I think this is reversing the role of words and concepts. You should not be seeking a crisp definition of a fuzzy concept, you should be seeking a crisp concept or concepts in the neighbourhood of your fuzzy one, that can better do the work of the fuzzy one.
The history of mathematics abounds in examples. Imagine yourself some centuries back and ask “what is a function?” (before the word was even introduced). Or “what is a polyhedron?”. Difficulties surfaced in reasoning about these imprecisely defined things, which led to the discovery of more precise concepts that put the knowledge previously built on the fuzzy ones on a clearer and stronger foundation. Mathematicians did not discover what their fuzzy concepts of functions and polyhedra “really were”, or what the words “really meant”, or discover “the right definitions” for the words. They discovered new concepts that served better.
In the space of psychology (cognition) and systems build of cognitive agents (such as the society), i.e., complex systems, crisp concepts “in the neighbourhood of our fuzzy ones” will tend simplify the reality too much, perhaps sometimes in detrimental or even catastrophic ways (cf. “Value is fragile”), rather than amplify your prediction and reasoning power thanks to formalisation.
I’ve discussed these problems here and the tradeoff in capabilities between formalisation and “intuitive”/”fuzzy”/connectionistic reasoning here. See also this recent Jim Rutt show with David Krakauer where they discuss related themes (philosophy of science and understanding in the AI age).
I think I agree with essentially everything you are saying here? Except that I was trying to emphasize something different from what you are emphasizing.
More specifically: I was trying to emphasize the point that [the concept that the word “cooperation” currently points to] is very fuzzy. Because it seemed to me that this was insufficiently clear (or at least not common knowledge). And appreciating this seemed necessary for ppl agreeing that (1) our mission should be to find crisp concepts in the vicinity of the fuzzy one (2) but that we shouldn’t be surprised when those concepts fail to fully capture everything we wanted. (And also (3) avoiding unnecessary arguments about which definition is better, at least to the extent that those only stem from (1) + (2).)
And to highlight a particular point: I endorse your claim about crisp concepts, but I think it should be ammended as follows:
You should not be seeking a crisp definition of a fuzzy concept, you should be seeking a crisp concept or concepts in the neighbourhood of your fuzzy one, that can better do the work of the fuzzy one. However, you should keep in mind that the given collection of crisp concepts might fail to capture some important nuances of the fuzzy concept.
(And it is fine that this difference is there—as long as we don’t forget about it.)
I think this is reversing the role of words and concepts. You should not be seeking a crisp definition of a fuzzy concept, you should be seeking a crisp concept or concepts in the neighbourhood of your fuzzy one, that can better do the work of the fuzzy one.
The history of mathematics abounds in examples. Imagine yourself some centuries back and ask “what is a function?” (before the word was even introduced). Or “what is a polyhedron?”. Difficulties surfaced in reasoning about these imprecisely defined things, which led to the discovery of more precise concepts that put the knowledge previously built on the fuzzy ones on a clearer and stronger foundation. Mathematicians did not discover what their fuzzy concepts of functions and polyhedra “really were”, or what the words “really meant”, or discover “the right definitions” for the words. They discovered new concepts that served better.
In the space of psychology (cognition) and systems build of cognitive agents (such as the society), i.e., complex systems, crisp concepts “in the neighbourhood of our fuzzy ones” will tend simplify the reality too much, perhaps sometimes in detrimental or even catastrophic ways (cf. “Value is fragile”), rather than amplify your prediction and reasoning power thanks to formalisation.
I’ve discussed these problems here and the tradeoff in capabilities between formalisation and “intuitive”/”fuzzy”/connectionistic reasoning here. See also this recent Jim Rutt show with David Krakauer where they discuss related themes (philosophy of science and understanding in the AI age).
I think I agree with essentially everything you are saying here? Except that I was trying to emphasize something different from what you are emphasizing.
More specifically: I was trying to emphasize the point that [the concept that the word “cooperation” currently points to] is very fuzzy. Because it seemed to me that this was insufficiently clear (or at least not common knowledge). And appreciating this seemed necessary for ppl agreeing that (1) our mission should be to find crisp concepts in the vicinity of the fuzzy one (2) but that we shouldn’t be surprised when those concepts fail to fully capture everything we wanted. (And also (3) avoiding unnecessary arguments about which definition is better, at least to the extent that those only stem from (1) + (2).)
And to highlight a particular point: I endorse your claim about crisp concepts, but I think it should be ammended as follows:
(And it is fine that this difference is there—as long as we don’t forget about it.)