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Warrigal comments on Concepts Don't Work That Way - Less Wrong
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Comments (88)
Then, if I'm not mistaken, the point being made here is that our idea of beauty is not a single, specific concept, but a vague feeling that could correspond to any of myriad different concepts. Therefore, we can't give necessary and sufficient conditions for a thing to be beautiful—unless, as you mention, we determine which concept of beauty we're referring to.
(It sounds to me like "concept" means one thing when lukeprog says it and something else when you say it.)
All that may be true - my beef is that we don't get that from cognitive science! Plain old philosophy gets us there.
Oh, my point was that (for me) 'beauty' isn't a concept but just a token that gets bandied about. I have some faith that there is a concept behind the token when other people use the word, and I have used the word in contexts where I've estimated that the concept is somehow 'close enough' to what might be meant by beauty ... but simultaneously I'm aware I'm not communicating any specific concept and probably not communicating the one I intend.
Even a vague feeling could point to a concept. If you have a vague feeling about 'beauty' that could correspond to any of a myriad of different concepts, then that is probably a set. (The set of all things you do tie or would tie to that feeling at that moment.)
I'm liking the idea that any concept must point to an actual set, though, and I think I'll go with that definition in my thoughts from now on. So: a 'concept' is something in my brain that defines a set.
... But now it is time to go back to lukeprog's post and check what he meant by concept and start using that token with his meaning in this context..
I don't think you do have anything in your brain that defines a set, except when you formulate a precise verbal or other description of an actual mathematical set. Which is not what you're doing when you ponder a concept like beauty.
In the instant that you think about whether something is "beautiful" the concept is a transient configuration of neuron state that at one particular point in time associates something in your memory or perception with the word "beautiful". In which case it's not any more meaningful than any other random association that happens to occur.
How would you tell this is what is happening instead of your brain containing a well-defined set? First note, it is not going to be consistent - you will change your mind. It's also not going to be complete - there will be things where you don't have any particular feeling about whether they are beautiful. Also, you will be able to say whether things are beautiful even when they aren't a discrete thing and have boundaries just as fuzzy as the concept you relate them to (e.g. a beach with surrounding landscape). And you will do this without even noticing.
In a way, I completely agree with you. I agree with you in the sense that I think you are slicing reality in exactly the right way, and any remaining disagreement is just definitional.
Agreed, we should distinguish this random-association-type thought from the brain process (however it may be done) of mentally defining a set.
What I want to do next is say that at this random-association stage of a thought process, you don't have a concept. Ithink you haven't seized a concept unless you've defined the set. The concept, if it is lurking there, hasn't been understood and hasn't been 'owned'.
Yes, I think this transience is what makes it difficult to recognize and discuss concepts correctly. For example, in several places 'concept families' have been mentioned, as though the primary object is a fuzzy set and at instances of thought we're picking out particular sets from this fuzzy family. I see this reversed: sets are always specific, but our thoughts transition so fluidly from one set to a nearby set that we imagine there is a single larger fuzzy set that these sets are coming from.
For example, when we think of the set of fish, we are likely to first consider something like 'the set of animals that look just like Nemo, but with any color variation'. (This is what was referred to as a 'most typical' member.) Then a few seconds later we remember sharks are also fish and throw them in. Both sets are called 'fish' in our minds from one moment to the next, but they were different sets and our brain can distinguish them, we just didn't bother to track the differences as our concept of 'fish' evolved. So a thought process will evolve a lineage of sets SetFish1-->SetFish2-->SetFish3 over the course of a few seconds.
I think the fact that our brain can easily distinguish them all (via necessary and sufficient conditions, if not actual single-word linguistic tokens) is evidence that we understand the individual sets first, and the understanding (concept) of a 'fuzzy set family' comes from the observation and generalization of this lineage.
Note: I mean, this is what I think now. I'd be interested in a different paradigm for how my brain understands a concept and/or a set.
Or it's any of myriad different sets.
But yes, trying to standardize our terminology will probably be helpful!