphysics – or even philosophy! – to come and save the day.

References:
Quine, Willard Van Orman (1981). What Price Bivalence?, in Theories and Things, Cambridge MA: Harvard University Press, 31–37.
Unger, Peter (1979). There Are No Ordinary Things, Synthese 41, No. 2, 117–154.
Williamson, Timothy (1994). Vagueness, London: Routledge.