Talk:Propositional calculus

Propositional calculus as branch of modern formal logic as branch of analytic philosophy
(moved from User_talk:Jochen_Burghardt:)

"Modern formal logic has its roots in the work of late 19th century mathematicians such as Gottlob Frege." https://en.wikipedia.org/wiki/Logic "...and is understood by many to be the father of analytic philosophy..." https://en.wikipedia.org/wiki/Gottlob_Frege — Preceding unsigned comment added by 150.135.165.49 (talk) 22:00, 19 October 2021 (UTC)


 * Propositional calculus originated in the 3rd century BC, according to Propositional_calculus. The main achievement of Frege is a formalization of first-order logic ("Begriffsschrift"); a formal treatment of propositional logic was already given by Chrysippus (according to Sect.2 of https://iep.utm.edu/prop-log). Subsuming the propositoinal calculus under analytical philosophy is therefore misleading. - Jochen Burghardt (talk) 11:04, 20 October 2021 (UTC)

I think that the school of thought in which propositional calculus exists should be included in the introduction. It is misleading to make it seem like it is merely a branch of logic when not all schools of philosophic thought include it. — Preceding unsigned comment added by 150.135.165.63 (talk) 16:59, 20 October 2021 (UTC)

Since no one has commented that this is incorrect I would like to make a change. — Preceding unsigned comment added by 150.135.165.40 (talk) 18:09, 29 November 2021 (UTC)


 * Silence is not consent, and for the record, I'm not even familiar with the article at hand. I just want to see some sources and justification before I see weirdly editorialized (?) content like "in some schools".--Megaman en m (talk) 22:23, 29 November 2021 (UTC)

How is "some schools" "weird"? Philosophy is composed of schools of philosophic thought from the the Pythagoreans, Platonists, Aristotelians, Lockeans, Kantians, on down through the ages. I think the idea that propositional calculus is in all schools of philosophy is complete ignorance of the history of philosophy. Check out any history of philosophy book (AC Grayling, Russell, Thilly). — Preceding unsigned comment added by 150.135.165.48 (talk) 22:42, 29 November 2021 (UTC)

Wikipedia list of schools of philosophic thought for reference: https://en.wikipedia.org/wiki/List_of_philosophies — Preceding unsigned comment added by 150.135.165.56 (talk) 16:24, 30 November 2021 (UTC)

https://en.wikipedia.org/wiki/Wikipedia:Please_do_not_bite_the_newcomers — Preceding unsigned comment added by 150.135.165.56 (talk) 16:27, 30 November 2021 (UTC)

Wikipedia article on what a school of thought is: https://en.wikipedia.org/wiki/School_of_thought — Preceding unsigned comment added by 150.135.165.17 (talk) 16:31, 30 November 2021 (UTC)
 * I too have no real stance in this, I just happened to pass by the AN post earlier, but strictly in the sense of writing and phrasing, the issue here in your proposed wording of "in some schools of thought" may be less about "schools of thought" and more about the "some " part. When you add qualifiers like "some" in there, it can somewhat suggest that there are differing or contentious views as well. It sheds some doubt on the statement, or at least gets the reader thinking "well, okay, what do others think then?" Is that accurate? I have no idea. My point is merely to point out that you're probably changing the meaning of the sentence more than you intended. Sergecross73   msg me  20:45, 30 November 2021 (UTC)

I appreciate the benefit of the doubt, but I use words precisely. When I say some, I mean some. Not all schools of thought have propositional calculus in them. There is no consensus in philosophy on what is included in logic. — Preceding unsigned comment added by 150.135.165.17 (talk) 21:27, 30 November 2021 (UTC)
 * Sure, but the problem is that you're not writing a note to yourself, you're writing to one of the largest general audiences in existence. And people may not be reading it to your intended meaning. And this is a collaborative project, so you do need other people buy in on this. Sergecross73   msg me  21:51, 30 November 2021 (UTC)

If anyone wants to look into which schools of thought do include propositional calculus in their view of logic that is fine. It would make it more detailed then using the word "some" but it still stands true that more than one school of thought has propositional calculus but not all schools of thought do. The way the article is currently worded implies that all schools of thought include it. — Preceding unsigned comment added by 150.135.165.10 (talk) 21:40, 30 November 2021 (UTC)

OED definition of the word "some". https://www.oed.com/view/Entry/184452?rskey=Zj9rzW&result=3&isAdvanced=false#eid The definition is pretty well established. This has nothing to do with writing a note to one's self but in using common sense. — Preceding unsigned comment added by 150.135.165.56 (talk) 22:07, 30 November 2021 (UTC)
 * I'm well aware of the definition of the word "some", but I'm beginning to see why you're blocked from editing the page. This is where I get off. Best of luck to you. You'll need it if this is how you interact and "collaborate" with people. Sergecross73   msg me  23:08, 30 November 2021 (UTC)

Cleanup
These are the talk-page topics I wrote while cleaning up the article between 2024-03-22 and 2024-07-02. I have made them into subsections of the same section to make it clear that they are related to each other, and that the first two are outdated. Thiagovscoelho (talk) 03:44, 2 July 2024 (UTC)

Cleanup I
I have cleaned up the article and changed its structure. Its current order and headings make clear that most of the current article content consists of highly developed example proof systems, which are given without sources because the authors were making them up from scratch. I'm not sure whether there should even be any proof systems in this article – in my opinion, proof systems should be left to the articles on Proof theory, Proof calculus, Natural deduction, Method of analytic tableaux, Truth table, Hilbert system, List of Hilbert systems, and possibly a new page besides these. But I have avoided removing material which could be seen as relevant without some consensus. Thiagovscoelho (talk) 05:02, 22 March 2024 (UTC)

Cleanup II
Now that I edited the coverage of natural deduction, I thought I should update this talk page. I thought that, since the article had so much coverage of proof systems, it was only fair that semantic proof be included, since proof with truth tables is covered by many sources such as Kleene and even Lemmon, and tableaux are the only kind of proof used by sources such as Beall & Logan (2017) and Howson (1997). The goal now, then, is to have one section on each proof system, with a short but complete specification of it, a proof example, and a link to the main article where the special properties of that proof system are (intended to be) laid out (such as, e.g., its extension into predicate logic, modal logic, etc.). Now that I found actual sources to treat of natural deduction, I have moved it off from the last, unsourced section of "example" proof systems, since it is no longer postulated from scratch, but rather derived from Reliable Sources, as befits a Wikipedia article. The updated natural deduction section, in addition to more clearly specifying how to build a natural deduction proof, also has the advantage of not defining the propositional language all over again – its set of variables, connectives, etc –, since this seems clearly redundant in an article where the formal language is so fully covered in its own proper section. Hopefully I can find sources to cite regarding axiomatic proof systems as well, so I can improve those sections. Once I find Reliable Sources to cite for the completeness and consistency theorems for propositional logic, I might move the theorems to a page of their own, reducing the mention of them in this article to a short note, thereby reducing the size of this page, which is already growing very large, as another editor pointed out elsewhere. But I am unable to perform such a page split yet, because it makes no sense to create a new page that cites no sources, whereas retaining that section without citations in this article is a tradition that I am loath to break with unilaterally. Thiagovscoelho (talk) 00:13, 20 April 2024 (UTC)

Cleanup III
I have written suitably-sourced material for a section on axiomatic proof, and I have moved much of the unsourced material that was there to Axiomatic system (logic), where I still hope to improve it by replacing it with sourced material. (Before, I hadn't noticed that there was already a separate article for axiomatic systems, because the relevant article had been given the unhelpful name "Hilbert system", which has been corrected.) But this article, at least, finally has decent enough coverage of axiomatic systems for what it is. My ambitions for it are finally pretty much fulfilled— I mean, I still want to write a section on "sequent calculus", and probably a section on any metalogical results that are independent of any specific proof system, such as conjunction/disjunction duality and the Disjunctive Normal Form Theorem. But at least all the unsourced material was finally removed from here, and the article consists fully of sections that are sourced from WP:RS. To make a pun on the article's topic, the article may not be "complete" yet, but now it is finally at least "sound". Thiagovscoelho (talk) 03:23, 2 July 2024 (UTC)