Though some situations will demand strict borders, in general the fuzzy region approach seems more beneficial, because it allows for quick low-level inductive reasoning
You’ve convinced me on the importance of fuzzy sets. I’m sure quick low-level inductive reasoning is of vital importance, but even more immediately it seems that flexibility in meaning is useful for communication. I don’t have to hunt for the exact right word, many approximate words will do, and I can describe new concepts by stretching an old one.
However, when you write:
It’s less brittle to use probabilities in situations like these than strict boolean sufficient-or-necessary values,
I don’t see how sufficient-or-necessary defined sets don’t allow fuzziness. For example, saying that a bird must have feathers (a necessary condition) and that a bluebird is a bird (sufficient condition) then there is still plenty of gray area for penguins and ostriches.
I think of sufficient conditions as being associations. We learn that penguins, ostriches and doves are all birds so those are sufficient conditions. A necessary conditions puts an edge on your set—staplers aren’t birds because they don’t have feathers.
On the other hand, a stapler that looks like a bird could be thought of as a bird to oneself. If anything has enough of the characteristics of a bird you could consider it one. For example a small plastic object with no feathers whatsoever is a ‘birdie’ because it moves like a bird.
So now I’m leaning towards agreeing. We just have associations, things are like other things if the characteristics overlap, and there aren’t any necessary conditions for deciding if something is ‘like’ something else.
[...]it seems that flexibility in meaning is useful for communication. I don’t have to hunt for the exact right word, many approximate words will do, and I can describe new concepts by stretching an old one.
Yes, strongly agreed. This idea makes me want to think of adjectives as tugging a concept-defining region of thing-space in a new direction.
That works especially well in languages like Lojban, where adjectives and nouns are not distinguished from each other. For example there is “blanu” which means “x is blue” and there is “zdani’ which means “x is a house”, and you can say “blanu zdani” (blueish-house) just as easily as “zdani blanu” (houseish-blue).
[...]saying that a bird must have feathers (a necessary condition)
That actually is a good example of a brittle requirement, in ways that are even more directly problematic than shuttlecocks and bird-shaped staplers. What about a plucked chicken? What about a duck that, due to a genetic disease, never had feathers? What about (NOTE: This example isn’t valid re: real evolutionary history) a member of an intermediary species between pterodactyl and modern birds?
Not that it particularly affects your point, but pterodactyls are not genetic precursors to birds (they split off before the clade Dinosauria,) and feathers predate the first true dinosaurs capable of flight.
That actually is a good example of a brittle requirement,
Yeah, good point. I’m entirely convinced. Even for an apparently straight-forward category like ‘bird’, there’s not a single necessary condition you can point to. Even if there are some examples of categories with necessary conditions (I don’t know), this is evidence that the necessary conditions aren’t an intrinsic part of the way we structure a concept.
You’ve convinced me on the importance of fuzzy sets. I’m sure quick low-level inductive reasoning is of vital importance, but even more immediately it seems that flexibility in meaning is useful for communication. I don’t have to hunt for the exact right word, many approximate words will do, and I can describe new concepts by stretching an old one.
However, when you write:
I don’t see how sufficient-or-necessary defined sets don’t allow fuzziness. For example, saying that a bird must have feathers (a necessary condition) and that a bluebird is a bird (sufficient condition) then there is still plenty of gray area for penguins and ostriches.
I think of sufficient conditions as being associations. We learn that penguins, ostriches and doves are all birds so those are sufficient conditions. A necessary conditions puts an edge on your set—staplers aren’t birds because they don’t have feathers.
On the other hand, a stapler that looks like a bird could be thought of as a bird to oneself. If anything has enough of the characteristics of a bird you could consider it one. For example a small plastic object with no feathers whatsoever is a ‘birdie’ because it moves like a bird.
So now I’m leaning towards agreeing. We just have associations, things are like other things if the characteristics overlap, and there aren’t any necessary conditions for deciding if something is ‘like’ something else.
Yes, strongly agreed. This idea makes me want to think of adjectives as tugging a concept-defining region of thing-space in a new direction.
That works especially well in languages like Lojban, where adjectives and nouns are not distinguished from each other. For example there is “blanu” which means “x is blue” and there is “zdani’ which means “x is a house”, and you can say “blanu zdani” (blueish-house) just as easily as “zdani blanu” (houseish-blue).
That actually is a good example of a brittle requirement, in ways that are even more directly problematic than shuttlecocks and bird-shaped staplers. What about a plucked chicken? What about a duck that, due to a genetic disease, never had feathers? What about (NOTE: This example isn’t valid re: real evolutionary history) a member of an intermediary species between pterodactyl and modern birds?
Not that it particularly affects your point, but pterodactyls are not genetic precursors to birds (they split off before the clade Dinosauria,) and feathers predate the first true dinosaurs capable of flight.
Whoops, didn’t know that, thanks.
Yeah, good point. I’m entirely convinced. Even for an apparently straight-forward category like ‘bird’, there’s not a single necessary condition you can point to. Even if there are some examples of categories with necessary conditions (I don’t know), this is evidence that the necessary conditions aren’t an intrinsic part of the way we structure a concept.