When Newton came up with his theory of gravitation, astrologers used it as evidence that they were right that the stars affect our actions on earth. They didn't calculate, as I have, that the moon has the equivalent pull on a person as the weight of half a teaspoon of dried parsley. Gravity was a fad. Gravity doesn't comfortably belong in astrology. What fads are misapplied these days?
One of the big candidates is geometry in prototypicality theory. Rosch devised the theory of prototypes by for example getting people to rank how much they thought something was a piece of furniture. She found that it was a spectrum, and with further research and thinking she was able to throw out the Aristotelian idea of necessary and sufficient conditions. Having done this, she needed a new metaphor to use for categorisation. What metaphor would you pick? She vacillated:
“The term prototype has been defined in Eleanor Rosch's study ‘Natural Categories’ (1973) and was first defined as a stimulus, which takes a salient position in the formation of a category as it is the first stimulus to be associated with that category. Later, she redefined it as the most central member of a category.” (Wikipedia)
Rosch started with a more narrative analogy (with some geometric constituents), and then switched to a purely geometric analogy. It seems very hard to avoid the geometric analogy when talking about classes. But I want to suggest that this is a blunder: that geometry is not the most natural or useful metaphor in prototypicality studies.
The most natural alternative metaphor to geometry is that of family resemblance, though there may be others even more productive. At any rate, the family metaphor was applied to non-Aristotelian classification before Rosch's theory, so it has historical precedence too.
The geometric metaphor for categorisation subsequently became attractive for many reasons. These are psychological, not scientific, reasons. We can, for example, ask with geometry what kind or kinds of geometry we have, which is an attractive proposition. It opens the door for further work, which is what academics want. We don't want to have an insight and say that there are no other insights. Application of an insight is not enough: we want further insights to can justify academic funding.
Another problem that I suspect contributed to the misapplication here of the spatial metaphor, the metaphor underlying geometry, is that it's a very common one. Space is so pervasive cognitively that it's not surprising that we apply it to all sorts of abstract things. Indeed, it was a common feature of Aristotelian classification too — think of venn diagrams and so on. And that's another problem: when you use a spatial metaphor for prototype theory, not only are you tempting people into a too detailed geometric analysis, but you're hinting at a link with Aristotelian classification.
Prototype theory is not a mere modification of Aristotelian classification. It is a different thing entirely. Because Rosch had a list of numbers, “table = 3, piano = 35”, because this was her way of measuring our activities associated with categorisation, this too was a step towards thinking of categorisation itself as being most naturally mathematical. But the family metaphor shows you that this need not be so natural. Indeed, the family metaphor feels to me more natural, and when I philosophise I find that it assists me a lot more than the mathematical metaphors. (The problems of overanalysis and the linking back to the Aristotelian points of view are the main stumbling blocks for me with the latter.)
We are addicted to mathematics, as we are addicted to science. Let us not be content in this. If we want to come to new realisations with respect to categorisation, we may have to search very hard for a new kind of metaphor to use.
We must also ask: what exactly do we want to achieve at the moment with our metaphors for classification? As far as I can tell, the primary goal is, or ought to be, to overturn the Aristotelian views which still so pervade the colloquial thinking. Categories as geometry takes us so far away from achieving this goal that I believe we ought to eschew it utterly, wherever this is indeed our goal.
by Sean B. Palmer