Talk:Rule of inference

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Changes to the article

I was thinking about implementing changes to this article with the hope of moving it in the direction of GA status. Most of the text is currently unreferenced. Usually, the lead should summarize information found in the body of the article, not present new information, like it is done here.

Contentwise, a lot of information is currently missing. There are countless rules of inference and at least the most important ones should be discussed. It should be better explained that rules of inference belong to systems of logic. Different systems of logic have different rules of inference, like the contrasts between propositional logic and predicate logic or between classical and intuitionistic logic. Another point to mention would be the different formalisms of Hilbert systems, natural deduction, and sequent calculus. Other things to discuss would be the relation between rules of inference and logical truths, the problem of fallacies, and the role of rules of inference in the philosophy of logic regarding the contrast between the semantic and the syntactic conception of logic. Since some of these topics are quite abstract, one could add a section called "Basic concepts" to explain what logic, systems of logic, propositions, and inferences are. It further wouldn't hurt to mention some applications in fields like mathematical reasoning, computer science, expert systems, automated theorem proving, etc.

There are more things to consider, but they can be addressed later since the ones mentioned so far will already involve a lot of work to implement. I was hoping to get some feedback on these ideas and possibly other suggestions. Phlsph7 (talk) 13:36, 16 March 2025 (UTC)

GA review

This review is transcluded from Talk:Rule of inference/GA1. The edit link for this section can be used to add comments to the review.

Nominator: Phlsph7 (talk · contribs) 17:09, 31 March 2025 (UTC)

Reviewer: Brent Silby (talk · contribs) 09:16, 3 April 2025 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
It is reasonably well written. a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists): It is factually accurate and verifiable, as shown by a source spot-check. a (references): b (citations to reliable sources): c (OR): d (copyvio and plagiarism): It is broad in its coverage. a (major aspects): b (focused): It follows the neutral point of view policy. Fair representation without bias: It is stable. No edit wars, etc.: It is illustrated by images, where possible and appropriate. a (images are tagged and non-free images have fair use rationales): b (appropriate use with suitable captions):
Overall: Pass/Fail:
· · ·

This article has excellent prose, no grammar mistakes, loads of reliable sources (even with pages mentioned!), no copyright issues, appropriate image captions and no edit wars in sight.

Hello Brent Silby and thanks for your review! Phlsph7 (talk) 12:02, 3 April 2025 (UTC)

That said I have two suggestions for improving the breadth of its coverage and one suggestion concerning the image in the lead section:

1) "Further rules include conjunction introduction, disjunction introduction, constructive dilemma, destructive dilemma, double negation elimination, and De Morgan's laws." could this sentence be expanded with more examples? Are there any more rules that can be mentioned here?

See below. Phlsph7 (talk) 12:02, 3 April 2025 (UTC)

2) This article has two tables titled "Notable rules of inference". However, they don't include such rules as (conjunction introduction, disjunction introduction, constructive dilemma, destructive dilemma, double negation elimination, and De Morgan's laws) that are mentioned elsewhere. Is it possible to create a separate table for them?

I expanded the list of rules of inference mentioned above and the table. There are many other rules of inference that could be included either in the list or the table, like several of the introduction and elimination rules discussed later in the context of natural deduction. In choosing which ones to mention, I tried to follow standard logic textbooks. I think the main purpose of the article is to explain the basic concept of rules of inference, clarify their role, and familiarize readers with notable rules. In this sense, the article is not a comprehensive reference work of every individual rule of inference. The purpose of the list article List of rules of inference is more closely aligned to this ideal, although it's still far from reaching it. Phlsph7 (talk) 12:02, 3 April 2025 (UTC)

3) In addition to that, I have noticed that the lead image is rectangular. This means that it gets badly cropped on the thumbnail. Is it possible to have image with the exact same content but in a square instead of a rectangle?

I replaced it with a more compact square version, I think it looks better this way. Phlsph7 (talk) 12:02, 3 April 2025 (UTC)

@Phlsph7 Yep, that addresses all the issues. It's a pleasure reviewing your articles. They are very well-written. Brent Silby (talk) 12:16, 3 April 2025 (UTC)

@Brent Silby: please perform a spot-check. 🌙Eclipse (she/they/all neos • talk • edits) 13:59, 18 April 2025 (UTC)

Alright

1 - verified

4 - verified

14 - verified

19 - verified

74 - verified Brent Silby (talk) 18:59, 18 April 2025 (UTC)

Did you know nomination

(

• Comment or view
• Article history

)

• ... that using classical rules of inference, logicians can prove from any contradiction that the Earth is flat?

• Source: Shapiro, Stewart; Kouri Kissel, Teresa (2024). "Classical Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. § 3. Deduction.

• ALT1: ... that rules of inference can be transformed into tautologies? Source:
  • Gossett, Eric (2009). Discrete Mathematics with Proof. John Wiley & Sons. pp. 50–51. ISBN 978-0-470-45793-1.
  • Carlson, Robert (2017). A Concrete Introduction to Real Analysis. CRC Press. p. 20. ISBN 978-1-4987-7815-2.
  • Hintikka, Jaakko; Sandu, Gabriel (2006). "What Is Logic?". In Jacquette, Dale (ed.). Philosophy of Logic. North Holland. p. 16. ISBN 978-0-444-51541-4.
• Reviewed: Template:Did you know nominations/Eleanor Island (Canada)

Improved to Good Article status by Phlsph7 (talk). Number of QPQs required: 1. Nominator has 30 past nominations.

Phlsph7 (talk) 09:14, 4 April 2025 (UTC).

• Comment: @Phlsph7: The hook facts have to both be 1) cited in the source, and 2) cited in the Wikipedia article. Viriditas (talk) 00:13, 21 April 2025 (UTC)

  Hello Viriditas and thanks for taking a look at this nomination. For ALT0, the relevant passage in the article is "Classical logic prohibits contradictions because classical rules of inference lead to the principle of explosion, an admissible rule of inference that makes it possible to infer $Q$ from the premises $P$ and $\lnot P$. Since $Q$ is unrelated to $P$, any arbitrary statement can be deduced from a contradiction". I chose the arbitrary statement "the Earth is flat" to make it more concrete, but any other statement would also work. For ALT1, the relevant passage in the article is "Every argument following a rule of inference can be transformed into a tautology". Both passages are supported by reliable sources. I could look up the sources to provide quotes if there are concrete doubts. Phlsph7 (talk) 08:26, 21 April 2025 (UTC)

  Review needed. Viriditas (talk) 23:42, 21 April 2025 (UTC)

General: Article is new enough and long enough
New enough: Long enough:

Policy: Article is sourced, neutral, and free of copyright problems
Adequate sourcing: Neutral: Free of copyright violations, plagiarism, and close paraphrasing:

Hook eligibility:

• Cited: - 0:N, 1:Y
• Interesting: - 0:Y, 1:N

QPQ: Done.

Overall: Hook ALT0 does not appear in the article or citations. Yes, I read the paragraph above that "any arbitrary statement can be deduced from a contradiction", but the rules for hooks are "Hooks should be definite facts that are verified by citations in the article. Hooks should be likely to be perceived as unusual or intriguing by readers with no special knowledge or interest." It is a fact, but, since basically any statement can be inserted in place of "earth is flat", it is not a definite one. And only a reader with special knowledge or interest in formal logic would understand that "earth is flat" is an example of "any arbitrary statement", and that reader would not find this specific example interesting. A reader without special knowledge would find this an interesting hook, but would be hard put to find "earth is flat" in the article, as they might not identify it with "any arbitrary statement", and the article is large.

• Hook ALT1 has the opposite problem: yes, it can be easily found in the article, and might even be interesting for readers interested in formal logic, but a reader without special knowledge or interest will read it as "words-I-don't-know can be transformed into another-word-I-don't-know" and their eyes will glaze over.
• Apart from the hook, it bothers me that the article title is "Rule of inference" while the term used is throughout the article, and in this DYK nomination, is "Rules of inference". If the term is generally used in the plural, we should make our article title be the plural, for example Americans; if the term is generally used in the singular, we should generally use it that way in the article. I'm not sure whether "article is poorly titled" is a formal blocker for DYK, but it really should be.

A hook that can be found in the article and citations and is interesting to a general audience is a formal requirement, though hopefully easily fixed. Maybe even just rephrase ALT0 to the general case, something like "...logicians can use a contradiction in roi to prove anything", which is more easily found in the article/citations. Or something about the many systems of logic, or fallacies, those are generally interesting to laypeople. GRuban (talk) 14:58, 22 May 2025 (UTC)