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Thus the classical picture, informed by a connection between concepts and sets present in the very word “classify”, sees the theoretical resources of set theory as the proper instruments for describing language and thought. Classes, and sets, have sharp boundaries… The concepts which classify without setting boundaries include the ones traditionally counted as vague: red, heap, child, bald, to take some famous examples. The first stage in showing that these are boundaryless concepts involves showing that there is no set of which they are true: they do not classify at all, if the only way to classify is to assign things to classes or sets.

Sainbsury, concepts without boundaries

I am not entirely sure, but Sainsbury seems to be saying that we can classify someone as bald or not bald, but there is no set of bald people, because baldness is vague. I think that's we can still say "I am bald" because the lack of a boundary is a mere semantic fact.

How would we ever infer that some lack of a boundary is a fact and not just conceptual?

Can qualia be vague: because if so that must be so independent of language, right, an actual fact? Would that mean the lack of a boundary is non-conceptual?

Mauro ALLEGRANZA
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  • prima facie, it is vague whether someone with green colour deficiency sees green or red, though i suppose it's easier to believe they only see red –  Jul 11 '23 at 03:27
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    Sainsbury doesn't sound like he understands the concept of sets, much less of (proper) classes. For one, fuzzy set theory allows for something equal to, or approximating, vagueness (first- or higher-order as it may be). Moreover, per interval notation, we can indicate half- or fully-open sets (...], [...), or (...), and indeed the notion of closed and unbounded sets has been given in set theory going back to Mahlo, if not earlier. – Kristian Berry Jul 11 '23 at 03:28
  • ok i have no idea, having no experience of logic whatsoever (beyond an introduction to syllogistic reasoning processes in psych class) @KristianBerry –  Jul 11 '23 at 03:29
  • Sainsbury might have a real point in mind, and perhaps he just made a poor choice of words (see about [nonconceptual mental content](https://plato.stanford.edu/entries/content-nonconceptual/), for example). – Kristian Berry Jul 11 '23 at 03:31
  • it's still being published, so probably the latter @KristianBerry ! –  Jul 11 '23 at 03:32
  • I don't *think* it makes sense to say "I am dead" and then infer we cannot "die" haha @KristianBerry probably just the wrong word for life –  Jul 11 '23 at 06:13
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    No, if they are "boundaryless concepts" you cannot classify every single instance as e.g. bald or not bald, otherwise you will be able to sort them into two mutually exclusive classes. – Mauro ALLEGRANZA Jul 11 '23 at 06:53
  • OK, but I don't understand what you are saying "No" to there @MauroALLEGRANZA do you mean we cannot ever infer such a thing? –  Jul 11 '23 at 07:01
  • Vague means that we cannot apply it in **every** case with a Y/N approach; of course, in e.g. 90% cases we can use it safely: we can assert correctly that Plato is bald and that Mike Jagger is not, but we cannot form the set of bald people an that of non-bald ones without a sort of "remainder" made of uncertain cases. For this, see Fuzzy sets. – Mauro ALLEGRANZA Jul 11 '23 at 07:07
  • this conversation is going on too long now but i was wondering if you mean qualia cannot be vague @MauroALLEGRANZA –  Jul 11 '23 at 07:09
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    But are [qualia](https://plato.stanford.edu/entries/qualia/) concepts? – Mauro ALLEGRANZA Jul 11 '23 at 10:14
  • Clearly, back when the Americas weren't yet discovered, peeps had a simpler view of the world. As for qualia, think of it as a competition. – Agent Smith Jul 12 '23 at 12:16

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