I think it's generally accepted that concepts or categories are *not* defined by necessary and sufficient conditions.
See the charmingly titled *The Big Book of Concepts 
*, 2002. It's a summary of the state of the knowledge back then.
Categories tend to have fuzzy edges. There are elements not clearly in or out of a category. Is a beanbag chair a chair? Is the pope a bachelor? Well, *technically*...
Together with fuzzy edges, there are also *central examples* or Prototypes for Concepts, ones that are in some sense the *best* examples. For example, in the 1970's, the canonical bachelor lived in the big city, probably read Playboy magazine (it did have good articles), prided himself on his knowledge of liquor and stereo systems, and so on.
Men without those attributes were less central to the concept of bachelor.
See also Wittgenstein and "family resemblance ".
> [Wittgenstein] argues that things which could be thought to be connected by one essential common feature may in fact be connected by a series of overlapping similarities, where no one feature is common to all of the things.
>