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1. • CommentRowNumber1.
   • CommentAuthorjonsterling
   • CommentTimeAug 3rd 2022
   • PermaLink
   Author: jonsterling
   Format: MarkdownItexThe shriek/star notation for existential and universal quantification was backwards from the usual conventions (which are: lower shriek for left adjoint to base change, lower star for right adjoint to base change). <a href="https://ncatlab.org/nlab/revision/diff/quantification/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantification/22">v22</a>, <a href="https://ncatlab.org/nlab/show/quantification">current</a>

   The shriek/star notation for existential and universal quantification was backwards from the usual conventions (which are: lower shriek for left adjoint to base change, lower star for right adjoint to base change).

   diff, v22, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexLooking at the section on "Guarded quantification" ([here](https://ncatlab.org/nlab/show/quantification#Guarded)), I find the language a little odd, in how it keeps referring to "types" but really speaks very much as of sets. I have adjusted wording slightly, but there remains room to improve the wording here, I think. Also, I touched the typesetting of the two formulas, in order to make the form of the syntax tree visually more manifest. <a href="https://ncatlab.org/nlab/revision/diff/quantification/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantification/28">v28</a>, <a href="https://ncatlab.org/nlab/show/quantification">current</a>

   Looking at the section on “Guarded quantification” (here), I find the language a little odd, in how it keeps referring to “types” but really speaks very much as of sets.

   I have adjusted wording slightly, but there remains room to improve the wording here, I think.

   Also, I touched the typesetting of the two formulas, in order to make the form of the syntax tree visually more manifest.

   diff, v28, current

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMay 24th 2024
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   Author: zskoda
   Format: MarkdownItexGeneral linguistical and philosophical discussion is in * [Quantifiers and quantification](https://plato.stanford.edu/entries/quantification) in Stanford Encyclopedia of Philosophy By the way, quite a few references do not consider $\exists!$ a quantifier but an abbreviation (as it is by definition). Maybe we should mention this. The point is that equality is, in this approach, considered a distinguished predicate satisfying the substitution rule, reflexivity, symmetricity and transitivity, and appears to be a syntactic tool rather than something about context, or talking about semantics/testing domain where the truth of the statement with a free variable is tested. <a href="https://ncatlab.org/nlab/revision/diff/quantification/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantification/30">v30</a>, <a href="https://ncatlab.org/nlab/show/quantification">current</a>

   General linguistical and philosophical discussion is in

   • Quantifiers and quantification in Stanford Encyclopedia of Philosophy

   By the way, quite a few references do not consider $\exists!$ a quantifier but an abbreviation (as it is by definition). Maybe we should mention this. The point is that equality is, in this approach, considered a distinguished predicate satisfying the substitution rule, reflexivity, symmetricity and transitivity, and appears to be a syntactic tool rather than something about context, or talking about semantics/testing domain where the truth of the statement with a free variable is tested.

   diff, v30, current