This question is in context of the umbrella view of objects, that there exists a general category that everything falls under. Here are the quote and link that peaked my curiosity.

Finally, note that there may be reason to be wary of any fully general category (whether expressed by ‘object’, ‘thing’, ‘entity’, or whatnot.). There may be reason, that is, to doubt the metaphysical conjunct of the Umbrella View. First and perhaps most importantly, there are paradoxes and puzzles associated with talking about. or ‘quantifying over’, literally every thing.


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    Are you including mathematical objects? If you use the von Neumann definition of ordinals where each ordinal is defined as the set of all smaller ordinals (the smallest one being the empty set), then you can't have a set of all ordinals since that would itself be a new ordinal larger than any of its members (apparently this is a specific version of the more general Burali-Forti paradox) – Hypnosifl Sep 18 '19 at 21:58
  • Russell's paradox , Berry paradox, the key problem is expressed in the vicious circle principle. Look at Williamson's Everything for trying to deal with that. – Conifold Sep 19 '19 at 2:42
  • @Hypnosifl "each ordinal is defined as the set of all smaller ordinals" -- You just quantified over the class of all ordinals. You made a statement about every ordinal. Yes? – user4894 Sep 19 '19 at 4:05
  • It's true that quantifying over a group in logical terms is not quite the same as treating them as a set mathematically, the problem with the ordinals only arises if you try to do the latter. Not sure if there are any basic paradoxes with quantifying over everything in the logical sense alone. – Hypnosifl Sep 19 '19 at 4:59
  • @Conifold I don't see how either Russell's or Berry's paradoxes are paradoxes of quantification. Russell shows that full comprehension isn't permissible, but says nothing about full quantification (although of course you can argue that the particular issue with the Russell set is that it's defined using full quantification, that's not necessary). Berry meanwhile has nothing to do with quantification at all that I can see, but rather the issue of defining definability. Since this is adequately treated in first-order logic, which does allow full quantification, I don't see the relevance. – Noah Schweber Sep 19 '19 at 21:38

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