Talk:Propositional calculus

Basic and derived argument forms

 Comment: The purpose of section Propositional calculus#Basic and derived argument forms is not quite clear, and I guess this is the reason for the dispute between Ans and JRSpriggs. The table lists more than a minimal ("basic") set of rules; there are many such minimal sets, anyway (one of them is the Huntington 1904 axiomatization, given, in algebraic form, in Boolean algebra (structure)#Axiomatics). On the other hand, the set of derived rules is infinite, so we can't list all of them. Which ones to select is then a matter of taste. Maybe, restricting to those rules that have an own article is (1) a good idea, and (2) closest to the current state of the table; however, I'm afraid some WP:EASTEREGGs need to be removed. — As for double negation elimination, if it is listed, I suggest to mention that it is not accepted in intuitionistic logic. - Jochen Burghardt (talk) 10:56, 3 February 2020 (UTC)

Merger proposal

I propose to merge Zeroth-order logic into Propositional calculus. I think that the content in the Zeroth-order logic article can easily be explained in the context of Propositional calculus, given that it is a synonym of propositional calculus, and the propositional calculus article is of a reasonable size that the merging of zeroth order logic will not cause any problems as far as article size is concerned. KazMalKen (talk) 20:35, 16 July 2020 (UTC)

Proving completeness

@Dan Gluck: In light of your recent change to the section on completeness, you may be interested in Talk:List of Hilbert systems#How to establish completeness in a two-valued (i.e. classical) logic. I am wondering whether you need to show p→¬¬p. JRSpriggs (talk) 00:48, 22 July 2020 (UTC)

Interesting, I'll try to have a thorough look at that. I'm currently working on inserting proofs for "simple" theorems in the Hilbert system propositional part (i.e. the one with only negation and "if-then"). Seems to me in place since this is a kind of a "standard" system but the proofs are highly non trivial. As a by-product, it will be a reference for this article to show that the theorems required for completeness indeed hold. The p→¬¬p proof happen to be extremely lengthy... It is needed as an intermediate for showing the several theorems needed for completeness indeed hold for that system. Not sure if you can circumvent it, but I don't think it's required by itself in the particular completeness proof appearing in this article (I think it IS needed for another proof I have seen).Dan Gluck (talk) 17:11, 22 July 2020 (UTC)

Propositional calculus as branch of modern formal logic as branch of analytic philosophy

(moved from User_talk:Jochen_Burghardt#Propositional_calculus_as_branch_of_modern_formal_logic_as_branch_of_analytic_philosophy:)

"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#History. 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).