Wikipedia:Notability comparison test

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This essay articulates a notability comparison test for articles on Wikipedia. It is based on the argument that another article B, which is less than or equally notable to an article currently nominated for deletion A, exists on Wikipedia, has survived one or more AfDs, has never been nominated for deletion, or never has its notability questioned via means other than an AfD(s); and thus A merits being kept for consistent application of policies.

In this essay, 'an article's notability' is a shorthand for 'the notability of an article's subject/topic.'


The argument on which this test is based is a parity thesis regarding an article's notability. It raises a possibility of double standard being used on Wikipedia at the time of a particular discussion. A person who would like to make the argument usually starts by asking ’what about article x?‘ or ‘the same can be said of x.’ The now-unused Pokémon test is one particular past example of this argument. This kind of arguments, namely a parity thesis, is of the following form:

  • Initial argument: It is the case that P, because of justification J.
  • Parity thesis: J also justifies Q. However, you deny Q. Therefore, you can either bite the bullet by accepting both P and Q, or deny Q and J.
    • If you deny that J also justifies Q, then you are employing a double standard.

Differences from tu quoque and whataboutism[edit]

What distinguish the parity theses from the ad hominem fallacy of tu quoque are given below (they have different structure compared to that of one another).

Parity thesis[edit]

Structure: see above

Example: see the above collapsed box

Ad hominem tu quoque[edit]


  1. Person A told person B that B ought to stop doing x because of justification j.
  2. A himself/herself also does x.
  3. If A argues that B ought to stop x because of j, and A himself/herself also does x, then j fails to justify that B ought to stop x.
  4. If j fails, then A's argument fails.
  5. If A argues that B ought to stop x because of j, and A also does x, then A's argument fails. (2,3 hypothetical syllogism)
  6. A argues that B ought to stop x because of j, and A himself/herself also does x. (1,2 conjunction introduction)
  7. Therefore, A's argument fails. (5,6 modus ponens)

Fallacious premise: 3rd

About whataboutism[edit]

The uses of the parity thesis by the former Soviet Union and modern-day Russia are sometimes called 'whataboutism'. Despite its notoriety, its examples are not always unsound. Their soundness depends on the similarities between the situational contexts (such as Crimea vs. Kosovo) used in them.

The test[edit]

The notability comparison test, like the direct comparison test in calculus, provides a way for determining whether or not a particular article whose topic's (or subject's) notability is being discussed, merits inclusion on Wikipedia. Most of the times, these discussions are made in the context of a nomination of that article for deletion.

Statement (informal)[edit]

Given that notability is graded (totally ordered) (like the integers) and that every article on Wikipedia is subjected to the same standard of notability,

If the article under consideration (A) is more notable than or equally notable to another article (B), then:

  • If B merits inclusion on Wikipedia, then A also merits inclusion on Wikipedia.
  • If A does not merit inclusion on Wikipedia, then B also does not merit inclusion on Wikipedia (meaning that both A and B must be deleted).

Statement (formal)[edit]

where is a notability function whose domain is a Wikipedia article and whose range is the set of natural numbers *, and is the set of articles worthy of inclusion in Wikipedia.


Empirical premises[edit]

  1. The notability of a subject/topic is graded and ordered from low to high, as can be seen when one compares the notability of the United States with the notability of Sacramento, California. Notability is the magnitude of how well known a subject/topic is, in other words, how many people know about it. The level of notability of a topic/subject can be zero when nobody has known about it before (for example, a single, specific tree somewhere within a forest), however, when it is under discussion on Wikipedia, it must have nonzero level of notability already because the user who brought to into a discussion on Wikipedia must have known about it, otherwise he/she could not have brought it into a discussion in the first place.
    Thus, the range the notability function is the set of natural numbers (non-zero positive integers) * = {1, 2, 3, …}. This also implies that is a totally ordered set.
  2. Every article on Wikipedia is subjected to the same standard of notability. The specific notability guidelines (such as that of astronomical objects) for different subjects are for determining an article's notability level given the context of the article within that subject.
    Thus, any article that is notable enough to be worthy of inclusion in Wikipedia must have a notability level higher than a certain threshold.

Axioms, theorems, syntaxes, and definitions used[edit]

Additional definitions used (based on the empirical premises)[edit]

  • represents an article/topic under consideration.
  • is a variable that can stand in for any .
  • is a notability function whose domain is a Wikipedia article and whose range is the set of natural numbers *
  • is the set of articles/topics worthy of inclusion in Wikipedia.
  • is the threshold notability level for inclusion.

Main body[edit]

Step Proposition Justification
1 Assumption for CP
2 1, simp.
3 2, def. of (x ∈ W)
4 3, simp.
5 1, simp.
6 4, 5, transitivity of ≤ (Theorem 9325)
7 Assumption for RAA
8 5, 7, substitution
9 4, 8 conj.
10 9, antisymmetry of ≤
11 3, simp.
12 10, 11 conj.
13 7 - 12, RAA
14 6, 13 conj.
15 14, def. of (x ∈ W)
16 1 - 15 CP (deduction theorem)
17 16, ≤ being a converse of ≥
18 17, commutative property of conjunction
19 18, exportation
20 Assumption for CP
21 19, 20 modus ponens
22 21, transposition
23 21, 22 conj.
24 23, def. of ∉
25 20 - 24, CP (deduction theorem)

End of proof

Using the test[edit]

Care must be taken when showing that the antecedent holds for two specific articles. While that n(United States) ≥ n(Sacramento) is easy to be established, that n(Justin Bieber) ≥ n(Kanye West) might not be.

See also[edit]