Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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
   • PermaLink
   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