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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.
   • CommentAuthornLab edit announcer
   • CommentTimeDec 1st 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting article on the statement "2 + 2 = 5", traditionally formulated in the natural numbers, and its status in some weak foundations of mathematics, before concluding with a section regarding its relevance to the philosophy of mathematics. Anonymous <a href="https://ncatlab.org/nlab/revision/2+%2B+2+%3D+5/1">v1</a>, <a href="https://ncatlab.org/nlab/show/2+%2B+2+%3D+5">current</a>

   starting article on the statement “2 + 2 = 5”, traditionally formulated in the natural numbers, and its status in some weak foundations of mathematics, before concluding with a section regarding its relevance to the philosophy of mathematics.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 1st 2022
   • (edited Dec 1st 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhat the technical part of the discussion in the entry really refers to is the fact that the term "2+2" and the term "5" are equal as proofs of the proposition that "$\mathbb{N}$ is inhabited". The text that is offered around this fact I find misleading and counterproductive. I vote for this entry being deleted.

   What the technical part of the discussion in the entry really refers to is the fact that the term “2+2” and the term “5” are equal as proofs of the proposition that “$\mathbb{N}$ is inhabited”.

   The text that is offered around this fact I find misleading and counterproductive. I vote for this entry being deleted.

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 1st 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThe fact that sets (i.e., homotopy 0-types) can be localized to get homotopy (-1)-types (i.e., truth values) is nice, but clearly does not belong in a separate article, and Section 3 (Philosophical consequences) is stretching things too far.

   The fact that sets (i.e., homotopy 0-types) can be localized to get homotopy (-1)-types (i.e., truth values) is nice, but clearly does not belong in a separate article, and Section 3 (Philosophical consequences) is stretching things too far.

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeDec 1st 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexAre the natural numbers actuslly the natural numbers if every type is (-1)-truncated? (similarly goes for the circle type in the presence of UIP)

   Are the natural numbers actuslly the natural numbers if every type is (-1)-truncated? (similarly goes for the circle type in the presence of UIP)

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 2nd 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI agree that this article is not a productive contribution to the nLab, and further, the title was the subject of a [wide-ranging debate](https://www.popularmechanics.com/science/math/a33547137/why-some-people-think-2-plus-2-equals-5/) spanning everything from maths education to hot-button political topics a couple of years ago. If one wants a technical discussion as at the page, then I think it _might_ fit on a different page that is about the overarching concept that is being interrogated (eg weak systems of arithmetic, or homotopy (-1)-types etc).

   I agree that this article is not a productive contribution to the nLab, and further, the title was the subject of a wide-ranging debate spanning everything from maths education to hot-button political topics a couple of years ago.

   If one wants a technical discussion as at the page, then I think it might fit on a different page that is about the overarching concept that is being interrogated (eg weak systems of arithmetic, or homotopy (-1)-types etc).

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 3rd 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have cleared the entry and renamed to a generic title. (That's the closest to deleting an entry here without logging into the server.) <a href="https://ncatlab.org/nlab/revision/diff/empty+215/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/empty+215/2">v2</a>, <a href="https://ncatlab.org/nlab/show/empty+215">current</a>

   Okay, I have cleared the entry and renamed to a generic title.

   (That’s the closest to deleting an entry here without logging into the server.)

   diff, v2, current