In my last post, I showed that the brain does not encode concepts in terms of necessary and sufficient conditions. So, any philosophical practice which assumes this — as much of 20th century conceptual analysis seems to do — is misguided.

This argument must be missing something crucial, because it fails to account for why the necessary-and-sufficient approach is so fantastically useful in mathematics. Mathematics deals with human concepts. Many of these concepts are very likely not stored in the brain as necessary and sufficient conditions. (Concepts learned in a formal setting might be stored that way, but there's little reason to think that a common concept like "triangle" is for most people.) And yet it proved incredibly fruitful to recast these concepts in terms of necessary and sufficient conditions.

In the case of mathematics, it turns out to be worthwhile to think about concepts in the decidedly unnatural mode of necessary and sufficient conditions. One might reasonably have hoped that the same admittedly unnatural mode would prove similarly worthwhile for concepts like "democracy". After all, unnatural doesn't necessarily mean worse. Now, for concepts like "democracy", the unnatural approach does prove to be worse. But it can't be simply because the approach was unnatural.