It’s not exactly the same, but I would argue that the issues with “Dog” versus “Cat” for the picture are best captured with that formalism—the boundaries between categories are not strict.
To be more technical, there are a couple locations where fuzziness can exist. First, the mapping in reality is potentially fuzzy since someone could, in theory, bio-engineer a kuppy or cat-dog. These would be partly members of the cat set, and partly members of the dog set, perhaps in proportion to the genetic resemblance to each of the parent categories.
Second, the process that leads to the picture, involving a camera and a physical item in space, is a mapping from reality to an image. That is, reality may have a sharp boundary between dogs and cats, but the space of possible pictures of a given resolution is far smaller than the space of physical configurations that can be photographed, so the mapping from reality->pictures is many-to-one, creating a different irresolvable fuzziness—perhaps 70% of the plausible configurations that lead to this set of pixels are cats, and 30% are dogs, so the picture has a fuzzy set membership.
Lastly, there is mental fuzziness, which usually captures the other two implicitly, but has the additional fuzziness created because the categories were made for man, not man for the categories. That is, the categories themselves may not map to reality coherently. This is different from the first issue, where “sharp” genetic boundaries like that between dogs and cats do map to reality correctly, but items can be made to sit on the line. This third issues is that the category may not map coherently to any actual distinction, or may be fundamentally ambiguous, as Scott’s post details for “Man vs. Woman” or “Planet vs. Planetoid”—items can partly match one or more than one category, and be fuzzy members of the set.
Each of these, it seems, can be captured fairly well as fuzzy sets, which is why I’m proposing that your usage has a high degree of membership in the fuzzy set of things that can be represented by fuzzy sets.
I’m not sure it maps exactly onto fuzzy sets the way I described it, but it does feel related to that area of research.
It’s not exactly the same, but I would argue that the issues with “Dog” versus “Cat” for the picture are best captured with that formalism—the boundaries between categories are not strict.
To be more technical, there are a couple locations where fuzziness can exist. First, the mapping in reality is potentially fuzzy since someone could, in theory, bio-engineer a kuppy or cat-dog. These would be partly members of the cat set, and partly members of the dog set, perhaps in proportion to the genetic resemblance to each of the parent categories.
Second, the process that leads to the picture, involving a camera and a physical item in space, is a mapping from reality to an image. That is, reality may have a sharp boundary between dogs and cats, but the space of possible pictures of a given resolution is far smaller than the space of physical configurations that can be photographed, so the mapping from reality->pictures is many-to-one, creating a different irresolvable fuzziness—perhaps 70% of the plausible configurations that lead to this set of pixels are cats, and 30% are dogs, so the picture has a fuzzy set membership.
Lastly, there is mental fuzziness, which usually captures the other two implicitly, but has the additional fuzziness created because the categories were made for man, not man for the categories. That is, the categories themselves may not map to reality coherently. This is different from the first issue, where “sharp” genetic boundaries like that between dogs and cats do map to reality correctly, but items can be made to sit on the line. This third issues is that the category may not map coherently to any actual distinction, or may be fundamentally ambiguous, as Scott’s post details for “Man vs. Woman” or “Planet vs. Planetoid”—items can partly match one or more than one category, and be fuzzy members of the set.
Each of these, it seems, can be captured fairly well as fuzzy sets, which is why I’m proposing that your usage has a high degree of membership in the fuzzy set of things that can be represented by fuzzy sets.
I agree with all this.